arXiv subjects

Richard G. Baraniuk

Publications and source records attributed to Richard G. Baraniuk.

At least 73 records · Page 4Linked to original sources

arXiv2022

Improving Transformers with Probabilistic Attention Keys

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.

cs.LG↗

arXiv2022

DeepTensor: Low-Rank Tensor Decomposition with Deep Network Priors

DeepTensor is a computationally efficient framework for low-rank decomposition of matrices and tensors using deep generative networks. We decompose a tensor as the product of low-rank tensor factors (e.g., a matrix as the outer product of two vectors), where each low-rank tensor is generated by a deep network (DN) that is trained in a self-supervised manner to minimize the mean-squared approximation error. Our key observation is that the implicit regularization inherent in DNs enables them to capture nonlinear signal structures (e.g., manifolds) that are out of the reach of classical linear methods like the singular value decomposition (SVD) and principal component analysis (PCA). Furthermore, in contrast to the SVD and PCA, whose performance deteriorates when the tensor's entries deviate from additive white Gaussian noise, we demonstrate that the performance of DeepTensor is robust to a wide range of distributions. We validate that DeepTensor is a robust and computationally efficient drop-in replacement for the SVD, PCA, nonnegative matrix factorization (NMF), and similar decompositions by exploring a range of real-world applications, including hyperspectral image denoising, 3D MRI tomography, and image classification. In particular, DeepTensor offers a 6dB signal-to-noise ratio improvement over standard denoising methods for signals corrupted by Poisson noise and learns to decompose 3D tensors 60 times faster than a single DN equipped with 3D convolutions.

stat.AP↗

arXiv2022

NeuroView-RNN: It's About Time

Recurrent Neural Networks (RNNs) are important tools for processing sequential data such as time-series or video. Interpretability is defined as the ability to be understood by a person and is different from explainability, which is the ability to be explained in a mathematical formulation. A key interpretability issue with RNNs is that it is not clear how each hidden state per time step contributes to the decision-making process in a quantitative manner. We propose NeuroView-RNN as a family of new RNN architectures that explains how all the time steps are used for the decision-making process. Each member of the family is derived from a standard RNN architecture by concatenation of the hidden steps into a global linear classifier. The global linear classifier has all the hidden states as the input, so the weights of the classifier have a linear mapping to the hidden states. Hence, from the weights, NeuroView-RNN can quantify how important each time step is to a particular decision. As a bonus, NeuroView-RNN also offers higher accuracy in many cases compared to the RNNs and their variants. We showcase the benefits of NeuroView-RNN by evaluating on a multitude of diverse time-series datasets.

cs.LG↗

arXiv2022

On Local Distributions in Graph Signal Processing

Graph filtering is the cornerstone operation in graph signal processing (GSP). Thus, understanding it is key in developing potent GSP methods. Graph filters are local and distributed linear operations, whose output depends only on the local neighborhood of each node. Moreover, a graph filter's output can be computed separately at each node by carrying out repeated exchanges with immediate neighbors. Graph filters can be compactly written as polynomials of a graph shift operator (typically, a sparse matrix description of the graph). This has led to relating the properties of the filters with the spectral properties of the corresponding matrix -- which encodes global structure of the graph. In this work, we propose a framework that relies solely on the local distribution of the neighborhoods of a graph. The crux of this approach is to describe graphs and graph signals in terms of a measurable space of rooted balls. Leveraging this, we are able to seamlessly compare graphs of different sizes and coming from different models, yielding results on the convergence of spectral densities, transferability of filters across arbitrary graphs, and continuity of graph signal properties with respect to the distribution of local substructures.

eess.SP↗

arXiv2022

The Flip Side of the Reweighted Coin: Duality of Adaptive Dropout and Regularization

Among the most successful methods for sparsifying deep (neural) networks are those that adaptively mask the network weights throughout training. By examining this masking, or dropout, in the linear case, we uncover a duality between such adaptive methods and regularization through the so-called "$η$-trick" that casts both as iteratively reweighted optimizations. We show that any dropout strategy that adapts to the weights in a monotonic way corresponds to an effective subquadratic regularization penalty, and therefore leads to sparse solutions. We obtain the effective penalties for several popular sparsification strategies, which are remarkably similar to classical penalties commonly used in sparse optimization. Considering variational dropout as a case study, we demonstrate similar empirical behavior between the adaptive dropout method and classical methods on the task of deep network sparsification, validating our theory.

cs.LG↗

arXiv2021

NeuroView: Explainable Deep Network Decision Making

Deep neural networks (DNs) provide superhuman performance in numerous computer vision tasks, yet it remains unclear exactly which of a DN's units contribute to a particular decision. NeuroView is a new family of DN architectures that are interpretable/explainable by design. Each member of the family is derived from a standard DN architecture by vector quantizing the unit output values and feeding them into a global linear classifier. The resulting architecture establishes a direct, causal link between the state of each unit and the classification decision. We validate NeuroView on standard datasets and classification tasks to show that how its unit/class mapping aids in understanding the decision-making process.

cs.CV↗

arXiv2021

NFT-K: Non-Fungible Tangent Kernels

Deep neural networks have become essential for numerous applications due to their strong empirical performance such as vision, RL, and classification. Unfortunately, these networks are quite difficult to interpret, and this limits their applicability in settings where interpretability is important for safety, such as medical imaging. One type of deep neural network is neural tangent kernel that is similar to a kernel machine that provides some aspect of interpretability. To further contribute interpretability with respect to classification and the layers, we develop a new network as a combination of multiple neural tangent kernels, one to model each layer of the deep neural network individually as opposed to past work which attempts to represent the entire network via a single neural tangent kernel. We demonstrate the interpretability of this model on two datasets, showing that the multiple kernels model elucidates the interplay between the layers and predictions.

cs.LG↗

arXiv2021

Unrolling Particles: Unsupervised Learning of Sampling Distributions

Particle filtering is used to compute good nonlinear estimates of complex systems. It samples trajectories from a chosen distribution and computes the estimate as a weighted average. Easy-to-sample distributions often lead to degenerate samples where only one trajectory carries all the weight, negatively affecting the resulting performance of the estimate. While much research has been done on the design of appropriate sampling distributions that would lead to controlled degeneracy, in this paper our objective is to \emph{learn} sampling distributions. Leveraging the framework of algorithm unrolling, we model the sampling distribution as a multivariate normal, and we use neural networks to learn both the mean and the covariance. We carry out unsupervised training of the model to minimize weight degeneracy, relying only on the observed measurements of the system. We show in simulations that the resulting particle filter yields good estimates in a wide range of scenarios.

cs.LG↗

arXiv2021

Math Word Problem Generation with Mathematical Consistency and Problem Context Constraints

We study the problem of generating arithmetic math word problems (MWPs) given a math equation that specifies the mathematical computation and a context that specifies the problem scenario. Existing approaches are prone to generating MWPs that are either mathematically invalid or have unsatisfactory language quality. They also either ignore the context or require manual specification of a problem template, which compromises the diversity of the generated MWPs. In this paper, we develop a novel MWP generation approach that leverages i) pre-trained language models and a context keyword selection model to improve the language quality of the generated MWPs and ii) an equation consistency constraint for math equations to improve the mathematical validity of the generated MWPs. Extensive quantitative and qualitative experiments on three real-world MWP datasets demonstrate the superior performance of our approach compared to various baselines.

cs.CL↗

arXiv2021

Extreme Compressed Sensing of Poisson Rates from Multiple Measurements

Compressed sensing (CS) is a signal processing technique that enables the efficient recovery of a sparse high-dimensional signal from low-dimensional measurements. In the multiple measurement vector (MMV) framework, a set of signals with the same support must be recovered from their corresponding measurements. Here, we present the first exploration of the MMV problem where signals are independently drawn from a sparse, multivariate Poisson distribution. We are primarily motivated by a suite of biosensing applications of microfluidics where analytes (such as whole cells or biomarkers) are captured in small volume partitions according to a Poisson distribution. We recover the sparse parameter vector of Poisson rates through maximum likelihood estimation with our novel Sparse Poisson Recovery (SPoRe) algorithm. SPoRe uses batch stochastic gradient ascent enabled by Monte Carlo approximations of otherwise intractable gradients. By uniquely leveraging the Poisson structure, SPoRe substantially outperforms a comprehensive set of existing and custom baseline CS algorithms. Notably, SPoRe can exhibit high performance even with one-dimensional measurements and high noise levels. This resource efficiency is not only unprecedented in the field of CS but is also particularly potent for applications in microfluidics in which the number of resolvable measurements per partition is often severely limited. We prove the identifiability property of the Poisson model under such lax conditions, analytically develop insights into system performance, and confirm these insights in simulated experiments. Our findings encourage a new approach to biosensing and are generalizable to other applications featuring spatial and temporal Poisson signals.

eess.SP↗

arXiv2021

Wearing a MASK: Compressed Representations of Variable-Length Sequences Using Recurrent Neural Tangent Kernels

High dimensionality poses many challenges to the use of data, from visualization and interpretation, to prediction and storage for historical preservation. Techniques abound to reduce the dimensionality of fixed-length sequences, yet these methods rarely generalize to variable-length sequences. To address this gap, we extend existing methods that rely on the use of kernels to variable-length sequences via use of the Recurrent Neural Tangent Kernel (RNTK). Since a deep neural network with ReLu activation is a Max-Affine Spline Operator (MASO), we dub our approach Max-Affine Spline Kernel (MASK). We demonstrate how MASK can be used to extend principal components analysis (PCA) and t-distributed stochastic neighbor embedding (t-SNE) and apply these new algorithms to separate synthetic time series data sampled from second-order differential equations.

eess.SP↗

arXiv2021

NePTuNe: Neural Powered Tucker Network for Knowledge Graph Completion

Knowledge graphs link entities through relations to provide a structured representation of real world facts. However, they are often incomplete, because they are based on only a small fraction of all plausible facts. The task of knowledge graph completion via link prediction aims to overcome this challenge by inferring missing facts represented as links between entities. Current approaches to link prediction leverage tensor factorization and/or deep learning. Factorization methods train and deploy rapidly thanks to their small number of parameters but have limited expressiveness due to their underlying linear methodology. Deep learning methods are more expressive but also computationally expensive and prone to overfitting due to their large number of trainable parameters. We propose Neural Powered Tucker Network (NePTuNe), a new hybrid link prediction model that couples the expressiveness of deep models with the speed and size of linear models. We demonstrate that NePTuNe provides state-of-the-art performance on the FB15K-237 dataset and near state-of-the-art performance on the WN18RR dataset.

cs.LG↗

arXiv2021

Instructions and Guide for Diagnostic Questions: The NeurIPS 2020 Education Challenge

Digital technologies are becoming increasingly prevalent in education, enabling personalized, high quality education resources to be accessible by students across the world. Importantly, among these resources are diagnostic questions: the answers that the students give to these questions reveal key information about the specific nature of misconceptions that the students may hold. Analyzing the massive quantities of data stemming from students' interactions with these diagnostic questions can help us more accurately understand the students' learning status and thus allow us to automate learning curriculum recommendations. In this competition, participants will focus on the students' answer records to these multiple-choice diagnostic questions, with the aim of 1) accurately predicting which answers the students provide; 2) accurately predicting which questions have high quality; and 3) determining a personalized sequence of questions for each student that best predicts the student's answers. These tasks closely mimic the goals of a real-world educational platform and are highly representative of the educational challenges faced today. We provide over 20 million examples of students' answers to mathematics questions from Eedi, a leading educational platform which thousands of students interact with daily around the globe. Participants to this competition have a chance to make a lasting, real-world impact on the quality of personalized education for millions of students across the world.

cs.CY↗

arXiv2021

Results and Insights from Diagnostic Questions: The NeurIPS 2020 Education Challenge

This competition concerns educational diagnostic questions, which are pedagogically effective, multiple-choice questions (MCQs) whose distractors embody misconceptions. With a large and ever-increasing number of such questions, it becomes overwhelming for teachers to know which questions are the best ones to use for their students. We thus seek to answer the following question: how can we use data on hundreds of millions of answers to MCQs to drive automatic personalized learning in large-scale learning scenarios where manual personalization is infeasible? Success in using MCQ data at scale helps build more intelligent, personalized learning platforms that ultimately improve the quality of education en masse. To this end, we introduce a new, large-scale, real-world dataset and formulate 4 data mining tasks on MCQs that mimic real learning scenarios and target various aspects of the above question in a competition setting at NeurIPS 2020. We report on our NeurIPS competition in which nearly 400 teams submitted approximately 4000 submissions, with encouragingly diverse and effective approaches to each of our tasks.

cs.CY↗

arXiv2021

Educational Question Mining At Scale: Prediction, Analysis and Personalization

Online education platforms enable teachers to share a large number of educational resources such as questions to form exercises and quizzes for students. With large volumes of available questions, it is important to have an automated way to quantify their properties and intelligently select them for students, enabling effective and personalized learning experiences. In this work, we propose a framework for mining insights from educational questions at scale. We utilize the state-of-the-art Bayesian deep learning method, in particular partial variational auto-encoders (p-VAE), to analyze real students' answers to a large collection of questions. Based on p-VAE, we propose two novel metrics that quantify question quality and difficulty, respectively, and a personalized strategy to adaptively select questions for students. We apply our proposed framework to a real-world dataset with tens of thousands of questions and tens of millions of answers from an online education platform. Our framework not only demonstrates promising results in terms of statistical metrics but also obtains highly consistent results with domain experts' evaluation.

cs.CY↗

arXiv2020

MomentumRNN: Integrating Momentum into Recurrent Neural Networks

Designing deep neural networks is an art that often involves an expensive search over candidate architectures. To overcome this for recurrent neural nets (RNNs), we establish a connection between the hidden state dynamics in an RNN and gradient descent (GD). We then integrate momentum into this framework and propose a new family of RNNs, called {\em MomentumRNNs}. We theoretically prove and numerically demonstrate that MomentumRNNs alleviate the vanishing gradient issue in training RNNs. We study the momentum long-short term memory (MomentumLSTM) and verify its advantages in convergence speed and accuracy over its LSTM counterpart across a variety of benchmarks. We also demonstrate that MomentumRNN is applicable to many types of recurrent cells, including those in the state-of-the-art orthogonal RNNs. Finally, we show that other advanced momentum-based optimization methods, such as Adam and Nesterov accelerated gradients with a restart, can be easily incorporated into the MomentumRNN framework for designing new recurrent cells with even better performance. The code is available at https://github.com/minhtannguyen/MomentumRNN.

cs.LG↗

arXiv2020

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

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.

cs.DS↗

arXiv2020

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

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.

cs.LG↗