Michael Mozer

NeurIPS Conference 2025 Conference Paper

From Dormant to Deleted: Tamper-Resistant Unlearning Through Weight-Space Regularization

• Shoaib Ahmed Siddiqui
• Adrian Weller
• David Krueger
• Gintare Karolina Dziugaite
• Michael Mozer
• Eleni Triantafillou

Recent unlearning methods for LLMs are vulnerable to relearning attacks: knowledge believed-to-be-unlearned re-emerges by fine-tuning on a small set of (even seemingly-unrelated) examples. We study this phenomenon in a controlled setting for example-level unlearning in vision classifiers. We make the surprising discovery that forget-set accuracy can recover from around 50\% post-unlearning to nearly 100\% with fine-tuning on just the *retain* set---i. e. , zero examples of the forget set. We observe this effect across a wide variety of unlearning methods, whereas for a model retrained from scratch excluding the forget set (gold standard), the accuracy remains at 50\%. We observe that resistance to relearning attacks can be predicted by weight-space properties, specifically, $L_2$-distance and linear mode connectivity between the original and the unlearned model. Leveraging this insight, we propose a new class of methods that achieve state-of-the-art resistance to relearning attacks.

ICLR Conference 2025 Conference Paper

On the Transfer of Object-Centric Representation Learning

• Aniket Rajiv Didolkar
• Andrii Zadaianchuk
• Anirudh Goyal
• Michael Mozer
• Yoshua Bengio
• Georg Martius
• Maximilian Seitzer

The goal of object-centric representation learning is to decompose visual scenes into a structured representation that isolates the entities into individual vectors. Recent successes have shown that object-centric representation learning can be scaled to real-world scenes by utilizing features from pre-trained foundation models like DINO. However, so far, these object-centric methods have mostly been applied in-distribution, with models trained and evaluated on the same dataset. This is in contrast to the underlying foundation models, which have been shown to be applicable to a wide range of data and tasks. Thus, in this work, we answer the question of whether current real-world capable object-centric methods exhibit similar levels of transferability by introducing a benchmark comprising seven different synthetic and real-world datasets. We analyze the factors influencing performance under transfer and find that training on diverse real-world images improves generalization to unseen scenarios. Furthermore, inspired by the success of task-specific fine-tuning in foundation models, we introduce a novel fine-tuning strategy to adapt pre-trained vision encoders for the task of object discovery. We find that the proposed approach results in state-of-the-art performance for unsupervised object discovery, exhibiting strong zero-shot transfer to unseen datasets.

NeurIPS Conference 2024 Conference Paper

Metacognitive Capabilities of LLMs: An Exploration in Mathematical Problem Solving

• Aniket Didolkar
• Anirudh Goyal
• Nan R. Ke
• Siyuan Guo
• Michal Valko
• Timothy Lillicrap
• Danilo Rezende
• Yoshua Bengio

\emph{Metacognitive knowledge} refers to humans' intuitive knowledge of their own thinking and reasoning processes. Today's best LLMs clearly possess some reasoning processes. The paper gives evidence that they also have metacognitive knowledge, including ability to name skills and procedures to apply given a task. We explore this primarily in context of math reasoning, developing a prompt-guided interaction procedure to get a powerful LLM to assign sensible skill labels to math questions, followed by having it perform semantic clustering to obtain coarser families of skill labels. These coarse skill labels look interpretable to humans. To validate that these skill labels are meaningful and relevant to the LLM's reasoning processes we perform the following experiments. (a) We ask GPT-4 to assign skill labels to training questions in math datasets GSM8K and MATH. (b) When using an LLM to solve the test questions, we present it with the full list of skill labels and ask it to identify the skill needed. Then it is presented with randomly selected exemplar solved questions associated with that skill label. This improves accuracy on GSM8k and MATH for several strong LLMs, including code-assisted models. The methodology presented is domain-agnostic, even though this article applies it to math problems.

ICLR Conference 2024 Conference Paper

On the Foundations of Shortcut Learning

• Katherine L. Hermann
• Hossein Mobahi
• Thomas Fel
• Michael Mozer

Deep-learning models can extract a rich assortment of features from data. Which features a model uses depends not only on *predictivity*---how reliably a feature indicates training-set labels---but also on *availability*---how easily the feature can be extracted from inputs. The literature on shortcut learning has noted examples in which models privilege one feature over another, for example texture over shape and image backgrounds over foreground objects. Here, we test hypotheses about which input properties are more available to a model, and systematically study how predictivity and availability interact to shape models' feature use. We construct a minimal, explicit generative framework for synthesizing classification datasets with two latent features that vary in predictivity and in factors we hypothesize to relate to availability, and we quantify a model's shortcut bias---its over-reliance on the shortcut (more available, less predictive) feature at the expense of the core (less available, more predictive) feature. We find that linear models are relatively unbiased, but introducing a single hidden layer with ReLU or Tanh units yields a bias. Our empirical findings are consistent with a theoretical account based on Neural Tangent Kernels. Finally, we study how models used in practice trade off predictivity and availability in naturalistic datasets, discovering availability manipulations which increase models' degree of shortcut bias. Taken together, these findings suggest that the propensity to learn shortcut features is a fundamental characteristic of deep nonlinear architectures warranting systematic study given its role in shaping how models solve tasks.

AAAI Conference 2023 Conference Paper

Adaptive Discrete Communication Bottlenecks with Dynamic Vector Quantization for Heterogeneous Representational Coarseness

• Dianbo Liu
• Alex Lamb
• Xu Ji
• Pascal Junior Tikeng Notsawo
• Michael Mozer
• Yoshua Bengio
• Kenji Kawaguchi

Vector Quantization (VQ) is a method for discretizing latent representations and has become a major part of the deep learning toolkit. It has been theoretically and empirically shown that discretization of representations leads to improved generalization, including in reinforcement learning where discretization can be used to bottleneck multi-agent communication to promote agent specialization and robustness. The discretization tightness of most VQ-based methods is defined by the number of discrete codes in the representation vector and the codebook size, which are fixed as hyperparameters. In this work, we propose learning to dynamically select discretization tightness conditioned on inputs, based on the hypothesis that data naturally contains variations in complexity that call for different levels of representational coarseness which is observed in many heterogeneous data sets. We show that dynamically varying tightness in communication bottlenecks can improve model performance on visual reasoning and reinforcement learning tasks with heterogeneity in representations.

ICML Conference 2023 Conference Paper

Can Neural Network Memorization Be Localized?

• Pratyush Maini
• Michael Mozer
• Hanie Sedghi
• Zachary C. Lipton
• J. Zico Kolter
• Chiyuan Zhang

Recent efforts at explaining the interplay of memorization and generalization in deep overparametrized networks have posited that neural networks memorize “hard” examples in the final few layers of the model. Memorization refers to the ability to correctly predict on atypical examples of the training set. In this work, we show that rather than being confined to individual layers, memorization is a phenomenon confined to a small set of neurons in various layers of the model. First, via three experimental sources of converging evidence, we find that most layers are redundant for the memorization of examples and the layers that contribute to example memorization are, in general, not the final layers. The three sources are gradient accounting (measuring the contribution to the gradient norms from memorized and clean examples), layer rewinding (replacing specific model weights of a converged model with previous training checkpoints), and retraining (training rewound layers only on clean examples). Second, we ask a more generic question: can memorization be localized anywhere in a model? We discover that memorization is often confined to a small number of neurons or channels (around 5) of the model. Based on these insights we propose a new form of dropout— example-tied dropout that enables us to direct the memorization of examples to an aprior determined set of neurons. By dropping out these neurons, we are able to reduce the accuracy on memorized examples from 100% to 3%, while also reducing the generalization gap.

ICML Conference 2023 Conference Paper

Discrete Key-Value Bottleneck

• Frederik Träuble
• Anirudh Goyal
• Nasim Rahaman
• Michael Mozer
• Kenji Kawaguchi
• Yoshua Bengio
• Bernhard Schölkopf

Deep neural networks perform well on classification tasks where data streams are i. i. d. and labeled data is abundant. Challenges emerge with non-stationary training data streams such as continual learning. One powerful approach that has addressed this challenge involves pre-training of large encoders on volumes of readily available data, followed by task-specific tuning. Given a new task, however, updating the weights of these encoders is challenging as a large number of weights needs to be fine-tuned, and as a result, they forget information about the previous tasks. In the present work, we propose a model architecture to address this issue, building upon a discrete bottleneck containing pairs of separate and learnable key-value codes. Our paradigm will be to encode; process the representation via a discrete bottleneck; and decode. Here, the input is fed to the pre-trained encoder, the output of the encoder is used to select the nearest keys, and the corresponding values are fed to the decoder to solve the current task. The model can only fetch and re-use a sparse number of these key-value pairs during inference, enabling localized and context-dependent model updates. We theoretically investigate the ability of the discrete key-value bottleneck to minimize the effect of learning under distribution shifts and show that it reduces the complexity of the hypothesis class. We empirically verify the proposed method under challenging class-incremental learning scenarios and show that the proposed model — without any task boundaries — reduces catastrophic forgetting across a wide variety of pre-trained models, outperforming relevant baselines on this task.

ICLR Conference 2023 Conference Paper

Learning in temporally structured environments

• Matt Jones 0001
• Tyler R. Scott
• Mengye Ren
• Gamaleldin Fathy Elsayed
• Katherine L. Hermann
• David Mayo
• Michael Mozer

Natural environments have temporal structure at multiple timescales. This property is reflected in biological learning and memory but typically not in machine learning systems. We advance a multiscale learning method in which each weight in a neural network is decomposed as a sum of subweights with different learning and decay rates. Thus knowledge becomes distributed across different timescales, enabling rapid adaptation to task changes while avoiding catastrophic interference. First, we prove previous models that learn at multiple timescales, but with complex coupling between timescales, are equivalent to multiscale learning via a reparameterization that eliminates this coupling. The same analysis yields a new characterization of momentum learning, as a fast weight with a negative learning rate. Second, we derive a model of Bayesian inference over $1/f$ noise, a common temporal pattern in many online learning domains that involves long-range (power law) autocorrelations. The generative side of the model expresses $1/f$ noise as a sum of diffusion processes at different timescales, and the inferential side tracks these latent processes using a Kalman filter. We then derive a variational approximation to the Bayesian model and show how it is an extension of the multiscale learner. The result is an optimizer that can be used as a drop-in replacement in an arbitrary neural network architecture. Third, we evaluate the ability of these methods to handle nonstationarity by testing them in online prediction tasks characterized by $1/f$ noise in the latent parameters. We find that the Bayesian model significantly outperforms online stochastic gradient descent and two batch heuristics that rely preferentially or exclusively on more recent data. Moreover, the variational approximation performs nearly as well as the full Bayesian model, and with memory requirements that are linear in the size of the network.

ICLR Conference 2023 Conference Paper

Learning to Induce Causal Structure

• Nan Rosemary Ke
• Silvia Chiappa
• Jane X. Wang
• Jörg Bornschein
• Anirudh Goyal
• Mélanie Rey
• Theophane Weber
• Matthew M. Botvinick

The fundamental challenge in causal induction is to infer the underlying graph structure given observational and/or interventional data. Most existing causal induction algorithms operate by generating candidate graphs and evaluating them using either score-based methods (including continuous optimization) or independence tests. In our work, we instead treat the inference process as a black box and design a neural network architecture that learns the mapping from both observational and interventional data to graph structures via supervised training on synthetic graphs. The learned model generalizes to new synthetic graphs, is robust to train-test distribution shifts, and achieves state-of-the-art performance on naturalistic graphs for low sample complexity.

ICLR Conference 2023 Conference Paper

Stateful Active Facilitator: Coordination and Environmental Heterogeneity in Cooperative Multi-Agent Reinforcement Learning

• Dianbo Liu
• Vedant Shah
• Oussama Boussif
• Cristian Meo
• Anirudh Goyal
• Tianmin Shu
• Michael Mozer
• Nicolas Heess

In cooperative multi-agent reinforcement learning, a team of agents works together to achieve a common goal. Different environments or tasks may require varying degrees of coordination among agents in order to achieve the goal in an optimal way. The nature of coordination will depend on properties of the environment—its spatial layout, distribution of obstacles, dynamics, etc. We term this variation of properties within an environment as heterogeneity. Existing literature has not sufficiently addressed the fact that different environments may have different levels of heterogeneity. We formalize the notions of coordination level and heterogeneity level of an environment and present HECOGrid, a suite of multi-agent RL environments that facilitates empirical evaluation of different MARL approaches across different levels of coordination and environmental heterogeneity by providing a quantitative control over coordination and heterogeneity levels of the environment. Further, we propose a Centralized Training Decentralized Execution learning approach called Stateful Active Facilitator (SAF) that enables agents to work efficiently in high-coordination and high-heterogeneity environments through a differentiable and shared knowledge source used during training and dynamic selection from a shared pool of policies. We evaluate SAF and compare its performance against baselines IPPO and MAPPO on HECOGrid. Our results show that SAF consistently outperforms the baselines across different tasks and different heterogeneity and coordination levels.

ICLR Conference 2022 Conference Paper

Coordination Among Neural Modules Through a Shared Global Workspace

• Anirudh Goyal
• Aniket Rajiv Didolkar
• Alex Lamb
• Kartikeya Badola
• Nan Rosemary Ke
• Nasim Rahaman
• Jonathan Binas
• Charles Blundell

Deep learning has seen a movement away from representing examples with a monolithic hidden state towards a richly structured state. For example, Transformers segment by position, and object-centric architectures decompose images into entities. In all these architectures, interactions between different elements are modeled via pairwise interactions: Transformers make use of self-attention to incorporate information from other positions and object-centric architectures make use of graph neural networks to model interactions among entities. We consider how to improve on pairwise interactions in terms of global coordination and a coherent, integrated representation that can be used for downstream tasks. In cognitive science, a global workspace architecture has been proposed in which functionally specialized components share information through a common, bandwidth-limited communication channel. We explore the use of such a communication channel in the context of deep learning for modeling the structure of complex environments. The proposed method includes a shared workspace through which communication among different specialist modules takes place but due to limits on the communication bandwidth, specialist modules must compete for access. We show that capacity limitations have a rational basis in that (1) they encourage specialization and compositionality and (2) they facilitate the synchronization of otherwise independent specialists.

ICML Conference 2022 Conference Paper

Head2Toe: Utilizing Intermediate Representations for Better Transfer Learning

• Utku Evci
• Vincent Dumoulin
• Hugo Larochelle
• Michael Mozer

Transfer-learning methods aim to improve performance in a data-scarce target domain using a model pretrained on a data-rich source domain. A cost-efficient strategy, linear probing, involves freezing the source model and training a new classification head for the target domain. This strategy is outperformed by a more costly but state-of-the-art method – fine-tuning all parameters of the source model to the target domain – possibly because fine-tuning allows the model to leverage useful information from intermediate layers which is otherwise discarded by the later previously trained layers. We explore the hypothesis that these intermediate layers might be directly exploited. We propose a method, Head-to-Toe probing (Head2Toe), that selects features from all layers of the source model to train a classification head for the target-domain. In evaluations on the Visual Task Adaptation Benchmark-1k, Head2Toe matches performance obtained with fine-tuning on average while reducing training and storage cost hundred folds or more, but critically, for out-of-distribution transfer, Head2Toe outperforms fine-tuning. Code used in our experiments can be found in supplementary materials.

ICML Conference 2021 Conference Paper

Characterizing Structural Regularities of Labeled Data in Overparameterized Models

• Ziheng Jiang
• Chiyuan Zhang
• Kunal Talwar
• Michael Mozer

Humans are accustomed to environments that contain both regularities and exceptions. For example, at most gas stations, one pays prior to pumping, but the occasional rural station does not accept payment in advance. Likewise, deep neural networks can generalize across instances that share common patterns or structures, yet have the capacity to memorize rare or irregular forms. We analyze how individual instances are treated by a model via a consistency score. The score characterizes the expected accuracy for a held-out instance given training sets of varying size sampled from the data distribution. We obtain empirical estimates of this score for individual instances in multiple data sets, and we show that the score identifies out-of-distribution and mislabeled examples at one end of the continuum and strongly regular examples at the other end. We identify computationally inexpensive proxies to the consistency score using statistics collected during training. We apply the score toward understanding the dynamics of representation learning and to filter outliers during training.

ICLR Conference 2021 Conference Paper

Factorizing Declarative and Procedural Knowledge in Structured, Dynamical Environments

• Anirudh Goyal
• Alex Lamb
• Phanideep Gampa
• Philippe Beaudoin
• Charles Blundell
• Sergey Levine
• Yoshua Bengio
• Michael Mozer

Modeling a structured, dynamic environment like a video game requires keeping track of the objects and their states (declarative knowledge) as well as predicting how objects behave (procedural knowledge). Black-box models with a monolithic hidden state often fail to apply procedural knowledge consistently and uniformly, i.e., they lack systematicity. For example, in a video game, correct prediction of one enemy's trajectory does not ensure correct prediction of another's. We address this issue via an architecture that factorizes declarative and procedural knowledge and that imposes modularity within each form of knowledge. The architecture consists of active modules called object files that maintain the state of a single object and invoke passive external knowledge sources called schemata that prescribe state updates. To use a video game as an illustration, two enemies of the same type will share schemata but will have separate object files to encode their distinct state (e.g., health, position). We propose to use attention to determine which object files to update, the selection of schemata, and the propagation of information between object files. The resulting architecture is a drop-in replacement conforming to the same input-output interface as normal recurrent networks (e.g., LSTM, GRU) yet achieves substantially better generalization on environments that have multiple object tokens of the same type, including a challenging intuitive physics benchmark.

NeurIPS Conference 2021 Conference Paper

Systematic Evaluation of Causal Discovery in Visual Model Based Reinforcement Learning

• Nan Rosemary Ke
• Aniket Didolkar
• Sarthak Mittal
• Anirudh Goyal ALIAS PARTH GOYAL
• Guillaume Lajoie
• Stefan Bauer
• Danilo Jimenez Rezende
• Michael Mozer

Inducing causal relationships from observations is a classic problem in machine learning. Most work in causality starts from the premise that the causal variables themselves are observed. However, for AI agents such as robots trying to make sense of their environment, the only observables are low-level variables like pixels in images. To generalize well, an agent must induce high-level variables, particularly those which are causal or are affected by causal variables. A central goal for AI and causality is thus the joint discovery of abstract representations and causal structure. However, we note that existing environments for studying causal induction are poorly suited for this objective because they have complicated task-specific causal graphs which are impossible to manipulate parametrically (e. g. , number of nodes, sparsity, causal chain length, etc. ). In this work, our goal is to facilitate research in learning representations of high-level variables as well as causal structures among them. In order to systematically probe the ability of methods to identify these variables and structures, we design a suite of benchmarking RL environments. We evaluate various representation learning algorithms from the literature and find that explicitly incorporating structure and modularity in models can help causal induction in model-based reinforcement learning.

ICML Conference 2021 Conference Paper

Understanding Invariance via Feedforward Inversion of Discriminatively Trained Classifiers

• Piotr Teterwak
• Chiyuan Zhang
• Dilip Krishnan
• Michael Mozer

A discriminatively trained neural net classifier can fit the training data perfectly if all information about its input other than class membership has been discarded prior to the output layer. Surprisingly, past research has discovered that some extraneous visual detail remains in the unnormalized logits. This finding is based on inversion techniques that map deep embeddings back to images. We explore this phenomenon further using a novel synthesis of methods, yielding a feedforward inversion model that produces remarkably high fidelity reconstructions, qualitatively superior to those of past efforts. When applied to an adversarially robust classifier model, the reconstructions contain sufficient local detail and global structure that they might be confused with the original image in a quick glance, and the object category can clearly be gleaned from the reconstruction. Our approach is based on BigGAN (Brock, 2019), with conditioning on logits instead of one-hot class labels. We use our reconstruction model as a tool for exploring the nature of representations, including: the influence of model architecture and training objectives (specifically robust losses), the forms of invariance that networks achieve, representational differences between correctly and incorrectly classified images, and the effects of manipulating logits and images. We believe that our method can inspire future investigations into the nature of information flow in a neural net and can provide diagnostics for improving discriminative models. We provide pre-trained models and visualizations at \url{https: //sites. google. com/view/understanding-invariance/home}.

ICLR Conference 2021 Conference Paper

Wandering within a world: Online contextualized few-shot learning

• Mengye Ren
• Michael L. Iuzzolino
• Michael Mozer
• Richard S. Zemel

We aim to bridge the gap between typical human and machine-learning environments by extending the standard framework of few-shot learning to an online, continual setting. In this setting, episodes do not have separate training and testing phases, and instead models are evaluated online while learning novel classes. As in the real world, where the presence of spatiotemporal context helps us retrieve learned skills in the past, our online few-shot learning setting also features an underlying context that changes throughout time. Object classes are correlated within a context and inferring the correct context can lead to better performance. Building upon this setting, we propose a new few-shot learning dataset based on large scale indoor imagery that mimics the visual experience of an agent wandering within a world. Furthermore, we convert popular few-shot learning approaches into online versions and we also propose a new model that can make use of spatiotemporal contextual information from the recent past.

ICLR Conference 2020 Conference Paper

Identity Crisis: Memorization and Generalization Under Extreme Overparameterization

• Chiyuan Zhang
• Samy Bengio
• Moritz Hardt
• Michael Mozer
• Yoram Singer

We study the interplay between memorization and generalization of overparameterized networks in the extreme case of a single training example and an identity-mapping task. We examine fully-connected and convolutional networks (FCN and CNN), both linear and nonlinear, initialized randomly and then trained to minimize the reconstruction error. The trained networks stereotypically take one of two forms: the constant function (memorization) and the identity function (generalization). We formally characterize generalization in single-layer FCNs and CNNs. We show empirically that different architectures exhibit strikingly different inductive biases. For example, CNNs of up to 10 layers are able to generalize from a single example, whereas FCNs cannot learn the identity function reliably from 60k examples. Deeper CNNs often fail, but nonetheless do astonishing work to memorize the training output: because CNN biases are location invariant, the model must progressively grow an output pattern from the image boundaries via the coordination of many layers. Our work helps to quantify and visualize the sensitivity of inductive biases to architectural choices such as depth, kernel width, and number of channels.

ICML Conference 2020 Conference Paper

Learning to Combine Top-Down and Bottom-Up Signals in Recurrent Neural Networks with Attention over Modules

• Sarthak Mittal
• Alex Lamb
• Anirudh Goyal
• Vikram Voleti
• Murray Shanahan
• Guillaume Lajoie
• Michael Mozer
• Yoshua Bengio

Robust perception relies on both bottom-up and top-down signals. Bottom-up signals consist of what’s directly observed through sensation. Top-down signals consist of beliefs and expectations based on past experience and the current reportable short-term memory, such as how the phrase ‘peanut butter and. .. ’ will be completed. The optimal combination of bottom-up and top-down information remains an open question, but the manner of combination must be dynamic and both context and task dependent. To effectively utilize the wealth of potential top-down information available, and to prevent the cacophony of intermixed signals in a bidirectional architecture, mechanisms are needed to restrict information flow. We explore deep recurrent neural net architectures in which bottom-up and top-down signals are dynamically combined using attention. Modularity of the architecture further restricts the sharing and communication of information. Together, attention and modularity direct information flow, which leads to reliable performance improvements in perceptual and language tasks, and in particular improves robustness to distractions and noisy data. We demonstrate on a variety of benchmarks in language modeling, sequential image classification, video prediction and reinforcement learning that the \emph{bidirectional} information flow can improve results over strong baselines.

ICML Conference 2019 Conference Paper

State-Reification Networks: Improving Generalization by Modeling the Distribution of Hidden Representations

• Alex Lamb
• Jonathan Binas
• Anirudh Goyal
• Sandeep Subramanian
• Ioannis Mitliagkas
• Yoshua Bengio
• Michael Mozer

Machine learning promises methods that generalize well from finite labeled data. However, the brittleness of existing neural net approaches is revealed by notable failures, such as the existence of adversarial examples that are misclassified despite being nearly identical to a training example, or the inability of recurrent sequence-processing nets to stay on track without teacher forcing. We introduce a method, which we refer to as _state reification_, that involves modeling the distribution of hidden states over the training data and then projecting hidden states observed during testing toward this distribution. Our intuition is that if the network can remain in a familiar manifold of hidden space, subsequent layers of the net should be well trained to respond appropriately. We show that this state-reification method helps neural nets to generalize better, especially when labeled data are sparse, and also helps overcome the challenge of achieving robust generalization with adversarial training.

NeurIPS Conference 2018 Conference Paper

Adapted Deep Embeddings: A Synthesis of Methods for k-Shot Inductive Transfer Learning

• Tyler Scott
• Karl Ridgeway
• Michael Mozer

The focus in machine learning has branched beyond training classifiers on a single task to investigating how previously acquired knowledge in a source domain can be leveraged to facilitate learning in a related target domain, known as inductive transfer learning. Three active lines of research have independently explored transfer learning using neural networks. In weight transfer, a model trained on the source domain is used as an initialization point for a network to be trained on the target domain. In deep metric learning, the source domain is used to construct an embedding that captures class structure in both the source and target domains. In few-shot learning, the focus is on generalizing well in the target domain based on a limited number of labeled examples. We compare state-of-the-art methods from these three paradigms and also explore hybrid adapted-embedding methods that use limited target-domain data to fine tune embeddings constructed from source-domain data. We conduct a systematic comparison of methods in a variety of domains, varying the number of labeled instances available in the target domain (k), as well as the number of target-domain classes. We reach three principal conclusions: (1) Deep embeddings are far superior, compared to weight transfer, as a starting point for inter-domain transfer or model re-use (2) Our hybrid methods robustly outperform every few-shot learning and every deep metric learning method previously proposed, with a mean error reduction of 34% over state-of-the-art. (3) Among loss functions for discovering embeddings, the histogram loss (Ustinova & Lempitsky, 2016) is most robust. We hope our results will motivate a unification of research in weight transfer, deep metric learning, and few-shot learning.

NeurIPS Conference 2018 Conference Paper

Learning Deep Disentangled Embeddings With the F-Statistic Loss

• Karl Ridgeway
• Michael Mozer

Deep-embedding methods aim to discover representations of a domain that make explicit the domain's class structure and thereby support few-shot learning. Disentangling methods aim to make explicit compositional or factorial structure. We combine these two active but independent lines of research and propose a new paradigm suitable for both goals. We propose and evaluate a novel loss function based on the $F$ statistic, which describes the separation of two or more distributions. By ensuring that distinct classes are well separated on a subset of embedding dimensions, we obtain embeddings that are useful for few-shot learning. By not requiring separation on all dimensions, we encourage the discovery of disentangled representations. Our embedding method matches or beats state-of-the-art, as evaluated by performance on recall@$k$ and few-shot learning tasks. Our method also obtains performance superior to a variety of alternatives on disentangling, as evaluated by two key properties of a disentangled representation: modularity and explicitness. The goal of our work is to obtain more interpretable, manipulable, and generalizable deep representations of concepts and categories.

NeurIPS Conference 2018 Conference Paper

Sparse Attentive Backtracking: Temporal Credit Assignment Through Reminding

• Nan Rosemary Ke
• Anirudh Goyal ALIAS PARTH GOYAL
• Olexa Bilaniuk
• Jonathan Binas
• Michael Mozer
• Chris Pal
• Yoshua Bengio

Learning long-term dependencies in extended temporal sequences requires credit assignment to events far back in the past. The most common method for training recurrent neural networks, back-propagation through time (BPTT), requires credit information to be propagated backwards through every single step of the forward computation, potentially over thousands or millions of time steps. This becomes computationally expensive or even infeasible when used with long sequences. Importantly, biological brains are unlikely to perform such detailed reverse replay over very long sequences of internal states (consider days, months, or years. ) However, humans are often reminded of past memories or mental states which are associated with the current mental state. We consider the hypothesis that such memory associations between past and present could be used for credit assignment through arbitrarily long sequences, propagating the credit assigned to the current state to the associated past state. Based on this principle, we study a novel algorithm which only back-propagates through a few of these temporal skip connections, realized by a learned attention mechanism that associates current states with relevant past states. We demonstrate in experiments that our method matches or outperforms regular BPTT and truncated BPTT in tasks involving particularly long-term dependencies, but without requiring the biologically implausible backward replay through the whole history of states. Additionally, we demonstrate that the proposed method transfers to longer sequences significantly better than LSTMs trained with BPTT and LSTMs trained with full self-attention.

RLDM Conference 2017 Conference Abstract

Overcoming Temptation: Incentive Design for Intertemporal Choice*

• Michael Mozer
• Camden Elliott-Williams
• Shabnam Hakimi
• Adrian Ward

Individuals are often faced with temptations that can lead them astray from long-term goals. We’re interested in developing interventions that steer individuals toward making good initial decisions and then maintaining those decisions over time. In the realm of financial decision making, a particularly successful approach is the prize-linked savings account: individuals are incentivized to make deposits by tying deposits to a periodic lottery that awards bonuses to the savers. Although these lotteries have been very effective in motivating savers across the globe, they are a one-size-fits-all solution. We investigate whether customized bonuses can be more effective in tasks involving delayed gratification. We formalize a delayed-gratification task as a Markov decision problem in which the agent must repeatedly choose between two actions: defecting, which obtains a small immediate reward, and persisting, which eventually obtains a large but delayed reward. We characterize individuals as rational agents subject to temporal discounting and stochastic fluctuations in willpower. Willpower is conceived of as modulating the subjective value of the small immediate reward. Our theory is able to explain key behavioral findings in intertemporal choice, including finish-line effects and the dependence of behavior on relative value of immediate and delayed rewards. We created an online delayed-gratification game in which players score points by selecting a queue to wait in and effortfully advancing to the front. Data collected from the game is fit to the model, and the instantiated model is then used to optimize predicted player performance over a space of incentives. We demonstrate that customized incentive structures can improve goal-directed decision making.

NeurIPS Conference 2014 Conference Paper

Automatic Discovery of Cognitive Skills to Improve the Prediction of Student Learning

• Robert Lindsey
• Mohammad Khajah
• Michael Mozer

To master a discipline such as algebra or physics, students must acquire a set of cognitive skills. Traditionally, educators and domain experts manually determine what these skills are and then select practice exercises to hone a particular skill. We propose a technique that uses student performance data to automatically discover the skills needed in a discipline. The technique assigns a latent skill to each exercise such that a student's expected accuracy on a sequence of same-skill exercises improves monotonically with practice. Rather than discarding the skills identified by experts, our technique incorporates a nonparametric prior over the exercise-skill assignments that is based on the expert-provided skills and a weighted Chinese restaurant process. We test our technique on datasets from five different intelligent tutoring systems designed for students ranging in age from middle school through college. We obtain two surprising results. First, in three of the five datasets, the skills inferred by our technique support significantly improved predictions of student performance over the expert-provided skills. Second, the expert-provided skills have little value: our technique predicts student performance nearly as well when it ignores the domain expertise as when it attempts to leverage it. We discuss explanations for these surprising results and also the relationship of our skill-discovery technique to alternative approaches.

NeurIPS Conference 2013 Conference Paper

Optimizing Instructional Policies

• Robert Lindsey
• Michael Mozer
• William Huggins
• Harold Pashler

Psychologists are interested in developing instructional policies that boost student learning. An instructional policy specifies the manner and content of instruction. For example, in the domain of concept learning, a policy might specify the nature of exemplars chosen over a training sequence. Traditional psychological studies compare several hand-selected policies, e. g. , contrasting a policy that selects only difficult-to-classify exemplars with a policy that gradually progresses over the training sequence from easy exemplars to more difficult (known as {\em fading}). We propose an alternative to the traditional methodology in which we define a parameterized space of policies and search this space to identify the optimum policy. For example, in concept learning, policies might be described by a fading function that specifies exemplar difficulty over time. We propose an experimental technique for searching policy spaces using Gaussian process surrogate-based optimization and a generative model of student performance. Instead of evaluating a few experimental conditions each with many human subjects, as the traditional methodology does, our technique evaluates many experimental conditions each with a few subjects. Even though individual subjects provide only a noisy estimate of the population mean, the optimization method allows us to determine the shape of the policy space and identify the global optimum, and is as efficient in its subject budget as a traditional A-B comparison. We evaluate the method via two behavioral studies, and suggest that the method has broad applicability to optimization problems involving humans in domains beyond the educational arena.

NeurIPS Conference 2011 Conference Paper

An Unsupervised Decontamination Procedure For Improving The Reliability Of Human Judgments

• Michael Mozer
• Benjamin Link
• Harold Pashler

Psychologists have long been struck by individuals' limitations in expressing their internal sensations, impressions, and evaluations via rating scales. Instead of using an absolute scale, individuals rely on reference points from recent experience. This relativity of judgment limits the informativeness of responses on surveys, questionnaires, and evaluation forms. Fortunately, the cognitive processes that map stimuli to responses are not simply noisy, but rather are influenced by recent experience in a lawful manner. We explore techniques to remove sequential dependencies, and thereby decontaminate a series of ratings to obtain more meaningful human judgments. In our formulation, the problem is to infer latent (subjective) impressions from a sequence of stimulus labels (e. g. , movie names) and responses. We describe an unsupervised approach that simultaneously recovers the impressions and parameters of a contamination model that predicts how recent judgments affect the current response. We test our iterated impression inference, or I^3, algorithm in three domains: rating the gap between dots, the desirability of a movie based on an advertisement, and the morality of an action. We demonstrate significant objective improvements in the quality of the recovered impressions.

NeurIPS Conference 2010 Conference Paper

Improving Human Judgments by Decontaminating Sequential Dependencies

• Michael Mozer
• Harold Pashler
• Matthew Wilder
• Robert Lindsey
• Matt Jones
• Michael Jones

For over half a century, psychologists have been struck by how poor people are at expressing their internal sensations, impressions, and evaluations via rating scales. When individuals make judgments, they are incapable of using an absolute rating scale, and instead rely on reference points from recent experience. This relativity of judgment limits the usefulness of responses provided by individuals to surveys, questionnaires, and evaluation forms. Fortunately, the cognitive processes that transform internal states to responses are not simply noisy, but rather are influenced by recent experience in a lawful manner. We explore techniques to remove sequential dependencies, and thereby decontaminate a series of ratings to obtain more meaningful human judgments. In our formulation, decontamination is fundamentally a problem of inferring latent states (internal sensations) which, because of the relativity of judgment, have temporal dependencies. We propose a decontamination solution using a conditional random field with constraints motivated by psychological theories of relative judgment. Our exploration of decontamination models is supported by two experiments we conducted to obtain ground-truth rating data on a simple length estimation task. Our decontamination techniques yield an over 20% reduction in the error of human judgments.

NeurIPS Conference 2009 Conference Paper

Predicting the Optimal Spacing of Study: A Multiscale Context Model of Memory

• Harold Pashler
• Nicholas Cepeda
• Robert Lindsey
• Ed Vul
• Michael Mozer

When individuals learn facts (e. g. , foreign language vocabulary) over multiple study sessions, the temporal spacing of study has a significant impact on memory retention. Behavioral experiments have shown a nonmonotonic relationship between spacing and retention: short or long intervals between study sessions yield lower cued-recall accuracy than intermediate intervals. Appropriate spacing of study can double retention on educationally relevant time scales. We introduce a Multiscale Context Model (MCM) that is able to predict the influence of a particular study schedule on retention for specific material. MCMs prediction is based on empirical data characterizing forgetting of the material following a single study session. MCM is a synthesis of two existing memory models (Staddon, Chelaru, & Higa, 2002; Raaijmakers, 2003). On the surface, these models are unrelated and incompatible, but we show they share a core feature that allows them to be integrated. MCM can determine study schedules that maximize the durability of learning, and has implications for education and training. MCM can be cast either as a neural network with inputs that fluctuate over time, or as a cascade of leaky integrators. MCM is intriguingly similar to a Bayesian multiscale model of memory (Kording, Tenenbaum, Shadmehr, 2007), yet MCM is better able to account for human declarative memory.

NeurIPS Conference 2009 Conference Paper

Sequential effects reflect parallel learning of multiple environmental regularities

• Matthew Wilder
• Matt Jones
• Michael Mozer

Across a wide range of cognitive tasks, recent experience influences behavior. For example, when individuals repeatedly perform a simple two-alternative forced-choice task (2AFC), response latencies vary dramatically based on the immediately preceding trial sequence. These sequential effects have been interpreted as adaptation to the statistical structure of an uncertain, changing environment (e. g. Jones & Sieck, 2003; Mozer, Kinoshita, & Shettel, 2007; Yu & Cohen, 2008). The Dynamic Belief Model (DBM) (Yu & Cohen, 2008) explains sequential effects in 2AFC tasks as a rational consequence of a dynamic internal representation that tracks second-order statistics of the trial sequence (repetition rates) and predicts whether the upcoming trial will be a repetition or an alternation of the previous trial. Experimental results suggest that first-order statistics (base rates) also influence sequential effects. We propose a model that learns both first- and second-order sequence properties, each according to the basic principles of the DBM but under a unified inferential framework. This model, the Dynamic Belief Mixture Model (DBM2), obtains precise, parsimonious fits to data. Furthermore, the model predicts dissociations in behavioral (Maloney, Dal Martello, Sahm, & Spillmann, 2005) and electrophysiological studies (Jentzsch & Sommer, 2002), supporting the psychological and neurobiological reality of its two components.

NeurIPS Conference 2008 Conference Paper

Optimal Response Initiation: Why Recent Experience Matters

• Matt Jones
• Sachiko Kinoshita
• Michael Mozer

In most cognitive and motor tasks, speed-accuracy tradeoffs are observed: Individuals can respond slowly and accurately, or quickly yet be prone to errors. Control mechanisms governing the initiation of behavioral responses are sensitive not only to task instructions and the stimulus being processed, but also to the recent stimulus history. When stimuli can be characterized on an easy-hard dimension (e. g. , word frequency in a naming task), items preceded by easy trials are responded to more quickly, and with more errors, than items preceded by hard trials. We propose a rationally motivated mathematical model of this sequential adaptation of control, based on a diffusion model of the decision process in which difficulty corresponds to the drift rate for the correct response. The model assumes that responding is based on the posterior distribution over which response is correct, conditioned on the accumulated evidence. We derive this posterior as a function of the drift rate, and show that higher estimates of the drift rate lead to (normatively) faster responding. Trial-by-trial tracking of difficulty thus leads to sequential effects in speed and accuracy. Simulations show the model explains a variety of phenomena in human speeded decision making. We argue this passive statistical mechanism provides a more elegant and parsimonious account than extant theories based on elaborate control structures.

NeurIPS Conference 2008 Conference Paper

Temporal Dynamics of Cognitive Control

• Jeremy Reynolds
• Michael Mozer

Cognitive control refers to the flexible deployment of memory and attention in response to task demands and current goals. Control is often studied experimentally by presenting sequences of stimuli, some demanding a response, and others modulating the stimulus-response mapping. In these tasks, participants must maintain information about the current stimulus-response mapping in working memory. Prominent theories of cognitive control use recurrent neural nets to implement working memory, and optimize memory utilization via reinforcement learning. We present a novel perspective on cognitive control in which working memory representations are intrinsically probabilistic, and control operations that maintain and update working memory are dynamically determined via probabilistic inference. We show that our model provides a parsimonious account of behavioral and neuroimaging data, and suggest that it offers an elegant conceptualization of control in which behavior can be cast as optimal, subject to limitations on learning and the rate of information processing. Moreover, our model provides insight into how task instructions can be directly translated into appropriate behavior and then efficiently refined with subsequent task experience.

NeurIPS Conference 2007 Conference Paper

Experience-Guided Search: A Theory of Attentional Control

• David Baldwin
• Michael Mozer

People perform a remarkable range of tasks that require search of the visual en- vironment for a target item among distractors. The Guided Search model (Wolfe, 1994, 2007), or GS, is perhaps the best developed psychological account of hu- man visual search. To prioritize search, GS assigns saliency to locations in the visual field. Saliency is a linear combination of activations from retinotopic maps representing primitive visual features. GS includes heuristics for setting the gain coefficient associated with each map. Variants of GS have formalized the notion of optimization as a principle of attentional control (e. g. , Baldwin & Mozer, 2006; Cave, 1999; Navalpakkam & Itti, 2006; Rao et al. , 2002), but every GS-like model must be ’dumbed down’ to match human data, e. g. , by corrupting the saliency map with noise and by imposing arbitrary restrictions on gain modulation. We propose a principled probabilistic formulation of GS, called Experience-Guided Search (EGS), based on a generative model of the environment that makes three claims: (1) Feature detectors produce Poisson spike trains whose rates are conditioned on feature type and whether the feature belongs to a target or distractor; (2) the en- vironment and/or task is nonstationary and can change over a sequence of trials; and (3) a prior specifies that features are more likely to be present for target than for distractors. Through experience, EGS infers latent environment variables that determine the gains for guiding search. Control is thus cast as probabilistic infer- ence, not optimization. We show that EGS can replicate a range of human data from visual search, including data that GS does not address.

NeurIPS Conference 2006 Conference Paper

Context Effects in Category Learning: An Investigation of Four Probabilistic Models

• Michael Mozer
• Michael Shettel
• Michael Holmes

Categorization is a central activity of human cognition. When an individual is asked to categorize a sequence of items, context effects arise: categorization of one item influences category decisions for subsequent items. Specifically, when experimental subjects are shown an exemplar of some target category, the category prototype appears to be pulled toward the exemplar, and the prototypes of all nontarget categories appear to be pushed away. These push and pull effects diminish with experience, and likely reflect long-term learning of category boundaries. We propose and evaluate four principled probabilistic (Bayesian) accounts of context effects in categorization. In all four accounts, the probability of an exemplar given a category is encoded as a Gaussian density in feature space, and categorization involves computing category posteriors given an exemplar. The models differ in how the uncertainty distribution of category prototypes is represented (localist or distributed), and how it is updated following each experience (using a maximum likelihood gradient ascent, or a Kalman filter update). We find that the distributed maximum-likelihood model can explain the key experimental phenomena. Further, the model predicts other phenomena that were confirmed via reanalysis of the experimental data. Categorization is a key cognitive activity. We continually make decisions about characteristics of objects and individuals: Is the fruit ripe? Does your friend seem unhappy? Is your car tire flat? When an individual is asked to categorize a sequence of items, context effects arise: categorization of one item influences category decisions for subsequent items. Intuitive naturalistic scenarios in which context effects occur are easy to imagine. For example, if one lifts a medium-weight object after lifting a light-weight or heavy-weight object, the medium weight feels heavier following the light weight than following the heavy weight. Although the object-contrast effect might be due to fatigue of sensory-motor systems, many context effects in categorization are purely cognitive and cannot easily be attributed to neural habituation. For example, if you are reviewing a set of conference papers, and the first three in the set are dreadful, then even a mediocre paper seems like it might be above threshold for acceptance. Another example of a category boundary shift due to context is the following. Suppose you move from San Diego to Pittsburgh and notice that your neighbors repeatedly describe muggy, somewhat overcast days as "lovely. " Eventually, your notion of what constitutes a lovely day accommodates to your new surroundings. As we describe shortly, experimental studies have shown a fundamental link between context effects in categorization and long-term learning of category boundaries. We believe that context effects can be viewed as a reflection of a trial-to-trial learning, and the cumulative effect of these trial-to-trial modulations corresponds to what we classically consider to be category learning. Consequently, any compelling model of category learning should also be capable of explaining context effects. 1 Experimental Studies of Context Effects in Categorization Consider a set of stimuli that vary along a single continuous dimension. Throughout this paper, we use as an illustration circles of varying diameters, and assume four categories of circles defined ranges of diameters; call them A, B, C, and D, in order from smallest to largest diameter. In a classification paradigm, experimental subjects are given an exemplar drawn from one category and are asked to respond with the correct category label (Zotov, Jones, & Mewhort, 2003). After making their response, subjects receive feedback as to the correct label, which we'll refer to as the target. In a production paradigm, subjects are given a target category label and asked to produce an exemplar of that category, e. g. , using a computer mouse to indicate the circle diameter (Jones & Mewhort, 2003). Once a response is made, subjects receive feedback as to the correct or true category label for the exemplar they produced. Neither classification nor production task has sequential structure, because the order of trial is random in both experiments. The production task provides direct information about the subjects' internal representations, because subjects are producing exemplars that they consider to be prototypes of a category, whereas the categorization task requires indirect inferences to be made about internal representations from reaction time and accuracy data. Nonetheless, the findings in the production and classification tasks mirror one another nicely, providing converging evidence as to the nature of learning. The production task reveals how mental representations shift as a function of trial-to-trial sequences, and these shifts cause the sequential pattern of errors and response times typically observed in the classification task. We focus on the production task in this paper because it provides a richer source of data. However, we address the categorization task with our models as well. Figure 1 provides a schematic depiction of the key sequential effects in categorization. The horizontal line represents the stimulus dimension, e. g. , circle diameter. The dimension is cut into four regions labeled with the corresponding category. The category center, which we'll refer to as the prototype, is indicated by a vertical dashed line. The long solid vertical line marks the current exemplar--whether it is an exemplar presented to subjects in the classification task or an exemplar generated by subjects in the production task. Following an experimental trial with this exemplar, category prototypes appear to shift: the target-category prototype moves toward the exemplar, which we refer to as a pull effect, and all nontarget-category prototypes move away from the exemplar, which we refer to as a push effect. Push and pull effects are assessed in the production task by examining the exemplar produced on the following trial, and in the categorization task by examining the likelihood of an error response near category boundaries. The set of phenomena to be explained are as follows, described in terms of the production task. All numerical results referred to are from Jones and Mewhort (2003). This experiment consisted of 12 blocks of 40 trials, with each category label given as target 10 times within a block. Within-category pull: When a target category is repeated on successive trials, the exemplar generated on the second trial moves toward the exemplar generated on the first trial, with respect to the true category prototype. Across the experiment, a correlation coefficient of 0. 524 is obtained, and remains fairly constant over trials. Between-category push: When the target category changes from one trial to the next, the exemplar generated on the second trial moves away from the exemplar generated on the first trial (or equivalently, from the prototype of the target category on the first trial). Figure 2a summarizes the sequential push effects from Jones and Mewhort. The diameter of the circle produced on trial t is plotted as a function of the target category on trial t - 1, with one line for each of the four trial t targets. The mean diameter for each target category is subtracted out, so the absolute vertical offset of each line is unimportant. The main feature of the data to note is that all four curves have a negative slope, which has the following meaning: the smaller that target t - 1 is (i. e. , the further to the left on the x axis in Figure 1), the larger the response to target t is (further to the right in Figure 1), and vice versa, reflecting a push away from target t - 1. Interestingly and importantly, the magnitude of the push increases with the ordinal distance between targets t - 1 and t. Figure 2a is based on data from only eight subjects and is therefore noisy, though the effect is statistically reliable. As further evidence, Figure 2b shows data from a categorization task (Zotov et al. , 2003), where the y-axis is a different dependent measure, but the negative slope has the same interpretation as in Figure 2a. example Figure 1: Schematic depiction of sequential effects in categorization

NeurIPS Conference 2005 Conference Paper

Top-Down Control of Visual Attention: A Rational Account

• Michael Shettel
• Shaun Vecera
• Michael Mozer

Theories of visual attention commonly posit that early parallel processes extract con- spicuous features such as color contrast and motion from the visual field. These features are then combined into a saliency map, and attention is directed to the most salient regions first. Top-down attentional control is achieved by modulating the contribution of different feature types to the saliency map. A key source of data concerning attentional control comes from behavioral studies in which the effect of recent experience is exam- ined as individuals repeatedly perform a perceptual discrimination task (e. g. , “what shape is the odd-colored object? ”). The robust finding is that repetition of features of recent trials (e. g. , target color) facilitates performance. We view this facilitation as an adaptation to the statistical structure of the environment. We propose a probabilistic model of the environment that is updated after each trial. Under the assumption that attentional control operates so as to make performance more efficient for more likely environmental states, we obtain parsimonious explanations for data from four different experiments. Further, our model provides a rational explanation for why the influence of past experience on attentional control is short lived.

NeurIPS Conference 2004 Conference Paper

Reducing Spike Train Variability: A Computational Theory Of Spike-Timing Dependent Plasticity

• Sander Bohte
• Michael Mozer

Experimental studies have observed synaptic potentiation when a presynaptic neuron fires shortly before a postsynaptic neuron, and synaptic depression when the presynaptic neuron fires shortly af- ter. The dependence of synaptic modulation on the precise tim- ing of the two action potentials is known as spike-timing depen- dent plasticity or STDP. We derive STDP from a simple compu- tational principle: synapses adapt so as to minimize the postsy- naptic neuron's variability to a given presynaptic input, causing the neuron's output to become more reliable in the face of noise. Using an entropy-minimization objective function and the biophys- ically realistic spike-response model of Gerstner (2001), we simu- late neurophysiological experiments and obtain the characteristic STDP curve along with other phenomena including the reduction in synaptic plasticity as synaptic efficacy increases. We compare our account to other efforts to derive STDP from computational princi- ples, and argue that our account provides the most comprehensive coverage of the phenomena. Thus, reliability of neural response in the face of noise may be a key goal of cortical adaptation. 1 Introduction Experimental studies have observed synaptic potentiation when a presynaptic neu- ron fires shortly before a postsynaptic neuron, and synaptic depression when the presynaptic neuron fires shortly after. The dependence of synaptic modulation on the precise timing of the two action potentials, known as spike-timing dependent plasticity or STDP, is depicted in Figure 1. Typically, plasticity is observed only when the presynaptic and postsynaptic spikes (hereafter, pre and post) occur within a 2030 ms time window, and the transition from potentiation to depression is very rapid. Another important observation is that synaptic plasticity decreases with in- creased synaptic efficacy. The effects are long lasting, and are therefore referred to as long-term potentiation (LTP) and depression (LTD). For detailed reviews of the evidence for STDP, see [1, 2]. Because these intriguing findings appear to describe a fundamental learning mech- anism in the brain, a flurry of models have been developed that focus on different aspects of STDP, from biochemical models that explain the underlying mechanisms giving rise to STDP [3], to models that explore the consequences of a STDP-like learning rules in an ensemble of spiking neurons [4, 5, 6, 7], to models that pro- pose fundamental computational justifications for STDP. Most commonly, STDP Figure 1: (a) Measuring STDP experimentally: pre-post spike pairs are repeatedly in- duced at a fixed interval tpre-post, and the resulting change to the strength of the synapse is assessed; (b) change in synaptic strength after repeated spike pairing as a function of the difference in time between the pre and post spikes (data from Zhang et al. , 1998). We have superimposed an exponential fit of LTP and LTD. is viewed as a type of asymmetric Hebbian learning with a temporal dimension. However, this perspective is hardly a fundamental computational rationale, and one would hope that such an intuitively sensible learning rule would emerge from a first-principle computational justification. Several researchers have tried to derive a learning rule yielding STDP from first principles. Rao and Sejnowski [8] show that STDP emerges when a neuron attempts to predict its membrane potential at some time t from the potential at time t - t. However, STDP emerges only for a narrow range of t values, and the qualitative nature of the modeling makes it unclear whether a quantitative fit can be obtained. Dayan and H ausser [9] show that STDP can be viewed as an optimal noise-removal filter for certain noise distributions. However, even small variation from these noise distributions yield quite different learning rules, and the noise statistics of biological neurons are unknown. Eisele (private communication) has shown that an STDP-like learning rule can be derived from the goal of maintaining the relevant connections in a network. Chechik [10] is most closely related to the present work. He relates STDP to information theory via maximization of mutual information between input and output spike trains. This approach derives the LTP portion of STDP, but fails to yield the LTD portion. The computational approach of Chechik (as well as Dayan and H ausser) is premised on a rate-coding neuron model that disregards the relative timing of spikes. It seems quite odd to argue for STDP using rate codes: if spike timing is irrelevant to information transmission, then STDP is likely an artifact and is not central to understanding mechanisms of neural computation. Further, as noted in [9], because STDP is not quite additive in the case of multiple input or output spikes that are near in time [11], one should consider interpretations that are based on individual spikes, not aggregates over spike trains. Here, we present an alternative computational motivation for STDP. We conjecture that a fundamental objective of cortical computation is to achieve reliable neural re- sponses, that is, neurons should produce the identical response--both in the number and timing of spikes--given a fixed input spike train. Reliability is an issue if neu- rons are affected by noise influences, because noise leads to variability in a neuron's dynamics and therefore in its response. Minimizing this variability will reduce the effect of noise and will therefore increase the informativeness of the neuron's output signal. The source of the noise is not important; it could be intrinsic to a neuron (e. g. , a noisy threshold) or it could originate in unmodeled external sources causing fluctuations in the membrane potential uncorrelated with a particular input. We are not suggesting that increasing neural reliability is the only learning objective. If it were, a neuron would do well to give no response regardless of the input. Rather, reliability is but one of many objectives that learning tries to achieve. This form of unsupervised learning must, of course, be complemented by supervised and reinforcement learning that allow an organism to achieve its goals and satisfy drives. We derive STDP from the following computational principle: synapses adapt so as to minimize the entropy of the postsynaptic neuron's output in response to a given presynaptic input. In our simulations, we follow the methodology of neurophysiolog- ical experiments. This approach leads to a detailed fit to key experimental results. We model not only the shape (sign and time course) of the STDP curve, but also the fact that potentiation of a synapse depends on the efficacy of the synapse--it decreases with increased efficacy. In addition to fitting these key STDP phenom- ena, the model allows us to make predictions regarding the relationship between properties of the neuron and the shape of the STDP curve. Before delving into the details of our approach, we attempt to give a basic intu- ition about the approach. Noise in spiking neuron dynamics leads to variability in the number and timing of spikes. Given a particular input, one spike train might be more likely than others, but the output is nondeterministic. By the entropy- minimization principle, adaptation should reduce the likelihood of these other pos- sibilities. To be concrete, consider a particular experimental paradigm. In [12], a pre neuron is identified with a weak synapse to a post neuron, such that the pre is unlikely to cause the post to fire. However, the post can be induced to fire via a second presynaptic connection. In a typical trial, the pre is induced to fire a single spike, and with a variable delay, the post is also induced to fire (typically) a single spike. To increase the likelihood of the observed post response, other response pos- sibilities must be suppressed. With presynaptic input preceding the postsynaptic spike, the most likely alternative response is no output spikes at all. Increasing the synaptic connection weight should then reduce the possibility of this alternative response. With presynaptic input following the postsynaptic spike, the most likely alternative response is a second output spike. Decreasing the synaptic connection weight should reduce the possibility of this alternative response. Because both of these alternatives become less likely as the lag between pre and post spikes is in- creased, one would expect that the magnitude of synaptic plasticity diminishes with the lag, as is observed in the STDP curve. Our approach to reducing response variability given a particular input pattern in- volves computing the gradient of synaptic weights with respect to a differentiable model of spiking neuron behavior. We use the Spike Response Model (SRM) of [13] with a stochastic threshold, where the stochastic threshold models fluctuations of the membrane potential or the threshold outside of experimental control. For the stochastic SRM, the response probability is differentiable with respect to the synap- tic weights, allowing us to calculate the entropy gradient with respect to the weights conditional on the presented input. Learning is presumed to take a gradient step to reduce this conditional entropy. In modeling neurophysiological experiments, we demonstrate that this learning rule yields the typical STDP curve. We can predict the relationship between the exact shape of the STDP curve and physiologically measurable parameters, and we show that our results are robust to the choice of the few free parameters of the model. Two papers in these proceedings are closely related to our work. They also find STDP-like curves when attempting to maximize an information-theoretic measure-- the mutual information between input and output--for a Spike Response Model [14, 15]. Bell & Parra [14] use a deterministic SRM model which does not model the LTD component of STDP properly. The derivation by Toyoizumi et al. [15] is valid only for an essentially constant membrane potential with small fluctuations. Neither of these approaches has succeeded in quantitatively modeling specific experimental data with neurobiologically-realistic timing parameters, and neither explains the saturation of LTD/LTP with increasing weights as we do. Nonetheless, these models make an interesting contrast to ours by suggesting a computational principle of optimization of information transmission, as contrasted with our principle of neural noise reduction. Perhaps experimental tests can be devised to distinguish between these competing theories. 2 The Stochastic Spike Response Model The Spike Response Model (SRM), defined by Gerstner [13], is a generic integrate- and-fire model of a spiking neuron that closely corresponds to the behavior of a biological spiking neuron and is characterized in terms of a small set of easily inter- pretable parameters [16]. The standard SRM formulation describes the temporal evolution of the membrane potential based on past neuronal events, specifically as a weighted sum of postsynaptic potentials (PSPs) modulated by reset and thresh- old effects of previous postsynaptic spiking events. Following [13], the membrane potential of cell i at time t, ui(t), is defined as: ui(t) = (t - ^ fi) + wij (t - ^ fi, t - fj), (1) ji fj F t j where i is the set of inputs connected to neuron i, Ft is the set of times prior to j t that neuron j has spiked, ^ fi is the time of the last spike of neuron i, wij is the synaptic weight from neuron j to neuron i, (t - ^ fi, t - fj) is the PSP in neuron i due to an input spike from neuron j at time fj, and (t - ^ fi) is the refractory response due to the postsynaptic spike at time ^ fi. Neuron i fires when the potential ui(t) exceeds a threshold () from below. The postsynaptic potential is modeled as the differential alpha function in [13], defined with respect to two variables: the time since the most recent postsynaptic spike, x, and the time since the presynaptic spike, s: 1 s s (x, s) = exp - - exp - H(s)H(x - s)+ (2) 1 - s m s m s - x x x +exp - exp - - exp - H(x)H(s - x), s m s where s and m are the rise and decay time-constants of the PSP, and H is the Heaviside function. The refractory reset function is defined to be [13]: x + x (x) = u abs absH(abs - x)H(-x) + uabsexp - + usexp -, (3) r f s r r where uabs is a large negative contribution to the potential to model the absolute refractory period, with duration abs. We smooth this refractory response by a fast decaying exponential with time constant f. The third term in the sum represents r the slow decaying exponential recovery of an elevated threshold, us, with time r constant s. (Graphs of these and functions can be found in [13]. ) We made r a minor modification to the SRM described in [13] by relaxing the constraint that s = r m; smoothing the absolute refractory function is mentioned in [13] but not explicitly defined as we do here. In all simulations presented, abs = 2ms, s = 4 r m, and f = 0. 1 r m. The SRM we just described is deterministic. Gerstner [13] introduces a stochas- tic variant of the SRM (sSRM) by incorporating the notion of a stochastic firing threshold: given membrane potential ui(t), the probability density of the neuron firing at time t is specified by (ui(t)). Herrmann & Gerstner [17] find that then for a realistic escape-rate noise model the firing probability density as a function of the potential is initially small and constant, transitioning to asymptotically linear increasing around threshold. In our simulations, we use such a function: (v) = (ln[1 + exp(( - v))] - ( - v)), (4) where is the firing threshold in the absence of noise, determines the abruptness of the constant-to-linear probability density transition around, and determines the slope of the increasing part. Experiments with sigmoidal and exponential density functions were found to not qualitatively affect the results. 3 Minimizing Conditional Entropy We now derive the rule for adjusting the weight from a presynaptic neuron j to a postsynaptic sSRM neuron i, so as to minimize the entropy of i's response given a particular spike sequence from j. A spike sequence is described by the set of all times at which spikes have occurred within some interval between 0 and T, denoted F T for neuron j. We assume the interval is wide enough that spikes outside the j interval do not influence the state of the neuron within the interval (e. g. , through threshold reset effects). We can then treat intervals as independent of each other. Let the postsynaptic neuron i produce a response i, where i is the set of all possible responses given the input, FT, and g() is the probability density over i responses. The differential conditional entropy h(i) of neuron i's response is then defined as: h(i) = - g()log g() d. (5) i To minimize the differential conditional entropy by adjusting the neuron's weights, we compute the gradient of the conditional entropy with respect to the weights: h(i) log(g()) = - g() log(g()) + 1 d. (6) wij wij i For a differentiable neuron model, log(g())/wij can be expressed as follows when neuron i fires once at time ^ fi [18]: log(g()) T (u u (t - ^ fi) - (ui(t)) = i(t)) i(t) dt, (7) wij t=0 ui(t) wij (ui(t)) where (. ) is the Dirac delta, and (ui(t)) is the firing probability-density of neuron i at time t. (See [18] for the generalization to multiple postsynaptic spikes. ) With the sSRM we can compute the partial derivatives (ui(t))/ui(t) and ui(t)/wij. Given the density function (4), (ui(t)) u =, i(t) = (t - ^ f u i, t - fj ). i(t) 1 + exp(( - ui(t)) wij To perform gradient descent in the conditional entropy, we use the weight update h( w i) ij - (8) wij T (t - ^ fi, t - fj) (t - ^ fi) - (ui(t)) g() log(g()) + 1 dt d. (1 + exp(( - ui(t)))(ui(t)) i t=0 We can use numerical methods to evaluate Equation (8). However, it seems bio- logically unrealistic to suppose a neuron can integrate over all possible responses. This dilemma can be circumvented in two ways. First, the resulting learning rule might be cached in some form through evolution so that the full computation is not necessary (e. g. , in an STDP curve). Second, the specific response produced by a neuron on a single trial might be considered to be a sample from the distribution g(), and the integration is performed by a sampling process over repeated trials; Figure 2: (a) Experimental setup of Zhang et al. and (b) their experimental STDP curve (small squares) vs. our model (solid line). Model parameters: s = 1. 5ms, m = 12. 25ms. each trial would produce a stochastic gradient step. 4 Simulation Methodology We model in detail the experiment of Zhang et al. [12] (Figure 2a). In this exper- iment, a post neuron is identified that has two neurons projecting to it, call them the pre and the driver. The pre is subthreshold: it produces depolarization but no spike. The driver is suprathreshold: it induces a spike in the post. Plasticity of the pre-post synapse is measured as a function of the timing between pre and post spikes (tpre-post) by varying the timing between induced spikes in the pre and the driver (tpre-driver). This measurement yields the well-known STDP curve (Figure 1b). 1 The experiment imposes several constraints on a simulation: The driver alone causes spiking > 70% of the time, the pre alone causes spiking < 10% of the time, synchronous firing of driver and pre cause LTP if and only if the post fires, and the time constants of the EPSPs--s and m in the sSRM--are in the range of 13ms and 1015ms respectively. These constraints remove many free parameters from our simulation. We do not explicitly model the two input cells; instead, we model the EPSPs they produce. The magnitude of these EPSPs are picked to satisfy the experimental constraints: the driver EPSP alone causes a spike in the post on 77. 4% of trials, and the pre EPSP alone causes a spike on fewer than 0. 1% of trials. Free parameters of the simulation are and in the spike-probability function ( can be folded into ), and the magnitude (us, u, f, r abs) and reset time constants ( s r r abs). The dependent variable of the simulation is tpre-driver, and we measure the time of the post spike to determine tpre-post. We estimate the weight update for a given tpre-driver using Equation 8, approximating the integral by a summation over all time-discretized output responses consisting of 0, 1, or 2 spikes. Three or more spikes have a probability that is vanishingly small.

NeurIPS Conference 2004 Conference Paper

Theories of Access Consciousness

• Michael Colagrosso
• Michael Mozer

Theories of access consciousness address how it is that some mental states but not others are available for evaluation, choice behavior, and verbal report. Farah, O'Reilly, and Vecera (1994) argue that quality of representation is critical; De- haene, Sergent, and Changeux (2003) argue that the ability to communicate rep- resentations is critical. We present a probabilistic information transmission or PIT model that suggests both of these conditions are essential for access con- sciousness. Having successfully modeled data from the repetition priming litera- ture in the past, we use the PIT model to account for data from two experiments on subliminal priming, showing that the model produces priming even in the ab- sence of accessibility and reportability of internal states. The model provides a mechanistic basis for understanding the dissociation of priming and awareness. Philosophy has made many attempts to identify distinct aspects of consciousness. Perhaps the most famous effort is Block's (1995) delineation of phenomenal and access conscious- ness. Phenomenal consciousness has to do with "what it is like" to experience chocolate or a pin prick. Access consciousness refers to internal states whose content is "(1) inferen- tially promiscuous, i. e. , poised to be used as a premise in reasoning, (2) poised for control of action, and (3) poised for rational control of speech. " (p. 230) The scientific study of con- sciousness has exploded in the past six years, and an important catalyst for this explosion has been the decision to focus on the problem of access consciousness: how is it that some mental states but not others become available for evaluation, choice behavior, verbal report, and storage in working memory. Another reason for the recent explosion of consciousness research is the availability of functional imaging techniques to explore differences in brain activation between conscious and unconscious states, as well as the development of clever psychological experiments that show that a stimulus that is not consciously perceived can nonetheless influence cognition, which we describe shortly. 1 Subliminal Priming The phenomena we address utilize an experimental paradigm known as repetition priming. Priming refers to an improvement in efficiency in processing a stimulus item as a result of previous exposure to the item. Efficiency is defined in terms of shorter response times, lower error rates, or both. A typical long-term perceptual priming experiment consists of a study phase during which participants are asked to read aloud a list of words, and a test phase during which participants must name or categorize a series of words, presented one at a time. Reaction time is lower and/or accuracy is higher for test words that were also on the study list. Repetition priming occurs without strategic effort on the part of participants, and therefore appears to be a low level mechanism of learning, which likely serves as the mechanism underlying the refinement of cognitive skills with practice. In traditional studies, priming is supraliminal--the prime is consciously perceived. In the studies we model here, primes are subliminal. Subliminal priming addresses fundamental issues concerning conscious access: How is it that a word or image that cannot be identified, detected, or even discriminated in forced choice can nonetheless influence the processing of a subsequent stimulus word? Answering this question in a computational framework would be a significant advance toward understanding the nature of access consciousness. 2 Models of Conscious and Unconscious Processing In contrast to the wealth of experimental data, and the large number of speculative and philosophical papers on consciousness, concrete computational models are rare. The do- main of consciousness is particularly ripe for theoretical perspectives, because it is a sig- nificant contribution to simply provide an existence proof of a mechanism that can explain specific experimental data. Ordinarily, a theorist faces skepticism when presenting a model; it often seems that hundreds of alternative, equally plausible accounts must exist. However, when addressing data deemed central to issues of consciousness, simply providing a con- crete handle on the phenomena serves to demystify consciousness and bring it into the realm of scientific understanding. We are familiar with only three computational models that address specific experimental data in the domain of consciousness. We summarize these models, and then present a novel model and describe its relationship to the previous efforts. Farah, O'Reilly, and Ve- cera (1994) were the first to model specific phenomena pertaining to consciousness in a computational framework. The phenomena involve prosopagnosia, a deficit of overt face recognition following brain damage. Nonetheless, prosopagnosia patients exhibit residual covert recognition by a variety of tests. For example, when patients are asked to categorize names as famous or nonfamous, their response times are faster to a famous name when the name is primed by a picture of a semantically related face (e. g. , the name "Bill Clinton" when preceded by a photograph of Hillary), despite the fact that they could not identify the related face. Farah et al. model face recognition in a neural network, and show that when the network is damaged, it loses the ability to perform tasks requiring high fidelity represen- tations (e. g. , identification) but not tasks requiring only coarse information (e. g. , semantic priming). They argue that conscious perception is associated with a certain minimal quality of representation. Dehaene and Naccache (2001) outline a framework based on Baars' (1989) notion of con- scious states as residing in a global workspace. They describe the workspace as a "dis- tributed neural system. .. with long-distance connectivity that can potentially interconnect multiple specialized brain areas in a coordinated, though variable manner. " (p. 13) De- haene, Sergent, and Changeaux (2003) implement this framework in a complicated archi- tecture of integrate-and-fire neurons and show that the model can qualitatively account for the attentional blink phenomenon. The attentional blink is observed in experiments where participants are shown a rapid series of stimuli, which includes two targets (T1 and T2). If T2 appears shortly after T1, the ability to report T2 drops, as if attention is distracted. Dehane et al. explain this phenomenon as follows. When T1 is presented, its activation propagates to frontal cortical areas (the global workspace). Feedback connections lead to a resonance between frontal and posterior areas, which strengthen T1 but block T2 from entering the workspace. If the T1-T2 lag is sufficiently great, habituation of T1 sufficiently weakens the representation such that T2 can enter the workspace and suppress T1. In this account, conscious access is achieved via resonance between posterior and frontal areas. Although the Farah et al. and Dehaene et al. models might not seem to have much in common, they both make claims concerning what is required to achieve functional con- nectivity between perceptual and response systems. Farah et al. focus on aspects of the representation; Dehaene et al. focus on a pathway through which representations can be communicated. These two aspects are not incompatible, and in fact, a third model incorpo- rates both. Mathis and Mozer (1996) describe an architecture with processing modules for perceptual and response processes, implemented as attractor neural nets. They argue that in order for a representation in some perceptual module to be assured of influencing a response module, (a) it must have certain characteristicstemporal persistence and well-formedness which is quite similar to Farah et al. 's notion of quality, and (b) the two modules must be interconnected--which is the purpose of Dehaene et al. 's global workspace. The model has two limitations that restrict its value as a contemporary account of conscious access. First, it addressed classical subliminal priming data, but more reliable data has recently been reported. Second, like the other two models, Mathis and Mozer used a complex neural network architecture with arbitrary assumptions built in, and the sensitivity of the model's behavior to these assumptions is far from clear. In this paper, we present a model that em- bodies the same assumptions as Mathis and Mozer, but overcomes its two limitations, and explains subliminal-priming data that has yet to be interpreted via a computational model. 3 The Probabilistic Information Transmission (PIT) Framework Our model is based on the probabilistic information transmission or PIT framework of Mozer, Colagrosso, and Huber (2002, 2003). The framework characterizes the transmission of information from perceptual to response systems, and how the time course of informa- tion transmission changes with experience (i. e. , priming). Mozer et al. used this framework to account for a variety of facilitation effects from supraliminal repetition priming. The framework describes cognition in terms of a collection of information-processing path- ways, and supposes that any act of cognition involves coordination among multiple path- ways. For example, to model a letter-naming task where a letter printed in upper or lower case is presented visually and the letter must be named, the framework would assume a perceptual pathway that maps the visual input to an identity representation, and a response pathway that maps a identity representation to a naming response. The framework is for- malized as a probabilistic model: the pathway input and output are random variables and microinference in a pathway is carried out by Bayesian belief revision. The framework captures the time course of information processing for a single experi- mental trial. To elaborate, consider a pathway whose input at time t is a discrete random variable, denoted X(t), which can assume values x1, x2, x3, .. ., xn corresponding to al- x ternative input states. Similarly, the output of the pathway at time t is a discrete random variable, denoted Y (t), which can assume values y1, y2, y3, .. ., yn. For example, in the y letter-naming task, the input to the perceptual pathway would be one of nx = 52 visual patterns corresponding to the upper- and lower-case letters of the alphabet, and the output is one of ny = 26 letter identities. To present a particular input alternative, say xi, to the model for T time steps, we specify X(t) = xi for t = 1. .. T, and allow the model to compute P(Y (t) | X(1). .. X(t)). A pathway is modeled as a dynamic Bayes network; the minimal version of the model used in the present simulations is simply a hidden Markov model, where the X(t) are observations and the Y (t) are inferred state (see Figure 1a). In typical usage, an HMM is presented with a sequence of distinct inputs, whereas we maintain the same input for many successive time steps; and an HMM transitions through a sequence of distinct hidden states, whereas we attempt to converge with increasing confidence on a single state. Figure 1b illustrates the time course of inference in a single pathway with 52 input and 26 output alternatives and two-to-one associations. The solid line in the Figure shows, as a function of time t, P(Y (t) = yi | X(1) = x2i. .. X(t) = x2i), i. e. , the probability that input i (say, the visual pattern of an upper case O) will produce its target output (the letter identity). Evidence for the target output accumulates gradually over time, yielding a speed-accuracy curve that relates the number of iterations to the accuracy of identification. 1 0. 8 Y Y 0 1 Y2 Y3 0. 6 O 0. 4 P(Output) 0. 2 Q X X 1 2 X3 0 (a) (b) Time Figure 1: (a) basic pathway architecture--a hidden Markov model; (b) time course of inference in a pathway when the letter O is presented, causing activation of both O and the visually similar Q. The exact shape of the speed-accuracy curve--the pathway dynamics--are determined by three probability distributions, which embody the knowledge and past experience of the model. First, P(Y (0)) is the prior distribution over outputs in the absence of any informa- tion about the input. Second, P(Y (t) | Y (t - 1)) characterizes how the pathway output evolves over time. We assume the transition probability matrix serves as a memory with diffusion, i. e. , P(Y (t) = yi|Y (t - 1) = yj) = (1 - )ij + P(Y (0) = yi), where is the diffusion constant and ij is the Kronecker delta. Third, P(X(t) | Y (t)) characterizes the strength of association between inputs and outputs. The greater the association strength, the more rapidly that information about X will be communicated to Y. We parameterize this distribution as P(X(t) = xi|Y (t) = yj) 1 + k ik kj, where ij indicates the frequency of experience with the association between states xi and yj, and ik specifies the similarity between states xi and xk. (Although the representation of states is localist, the terms allow us to design in the similarity structure inherent in a distributed representation. ) These association strengths are highly constrained by the task structure and the similarity structure and familiarity of the inputs. Fundamental to the framework is the assumption that with each experience, a pathway be- comes more efficient at processing an input. Efficiency is reflected by a shift in the speed- accuracy curve to the left. In Mozer, Colagrosso, and Huber (2002, 2003), we propose two distinct mechanisms to model phenomena of supraliminal priming. First, the association frequencies, ij, are increased following a trial in which xi leads to activation of yj, re- sulting in more efficient transmission of information, corresponding to an increased slope of the solid line in Figure 1b. The increase is Hebbian, based on the maximum activation achieved by xi and yj: ij = maxt P(X(t) = xi)P(Y (t) = yj), where is a step size. Second, the priors, which serve as a model of the environment, are increased to indicate a greater likelihood of the same output occurring again in the future. In modeling data from supraliminal priming, we found that the increases to association frequencies are long last- ing, but the increases to the priors decay over the course of a few minutes or a few trials. As a result, the prior updating does not play into the simulation we report here; we refer the reader to Mozer, Colagrosso, and Huber (2003) for details. 4 Access Consciousness and PIT We have described the operation of a single pathway, but to model any cognitive task, we require a series of pathways in cascade. For a simple choice task, we use a percpet- ual pathway cascaded to a response pathway. The interconnection between the pathways is achieved by copying the output of the perceptual pathway, Y p(t), to the input of the response pathway, Xr(t), at each time t. This multiple-pathway architecture allows us to characterize the notion of access con- sciousness. Considering the output of the perceptual pathway, access is achieved when: (1) the output representation is sufficient to trigger the correct behavior in the response pathway, and (2) the perceptual and response pathways are functionally interconnected. In more general terms, access for a perceptual pathway output requires that these two condi- tions be met not just for a specific response pathway, but for arbitrary response pathways (e. g. , pathways for naming, choice, evaluation, working memory, etc. ). In Mozer and Co- lagrosso (in preparation) we characterize the sufficiency requirements of condition 1; they involve a representation of low entropy that stays active for long enough that the represen- tation can propagate to the next pathway. As we will show, a briefly presented stimulus fails to achieve a representation that supports choice and naming responses. Nonetheless, the stimulus evokes activity in the perceptual pathway. Because perceptual priming depends on the magnitude of the activation in the perceptual pathway, not on the activation being communicated to response pathways, the framework is consistent with the notion of priming occurring in the absence of awareness. 4. 1 Simulation of Bar and Biederman (1998) Bar and Biederman (1998) presented a sequence of masked line drawings of objects and asked participants to name the objects, even if they had to guess. If the guess was incorrect, participants were required to choose the object name from a set of four alternatives. Unbe- knownst to the participant, some of the drawings in the series were repeated, and Bar and Biederman were interested in whether participants would benefit from the first presenta- tion even if it could not be identified. The repeated objects could be the same or a different exemplar of the object, and it could appear in either the same or a different display position. Participants were able to name 13. 5% of drawings on presentation 1, but accuracy jumped to 34. 5% on presentation 2. Accuracy did improve, though not as much, if the same shape was presented in a different position, but not if a different drawing of the same object was presented, suggesting a locus of priming early in the visual stream. The improvement in accuracy is not due to practice in general, because accuracy rose only 4. 0% for novel control objects over the course of the experiment. The priming is firmly subliminal, because participants were not only unable to name objects on the first presentation, but their four- alternative forced choice (4AFC) performance was not much above chance (28. 5%). To model these phenomena, we created a response pathway with fifty states representing names of objects that are used in the experiment, e. g. , chair and lamp. We also created a perceptual pathway with states representing visual patterns that correspond to the names in the response pathway. Following the experimental design, every object identity was instantiated in two distinct shapes, and every shape could be in one of nine different visual- field positions, leading to 900 distinct states in the perceptual pathway to model the possible visual stimuli. The following parameters were fit to the data. If two perceptual states, xi and xk are the same shape in different positions, they are assigned a similarity coefficient ik = 0. 95; all other similarity coefficients are zero. The association frequency, , for valid associations in the perceptual pathway was 22, and the response pathway 18. Other parameters were p =. 05, r =. 01, and = 1. 0. The PIT model achieves a good fit to the human experimental data (Figure 2). Specifi- cally, priming is greatest for the same shape in the same position, some priming occurs for the same shape in a different position, and no substantial priming occurs for the different shape. Figure 3a shows the time course of activation of a stimulus representation in the perceptual pathway when the stimulus is presented for 50 iterations, on both the first and third presentations. The third presentation was chosen instead of the second to make the effect of priming clearer. Even though a shape cannot be named on the first presentation, partial information about the shape may nonetheless be available for report. The 4AFC test of Bar and Bieder- man provides a more sensitive measure of residual stimulus information. In past work, we modeled forced-choice tasks using a response pathway with only the alternatives under consideration. However, in this experiment, forced-choice performance must be estimated conditional on incorrect naming. In PIT framework, we achieve this using naming and 40 40 First Block First Block 35 Second Block 35 Second Block 30 30 25 25 20 20 15 15 10 Percent Correct Naming 10 Percent Correct Naming 5 5 0 0 Control Prime SHAPE: Same Same Different Different Second Control Prime SHAPE: Same Same Different Different Second Objects Objects POSITION: Same Different Same Different Control Objects Objects POSITION: Same Different Same Different Control Figure 2: (left panel) Data from Bar and Biederman (1998) (right panel) Simulation of PIT. White bar: accuracy on first presentation of a prime object. Black bars: the accuracy when the object is repeated, either with the same or different shape, and in the same or different position. Grey bars: accuracy for control objects at the beginning and the end of the experiment. forced-choice output pathways having output distributions N (t) and F (t), which are linked via the perceptual state, Y p(t). F (t) must be reestimated with the evidence that N (t) is not the target state. This inference problem is intractable. We therefore used a shortcut in which a single response pathway is used, augmented with a simple three-node belief net (Figure 3b) to capture the dependence between naming and forced choice. The belief net has a response pathway node Y r(t) connected to F (t) and N (t), with conditional distribu- tion P (N (t) = ni|Y r(t) = yj) = ij + (1 - )/|Y r|, and an analogous distribution for P (F (t) = fi|Y r(t) = yj). The free parameter determines how veridically naming and forced-choice actions reflect response-pathway output. Over a range of, 0. 6 object, first presentation 0. 5 object, third presentation 0. 4 N(t) F(t) different object 0. 3 0. 2 Probability 0. 1 0 1 Yr(t) (a) 50 1000 (b) Time (msec) Figure 3: (a) Activation of the perceptual representation in PIT as a function of processing iterations on the first (thin solid line) and third (thick solid line) presentations of target. (b) Bayes net for performing 4AFC conditional on incorrect naming response. 0. 4 Experiment 0. 3 Model alence 0. 2 0. 1 fective VEf 0 targets hulip-type tumor-type orphans Figure 4: Effective valence of primes in the Abrams and Greenwald (2000) experiment for human subjects (black bars) and PIT model (grey bars). HULIP-type primes are almost as strong as target repetitions, and TUMOR-type primes have a positive valence, contrary to the meaning of the word. no significant EV effect when used as primes. In this simulation, we used a three pathway model: a perceptual pathway that maps vi- sual patterns to orthography with 200 input states corresponding both to words, nonwords, and nonword recombinations of words; a semantic pathway that maps to 100 distinct lex- ical/semantic states; and a judgement pathway that maps to two responses, pleasant and unpleasant. In the perceptual pathway, similarity structure was based on letter overlap, so that HULIP was similar to both TULIP and HUMOR, with = 0. 837. No similarity was assumed in the semantic state representation; consistent with the previous simulation, p =. 05, s =. 01, j =. 01, and =. 01. At the outset of the simulation, frequencies for correct associations were 15, 19, and 25 in the perceptual, semantic, and judgement pathways. The initial phase of the experiment was simulated by repeated supraliminal presentation of words, which increased the association frequencies in all three pathways through the ij learning rule. Long-term supraliminal priming is essential in establishing the association strengths, as we'll explain. Short-term subliminal priming also plays a key role in the experiment. Dur- ing the second phase of the experiment, residual activity from the prime--primarily in the judgement pathway--biases the response to the target. Residual activation of the prime is present even if the representation of the prime does not reach sufficient strength that it could be named or otherwise reported. The outcome of the simulation is consistent with the human data (Figure 4). When a HULIP-type prime is presented, HUMOR and TULIP become active in the semantic path- way because of their visual similarity to HULIP. Partial activation of these two practiced words pushes the judgement pathway toward a pleasant response, resulting in a positive EV. When a TUMOR-type prime is presented, three different words become active in the semantic pathway: HUMOR, TULIP, and TUMOR itself. Although TUMOR is more active, it was not one of the words studied during the initial phase of the experiment, and as a result, it has a relatively weak association to the unpleasant judgement, in contrast to the other two words which have strong associations to the pleasant judgement. Orphan primes have little effect because they were not studied during the initial phase of the experiment, and consequently their association to pleasant and unpleasant judgements is also weak. In sum- mary, activation of the prime along a critical, well-practiced pathway may not be sufficient to support an overt naming response, yet it may be sufficient to bias the processing of the immediately following target.

ICML Conference 2003 Conference Paper

Optimizing Classifier Performance via an Approximation to the Wilcoxon-Mann-Whitney Statistic

• Lian Yan
• Robert H. Dodier
• Michael Mozer
• Richard H. Wolniewicz

NeurIPS Conference 2002 Conference Paper

Coulomb Classifiers: Generalizing Support Vector Machines via an Analogy to Electrostatic Systems

• Sepp Hochreiter
• Michael Mozer
• Klaus Obermayer

We introduce a family of classiflers based on a physical analogy to an electrostatic system of charged conductors. The family, called Coulomb classiflers, includes the two best-known support-vector machines (SVMs), the ”{SVM and the C{SVM. In the electrostat- ics analogy, a training example corresponds to a charged conductor at a given location in space, the classiflcation function corresponds to the electrostatic potential function, and the training objective function corresponds to the Coulomb energy. The electrostatic framework provides not only a novel interpretation of existing algo- rithms and their interrelationships, but it suggests a variety of new methods for SVMs including kernels that bridge the gap between polynomial and radial-basis functions, objective functions that do not require positive-deflnite kernels, regularization techniques that allow for the construction of an optimal classifler in Minkowski space. Based on the framework, we propose novel SVMs and per- form simulation studies to show that they are comparable or su- perior to standard SVMs. The experiments include classiflcation tasks on data which are represented in terms of their pairwise prox- imities, where a Coulomb Classifler outperformed standard SVMs.

NeurIPS Conference 2001 Conference Paper

A Rational Analysis of Cognitive Control in a Speeded Discrimination Task

• Michael Mozer
• Michael Colagrosso
• David Huber

We are interested in the mechanisms by which individuals monitor and adjust their performance of simple cognitive tasks. We model a speeded discrimination task in which individuals are asked to classify a sequence of stimuli (Jones & Braver, 2001). Response conflict arises when one stimulus class is infrequent relative to another, resulting in more errors and slower reaction times for the infrequent class. How do control pro- cesses modulate behavior based on the relative class frequencies? We explain performance from a rational perspective that casts the goal of individuals as minimizing a cost that depends both on error rate and re- action time. With two additional assumptions of rationality—that class prior probabilities are accurately estimated and that inference is optimal subject to limitations on rate of information transmission—we obtain a good fit to overall RT and error data, as well as trial-by-trial variations in performance. Consider the following scenario: While driving, you approach an intersection at which the traffic light has already turned yellow, signaling that it is about to turn red. You also notice that a car is approaching you rapidly from behind, with no indication of slowing. Should you stop or speed through the intersection? The decision is difficult due to the presence of two conflicting signals. Such response conflict can be produced in a psychological labo- ratory as well. For example, Stroop (1935) asked individuals to name the color of ink on which a word is printed. When the words are color names incongruous with the ink color— e. g. , “blue” printed in red—reaction times are slower and error rates are higher. We are in- terested in the control mechanisms underlying performance of high-conflict tasks. Conflict requires individuals to monitor and adjust their behavior, possibly responding more slowly if errors are too frequent. In this paper, we model a speeded discrimination paradigm in which individuals are asked to classify a sequence of stimuli (Jones & Braver, 2001). The stimuli are letters of the alphabet, A–Z, presented in rapid succession. In a choice task, individuals are asked to press one response key if the letter is an X or another response key for any letter other than X (as a shorthand, we will refer to non-X stimuli as Y). In a go/no-go task, individuals
 are asked to press a response key when X is presented and to make no response otherwise. We address both tasks because they elicit slightly different decision-making behavior. In both tasks, Jones and Braver (2001) manipulated the relative frequency of the X and Y stimuli; the ratio of presentation frequency was either 17: 83, 50: 50, or 83: 17. Response conflict arises when the two stimulus classes are unbalanced in frequency, resulting in more errors and slower reaction times. For example, when X’s are frequent but Y is presented, individuals are predisposed toward producing the X response, and this predisposition must be overcome by the perceptual evidence from the Y. Jones and Braver (2001) also performed an fMRI study of this task and found that anterior cingulate cortex (ACC) becomes activated in situations involving response conflict. Specif- ically, when one stimulus occurs infrequently relative to the other, event-related fMRI re- sponse in the ACC is greater for the low frequency stimulus. Jones and Braver also ex- tended a neural network model of Botvinick, Braver, Barch, Carter, and Cohen (2001) to account for human performance in the two discrimination tasks. The heart of the model is a mechanism that monitors conflict—the posited role of the ACC—and adjusts response biases accordingly. In this paper, we develop a parsimonious alternative account of the role of the ACC and of how control processes modulate behavior when response conflict arises. 1 A RATIONAL ANALYSIS Our account is based on a rational analysis of human cognition, which views cognitive processes as being optimized with respect to certain task-related goals, and being adaptive to the structure of the environment (Anderson, 1990). We make three assumptions of ratio- nality: (1) perceptual inference is optimal but is subject to rate limitations on information transmission, (2) response class prior probabilities are accurately estimated, and (3) the goal of individuals is to minimize a cost that depends both on error rate and reaction time. The heart of our account is an existing probabilistic model that explains a variety of fa- cilitation effects that arise from long-term repetition priming (Colagrosso, in preparation; Mozer, Colagrosso, & Huber, 2000), and more broadly, that addresses changes in the na- ture of information transmission in neocortex due to experience. We give a brief overview of this model; the details are not essential for the present work. The model posits that neocortex can be characterized by a collection of information- processing pathways, and any act of cognition involves coordination among pathways. To model a simple discrimination task, we might suppose a perceptual pathway to map the visual input to a semantic representation, and a response pathway to map the semantic representation to a response. The choice and go/no-go tasks described earlier share a per- ceptual pathway, but require different response pathways. The model is framed in terms of probability theory: pathway inputs and outputs are random variables and microinference in a pathway is carried out by Bayesian belief revision.

NeurIPS Conference 2001 Conference Paper

Prodding the ROC Curve: Constrained Optimization of Classifier Performance

• Michael Mozer
• Robert Dodier
• Michael Colagrosso
• Cesar Guerra-Salcedo
• Richard Wolniewicz

When designing a two-alternative classifier, one ordinarily aims to maximize the classifier’s ability to discriminate between members of the two classes. We describe a situation in a real-world business application of machine-learning prediction in which an additional constraint is placed on the nature of the solu- tion: that the classifier achieve a specified correct acceptance or correct rejection rate (i. e. , that it achieve a fixed accuracy on members of one class or the other). Our domain is predicting churn in the telecommunications industry. Churn refers to customers who switch from one service provider to another. We pro- pose four algorithms for training a classifier subject to this domain constraint, and present results showing that each algorithm yields a reliable improvement in performance. Although the improvement is modest in magnitude, it is nonethe- less impressive given the difficulty of the problem and the financial return that it achieves to the service provider. When designing a classifier, one must specify an objective measure by which the classi- fier’s performance is to be evaluated. One simple objective measure is to minimize the number of misclassifications. If the cost of a classification error depends on the target and/ or response class, one might utilize a risk-minimization framework to reduce the expected loss. A more general approach is to maximize the classifier’s ability to discriminate one class from another class (e. g. , Chang & Lippmann, 1994). An ROC curve (Green & Swets, 1966) can be used to visualize the discriminative performance of a two-alternative classifier that outputs class posteriors. To explain the ROC curve, a classifier can be thought of as making a positive/negative judgement as to whether an input is a member of some class. Two different accuracy measures can be obtained from the classifier: the accuracy of correctly identifying an input as a member of the class (a correct acceptance or CA), and the accuracy of correctly identifying an input as a nonmember of the class (a correct rejection or CR). To evaluate the CA and CR rates, it is necessary to pick a threshold above which the classifier’s probability estimate is inter- preted as an “accept, ” and below which is interpreted as a “reject”—call this the criterion. The ROC curve plots CA against CR rates for various criteria (Figure 1a). Note that as the threshold is lowered, the CA rate increases and the CR rate decreases. For a criterion of 1, the CA rate approaches 0 and the CR rate 1; for a criterion of 0, the CA rate approaches 1

NeurIPS Conference 2000 Conference Paper

Beyond Maximum Likelihood and Density Estimation: A Sample-Based Criterion for Unsupervised Learning of Complex Models

• Sepp Hochreiter
• Michael Mozer

The goal of many unsupervised learning procedures is to bring two probability distributions into alignment. Generative models such as Gaussian mixtures and Boltzmann machines can be cast in this light, as can recoding models such as ICA and projection pursuit. We propose a novel sample-based error measure for these classes of models, which applies even in situations where maximum likelihood (ML) and probability density estimation-based formulations can(cid: 173) not be applied, e. g. , models that are nonlinear or have intractable posteriors. Furthermore, our sample-based error measure avoids the difficulties of approximating a density function. We prove that with an unconstrained model, (1) our approach converges on the correct solution as the number of samples goes to infinity, and (2) the expected solution of our approach in the generative framework is the ML solution. Finally, we evaluate our approach via simula(cid: 173) tions of linear and nonlinear models on mixture of Gaussians and ICA problems. The experiments show the broad applicability and generality of our approach.

NeurIPS Conference 2000 Conference Paper

The Interplay of Symbolic and Subsymbolic Processes in Anagram Problem Solving

• David Grimes
• Michael Mozer

Although connectionist models have provided insights into the nature of perception and motor control, connectionist accounts of higher cognition seldom go beyond an implementation of traditional symbol-processing theories. We describe a connectionist constraint satisfaction model of how people solve anagram problems. The model exploits statistics of English orthography, but also addresses the interplay of sub symbolic and symbolic computation by a mechanism that extracts approximate symbolic representations (partial orderings of letters) from sub symbolic structures and injects the extracted representation back into the model to assist in the solution of the anagram. We show the computational benefit of this extraction-injection process and discuss its relationship to conscious mental processes and working memory. We also account for experimental data concerning the difficulty of anagram solution based on the orthographic structure of the anagram string and the target word. Historically, the mind has been viewed from two opposing computational perspectives. The symbolic perspective views the mind as a symbolic information processing engine. According to this perspective, cognition operates on representations that encode logical relationships among discrete symbolic elements, such as stacks and structured trees, and cognition involves basic operations such as means-ends analysis and best-first search. In contrast, the subsymbolic perspective views the mind as performing statistical inference, and involves basic operations such as constraint-satisfaction search. The data structures on which these operations take place are numerical vectors. In some domains of cognition, significant progress has been made through analysis from one computational perspective or the other. The thesis of our work is that many of these do(cid: 173) mains might be understood more completely by focusing on the interplay of subsymbolic and symbolic information processing. Consider the higher-cognitive domain of problem solving. At an abstract level of description, problem solving tasks can readily be formal(cid: 173) ized in terms of symbolic representations and operations. However, the neurobiological hardware that underlies human cognition appears to be subsymbolic-representations are noisy and graded, and the brain operates and adapts in a continuous fashion that is diffi(cid: 173) cult to characterize in discrete symbolic terms. At some level-between the computational level of the task description and the implementation level of human neurobiology-the symbolic and subsymbolic accounts must come into contact with one another. We focus on this point of contact by proposing mechanisms by which symbolic representations can modulate sub symbolic processing, and mechanisms by which subsymbolic representations are made symbolic. We conjecture that these mechanisms can not only provide an account for the interplay of symbolic and sub symbolic processes in cognition, but that they form a sensible computational strategy that outperforms purely subsymbolic computation, and hence, symbolic reasoning makes sense from an evolutionary perspective. In this paper, we apply our approach to a high-level cognitive task, anagram problem solv(cid: 173) ing. An anagram is a nonsense string of letters whose letters can be rearranged to form a word. For example, the solution to the anagram puzzle RYTEHO is THEORY. Anagram solving is a interesting task because it taps higher cognitive abilities and issues of aware(cid: 173) ness, it has a tractable state space, and interesting psychological data is available to model. 1 A Sub symbolic Computational Model We start by presenting a purely subsymbolic model of anagram processing. By subsym(cid: 173) bolic, we mean that the model utilizes only English orthographic statistics and does not have access to an English lexicon. We will argue that this model proves insufficient to ex(cid: 173) plain human performance on anagram problem solving. However, it is a key component of a hybrid symbolic-subsymbolic model we propose, and is thus described in detail. 1. 1 Problem Representation A computational model of anagram processing must represent letter orderings. For ex(cid: 173) ample, the model must be capable of representing a solution such as, or any permutation of the letters such as. (The symbols " " will be used to delimit the beginning and end of a string, respectively. ) We adopted a representation of letter strings in which a string is encoded by the set of letter pairs (hereafter, bigrams) contained in the string; for example, the bigrams in are: . The delimiters are treated as ordinary symbols of the alphabet. We capture letter pairings in a symbolic letter-ordering matrix, or symbolic ordering for short. Figure lea) shows the matrix, in which the rows indicate the first letter of the bigram, and the columns indicate the second. A cell of the matrix contains a value of I if the corre(cid: 173) sponding bigram is present in the string. (This matrix formalism and all procedures in the paper can be extended to handle strings with repeated letters, which we do not have space to discuss. ) The matrix columns and rows can be thought of as consisting of all letters from A to z, along with the delimiters. However, in the Figure we have omitted rows and columns corresponding to letters not present in the anagram. Similarly, we have omitted the from row space, as they could not by definition be part of any bigram. The seven bigrams indicated by the seven ones in the Figure uniquely specify the string THEORY. As we've described the matrix, cells contain the truth value of the proposition that a par(cid: 173) ticular bigram appears in the string being represented. However, the cell values have an interesting alternative interpretation: as the probability that a particular bigram is present. Figure l(b) illustrates a matrix of this sort, which we call a subsymbolic letter ordering matrix, or subsymbolic ordering for short. In the Figure, the bigram TH occurs with prob(cid: 173) ability 0. 8. Although the symbolic orderings are obviously a subset of the sub symbolic orderings, the two representations play critically disparate roles in our model, and thus are treated as separate entities. To formally characterize symbolic and subsymbolic ordering matrices, we define a mask vector, /-£, having N = 28 elements, corresponding to the 26 letters of the alphabet plus the two delimiters. Element i of the mask, /-£i, is set to one if the corresponding letter appears in the anagram string and zero if it does not. In both the symbolic and sub symbolic orderings, the matrices are constrained such that elements in row i and column i must sum E H 0 R T Y > 1 0 0 < 0 0 0 0 E H

NeurIPS Conference 1999 Conference Paper

A Generative Model for Attractor Dynamics

• Richard Zemel
• Michael Mozer

Attractor networks, which map an input space to a discrete out(cid: 173) put space, are useful for pattern completion. However, designing a net to have a given set of attractors is notoriously tricky; training procedures are CPU intensive and often produce spurious afuac(cid: 173) tors and ill-conditioned attractor basins. These difficulties occur because each connection in the network participates in the encod(cid: 173) ing of multiple attractors. We describe an alternative formulation of attractor networks in which the encoding of knowledge is local, not distributed. Although localist attractor networks have similar dynamics to their distributed counterparts, they are much easier to work with and interpret. We propose a statistical formulation of localist attract or net dynamics, which yields a convergence proof and a mathematical interpretation of model parameters. Attractor networks map an input space, usually continuous, to a sparse output space composed of a discrete set of alternatives. Attractor networks have a long history in neural network research. Attractor networks are often used for pattern completion, which involves filling in missing, noisy, or incorrect features in an input pattern. The initial state of the attractor net is typically determined by the input pattern. Over time, the state is drawn to one of a predefined set of states-the attractors. Attractor net dynam(cid: 173) ics can be described by a state trajectory (Figure 1a). An attractor net is generally implemented by a set of visible units whose activity represents the instantaneous state, and optionally, a set of hidden units that assist in the computation. Attractor dynamics arise from interactions among the units. In most formulations of afuac(cid: 173) tor nets, 2, 3 the dynamics can be characterized by gradient descent in an energy landscape, allowing one to partition the output space into attractor basins. Instead of homogeneous attractor basins, it is often desirable to sculpt basins that depend on the recent history of the network and the arrangement of attractors in the space. In psychological models of human cognition, for example, priming is fundamental: after the model visits an attractor, it should be faster to fall into the same attractor in the near future, i. e. , the attractor basin should be broadened. 1, 6 Another property of attractor nets is key to explaining behavioral data in psycho(cid: 173) logical and neurobiological models: the gang effect, in which the strength of an attractor is influenced by other attractors in its neighborhood. Figure 1b illustrates the gang effect: the proximity of the two rightmost afuactors creates a deeper at(cid: 173) tractor basin, so that if the input starts at the origin it will get pulled to the right. A Generative Model for Attractor Dynamics 81

NeurIPS Conference 1999 Conference Paper

Churn Reduction in the Wireless Industry

• Michael Mozer
• Richard Wolniewicz
• David Grimes
• Eric Johnson
• Howard Kaushansky

Competition in the wireless telecommunications industry is rampant. To main(cid: 173) tain profitability, wireless carriers must control chum, the loss of subscribers who switch from one carrier to another. We explore statistical techniques for chum prediction and, based on these predictions. an optimal policy for identify(cid: 173) ing customers to whom incentives should be offered to increase retention. Our experiments are based on a data base of nearly 47, 000 U. S. domestic subscrib(cid: 173) ers, and includes information about their usage, billing, credit, application, and complaint history. We show that under a wide variety of assumptions concerning the cost of intervention and the retention rate resulting from intervention, chum prediction and remediation can yield significant savings to a carrier. We also show the importance of a data representation crafted by domain experts. Competition in the wireless telecommunications industry is rampant. As many as seven competing carriers operate in each market. The industry is extremely dynamic, with new services, technologies, and carriers constantly altering the landscape. Carriers announce new rates and incentives weekly, hoping to entice new subscribers and to lure subscribers away from the competition. The extent of rivalry is reflected in the deluge of advertise(cid: 173) ments for wireless service in the daily newspaper and other mass media. The United States had 69 million wireless subscribers in 1998, roughly 25% of the population. Some markets are further developed; for example, the subscription rate in Fin(cid: 173) land is 53%. Industry forecasts are for a U. S. penetration rate of 48% by 2003. Although there is significant room for growth in most markets, the industry growth rate is declining and competition is rising. Consequently, it has become crucial for wireless carriers to con(cid: 173) trol chum-the loss of customers who switch from one carrier to another. At present, domestic monthly chum rates are 2-3% of the customer base. At an average cost of $400 to acquire a subscriber, churn cost the industry nearly $6. 3 bilIion in 1998; the total annual loss rose to nearly $9. 6 billion when lost monthly revenue from subscriber cancellations is considered (Luna, 1998). It costs roughly five times as much to sign on a new subscriber as to retain an existing one. Consequently, for a carrier with 1. 5 milIion subscribers, reduc(cid: 173) ing the monthly churn' rate from 2% to 1 % would yield an increase in annual earnings of at least $54 milIion, and an increase in shareholder value of approximately $150 million. (Estimates are even higher when lost monthly revenue is considered; see Fowlkes, Madan, Andrew, & Jensen, 1999; Luna, 1998. ) The goal of our research is to evaluate the benefits of predicting churn using tech(cid: 173) niques from statistical machine learning. We designed models that predict the probability 936 M. C. Mozer, R. Wolniewicz. D. B. Grimes. E. Johnson and H. Kaushansky of a subscriber churning within a short time window, and we evaluated how well these pre(cid: 173) dictions could be used for decision making by estimating potential cost savings to the wireless carrier under a variety of assumptions concerning subscriber behavior.

NeurIPS Conference 1999 Conference Paper

Robust Recognition of Noisy and Superimposed Patterns via Selective Attention

• Soo-Young Lee
• Michael Mozer

In many classification tasks, recognition accuracy is low because input patterns are corrupted by noise or are spatially or temporally overlapping. We propose an approach to overcoming these limitations based on a model of human selective attention. The model, an early selection filter guided by top-down attentional control, entertains each candidate output class in sequence and adjusts attentional gain coefficients in order to produce a strong response for that class. The chosen class is then the one that obtains the strongest response with the least modulation of attention. We present simulation results on classification of corrupted and superimposed handwritten digit patterns, showing a significant improvement in recognition rates. The algorithm has also been applied in the domain of speech recognition, with comparable results.

NeurIPS Conference 1998 Conference Paper

A Principle for Unsupervised Hierarchical Decomposition of Visual Scenes

• Michael Mozer

Structure in a visual scene can be described at many levels of granular(cid: 173) ity. At a coarse level, the scene is composed of objects; at a finer level, each object is made up of parts, and the parts of subparts. In this work, I propose a simple principle by which such hierarchical structure can be extracted from visual scenes: Regularity in the relations among different parts of an object is weaker than in the internal structure of a part. This principle can be applied recursively to define part-whole relationships among elements in a scene. The principle does not make use of object models, categories, or other sorts of higher-level knowledge; rather, part-whole relationships can be established based on the statistics of a set of sample visual scenes. I illustrate with a model that performs unsu(cid: 173) pervised decomposition of simple scenes. The model can account for the results from a human learning experiment on the ontogeny of part(cid: 173) whole relationships.

NeurIPS Conference 1997 Conference Paper

A Superadditive-Impairment Theory of Optic Aphasia

• Michael Mozer
• Mark Sitton
• Martha Farah

Accounts of neurological disorders often posit damage to a specific functional pathway of the brain. Farah (1990) has proposed an alterna(cid: 173) tive class of explanations involving partial damage to multiple path(cid: 173) ways. We explore this explanation for optic aphasia, a disorder in which severe perfonnance deficits are observed when patients are asked to name visually presented objects, but surprisingly, performance is rela(cid: 173) tively nonnal on naming objects from auditory cues and on gesturing the appropriate use of visually presented objects. We model this highly specific deficit through partial damage to two pathways-one that maps visual input to semantics, and the other that maps semantics to naming responses. The effect of this damage is superadditive, meaning that tasks which require one pathway or the other show little or no perfor(cid: 173) mance deficit, but the damage is manifested when a task requires both pathways (i. e. , naming visually presented objects). Our model explains other phenomena associated with optic aphasia, and makes testable experimental predictions. Neuropsychology is the study of disrupted cognition resulting from damage to functional systems in the brain. Generally, accounts of neuropsychological disorders posit damage to a particular functional system or a disconnection between systems. Farah (1990) sug(cid: 173) gested an alternative class of explanations for neuropsychological disorders: partial dam(cid: 173) age to multiple systems, which is manifested through interactions among the loci of damage. We explore this explanation for the neuropsychological disorder of optic aphasia. Optic aphasia, arising from unilateral left posterior lesions, including occipital cortex and the splenium of the corpus callosum (Schnider, Benson, & Scharre, 1994), is marked by a deficit in naming visually presented objects, hereafter referred to as visual naming (Farah, 1990). However, patients can demonstrate recognition of visually presented objects nonverbally, for example, by gesturing the appropriate use of an object or sorting visual items into their proper superordinate categories (hereafter, visual gesturing). Patients can also name objects by nonvisual cues such as a verbal definition or typical sounds made by the objects (hereafter, auditory naming). The highly specific nature of the deficit rules out an explanation in terms of damage to a single pathway in a standard model of visual naming (Figure 1), suggesting that a more complex model is required, involving A Superadditive-Impainnent Theory of Optic Aphasia 67 FIGURE 1. A standard box-and-arrow model of visual naming. The boxes denote levels of representation, and the arrows denote pathways mapping from one level of representation to another. Although optic aphasia cannot be explained by damage to the vision-to-semantics pathway or the semantics-ta-naming Farah (1990) proposed an explanation in terms of partial damage to both pathways (the X's).

NeurIPS Conference 1996 Conference Paper

The Neurothermostat: Predictive Optimal Control of Residential Heating Systems

• Michael Mozer
• Lucky Vidmar
• Robert Dodier

The Neurothermostat is an adaptive controller that regulates in(cid: 173) door air temperature in a residence by switching a furnace on or off. The task is framed as an optimal control problem in which both comfort and energy costs are considered as part of the con(cid: 173) trol objective. Because the consequences of control decisions are delayed in time, the N eurothermostat must anticipate heating de(cid: 173) mands with predictive models of occupancy patterns and the ther(cid: 173) mal response of the house and furnace. Occupancy pattern predic(cid: 173) tion is achieved by a hybrid neural net / look-up table. The Neu(cid: 173) rothermostat searches, at each discrete time step, for a decision sequence that minimizes the expected cost over a fixed planning horizon. The first decision in this sequence is taken, and this pro(cid: 173) cess repeats. Simulations of the Neurothermostat were conducted using artificial occupancy data in which regularity was systemat(cid: 173) ically varied, as well as occupancy data from an actual residence. The Neurothermostat is compared against three conventional poli(cid: 173) cies, and achieves reliably lower costs. This result is robust to the relative weighting of comfort and energy costs and the degree of variability in the occupancy patterns. For over a quarter century, the home automation industry has promised to revolu(cid: 173) tionize our lifestyle with the so-called Smart House@ in which appliances, lighting, stereo, video, and security systems are integrated under computer control. How(cid: 173) ever, home automation has yet to make significant inroads, at least in part because software must be tailored to the home occupants. Instead of expecting the occupants to program their homes or to hire someone to do so, one would ideally like the home to essentially program itself by observing the lifestyle of the occupants. This is the goal of the Neural Network House (Mozer et al. , 1995), an actual residence that has been outfitted with over 75 sensors(cid: 173) including temperature, light, sound, motion-and actua. tors to control air heating, water heating, lighting, and ventilation. In this paper, we describe one research 954 M. C. Mozer. L. Vidmar and R. H. Dodier project within the house, the Neurothermostat, that learns to regulate the indoor air temperature automatically by observing and detecting patterns in the occupants' schedules and comfort preferences. We focus on the problem of air heating with a whole-house furnace, but the same approach can be taken with alternative or multiple heating devices, and to the problems of cooling and ventilation. 1 TEMPERATURE REGULATION AS AN OPTIMAL

NeurIPS Conference 1994 Conference Paper

On the Computational Utility of Consciousness

• Donald Mathis
• Michael Mozer

We propose a computational framework for understanding and modeling human consciousness. This framework integrates many existing theoretical perspectives, yet is sufficiently concrete to allow simulation experiments. We do not attempt to explain qualia (sub(cid: 173) jective experience), but instead ask what differences exist within the cognitive information processing system when a person is con(cid: 173) scious of mentally-represented information versus when that infor(cid: 173) mation is unconscious. The central idea we explore is that the con(cid: 173) tents of consciousness correspond to temporally persistent states in a network of computational modules. Three simulations are de(cid: 173) scribed illustrating that the behavior of persistent states in the models corresponds roughly to the behavior of conscious states people experience when performing similar tasks. Our simulations show that periodic settling to persistent (i. e. , conscious) states im(cid: 173) proves performance by cleaning up inaccuracies and noise, forcing decisions, and helping keep the system on track toward a solution.

NeurIPS Conference 1994 Conference Paper

Template-Based Algorithms for Connectionist Rule Extraction

• Jay Alexander
• Michael Mozer

Casting neural network weights in symbolic terms is crucial for interpreting and explaining the behavior of a network. Additionally, in some domains, a symbolic description may lead to more robust generalization. We present a principled approach to symbolic rule extraction based on the notion of weight templates, parameterized regions of weight space corresponding to specific symbolic expressions. With an appropriate choice of representation, we show how template parameters may be efficiently identified and instantiated to yield the optimal match to a unit's actual weights. Depending on the requirements of the application domain, our method can accommodate arbitrary disjunctions and conjunctions with O(k) complexity, simple n-of-m expressions with O( k! ) complexity, or a more general class of recursive n-of-m expressions with O(k! ) complexity, where k is the number of inputs to a unit. Our method of rule extraction offers several benefits over alternative approaches in the literature, and simulation results on a variety of problems demonstrate its effectiveness.

NeurIPS Conference 1993 Conference Paper

A Unified Gradient-Descent/Clustering Architecture for Finite State Machine Induction

• Sreerupa Das
• Michael Mozer

Although recurrent neural nets have been moderately successful in learning to emulate finite-state machines (FSMs), the continu(cid: 173) ous internal state dynamics of a neural net are not well matched to the discrete behavior of an FSM. We describe an architecture, called DOLCE, that allows discrete states to evolve in a net as learn(cid: 173) ing progresses. DOLCE consists of a standard recurrent neural net trained by gradient descent and an adaptive clustering technique that quantizes the state space. DOLCE is based on the assumption that a finite set of discrete internal states is required for the task, and that the actual network state belongs to this set but has been corrupted by noise due to inaccuracy in the weights. DOLCE learns to recover the discrete state with maximum a posteriori probabil(cid: 173) ity from the noisy state. Simulations show that DOLCE leads to a significant improvement in generalization performance over earlier neural net approaches to FSM induction.

NeurIPS Conference 1992 Conference Paper

A Connectionist Symbol Manipulator That Discovers the Structure of Context-Free Languages

• Michael Mozer
• Sreerupa Das

We present a neural net architecture that can discover hierarchical and re(cid: 173) cursive structure in symbol strings. To detect structure at multiple levels, the architecture has the capability of reducing symbols substrings to single symbols, and makes use of an external stack memory. In terms of formal languages, the architecture can learn to parse strings in an LR(O) context(cid: 173) free grammar. Given training sets of positive and negative exemplars, the architecture has been trained to recognize many different grammars. The architecture has only one layer of modifiable weights, allowing for a straightforward interpretation of its behavior. Many cognitive domains involve complex sequences that contain hierarchical or recursive structure, e. g. , music, natural language parsing, event perception. To il(cid: 173) lustrate, "the spider that ate the hairy fly" is a noun phrase containing the embed(cid: 173) ded noun phrase "the hairy fly. " Understanding such multilevel structures requires forming reduced descriptions (Hinton, 1988) in which a string of symbols or states ("the hairy fly") is reduced to a single symbolic entity (a noun phrase). We present a neural net architecture that learns to encode the structure of symbol strings via such red uction transformations. The difficult problem of extracting multilevel structure from complex, extended sequences has been studied by Mozer (1992), Ring (1993), Rohwer (1990), and Schmidhuber (1992), among others. While these previous efforts have made some

NeurIPS Conference 1992 Conference Paper

Directional-Unit Boltzmann Machines

• Richard Zemel
• Christopher Williams
• Michael Mozer

We present a general formulation for a network of stochastic di(cid: 173) rectional units. This formulation is an extension of the Boltzmann machine in which the units are not binary, but take on values in a cyclic range, between 0 and 271' radians. The state of each unit in a Directional-Unit Boltzmann Machine (DUBM) is described by a complex variable, where the phase component specifies a direction; the weights are also complex variables. We associate a quadratic energy function, and corresponding probability, with each DUBM configuration. The conditional distribution of a unit's stochastic state is a circular version of the Gaussian probability distribution, known as the von Mises distribution. In a mean-field approxima(cid: 173) tion to a stochastic DUBM, the phase component of a unit's state represents its mean direction, and the magnitude component spec(cid: 173) ifies the degree of certainty associated with this direction. This combination of a value and a certainty provides additional repre(cid: 173) sentational power in a unit. We describe a learning algorithm and simulations that demonstrate a mean-field DUBM'S ability to learn interesting mappings. Many kinds of information can naturally be represented in terms of angular, or directional, variables. A circular range forms a suitable representation for explicitly directional information, such as wind direction, as well as for information where the underlying range is periodic, such as days of the week or months of the year. In computer vision, tangent fields and optic flow fields are represented as fields of oriented line segments, each of which can be described by a magnitude and direction. Directions can also be used to represent a set of symbolic labels, e. g. , object label A at 0, and object label B at 71'/2 radians. We discuss below some advantages of representing symbolic labels with directional units.

NeurIPS Conference 1992 Conference Paper

Metamorphosis Networks: An Alternative to Constructive Models

• Brian Bonnlander
• Michael Mozer

Given a set oft raining examples, determining the appropriate num(cid: 173) ber of free parameters is a challenging problem. Constructive learning algorithms attempt to solve this problem automatically by adding hidden units, and therefore free parameters, during learn(cid: 173) ing. We explore an alternative class of algorithms-called meta(cid: 173) morphosis algorithms-in which the number of units is fixed, but the number of free parameters gradually increases during learning. The architecture we investigate is composed of RBF units on a lat(cid: 173) tice, which imposes flexible constraints on the parameters of the network. Virtues of this approach include variable subset selec(cid: 173) tion, robust parameter selection, multiresolution processing, and interpolation of sparse training data.

NeurIPS Conference 1991 Conference Paper

Induction of Multiscale Temporal Structure

• Michael Mozer

Learning structure in temporally-extended sequences is a difficult com(cid: 173) putational problem because only a fraction of the relevant information is available at any instant. Although variants of back propagation can in principle be used to find structure in sequences, in practice they are not sufficiently powerful to discover arbitrary contingencies, especially those spanning long temporal intervals or involving high order statistics. For example, in designing a connectionist network for music composition, we have encountered the problem that the net is able to learn musical struc(cid: 173) ture that occurs locally in time-e. g. , relations among notes within a mu(cid: 173) sical phrase-but not structure that occurs over longer time periods--e. g. , relations among phrases. To address this problem, we require a means of constructing a reduced deacription of the sequence that makes global aspects more explicit or more readily detectable. I propose to achieve this using hidden units that operate with different time constants. Simulation experiments indicate that slower time-scale hidden units are able to pick up global structure, structure that simply can not be learned by standard back propagation. Many patterns in the world are intrinsically temporal, e. g. , speech, music, the un(cid: 173) folding of events. Recurrent neural net architectures have been devised to accom(cid: 173) modate time-varying sequences. For example, the architecture shown in Figure 1 can map a sequence of inputs to a sequence of outputs. Learning structure in temporally-extended sequences is a difficult computational problem because the in(cid: 173) put pattern may not contain all the task-relevant information at any instant. Thus, 275

NeurIPS Conference 1991 Conference Paper

Learning to Segment Images Using Dynamic Feature Binding

• Michael Mozer
• Richard Zemel
• Marlene Behrmann

Despite the fact that complex visual scenes contain multiple, overlapping objects, people perform object recognition with ease and accuracy. One operation that facilitates recognition is an early segmentation process in which features of objects are grouped and labeled according to which ob(cid: 173) ject they belong. Current computational systems that perform this oper(cid: 173) ation are based on predefined grouping heuristics. We describe a system called MAGIC that learn. how to group features based on a set of pre(cid: 173) segmented examples. In many cases, MAGIC discovers grouping heuristics similar to those previously proposed, but it also has the capability of find(cid: 173) ing nonintuitive structural regularities in images. Grouping is performed by a relaxation network that aUempts to dynamically bind related fea(cid: 173) tures. Features transmit a complex-valued signal (amplitude and phase) to one another; binding can thus be represented by phase locking related features. MAGIC'S training procedure is a generalization of recurrent back propagation to complex-valued units. When a visual image contains multiple, overlapping objects, recognition is difficult because features in the image are not grouped according to which object they belong. Without the capability to form such groupings, it would be necessary to undergo a massive search through all subsets of image features. For this reason, most machine vision recognition systems include a component that performs feature grouping or image. egmentation (e. g. , Guzman, 1968; Lowe, 1985; Marr, 1982).

NeurIPS Conference 1991 Conference Paper

Rule Induction through Integrated Symbolic and Subsymbolic Processing

• Clayton McMillan
• Michael Mozer
• Paul Smolensky

We describe a neural network, called RufeNet, that learns explicit, sym(cid: 173) bolic condition-action rules in a formal string manipulation domain. RuleNet discovers functional categories over elements of the domain, and, at various points during learning, extracts rules that operate on these categories. The rules are then injected back into RuleNet and training continues, in a process called iterative projection. By incorpo(cid: 173) rating rules in this way, RuleNet exhibits enhanced learning and gener(cid: 173) alization performance over alternative neural net approaches. By integrating symbolic rule learning and subsymbolic category learning, RuleNet has capabilities that go beyond a purely symbolic system. We show how this architecture can be applied to the problem of case-role assignment in natural language processing, yielding a novel rule-based solution.

NeurIPS Conference 1990 Conference Paper

Connectionist Music Composition Based on Melodic and Stylistic Constraints

• Michael Mozer
• Todd Soukup

We describe a recurrent connectionist network, called CONCERT, that uses a set of melodies written in a given style to compose new melodies in that style. CONCERT is an extension of a traditional algorithmic composition tech(cid: 173) nique in which transition tables specify the probability of the next note as a function of previous context. A central ingredient of CONCERT is the use of a psychologically-grounded representation of pitch.

NeurIPS Conference 1990 Conference Paper

Discovering Discrete Distributed Representations with Iterative Competitive Learning

• Michael Mozer

Competitive learning is an unsupervised algorithm that classifies input pat(cid: 173) terns into mutually exclusive clusters. In a neural net framework, each clus(cid: 173) ter is represented by a processing unit that competes with others in a winner(cid: 173) take-all pool for an input pattern. I present a simple extension to the algo(cid: 173) rithm that allows it to construct discrete, distributed representations. Discrete representations are useful because they are relatively easy to analyze and their information content can readily be measured. Distributed representa(cid: 173) tions are useful because they explicitly encode similarity. The basic idea is to apply competitive learning iteratively to an input pattern, and after each stage to subtract from the input pattern the component that was captured in the representation at that stage. This component is simply the weight vector of the winning unit of the competitive pool. The subtraction procedure forces competitive pools at different stages to encode different aspects of the input. The algorithm is essentially the same as a traditional data compression tech(cid: 173) nique known as multistep vector quantization, although the neural net per(cid: 173) spective suggests potentially powerful extensions to that approach.

NeurIPS Conference 1989 Conference Paper

Discovering the Structure of a Reactive Environment by Exploration

• Michael Mozer
• Jonathan Bachrach

Consider a robot wandering around an unfamiliar environment. performing ac(cid: 173) tions and sensing the resulting environmental states. The robot's task is to con(cid: 173) struct an internal model of its environment. a model that will allow it to predict the consequences of its actions and to determine what sequences of actions to take to reach particular goal states. Rivest and Schapire (1987&, 1987b; Schapire. 1988) have studied this problem and have designed a symbolic algo(cid: 173) rithm to strategically explore and infer the structure of "finite state" environ(cid: 173) ments. The heart of this algorithm is a clever representation of the environment called an update graph. We have developed a connectionist implementation of the update graph using a highly-specialized network architecture. With back propagation learning and a trivial exploration strategy - tions - gorithm on simple problems. The network has the additional strength that it can accommodate stochastic environments. Perhaps the greatest virtue of the connectionist approach is that it suggests generalizations of the update graph representation that do not arise from a traditional, symbolic perspective. choosing random ac(cid: 173) the connectionist network can outperfonn the Rivest and Schapire al(cid: 173)

NeurIPS Conference 1989 Conference Paper

TRAFFIC: Recognizing Objects Using Hierarchical Reference Frame Transformations

• Richard Zemel
• Michael Mozer
• Geoffrey Hinton

We describe a model that can recognize two-dimensional shapes in an unsegmented image, independent of their orientation, position, and scale. The model, called TRAFFIC, efficiently represents the structural relation between an object and each of its component features by encoding the fixed viewpoint-invariant transformation from the feature's reference frame to the object's in the weights of a connectionist network. Using a hierarchy of such transformations, with increasing complexity of features at each successive layer, the network can recognize multiple objects in parallel. An implemen(cid: 173) tation of TRAFFIC is described, along with experimental results demonstrating the network's ability to recognize constellations of stars in a viewpoint-invariant manner.

NeurIPS Conference 1988 Conference Paper

Skeletonization: A Technique for Trimming the Fat from a Network via Relevance Assessment

• Michael Mozer
• Paul Smolensky

This paper proposes a means of using the knowledge in a network to determine the functionality or relevance of individual units, both for the purpose of understanding the network's behavior and improving its performance. The basic idea is to iteratively train the network to a cer(cid: 173) tain performance criterion, compute a measure of relevance that identi(cid: 173) fies which input or hidden units are most critical to performance, and automatically trim the least relevant units. This skeletonization tech(cid: 173) nique can be used to simplify networks by eliminating units that con(cid: 173) vey redundant information; to improve learning performance by first learning with spare hidden units and then trimming the unnecessary ones away, thereby constraining generalization; and to understand the behavior of networks in terms of minimal "rules. "