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Richard G. Baraniuk

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21 papers

2 author rows

ICML Conference 2025 Conference Paper

Mitigating over-Exploration in Latent Space Optimization using les

Omer Ronen
Ahmed Imtiaz Humayun
Richard G. Baraniuk
Randall Balestriero
Bin Yu 0001

We develop Latent Exploration Score (LES) to mitigate over-exploration in Latent Space Optimization (LSO), a popular method for solving black-box discrete optimization problems. LSO utilizes continuous optimization within the latent space of a Variational Autoencoder (VAE) and is known to be susceptible to over-exploration, which manifests in unrealistic solutions that reduce its practicality. LES leverages the trained decoder’s approximation of the data distribution, and can be employed with any VAE decoder–including pretrained ones–without additional training, architectural changes or access to the training data. Our evaluation across five LSO benchmark tasks and twenty-two VAE models demonstrates that LES always enhances the quality of the solutions while maintaining high objective values, leading to improvements over existing solutions in most cases. We believe that new avenues to LSO will be opened by LES’ ability to identify out of distribution areas, differentiability, and computational tractability.

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ICML Conference 2024 Conference Paper

Deep Networks Always Grok and Here is Why

Ahmed Imtiaz Humayun
Randall Balestriero
Richard G. Baraniuk

Grokking, or delayed generalization, is a phenomenon where generalization in a deep neural network (DNN) occurs long after achieving near zero training error. Previous studies have reported the occurrence of grokking in specific controlled settings, such as DNNs initialized with large-norm parameters or transformers trained on algorithmic datasets. We demonstrate that grokking is actually much more widespread and materializes in a wide range of practical settings, such as training of a convolutional neural network (CNN) on CIFAR10 or a Resnet on Imagenette. We introduce the new concept of delayed robustness, whereby a DNN groks adversarial examples and becomes robust, long after interpolation and/or generalization. We develop an analytical explanation for the emergence of both delayed generalization and delayed robustness based on the local complexity of a DNN’s input-output mapping. Our local complexity measures the density of so-called “linear regions’’ (aka, spline partition regions) that tile the DNN input space and serves as a utile progress measure for training. We provide the first evidence that, for classification problems, the linear regions undergo a phase transition during training whereafter they migrate away from the training samples (making the DNN mapping smoother there) and towards the decision boundary (making the DNN mapping less smooth there). Grokking occurs post phase transition as a robust partition of the input space thanks to the linearization of the DNN mapping around the training points. Web: https: //bit. ly/grok-adversarial.

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ICLR Conference 2024 Conference Paper

Implicit Neural Representations and the Algebra of Complex Wavelets

T. Mitchell Roddenberry
Vishwanath Saragadam
Maarten V. de Hoop
Richard G. Baraniuk

Implicit neural representations (INRs) have arisen as useful methods for representing signals on Euclidean domains. By parameterizing an image as a multilayer perceptron (MLP) on Euclidean space, INRs effectively couple spatial and spectral features of the represented signal in a way that is not obvious in the usual discrete representation. Although INRs using sinusoidal activation functions have been studied in terms of Fourier theory, recent works have shown the advantage of using wavelets instead of sinusoids as activation functions, due to their ability to simultaneously localize in both frequency and space. In this work, we approach such INRs and demonstrate how they resolve high-frequency features of signals from coarse approximations performed in the first layer of the MLP. This leads to multiple prescriptions for the design of INR architectures, including the use of progressive wavelets, decoupling of low and high-pass approximations, and initialization schemes based on the singularities of the target signal.

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NeurIPS Conference 2024 Conference Paper

Learning Transferable Features for Implicit Neural Representations

Kushal Vyas
Ahmed I. Humayun
Aniket Dashpute
Richard G. Baraniuk
Ashok Veeraraghavan
Guha Balakrishnan

Implicit neural representations (INRs) have demonstrated success in a variety of applications, including inverse problems and neural rendering. An INR is typically trained to capture one signal of interest, resulting in learned neural features that are highly attuned to that signal. Assumed to be less generalizable, we explore the aspect of transferability of such learned neural features for fitting similar signals. We introduce a new INR training framework, STRAINER that learns transferable features for fitting INRs to new signals from a given distribution, faster and with better reconstruction quality. Owing to the sequential layer-wise affine operations in an INR, we propose to learn transferable representations by sharing initial encoder layers across multiple INRs with independent decoder layers. At test time, the learned encoder representations are transferred as initialization for an otherwise randomly initialized INR. We find STRAINER to yield extremely powerful initialization for fitting images from the same domain and allow for a ≈ +10dB gain in signal quality early on compared to an untrained INR itself. STRAINER also provides a simple way to encode data-driven priors in INRs. We evaluate STRAINER on multiple in-domain and out-of-domain signal fitting tasks and inverse problems and further provide detailed analysis and discussion on the transferability of STRAINER’s features.

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ICML Conference 2024 Conference Paper

PIDformer: Transformer Meets Control Theory

Tam Minh Nguyen
Cesar A. Uribe
Tan Minh Nguyen
Richard G. Baraniuk

In this work, we address two main shortcomings of transformer architectures: input corruption and rank collapse in their output representation. We unveil self-attention as an autonomous state-space model that inherently promotes smoothness in its solutions, leading to lower-rank outputs and diminished representation capacity. Moreover, the steady-state solution of the model is sensitive to input perturbations. We incorporate a Proportional-Integral-Derivative (PID) closed-loop feedback control system with a reference point into the model to improve robustness and representation capacity. This integration aims to preserve high-frequency details while bolstering model stability, rendering it more noise-resilient. The resulting controlled state-space model is theoretically proven robust and adept at addressing the rank collapse. Motivated by this control framework, we derive a novel class of transformers, PID-controlled Transformer (PIDformer), aimed at improving robustness and mitigating the rank-collapse issue inherent in softmax transformers. We empirically evaluate the model for advantages and robustness against baseline transformers across various practical tasks, including object classification, image segmentation, and language modeling.

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ICLR Conference 2024 Conference Paper

Self-Consuming Generative Models Go MAD

Sina Alemohammad
Josue Casco-Rodriguez
Lorenzo Luzi
Ahmed Imtiaz Humayun
Hossein Babaei
Daniel LeJeune
Ali Siahkoohi
Richard G. Baraniuk

Seismic advances in generative AI algorithms for imagery, text, and other data types have led to the temptation to use AI-synthesized data to train next-generation models. Repeating this process creates an autophagous ("self-consuming") loop whose properties are poorly understood. We conduct a thorough analytical and empirical analysis using state-of-the-art generative image models of three families of autophagous loops that differ in how fixed or fresh real training data is available through the generations of training and whether the samples from previous-generation models have been biased to trade off data quality versus diversity. Our primary conclusion across all scenarios is that *without enough fresh real data in each generation of an autophagous loop, future generative models are doomed to have their quality (precision) or diversity (recall) progressively decrease.* We term this condition Model Autophagy Disorder (MAD), by analogy to mad cow disease, and show that appreciable MADness arises in just a few generations.

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ICLR Conference 2023 Conference Paper

A Primal-Dual Framework for Transformers and Neural Networks

Tan Minh Nguyen
Tam Minh Nguyen
Nhat Ho
Andrea L. Bertozzi
Richard G. Baraniuk
Stanley J. Osher

Self-attention is key to the remarkable success of transformers in sequence modeling tasks including many applications in natural language processing and computer vision. Like neural network layers, these attention mechanisms are often developed by heuristics and experience. To provide a principled framework for constructing attention layers in transformers, we show that the self-attention corresponds to the support vector expansion derived from a support vector regression problem, whose primal formulation has the form of a neural network layer. Using our framework, we derive popular attention layers used in practice and propose two new attentions: 1) the Batch Normalized Attention (Attention-BN) derived from the batch normalization layer and 2) the Attention with Scaled Head (Attention-SH) derived from using less training data to fit the SVR model. We empirically demonstrate the advantages of the Attention-BN and Attention-SH in reducing head redundancy, increasing the model's accuracy, and improving the model's efficiency in a variety of practical applications including image and time-series classification.

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ICLR Conference 2023 Conference Paper

Retrieval-based Controllable Molecule Generation

Zichao Wang 0001
Weili Nie
Zhuoran Qiao
Chaowei Xiao
Richard G. Baraniuk
Anima Anandkumar

Generating new molecules with specified chemical and biological properties via generative models has emerged as a promising direction for drug discovery. However, existing methods require extensive training/fine-tuning with a large dataset, often unavailable in real-world generation tasks. In this work, we propose a new retrieval-based framework for controllable molecule generation. We use a small set of exemplar molecules, i.e., those that (partially) satisfy the design criteria, to steer the pre-trained generative model towards synthesizing molecules that satisfy the given design criteria. We design a retrieval mechanism that retrieves and fuses the exemplar molecules with the input molecule, which is trained by a new self-supervised objective that predicts the nearest neighbor of the input molecule. We also propose an iterative refinement process to dynamically update the generated molecules and retrieval database for better generalization. Our approach is agnostic to the choice of generative models and requires no task-specific fine-tuning. On various tasks ranging from simple design criteria to a challenging real-world scenario for designing lead compounds that bind to the SARS-CoV-2 main protease, we demonstrate our approach extrapolates well beyond the retrieval database, and achieves better performance and wider applicability than previous methods.

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ICML Conference 2022 Conference Paper

Improving Transformers with Probabilistic Attention Keys

Tam Minh Nguyen
Tan Minh Nguyen
Dung D. Le
Duy Khuong Nguyen
Viet-Anh Tran
Richard G. Baraniuk
Nhat Ho
Stanley J. Osher

Multi-head attention is a driving force behind state-of-the-art transformers, which achieve remarkable performance across a variety of natural language processing (NLP) and computer vision tasks. It has been observed that for many applications, those attention heads learn redundant embedding, and most of them can be removed without degrading the performance of the model. Inspired by this observation, we propose Transformer with a Mixture of Gaussian Keys (Transformer-MGK), a novel transformer architecture that replaces redundant heads in transformers with a mixture of keys at each head. These mixtures of keys follow a Gaussian mixture model and allow each attention head to focus on different parts of the input sequence efficiently. Compared to its conventional transformer counterpart, Transformer-MGK accelerates training and inference, has fewer parameters, and requires fewer FLOPs to compute while achieving comparable or better accuracy across tasks. Transformer-MGK can also be easily extended to use with linear attention. We empirically demonstrate the advantage of Transformer-MGK in a range of practical applications, including language modeling and tasks that involve very long sequences. On the Wikitext-103 and Long Range Arena benchmark, Transformer-MGKs with 4 heads attain comparable or better performance to the baseline transformers with 8 heads.

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ICLR Conference 2022 Conference Paper

MaGNET: Uniform Sampling from Deep Generative Network Manifolds Without Retraining

Ahmed Imtiaz Humayun
Randall Balestriero
Richard G. Baraniuk

Deep Generative Networks (DGNs) are extensively employed in Generative Adversarial Networks (GANs), Variational Autoencoders (VAEs), and their variants to approximate the data manifold, and data distribution on that manifold. However, training samples are often obtained based on preferences, costs, or convenience producing artifacts in the empirical data distribution e.g. the large fraction of smiling faces in the CelebA dataset or the large fraction of dark-haired individuals in FFHQ). {\em These inconsistencies will be reproduced when sampling from the trained DGN, which has far-reaching potential implications for fairness, data augmentation, anomaly detection, domain adaptation, and beyond.} In response, we develop a differential geometry based sampler -coined MaGNET- that, given any trained DGN, produces samples that are uniformly distributed on the learned manifold. We prove theoretically and empirically that our technique produces a uniform distribution on the manifold regardless of the training set distribution. We perform a range of experiments on various datasets and DGNs. One of them considers the state-of-the-art StyleGAN2 trained on FFHQ dataset, where uniform sampling via MaGNET increases distribution precision \& recall by 4.12\% \& 3.01\% and decreases gender bias by 41.2\%, without requiring labels or retraining.

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ICLR Conference 2021 Conference Paper

The Recurrent Neural Tangent Kernel

Sina Alemohammad
Zichao Wang 0001
Randall Balestriero
Richard G. Baraniuk

The study of deep neural networks (DNNs) in the infinite-width limit, via the so-called neural tangent kernel (NTK) approach, has provided new insights into the dynamics of learning, generalization, and the impact of initialization. One key DNN architecture remains to be kernelized, namely, the recurrent neural network (RNN). In this paper we introduce and study the Recurrent Neural Tangent Kernel (RNTK), which provides new insights into the behavior of overparametrized RNNs. A key property of the RNTK should greatly benefit practitioners is its ability to compare inputs of different length. To this end, we characterize how the RNTK weights different time steps to form its output under different initialization parameters and nonlinearity choices. A synthetic and 56 real-world data experiments demonstrate that the RNTK offers significant performance gains over other kernels, including standard NTKs, across a wide array of data sets.

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ICLR Conference 2020 Conference Paper

Drawing Early-Bird Tickets: Toward More Efficient Training of Deep Networks

Haoran You
Chaojian Li
Pengfei Xu 0011
Yonggan Fu
Yue Wang 0036
Xiaohan Chen 0001
Richard G. Baraniuk
Zhangyang Wang

(Frankle & Carbin, 2019) shows that there exist winning tickets (small but critical subnetworks) for dense, randomly initialized networks, that can be trained alone to achieve comparable accuracies to the latter in a similar number of iterations. However, the identification of these winning tickets still requires the costly train-prune-retrain process, limiting their practical benefits. In this paper, we discover for the first time that the winning tickets can be identified at the very early training stage, which we term as Early-Bird (EB) tickets, via low-cost training schemes (e.g., early stopping and low-precision training) at large learning rates. Our finding of EB tickets is consistent with recently reported observations that the key connectivity patterns of neural networks emerge early. Furthermore, we propose a mask distance metric that can be used to identify EB tickets with low computational overhead, without needing to know the true winning tickets that emerge after the full training. Finally, we leverage the existence of EB tickets and the proposed mask distance to develop efficient training methods, which are achieved by first identifying EB tickets via low-cost schemes, and then continuing to train merely the EB tickets towards the target accuracy. Experiments based on various deep networks and datasets validate: 1) the existence of EB tickets and the effectiveness of mask distance in efficiently identifying them; and 2) that the proposed efficient training via EB tickets can achieve up to 5.8x ~ 10.7x energy savings while maintaining comparable or even better accuracy as compared to the most competitive state-of-the-art training methods, demonstrating a promising and easily adopted method for tackling cost-prohibitive deep network training.

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ICML Conference 2020 Conference Paper

Sub-linear Memory Sketches for Near Neighbor Search on Streaming Data

Benjamin Coleman
Richard G. Baraniuk
Anshumali Shrivastava

We present the first sublinear memory sketch that can be queried to find the nearest neighbors in a dataset. Our online sketching algorithm compresses an N element dataset to a sketch of size $O(N^b \log^3 N)$ in $O(N^{(b+1)} \log^3 N)$ time, where $b < 1$. This sketch can correctly report the nearest neighbors of any query that satisfies a stability condition parameterized by $b$. We achieve sublinear memory performance on stable queries by combining recent advances in locality sensitive hash (LSH)-based estimators, online kernel density estimation, and compressed sensing. Our theoretical results shed new light on the memory-accuracy tradeoff for nearest neighbor search, and our sketch, which consists entirely of short integer arrays, has a variety of attractive features in practice. We evaluate the memory-recall tradeoff of our method on a friend recommendation task in the Google plus social media network. We obtain orders of magnitude better compression than the random projection based alternative while retaining the ability to report the nearest neighbors of practical queries.

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ICML Conference 2020 Conference Paper

Subspace Fitting Meets Regression: The Effects of Supervision and Orthonormality Constraints on Double Descent of Generalization Errors

Yehuda Dar
Paul M. Mayer
Lorenzo Luzi
Richard G. Baraniuk

We study the linear subspace fitting problem in the overparameterized setting, where the estimated subspace can perfectly interpolate the training examples. Our scope includes the least-squares solutions to subspace fitting tasks with varying levels of supervision in the training data (i. e. , the proportion of input-output examples of the desired low-dimensional mapping) and orthonormality of the vectors defining the learned operator. This flexible family of problems connects standard, unsupervised subspace fitting that enforces strict orthonormality with a corresponding regression task that is fully supervised and does not constrain the linear operator structure. This class of problems is defined over a supervision-orthonormality plane, where each coordinate induces a problem instance with a unique pair of supervision level and softness of orthonormality constraints. We explore this plane and show that the generalization errors of the corresponding subspace fitting problems follow double descent trends as the settings become more supervised and less orthonormally constrained.

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ICML Conference 2018 Conference Paper

A Spline Theory of Deep Networks

Randall Balestriero
Richard G. Baraniuk

We build a rigorous bridge between deep networks (DNs) and approximation theory via spline functions and operators. Our key result is that a large class of DNs can be written as a composition of max-affine spline operators (MASOs), which provide a powerful portal through which to view and analyze their inner workings. For instance, conditioned on the input signal, the output of a MASO DN can be written as a simple affine transformation of the input. This implies that a DN constructs a set of signal-dependent, class-specific templates against which the signal is compared via a simple inner product; we explore the links to the classical theory of optimal classification via matched filters and the effects of data memorization. Going further, we propose a simple penalty term that can be added to the cost function of any DN learning algorithm to force the templates to be orthogonal with each other; this leads to significantly improved classification performance and reduced overfitting with no change to the DN architecture. The spline partition of the input signal space opens up a new geometric avenue to study how DNs organize signals in a hierarchical fashion. As an application, we develop and validate a new distance metric for signals that quantifies the difference between their partition encodings.

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ICML Conference 2018 Conference Paper

MISSION: Ultra Large-Scale Feature Selection using Count-Sketches

Amirali Aghazadeh
Ryan Spring
Daniel LeJeune
Gautam Dasarathy
Anshumali Shrivastava
Richard G. Baraniuk

Feature selection is an important challenge in machine learning. It plays a crucial role in the explainability of machine-driven decisions that are rapidly permeating throughout modern society. Unfortunately, the explosion in the size and dimensionality of real-world datasets poses a severe challenge to standard feature selection algorithms. Today, it is not uncommon for datasets to have billions of dimensions. At such scale, even storing the feature vector is impossible, causing most existing feature selection methods to fail. Workarounds like feature hashing, a standard approach to large-scale machine learning, helps with the computational feasibility, but at the cost of losing the interpretability of features. In this paper, we present MISSION, a novel framework for ultra large-scale feature selection that performs stochastic gradient descent while maintaining an efficient representation of the features in memory using a Count-Sketch data structure. MISSION retains the simplicity of feature hashing without sacrificing the interpretability of the features while using only O(log^2(p)) working memory. We demonstrate that MISSION accurately and efficiently performs feature selection on real-world, large-scale datasets with billions of dimensions.

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ICML Conference 2018 Conference Paper

prDeep: Robust Phase Retrieval with a Flexible Deep Network

Christopher A. Metzler
Philip Schniter
Ashok Veeraraghavan
Richard G. Baraniuk

Phase retrieval algorithms have become an important component in many modern computational imaging systems. For instance, in the context of ptychography and speckle correlation imaging, they enable imaging past the diffraction limit and through scattering media, respectively. Unfortunately, traditional phase retrieval algorithms struggle in the presence of noise. Progress has been made recently on developing more robust algorithms using signal priors, but at the expense of limiting the range of supported measurement models (e. g. , to Gaussian or coded diffraction patterns). In this work we leverage the regularization-by-denoising framework and a convolutional neural network denoiser to create prDeep, a new phase retrieval algorithm that is both robust and broadly applicable. We test and validate prDeep in simulation to demonstrate that it is robust to noise and can handle a variety of system models.

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ICML Conference 2018 Conference Paper

Spline Filters For End-to-End Deep Learning

Randall Balestriero
Romain Cosentino
Hervé Glotin
Richard G. Baraniuk

We propose to tackle the problem of end-to-end learning for raw waveform signals by introducing learnable continuous time-frequency atoms. The derivation of these filters is achieved by defining a functional space with a given smoothness order and boundary conditions. From this space, we derive the parametric analytical filters. Their differentiability property allows gradient-based optimization. As such, one can utilize any Deep Neural Network (DNN) with these filters. This enables us to tackle in a front-end fashion a large scale bird detection task based on the freefield1010 dataset known to contain key challenges, such as the dimensionality of the inputs data ($>100, 000$) and the presence of additional noises: multiple sources and soundscapes.

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ICML Conference 2016 Conference Paper

Dealbreaker: A Nonlinear Latent Variable Model for Educational Data

Andrew S. Lan
Tom Goldstein
Richard G. Baraniuk
Christoph Studer

Statistical models of student responses on assessment questions, such as those in homeworks and exams, enable educators and computer-based personalized learning systems to gain insights into students’ knowledge using machine learning. Popular student-response models, including the Rasch model and item response theory models, represent the probability of a student answering a question correctly using an affine function of latent factors. While such models can accurately predict student responses, their ability to interpret the underlying knowledge structure (which is certainly nonlinear) is limited. In response, we develop a new, nonlinear latent variable model that we call the dealbreaker model, in which a student’s success probability is determined by their weakest concept mastery. We develop efficient parameter inference algorithms for this model using novel methods for nonconvex optimization. We show that the dealbreaker model achieves comparable or better prediction performance as compared to affine models with real-world educational datasets. We further demonstrate that the parameters learned by the dealbreaker model are interpretable—they provide key insights into which concepts are critical (i. e. , the “dealbreaker”) to answering a question correctly. We conclude by reporting preliminary results for a movie-rating dataset, which illustrate the broader applicability of the dealbreaker model.

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JMLR Journal 2014 Journal Article

Sparse Factor Analysis for Learning and Content Analytics

Andrew S. Lan
Andrew E. Waters
Christoph Studer
Richard G. Baraniuk

We develop a new model and algorithms for machine learning-based learning analytics, which estimate a learner's knowledge of the concepts underlying a domain, and {\em{content analytics}}, which estimate the relationships among a collection of questions and those concepts. Our model represents the probability that a learner provides the correct response to a question in terms of three factors: their understanding of a set of underlying concepts, the concepts involved in each question, and each question's intrinsic difficulty. We estimate these factors given the graded responses to a collection of questions. The underlying estimation problem is ill-posed in general, especially when only a subset of the questions are answered. The key observation that enables a well-posed solution is the fact that typical educational domains of interest involve only a small number of key concepts. Leveraging this observation, we develop both a bi-convex maximum-likelihood-based solution and a Bayesian solution to the resulting SPARse Factor Analysis (SPARFA) problem. We also incorporate user-defined tags on questions to facilitate the interpretability of the estimated factors. Experiments with synthetic and real-world data demonstrate the efficacy of our approach. Finally, we make a connection between SPARFA and noisy, binary-valued (1-bit) dictionary learning that is of independent interest. [abs] [ pdf ][ bib ] &copy JMLR 2014. ( edit, beta )

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JMLR Journal 2013 Journal Article

Greedy Feature Selection for Subspace Clustering

Eva L. Dyer
Aswin C. Sankaranarayanan
Richard G. Baraniuk

Unions of subspaces provide a powerful generalization of single subspace models for collections of high-dimensional data; however, learning multiple subspaces from data is challenging due to the fact that segmentation---the identification of points that live in the same subspace---and subspace estimation must be performed simultaneously. Recently, sparse recovery methods were shown to provide a provable and robust strategy for exact feature selection (EFS)---recovering subsets of points from the ensemble that live in the same subspace. In parallel with recent studies of EFS with $\ell_1$-minimization, in this paper, we develop sufficient conditions for EFS with a greedy method for sparse signal recovery known as orthogonal matching pursuit (OMP). Following our analysis, we provide an empirical study of feature selection strategies for signals living on unions of subspaces and characterize the gap between sparse recovery methods and nearest neighbor (NN)-based approaches. In particular, we demonstrate that sparse recovery methods provide significant advantages over NN methods and that the gap between the two approaches is particularly pronounced when the sampling of subspaces in the data set is sparse. Our results suggest that OMP may be employed to reliably recover exact feature sets in a number of regimes where NN approaches fail to reveal the subspace membership of points in the ensemble. [abs] [ pdf ][ bib ] &copy JMLR 2013. ( edit, beta )

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