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Roger B. Grosse

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35 papers

2 author rows

NeurIPS Conference 2024 Conference Paper

Many-shot Jailbreaking

Cem Anil
Esin Durmus
Nina Panickssery
Mrinank Sharma
Joe Benton
Sandipan Kundu
Joshua Batson
Meg Tong

We investigate a family of simple long-context attacks on large language models: prompting with hundreds of demonstrations of undesirable behavior. This attack is newly feasible with the larger context windows recently deployed by language model providers like Google DeepMind, OpenAI and Anthropic. We find that in diverse, realistic circumstances, the effectiveness of this attack follows a power law, up to hundreds of shots. We demonstrate the success of this attack on the most widely used state-of-the-art closed-weight models, and across various tasks. Our results suggest very long contexts present a rich new attack surface for LLMs.

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ICML Conference 2024 Conference Paper

Measuring Stochastic Data Complexity with Boltzmann Influence Functions

Nathan H. Ng
Roger B. Grosse
Marzyeh Ghassemi

Estimating the uncertainty of a model’s prediction on a test point is a crucial part of ensuring reliability and calibration under distribution shifts. A minimum description length approach to this problem uses the predictive normalized maximum likelihood (pNML) distribution, which considers every possible label for a data point, and decreases confidence in a prediction if other labels are also consistent with the model and training data. In this work we propose IF-COMP, a scalable and efficient approximation of the pNML distribution that linearizes the model with a temperature-scaled Boltzmann influence function. IF-COMP can be used to produce well-calibrated predictions on test points as well as measure complexity in both labelled and unlabelled settings. We experimentally validate IF-COMP on uncertainty calibration, mislabel detection, and OOD detection tasks, where it consistently matches or beats strong baseline methods.

ICML Conference 2024 Conference Paper

Probabilistic Inference in Language Models via Twisted Sequential Monte Carlo

Stephen Zhao
Rob Brekelmans
Alireza Makhzani
Roger B. Grosse

Numerous capability and safety techniques of Large Language Models (LLMs), including RLHF, automated red-teaming, prompt engineering, and infilling, can be cast as sampling from an unnormalized target distribution defined by a given reward or potential function over the full sequence. In this work, we leverage the rich toolkit of Sequential Monte Carlo (SMC) for these probabilistic inference problems. In particular, we use learned twist functions to estimate the expected future value of the potential at each timestep, which enables us to focus inference-time computation on promising partial sequences. We propose a novel contrastive method for learning the twist functions, and establish connections with the rich literature of soft reinforcement learning. As a complementary application of our twisted SMC framework, we present methods for evaluating the accuracy of language model inference techniques using novel bidirectional SMC bounds on the log partition function. These bounds can be used to estimate the KL divergence between the inference and target distributions in both directions. We apply our inference evaluation techniques to show that twisted SMC is effective for sampling undesirable outputs from a pretrained model (a useful component of harmlessness training and automated red-teaming), generating reviews with varied sentiment, and performing infilling tasks.

ICLR Conference 2024 Conference Paper

REFACTOR: Learning to Extract Theorems from Proofs

Jin Peng Zhou
Yuhuai Wu
Qiyang Li
Roger B. Grosse

Human mathematicians are often good at recognizing modular and reusable theorems that make complex mathematical results within reach. In this paper, we propose a novel method called theoREm-from-prooF extrACTOR (REFACTOR) for training neural networks to mimic this ability in formal mathematical theorem proving. We show on a set of unseen proofs, REFACTOR is able to extract 19.6\% of the theorems that humans would use to write the proofs. When applying the model to the existing Metamath library, REFACTOR extracted 16 new theorems. With newly extracted theorems, we show that the existing proofs in the MetaMath database can be refactored. The new theorems are used very frequently after refactoring, with an average usage of 733.5 times, and help shorten the proof lengths. Lastly, we demonstrate that the prover trained on the new-theorem refactored dataset proves more test theorems and outperforms state-of-the-art baselines by frequently leveraging a diverse set of newly extracted theorems. Code can be found at https://github.com/jinpz/refactor.

ICML Conference 2023 Conference Paper

Efficient Parametric Approximations of Neural Network Function Space Distance

Nikita Dhawan
Sicong Huang 0001
Juhan Bae
Roger B. Grosse

It is often useful to compactly summarize important properties of model parameters and training data so that they can be used later without storing and/or iterating over the entire dataset. As a specific case, we consider estimating the Function Space Distance (FSD) over a training set, i. e. the average discrepancy between the outputs of two neural networks. We propose a Linearized Activation Function TRick (LAFTR) and derive an efficient approximation to FSD for ReLU neural networks. The key idea is to approximate the architecture as a linear network with stochastic gating. Despite requiring only one parameter per unit of the network, our approach outcompetes other parametric approximations with larger memory requirements. Applied to continual learning, our parametric approximation is competitive with state-of-the-art nonparametric approximations, which require storing many training examples. Furthermore, we show its efficacy in estimating influence functions accurately and detecting mislabeled examples without expensive iterations over the entire dataset.

ICLR Conference 2023 Conference Paper

Multi-Rate VAE: Train Once, Get the Full Rate-Distortion Curve

Juhan Bae
Michael R. Zhang
Michael Ruan
Eric Wang
So Hasegawa
Jimmy Ba
Roger B. Grosse

Variational autoencoders (VAEs) are powerful tools for learning latent representations of data used in a wide range of applications. In practice, VAEs usually require multiple training rounds to choose the amount of information the latent variable should retain. This trade-off between the reconstruction error (distortion) and the KL divergence (rate) is typically parameterized by a hyperparameter $\beta$. In this paper, we introduce Multi-Rate VAE (MR-VAE), a computationally efficient framework for learning optimal parameters corresponding to various $\beta$ in a single training run. The key idea is to explicitly formulate a response function using hypernetworks that maps $\beta$ to the optimal parameters. MR-VAEs construct a compact response hypernetwork where the pre-activations are conditionally gated based on $\beta$. We justify the proposed architecture by analyzing linear VAEs and showing that it can represent response functions exactly for linear VAEs. With the learned hypernetwork, MR-VAEs can construct the rate-distortion curve without additional training and can be deployed with significantly less hyperparameter tuning. Empirically, our approach is competitive and often exceeds the performance of multiple $\beta$-VAEs training with minimal computation and memory overheads.

NeurIPS Conference 2023 Conference Paper

Similarity-based cooperative equilibrium

Caspar Oesterheld
Johannes Treutlein
Roger B. Grosse
Vincent Conitzer
Jakob Foerster

As machine learning agents act more autonomously in the world, they will increasingly interact with each other. Unfortunately, in many social dilemmas like the one-shot Prisoner’s Dilemma, standard game theory predicts that ML agents will fail to cooperate with each other. Prior work has shown that one way to enable cooperative outcomes in the one-shot Prisoner’s Dilemma is to make the agents mutually transparent to each other, i. e. , to allow them to access one another’s source code (Rubinstein, 1998; Tennenholtz, 2004) – or weights in the case of ML agents. However, full transparency is often unrealistic, whereas partial transparency is commonplace. Moreover, it is challenging for agents to learn their way to cooperation in the full transparency setting. In this paper, we introduce a more realistic setting in which agents only observe a single number indicating how similar they are to each other. We prove that this allows for the same set of cooperative outcomes as the full transparency setting. We also demonstrate experimentally that cooperation can be learned using simple ML methods.

NeurIPS Conference 2022 Conference Paper

Amortized Proximal Optimization

Juhan Bae
Paul Vicol
Jeff Z. HaoChen
Roger B. Grosse

We propose a framework for online meta-optimization of parameters that govern optimization, called Amortized Proximal Optimization (APO). We first interpret various existing neural network optimizers as approximate stochastic proximal point methods which trade off the current-batch loss with proximity terms in both function space and weight space. The idea behind APO is to amortize the minimization of the proximal point objective by meta-learning the parameters of an update rule. We show how APO can be used to adapt a learning rate or a structured preconditioning matrix. Under appropriate assumptions, APO can recover existing optimizers such as natural gradient descent and KFAC. It enjoys low computational overhead and avoids expensive and numerically sensitive operations required by some second-order optimizers, such as matrix inverses. We empirically test APO for online adaptation of learning rates and structured preconditioning matrices for regression, image reconstruction, image classification, and natural language translation tasks. Empirically, the learning rate schedules found by APO generally outperform optimal fixed learning rates and are competitive with manually tuned decay schedules. Using APO to adapt a structured preconditioning matrix generally results in optimization performance competitive with second-order methods. Moreover, the absence of matrix inversion provides numerical stability, making it effective for low-precision training.

NeurIPS Conference 2022 Conference Paper

If Influence Functions are the Answer, Then What is the Question?

Juhan Bae
Nathan Ng
Alston Lo
Marzyeh Ghassemi
Roger B. Grosse

Influence functions efficiently estimate the effect of removing a single training data point on a model's learned parameters. While influence estimates align well with leave-one-out retraining for linear models, recent works have shown this alignment is often poor in neural networks. In this work, we investigate the specific factors that cause this discrepancy by decomposing it into five separate terms. We study the contributions of each term on a variety of architectures and datasets and how they vary with factors such as network width and training time. While practical influence function estimates may be a poor match to leave-one-out retraining for nonlinear networks, we show that they are often a good approximation to a different object we term the proximal Bregman response function (PBRF). Since the PBRF can still be used to answer many of the questions motivating influence functions, such as identifying influential or mislabeled examples, our results suggest that current algorithms for influence function estimation give more informative results than previous error analyses would suggest.

ICLR Conference 2022 Conference Paper

Improving Mutual Information Estimation with Annealed and Energy-Based Bounds

Rob Brekelmans
Sicong Huang 0001
Marzyeh Ghassemi
Greg Ver Steeg
Roger B. Grosse
Alireza Makhzani

Mutual information (MI) is a fundamental quantity in information theory and machine learning. However, direct estimation of MI is intractable, even if the true joint probability density for the variables of interest is known, as it involves estimating a potentially high-dimensional log partition function. In this work, we present a unifying view of existing MI bounds from the perspective of importance sampling, and propose three novel bounds based on this approach. Since a tight MI bound without density information requires a sample size exponential in the true MI, we assume either a single marginal or the full joint density information is known. In settings where the full joint density is available, we propose Multi-Sample Annealed Importance Sampling (AIS) bounds on MI, which we demonstrate can tightly estimate large values of MI in our experiments. In settings where only a single marginal distribution is known, we propose Generalized IWAE (GIWAE) and MINE-AIS bounds. Our GIWAE bound unifies variational and contrastive bounds in a single framework that generalizes InfoNCE, IWAE, and Barber-Agakov bounds. Our MINE-AIS method improves upon existing energy-based methods such as MINE-DV and MINE-F by directly optimizing a tighter lower bound on MI. MINE-AIS uses MCMC sampling to estimate gradients for training and Multi-Sample AIS for evaluating the bound. Our methods are particularly suitable for evaluating MI in deep generative models, since explicit forms of the marginal or joint densities are often available. We evaluate our bounds on estimating the MI of VAEs and GANs trained on the MNIST and CIFAR datasets, and showcase significant gains over existing bounds in these challenging settings with high ground truth MI.

ICML Conference 2022 Conference Paper

On Implicit Bias in Overparameterized Bilevel Optimization

Paul Vicol
Jonathan P. Lorraine
Fabian Pedregosa
David Duvenaud
Roger B. Grosse

Many problems in machine learning involve bilevel optimization (BLO), including hyperparameter optimization, meta-learning, and dataset distillation. Bilevel problems involve inner and outer parameters, each optimized for its own objective. Often, at least one of the two levels is underspecified and there are multiple ways to choose among equivalent optima. Inspired by recent studies of the implicit bias induced by optimization algorithms in single-level optimization, we investigate the implicit bias of different gradient-based algorithms for jointly optimizing the inner and outer parameters. We delineate two standard BLO methods—cold-start and warm-start BLO—and show that the converged solution or long-run behavior depends to a large degree on these and other algorithmic choices, such as the hypergradient approximation. We also show that the solutions from warm-start BLO can encode a surprising amount of information about the outer objective, even when the outer optimization variables are low-dimensional. We believe that implicit bias deserves as central a role in the study of bilevel optimization as it has attained in the study of single-level neural net optimization.

NeurIPS Conference 2022 Conference Paper

Path Independent Equilibrium Models Can Better Exploit Test-Time Computation

Cem Anil
Ashwini Pokle
Kaiqu Liang
Johannes Treutlein
Yuhuai Wu
Shaojie Bai
J. Zico Kolter
Roger B. Grosse

Designing networks capable of attaining better performance with an increased inference budget is important to facilitate generalization to harder problem instances. Recent efforts have shown promising results in this direction by making use of depth-wise recurrent networks. In this work, we reproduce the performance of the prior art using a broader class of architectures called equilibrium models, and find that stronger generalization performance on harder examples (which require more iterations of inference to get correct) strongly correlates with the path independence of the system—its ability to converge to the same attractor (or limit cycle) regardless of initialization, given enough computation. Experimental interventions made to promote path independence result in improved generalization on harder (and thus more compute-hungry) problem instances, while those that penalize it degrade this ability. Path independence analyses are also useful on a per-example basis: for equilibrium models that have good in-distribution performance, path independence on out-of-distribution samples strongly correlates with accuracy. Thus, considering equilibrium models and path independence jointly leads to a valuable new viewpoint under which we can study the generalization performance of these networks on hard problem instances.

NeurIPS Conference 2022 Conference Paper

Proximal Learning With Opponent-Learning Awareness

Stephen Zhao
Chris Lu
Roger B. Grosse
Jakob Foerster

Learning With Opponent-Learning Awareness (LOLA) (Foerster et al. [2018a]) is a multi-agent reinforcement learning algorithm that typically learns reciprocity-based cooperation in partially competitive environments. However, LOLA often fails to learn such behaviour on more complex policy spaces parameterized by neural networks, partly because the update rule is sensitive to the policy parameterization. This problem is especially pronounced in the opponent modeling setting, where the opponent's policy is unknown and must be inferred from observations; in such settings, LOLA is ill-specified because behaviorally equivalent opponent policies can result in non-equivalent updates. To address this shortcoming, we reinterpret LOLA as approximating a proximal operator, and then derive a new algorithm, proximal LOLA (POLA), which uses the proximal formulation directly. Unlike LOLA, the POLA updates are parameterization invariant, in the sense that when the proximal objective has a unique optimum, behaviorally equivalent policies result in behaviorally equivalent updates. We then present practical approximations to the ideal POLA update, which we evaluate in several partially competitive environments with function approximation and opponent modeling. This empirically demonstrates that POLA achieves reciprocity-based cooperation more reliably than LOLA.

NeurIPS Conference 2021 Conference Paper

Differentiable Annealed Importance Sampling and the Perils of Gradient Noise

Guodong Zhang
Kyle Hsu
Jianing Li
Chelsea Finn
Roger B. Grosse

Annealed importance sampling (AIS) and related algorithms are highly effective tools for marginal likelihood estimation, but are not fully differentiable due to the use of Metropolis-Hastings correction steps. Differentiability is a desirable property as it would admit the possibility of optimizing marginal likelihood as an objective using gradient-based methods. To this end, we propose Differentiable AIS (DAIS), a variant of AIS which ensures differentiability by abandoning the Metropolis-Hastings corrections. As a further advantage, DAIS allows for mini-batch gradients. We provide a detailed convergence analysis for Bayesian linear regression which goes beyond previous analyses by explicitly accounting for the sampler not having reached equilibrium. Using this analysis, we prove that DAIS is consistent in the full-batch setting and provide a sublinear convergence rate. Furthermore, motivated by the problem of learning from large-scale datasets, we study a stochastic variant of DAIS that uses mini-batch gradients. Surprisingly, stochastic DAIS can be arbitrarily bad due to a fundamental incompatibility between the goals of last-iterate convergence to the posterior and elimination of the accumulated stochastic error. This is in stark contrast with other settings such as gradient-based optimization and Langevin dynamics, where the effect of gradient noise can be washed out by taking smaller steps. This indicates that annealing-based marginal likelihood estimation with stochastic gradients may require new ideas.

ICLR Conference 2021 Conference Paper

INT: An Inequality Benchmark for Evaluating Generalization in Theorem Proving

Yuhuai Wu
Albert Q. Jiang
Jimmy Ba
Roger B. Grosse

In learning-assisted theorem proving, one of the most critical challenges is to generalize to theorems unlike those seen at training time. In this paper, we introduce INT, an INequality Theorem proving benchmark designed to test agents’ generalization ability. INT is based on a theorem generator, which provides theoretically infinite data and allows us to measure 6 different types of generalization, each reflecting a distinct challenge, characteristic of automated theorem proving. In addition, provides a fast theorem proving environment with sequence-based and graph-based interfaces, conducive to performing learning-based research. We introduce base-lines with architectures including transformers and graph neural networks (GNNs)for INT. Using INT, we find that transformer-based agents achieve stronger test performance for most of the generalization tasks, despite having much larger out-of-distribution generalization gaps than GNNs. We further find that the addition of Monte Carlo Tree Search (MCTS) at test time helps to prove new theorems.

ICML Conference 2021 Conference Paper

LIME: Learning Inductive Bias for Primitives of Mathematical Reasoning

Yuhuai Wu
Markus N. Rabe
Wenda Li
Jimmy Ba
Roger B. Grosse
Christian Szegedy

While designing inductive bias in neural architectures has been widely studied, we hypothesize that transformer networks are flexible enough to learn inductive bias from suitable generic tasks. Here, we replace architecture engineering by encoding inductive bias in the form of datasets. Inspired by Peirce’s view that deduction, induction, and abduction are the primitives of reasoning, we design three synthetic tasks that are intended to require the model to have these three abilities. We specifically design these tasks to be synthetic and devoid of mathematical knowledge to ensure that only the fundamental reasoning biases can be learned from these tasks. This defines a new pre-training methodology called "LIME" (Learning Inductive bias for Mathematical rEasoning). Models trained with LIME significantly outperform vanilla transformers on four very different large mathematical reasoning benchmarks. Unlike dominating the computation cost as traditional pre-training approaches, LIME requires only a small fraction of the computation cost of the typical downstream task. The code for generating LIME tasks is available at https: //github. com/tonywu95/LIME.

ICML Conference 2021 Conference Paper

On Monotonic Linear Interpolation of Neural Network Parameters

James Lucas
Juhan Bae
Michael R. Zhang
Stanislav Fort
Richard S. Zemel
Roger B. Grosse

Linear interpolation between initial neural network parameters and converged parameters after training with stochastic gradient descent (SGD) typically leads to a monotonic decrease in the training objective. This Monotonic Linear Interpolation (MLI) property, first observed by Goodfellow et al. 2014, persists in spite of the non-convex objectives and highly non-linear training dynamics of neural networks. Extending this work, we evaluate several hypotheses for this property that, to our knowledge, have not yet been explored. Using tools from differential geometry, we draw connections between the interpolated paths in function space and the monotonicity of the network — providing sufficient conditions for the MLI property under mean squared error. While the MLI property holds under various settings (e. g. , network architectures and learning problems), we show in practice that networks violating the MLI property can be produced systematically, by encouraging the weights to move far from initialization. The MLI property raises important questions about the loss landscape geometry of neural networks and highlights the need to further study their global properties.

ICML Conference 2021 Conference Paper

Scalable Variational Gaussian Processes via Harmonic Kernel Decomposition

Shengyang Sun
Jiaxin Shi
Andrew Gordon Wilson
Roger B. Grosse

We introduce a new scalable variational Gaussian process approximation which provides a high fidelity approximation while retaining general applicability. We propose the harmonic kernel decomposition (HKD), which uses Fourier series to decompose a kernel as a sum of orthogonal kernels. Our variational approximation exploits this orthogonality to enable a large number of inducing points at a low computational cost. We demonstrate that, on a range of regression and classification problems, our approach can exploit input space symmetries such as translations and reflections, and it significantly outperforms standard variational methods in scalability and accuracy. Notably, our approach achieves state-of-the-art results on CIFAR-10 among pure GP models.

ICLR Conference 2021 Conference Paper

When does preconditioning help or hurt generalization?

Shun-ichi Amari
Jimmy Ba
Roger B. Grosse
Xuechen Li 0005
Atsushi Nitanda
Taiji Suzuki
Denny Wu
Ji Xu

While second order optimizers such as natural gradient descent (NGD) often speed up optimization, their effect on generalization has been called into question. This work presents a more nuanced view on how the \textit{implicit bias} of optimizers affects the comparison of generalization properties. We provide an exact asymptotic bias-variance decomposition of the generalization error of preconditioned ridgeless regression in the overparameterized regime, and consider the inverse population Fisher information matrix (used in NGD) as a particular example. We determine the optimal preconditioner $\boldsymbol{P}$ for both the bias and variance, and find that the relative generalization performance of different optimizers depends on label noise and ``shape'' of the signal (true parameters): when the labels are noisy, the model is misspecified, or the signal is misaligned with the features, NGD can achieve lower risk; conversely, GD generalizes better under clean labels, a well-specified model, or aligned signal. Based on this analysis, we discuss several approaches to manage the bias-variance tradeoff, and the potential benefit of interpolating between first- and second-order updates. We then extend our analysis to regression in the reproducing kernel Hilbert space and demonstrate that preconditioning can lead to more efficient decrease in the population risk. Lastly, we empirically compare the generalization error of first- and second-order optimizers in neural network experiments, and observe robust trends matching our theoretical analysis.

NeurIPS Conference 2020 Conference Paper

Delta-STN: Efficient Bilevel Optimization for Neural Networks using Structured Response Jacobians

Juhan Bae
Roger B. Grosse

Hyperparameter optimization of neural networks can be elegantly formulated as a bilevel optimization problem. While research on bilevel optimization of neural networks has been dominated by implicit differentiation and unrolling, hypernetworks such as Self-Tuning Networks (STNs) have recently gained traction due to their ability to amortize the optimization of the inner objective. In this paper, we diagnose several subtle pathologies in the training of STNs. Based on these observations, we propose the Delta-STN, an improved hypernetwork architecture which stabilizes training and optimizes hyperparameters much more efficiently than STNs. The key idea is to focus on accurately approximating the best-response Jacobian rather than the full best-response function; we achieve this by reparameterizing the hypernetwork and linearizing the network around the current parameters. We demonstrate empirically that our Delta-STN can tune regularization hyperparameters (e. g. weight decay, dropout, number of cutout holes) with higher accuracy, faster convergence, and improved stability compared to existing approaches.

ICML Conference 2020 Conference Paper

Evaluating Lossy Compression Rates of Deep Generative Models

Sicong Huang 0001
Alireza Makhzani
Yanshuai Cao
Roger B. Grosse

The field of deep generative modeling has succeeded in producing astonishingly realistic-seeming images and audio, but quantitative evaluation remains a challenge. Log-likelihood is an appealing metric due to its grounding in statistics and information theory, but it can be challenging to estimate for implicit generative models, and scalar-valued metrics give an incomplete picture of a model’s quality. In this work, we propose to use rate distortion (RD) curves to evaluate and compare deep generative models. While estimating RD curves is seemingly even more computationally demanding than log-likelihood estimation, we show that we can approximate the entire RD curve using nearly the same computations as were previously used to achieve a single log-likelihood estimate. We evaluate lossy compression rates of VAEs, GANs, and adversarial autoencoders (AAEs) on the MNIST and CIFAR10 datasets. Measuring the entire RD curve gives a more complete picture than scalar-valued metrics, and we arrive at a number of insights not obtainable from log-likelihoods alone.

ICLR Conference 2020 Conference Paper

Picking Winning Tickets Before Training by Preserving Gradient Flow

Chaoqi Wang
Guodong Zhang 0006
Roger B. Grosse

Overparameterization has been shown to benefit both the optimization and generalization of neural networks, but large networks are resource hungry at both training and test time. Network pruning can reduce test-time resource requirements, but is typically applied to trained networks and therefore cannot avoid the expensive training process. We aim to prune networks at initialization, thereby saving resources at training time as well. Specifically, we argue that efficient training requires preserving the gradient flow through the network. This leads to a simple but effective pruning criterion we term Gradient Signal Preservation (GraSP). We empirically investigate the effectiveness of the proposed method with extensive experiments on CIFAR-10, CIFAR-100, Tiny-ImageNet and ImageNet, using VGGNet and ResNet architectures. Our method can prune 80% of the weights of a VGG-16 network on ImageNet at initialization, with only a 1.6% drop in top-1 accuracy. Moreover, our method achieves significantly better performance than the baseline at extreme sparsity levels. Our code is made public at: https://github.com/alecwangcq/GraSP.

NeurIPS Conference 2020 Conference Paper

Regularized linear autoencoders recover the principal components, eventually

Xuchan Bao
James Lucas
Sushant Sachdeva
Roger B. Grosse

Our understanding of learning input-output relationships with neural nets has improved rapidly in recent years, but little is known about the convergence of the underlying representations, even in the simple case of linear autoencoders (LAEs). We show that when trained with proper regularization, LAEs can directly learn the optimal representation -- ordered, axis-aligned principal components. We analyze two such regularization schemes: non-uniform L2 regularization and a deterministic variant of nested dropout [Rippel et al, ICML' 2014]. Though both regularization schemes converge to the optimal representation, we show that this convergence is slow due to ill-conditioning that worsens with increasing latent dimension. We show that the inefficiency of learning the optimal representation is not inevitable -- we present a simple modification to the gradient descent update that greatly speeds up convergence empirically.

ICML Conference 2019 Conference Paper

EigenDamage: Structured Pruning in the Kronecker-Factored Eigenbasis

Chaoqi Wang
Roger B. Grosse
Sanja Fidler
Guodong Zhang 0006

Reducing the test time resource requirements of a neural network while preserving test accuracy is crucial for running inference on resource-constrained devices. To achieve this goal, we introduce a novel network reparameterization based on the Kronecker-factored eigenbasis (KFE), and then apply Hessian-based structured pruning methods in this basis. As opposed to existing Hessian-based pruning algorithms which do pruning in parameter coordinates, our method works in the KFE where different weights are approximately independent, enabling accurate pruning and fast computation. We demonstrate empirically the effectiveness of the proposed method through extensive experiments. In particular, we highlight that the improvements are especially significant for more challenging datasets and networks. With negligible loss of accuracy, an iterative-pruning version gives a 10x reduction in model size and a 8x reduction in FLOPs on wide ResNet32.

ICML Conference 2019 Conference Paper

Sorting Out Lipschitz Function Approximation

Cem Anil
James Lucas
Roger B. Grosse

Training neural networks under a strict Lipschitz constraint is useful for provable adversarial robustness, generalization bounds, interpretable gradients, and Wasserstein distance estimation. By the composition property of Lipschitz functions, it suffices to ensure that each individual affine transformation or nonlinear activation is 1-Lipschitz. The challenge is to do this while maintaining the expressive power. We identify a necessary property for such an architecture: each of the layers must preserve the gradient norm during backpropagation. Based on this, we propose to combine a gradient norm preserving activation function, GroupSort, with norm-constrained weight matrices. We show that norm-constrained GroupSort architectures are universal Lipschitz function approximators. Empirically, we show that norm-constrained GroupSort networks achieve tighter estimates of Wasserstein distance than their ReLU counterparts and can achieve provable adversarial robustness guarantees with little cost to accuracy.

ICML Conference 2018 Conference Paper

Adversarial Distillation of Bayesian Neural Network Posteriors

Kuan-Chieh Wang
Paul Vicol
James Lucas
Li Gu
Roger B. Grosse
Richard S. Zemel

Bayesian neural networks (BNNs) allow us to reason about uncertainty in a principled way. Stochastic Gradient Langevin Dynamics (SGLD) enables efficient BNN learning by drawing samples from the BNN posterior using mini-batches. However, SGLD and its extensions require storage of many copies of the model parameters, a potentially prohibitive cost, especially for large neural networks. We propose a framework, Adversarial Posterior Distillation, to distill the SGLD samples using a Generative Adversarial Network (GAN). At test-time, samples are generated by the GAN. We show that this distillation framework incurs no loss in performance on recent BNN applications including anomaly detection, active learning, and defense against adversarial attacks. By construction, our framework distills not only the Bayesian predictive distribution, but the posterior itself. This allows one to compute quantities such as the approximate model variance, which is useful in downstream tasks. To our knowledge, these are the first results applying MCMC-based BNNs to the aforementioned applications.

ICML Conference 2018 Conference Paper

Differentiable Compositional Kernel Learning for Gaussian Processes

Shengyang Sun
Guodong Zhang 0006
Chaoqi Wang
Wenyuan Zeng
Jiaman Li
Roger B. Grosse

The generalization properties of Gaussian processes depend heavily on the choice of kernel, and this choice remains a dark art. We present the Neural Kernel Network (NKN), a flexible family of kernels represented by a neural network. The NKN’s architecture is based on the composition rules for kernels, so that each unit of the network corresponds to a valid kernel. It can compactly approximate compositional kernel structures such as those used by the Automatic Statistician (Lloyd et al. , 2014), but because the architecture is differentiable, it is end-to-end trainable with gradient- based optimization. We show that the NKN is universal for the class of stationary kernels. Empirically we demonstrate NKN’s pattern discovery and extrapolation abilities on several tasks that depend crucially on identifying the underlying structure, including time series and texture extrapolation, as well as Bayesian optimization.

ICML Conference 2018 Conference Paper

Noisy Natural Gradient as Variational Inference

Guodong Zhang 0006
Shengyang Sun
David Duvenaud
Roger B. Grosse

Variational Bayesian neural nets combine the flexibility of deep learning with Bayesian uncertainty estimation. Unfortunately, there is a tradeoff between cheap but simple variational families (e. g. fully factorized) or expensive and complicated inference procedures. We show that natural gradient ascent with adaptive weight noise implicitly fits a variational posterior to maximize the evidence lower bound (ELBO). This insight allows us to train full-covariance, fully factorized, or matrix-variate Gaussian variational posteriors using noisy versions of natural gradient, Adam, and K-FAC, respectively, making it possible to scale up to modern-size ConvNets. On standard regression benchmarks, our noisy K-FAC algorithm makes better predictions and matches Hamiltonian Monte Carlo’s predictive variances better than existing methods. Its improved uncertainty estimates lead to more efficient exploration in active learning, and intrinsic motivation for reinforcement learning.

ICML Conference 2016 Conference Paper

A Kronecker-factored approximate Fisher matrix for convolution layers

Roger B. Grosse
James Martens

Second-order optimization methods such as natural gradient descent have the potential to speed up training of neural networks by correcting for the curvature of the loss function. Unfortunately, the exact natural gradient is impractical to compute for large models, and most approximations either require an expensive iterative procedure or make crude approximations to the curvature. We present Kronecker Factors for Convolution (KFC), a tractable approximation to the Fisher matrix for convolutional networks based on a structured probabilistic model for the distribution over backpropagated derivatives. Similarly to the recently proposed Kronecker-Factored Approximate Curvature (K-FAC), each block of the approximate Fisher matrix decomposes as the Kronecker product of small matrices, allowing for efficient inversion. KFC captures important curvature information while still yielding comparably efficient updates to stochastic gradient descent (SGD). We show that the updates are invariant to commonly used reparameterizations, such as centering of the activations. In our experiments, approximate natural gradient descent with KFC was able to train convolutional networks several times faster than carefully tuned SGD. Furthermore, it was able to train the networks in 10-20 times fewer iterations than SGD, suggesting its potential applicability in a distributed setting.

ICML Conference 2015 Conference Paper

Optimizing Neural Networks with Kronecker-factored Approximate Curvature

James Martens
Roger B. Grosse

We propose an efficient method for approximating natural gradient descent in neural networks which we call Kronecker-factored Approximate Curvature (K-FAC). K-FAC is based on an efficiently invertible approximation of a neural network’s Fisher information matrix which is neither diagonal nor low-rank, and in some cases is completely non-sparse. It is derived by approximating various large blocks of the Fisher (corresponding to entire layers) as being the Kronecker product of two much smaller matrices. While only several times more expensive to compute than the plain stochastic gradient, the updates produced by K-FAC make much more progress optimizing the objective, which results in an algorithm that can be much faster than stochastic gradient descent with momentum in practice. And unlike some previously proposed approximate natural-gradient/Newton methods which use high-quality non-diagonal curvature matrices (such as Hessian-free optimization), K-FAC works very well in highly stochastic optimization regimes. This is because the cost of storing and inverting K-FAC’s approximation to the curvature matrix does not depend on the amount of data used to estimate it, which is a feature typically associated only with diagonal or low-rank approximations to the curvature matrix.

ICML Conference 2015 Conference Paper

Scaling up Natural Gradient by Sparsely Factorizing the Inverse Fisher Matrix

Roger B. Grosse
Ruslan Salakhutdinov

Second-order optimization methods, such as natural gradient, are difficult to apply to high-dimensional problems, because they require approximately solving large linear systems. We present FActorized Natural Gradient (FANG), an approximation to natural gradient descent where the Fisher matrix is approximated with a Gaussian graphical model whose precision matrix can be computed efficiently. We analyze the Fisher matrix for a small RBM and derive an extremely sparse graphical model which is a good match to the covariance of the sufficient statistics. Our experiments indicate that FANG allows RBMs to be trained more efficiently compared with stochastic gradient descent. Additionally, our analysis yields insight into the surprisingly good performance of the “centering trick” for training RBMs.

ICML Conference 2013 Conference Paper

Structure Discovery in Nonparametric Regression through Compositional Kernel Search

David Duvenaud
James Robert Lloyd
Roger B. Grosse
Joshua B. Tenenbaum
Zoubin Ghahramani

Despite its importance, choosing the structural form of the kernel in nonparametric regression remains a black art. We define a space of kernel structures which are built compositionally by adding and multiplying a small number of base kernels. We present a method for searching over this space of structures which mirrors the scientific discovery process. The learned structures can often decompose functions into interpretable components and enable long-range extrapolation on time-series datasets. Our structure search method outperforms many widely used kernels and kernel combination methods on a variety of prediction tasks.

UAI Conference 2012 Conference Paper

Exploiting compositionality to explore a large space of model structures

Roger B. Grosse
Ruslan Salakhutdinov
William T. Freeman
Joshua B. Tenenbaum

The recent proliferation of richly structured probabilistic models raises the question of how to automatically determine an appropriate model for a dataset. We investigate this question for a space of matrix decomposition models which can express a variety of widely used models from unsupervised learning. To enable model selection, we organize these models into a context-free grammar which generates a wide variety of structures through the compositional application of a few simple rules. We use our grammar to generically and efficiently infer latent components and estimate predictive likelihood for nearly 2500 structures using a small toolbox of reusable algorithms. Using a greedy search over our grammar, we automatically choose the decomposition structure from raw data by evaluating only a small fraction of all models. The proposed method typically finds the correct structure for synthetic data and backs off gracefully to simpler models under heavy noise. It learns sensible structures for datasets as diverse as image patches, motion capture, 20 Questions, and U.S. Senate votes, all using exactly the same code.

ICML Conference 2009 Conference Paper

Convolutional deep belief networks for scalable unsupervised learning of hierarchical representations

Honglak Lee
Roger B. Grosse
Rajesh Ranganath
Andrew Y. Ng

There has been much interest in unsupervised learning of hierarchical generative models such as deep belief networks. Scaling such models to full-sized, high-dimensional images remains a difficult problem. To address this problem, we present the convolutional deep belief network , a hierarchical generative model which scales to realistic image sizes. This model is translation-invariant and supports efficient bottom-up and top-down probabilistic inference. Key to our approach is probabilistic max-pooling , a novel technique which shrinks the representations of higher layers in a probabilistically sound way. Our experiments show that the algorithm learns useful high-level visual features, such as object parts, from unlabeled images of objects and natural scenes. We demonstrate excellent performance on several visual recognition tasks and show that our model can perform hierarchical (bottom-up and top-down) inference over full-sized images.

UAI Conference 2007 Conference Paper

Shift-Invariance Sparse Coding for Audio Classification

Roger B. Grosse
Rajat Raina
Helen Kwong
Andrew Y. Ng

Sparse coding is an unsupervised learning algorithm that learns a succinct high-level representation of the inputs given only unlabeled data; it represents each input as a sparse linear combination of a set of basis functions. Originally applied to modeling the human visual cortex, sparse coding has also been shown to be useful for self-taught learning, in which the goal is to solve a supervised classification task given access to additional unlabeled data drawn from different classes than that in the supervised learning problem. Shift-invariant sparse coding (SISC) is an extension of sparse coding which reconstructs a (usually time-series) input using all of the basis functions in all possible shifts. In this paper, we present an efficient algorithm for learning SISC bases. Our method is based on iteratively solving two large convex optimization problems: The first, which computes the linear coefficients, is an L 1 -regularized linear least squares problem with potentially hundreds of thousands of variables. Existing methods typically use a heuristic to select a small subset of the variables to optimize, but we present a way to efficiently compute the exact solution. The second, which solves for bases, is a constrained linear least squares problem. By optimizing over complex-valued variables in the Fourier domain, we reduce the coupling between the different variables, allowing the problem to be solved efficiently. We show that SISC's learned high-level representations of speech and music provide useful features for classification tasks within those domains. When applied to classification, under certain conditions the learned features outperform state of the art spectral and cepstral features.