pwc-archive/papers-with-abstracts huggingface dataset:
Rejection sampling from shape-constrained distributions in sublinear time
Authors: Sinho Chewi, Patrik Gerber, Chen Lu, Thibaut Le Gouic, Philippe Rigollet
Date: 2021-05-29 00:00:00

We consider the task of generating exact samples from a target distribution, known up to normalization, over a finite alphabet. The classical algorithm for this task is rejection sampling, and although it has been used in practice for decades, there is surprisingly little study of its fundamental limitations. In this work, we study the query complexity of rejection sampling in a minimax framework for various classes of discrete distributions. Our results provide new algorithms for sampling whose complexity scales sublinearly with the alphabet size. When applied to adversarial bandits, we show that a slight modification of the Exp3 algorithm reduces the per-iteration complexity from $\mathcal O(K)$ to $\mathcal O(\log^2 K)$, where $K$ is the number of arms.
The query complexity of sampling from strongly log-concave distributions in one dimension
Authors: Sinho Chewi, Patrik Gerber, Chen Lu, Thibaut Le Gouic, Philippe Rigollet
Date: 2021-05-29 00:00:00

We establish the first tight lower bound of $\Omega(\log\log\kappa)$ on the query complexity of sampling from the class of strongly log-concave and log-smooth distributions with condition number $\kappa$ in one dimension. Whereas existing guarantees for MCMC-based algorithms scale polynomially in $\kappa$, we introduce a novel algorithm based on rejection sampling that closes this doubly exponential gap.
SMASH: Sparse Matrix Atomic Scratchpad Hashing
Authors: Kaustubh Shivdikar
Date: 2021-05-29 00:00:00

Sparse matrices, more specifically SpGEMM kernels, are commonly found in a wide range of applications, spanning graph-based path-finding to machine learning algorithms (e.g., neural networks). A particular challenge in implementing SpGEMM kernels has been the pressure placed on DRAM memory. One approach to tackle this problem is to use an inner product method for the SpGEMM kernel implementation. While the inner product produces fewer intermediate results, it can end up saturating the memory bandwidth, given the high number of redundant fetches of the input matrix elements. Using an outer product-based SpGEMM kernel can reduce redundant fetches, but at the cost of increased overhead due to extra computation and memory accesses for producing/managing partial products. In this thesis, we introduce a novel SpGEMM kernel implementation based on the row-wise product approach. We leverage atomic instructions to merge intermediate partial products as they are generated. The use of atomic instructions eliminates the need to create partial product matrices. To evaluate our row-wise product approach, we map an optimized SpGEMM kernel to a custom accelerator designed to accelerate graph-based applications. The targeted accelerator is an experimental system named PIUMA, being developed by Intel. PIUMA provides several attractive features, including fast context switching, user-configurable caches, globally addressable memory, non-coherent caches, and asynchronous pipelines. We tailor our SpGEMM kernel to exploit many of the features of the PIUMA fabric. This thesis compares our SpGEMM implementation against prior solutions, all mapped to the PIUMA framework. We briefly describe some of the PIUMA architecture features and then delve into the details of our optimized SpGEMM kernel. Our SpGEMM kernel can achieve 9.4x speedup as compared to competing approaches.
Deep Fair Discriminative Clustering
Authors: Hongjing Zhang, Ian Davidson
Date: 2021-05-28 00:00:00
Tasks: Clustering, Deep Clustering, Fairness, Representation Learning

Deep clustering has the potential to learn a strong representation and hence better clustering performance compared to traditional clustering methods such as $k$-means and spectral clustering. However, this strong representation learning ability may make the clustering unfair by discovering surrogates for protected information which we empirically show in our experiments. In this work, we study a general notion of group-level fairness for both binary and multi-state protected status variables (PSVs). We begin by formulating the group-level fairness problem as an integer linear programming formulation whose totally unimodular constraint matrix means it can be efficiently solved via linear programming. We then show how to inject this solver into a discriminative deep clustering backbone and hence propose a refinement learning algorithm to combine the clustering goal with the fairness objective to learn fair clusters adaptively. Experimental results on real-world datasets demonstrate that our model consistently outperforms state-of-the-art fair clustering algorithms. Our framework shows promising results for novel clustering tasks including flexible fairness constraints, multi-state PSVs and predictive clustering.
ARMS: Antithetic-REINFORCE-Multi-Sample Gradient for Binary Variables
Authors: Alek Dimitriev, Mingyuan Zhou
Date: 2021-05-28 00:00:00

Estimating the gradients for binary variables is a task that arises frequently in various domains, such as training discrete latent variable models. What has been commonly used is a REINFORCE based Monte Carlo estimation method that uses either independent samples or pairs of negatively correlated samples. To better utilize more than two samples, we propose ARMS, an Antithetic REINFORCE-based Multi-Sample gradient estimator. ARMS uses a copula to generate any number of mutually antithetic samples. It is unbiased, has low variance, and generalizes both DisARM, which we show to be ARMS with two samples, and the leave-one-out REINFORCE (LOORF) estimator, which is ARMS with uncorrelated samples. We evaluate ARMS on several datasets for training generative models, and our experimental results show that it outperforms competing methods. We also develop a version of ARMS for optimizing the multi-sample variational bound, and show that it outperforms both VIMCO and DisARM. The code is publicly available.
On a class of data-driven mixed-integer programming problems under uncertainty: a distributionally robust approach
Authors: Sergey S. Ketkov, Andrei S. Shilov
Date: 2021-05-28 00:00:00
Tasks: Combinatorial Optimization

In this study we analyze linear mixed-integer programming problems, in which the distribution of the cost vector is only observable through a finite training data set. In contrast to the related studies, we assume that the number of random observations for each component of the cost vector may vary. Then the goal is to find a prediction rule that converts the data set into an estimate of the expected value of the objective function and a prescription rule that provides an associated estimate of the optimal decision. We aim at finding the least conservative prediction and prescription rules, which satisfy some specified asymptotic guarantees as the sample size tends to infinity. We demonstrate that under some mild assumption the resulting vector optimization problems admit a Pareto optimal solution with some attractive theoretical properties. In particular, this solution can be obtained by solving a distributionally robust optimization (DRO) problem with respect to all probability distributions with given component-wise relative entropy distances from the empirical marginal distributions. It turns out that the outlined DRO problem can be solved rather effectively whenever there exists an effective algorithm for the respective deterministic problem. In addition, we perform numerical experiments where the out-of-sample performance of the proposed approach is analyzed.
Visualizing Representations of Adversarially Perturbed Inputs
Authors: Daniel Steinberg, Paul Munro
Date: 2021-05-28 00:00:00
Tasks: Dimensionality Reduction

It has been shown that deep learning models are vulnerable to adversarial attacks. We seek to further understand the consequence of such attacks on the intermediate activations of neural networks. We present an evaluation metric, POP-N, which scores the effectiveness of projecting data to N dimensions under the context of visualizing representations of adversarially perturbed inputs. We conduct experiments on CIFAR-10 to compare the POP-2 score of several dimensionality reduction algorithms across various adversarial attacks. Finally, we utilize the 2D data corresponding to high POP-2 scores to generate example visualizations.
Asymptotically Optimal Bandits under Weighted Information
Authors: Matias I. Müller, Cristian R. Rojas
Date: 2021-05-28 00:00:00
Tasks: Thompson Sampling

We study the problem of regret minimization in a multi-armed bandit setup where the agent is allowed to play multiple arms at each round by spreading the resources usually allocated to only one arm. At each iteration the agent selects a normalized power profile and receives a Gaussian vector as outcome, where the unknown variance of each sample is inversely proportional to the power allocated to that arm. The reward corresponds to a linear combination of the power profile and the outcomes, resembling a linear bandit. By spreading the power, the agent can choose to collect information much faster than in a traditional multi-armed bandit at the price of reducing the accuracy of the samples. This setup is fundamentally different from that of a linear bandit -- the regret is known to scale as $\Theta(\sqrt{T})$ for linear bandits, while in this setup the agent receives a much more detailed feedback, for which we derive a tight $\log(T)$ problem-dependent lower-bound. We propose a Thompson-Sampling-based strategy, called Weighted Thompson Sampling (\WTS), that designs the power profile as its posterior belief of each arm being the best arm, and show that its upper bound matches the derived logarithmic lower bound. Finally, we apply this strategy to a problem of control and system identification, where the goal is to estimate the maximum gain (also called $\mathcal{H}_\infty$-norm) of a linear dynamical system based on batches of input-output samples.
Reinforcement Learning reveals fundamental limits on the mixing of active particles
Authors: Dominik Schildknecht, Anastasia N. Popova, Jack Stellwagen, Matt Thomson
Date: 2021-05-28 00:00:00
Tasks: Open-Ended Question Answering, reinforcement-learning, Reinforcement Learning (RL)

The control of far-from-equilibrium physical systems, including active materials, has emerged as an important area for the application of reinforcement learning (RL) strategies to derive control policies for physical systems. In active materials, non-linear dynamics and long-range interactions between particles prohibit closed-form descriptions of the system's dynamics and prevent explicit solutions to optimal control problems. Due to fundamental challenges in solving for explicit control strategies, RL has emerged as an approach to derive control strategies for far-from-equilibrium active matter systems. However, an important open question is how the mathematical structure and the physical properties of the active matter systems determine the tractability of RL for learning control policies. In this work, we show that RL can only find good strategies to the canonical active matter task of mixing for systems that combine attractive and repulsive particle interactions. Using mathematical results from dynamical systems theory, we relate the availability of both interaction types with the existence of hyperbolic dynamics and the ability of RL to find homogeneous mixing strategies. In particular, we show that for drag-dominated translational-invariant particle systems, hyperbolic dynamics and, therefore, mixing requires combining attractive and repulsive interactions. Broadly, our work demonstrates how fundamental physical and mathematical properties of dynamical systems can enable or constrain reinforcement learning-based control.
Bridging the Gap Between Practice and PAC-Bayes Theory in Few-Shot Meta-Learning
Authors: Nan Ding, Xi Chen, Tomer Levinboim, Sebastian Goodman, Radu Soricut
Date: 2021-05-28 00:00:00
Proceeding: NeurIPS 2021 12
Tasks: Few-Shot Learning, Meta-Learning

Despite recent advances in its theoretical understanding, there still remains a significant gap in the ability of existing PAC-Bayesian theories on meta-learning to explain performance improvements in the few-shot learning setting, where the number of training examples in the target tasks is severely limited. This gap originates from an assumption in the existing theories which supposes that the number of training examples in the observed tasks and the number of training examples in the target tasks follow the same distribution, an assumption that rarely holds in practice. By relaxing this assumption, we develop two PAC-Bayesian bounds tailored for the few-shot learning setting and show that two existing meta-learning algorithms (MAML and Reptile) can be derived from our bounds, thereby bridging the gap between practice and PAC-Bayesian theories. Furthermore, we derive a new computationally-efficient PACMAML algorithm, and show it outperforms existing meta-learning algorithms on several few-shot benchmark datasets.
Reinforcement Learning for on-line Sequence Transformation
Authors: Grzegorz Rypeść, Łukasz Lepak, Paweł Wawrzyński
Date: 2021-05-28 00:00:00
Tasks: Machine Translation, reinforcement-learning, Reinforcement Learning, Reinforcement Learning (RL), Translation

A number of problems in the processing of sound and natural language, as well as in other areas, can be reduced to simultaneously reading an input sequence and writing an output sequence of generally different length. There are well developed methods that produce the output sequence based on the entirely known input. However, efficient methods that enable such transformations on-line do not exist. In this paper we introduce an architecture that learns with reinforcement to make decisions about whether to read a token or write another token. This architecture is able to transform potentially infinite sequences on-line. In an experimental study we compare it with state-of-the-art methods for neural machine translation. While it produces slightly worse translations than Transformer, it outperforms the autoencoder with attention, even though our architecture translates texts on-line thereby solving a more difficult problem than both reference methods.
Weighted Training for Cross-Task Learning
Authors: Shuxiao Chen, Koby Crammer, Hangfeng He, Dan Roth, Weijie J. Su
Date: 2021-05-28 00:00:00
Proceeding: ICLR 2022 4
Tasks: Chunking, named-entity-recognition, Named Entity Recognition, Named Entity Recognition (NER), NER, Part-Of-Speech Tagging, POS, POS Tagging, Predicate Detection

In this paper, we introduce Target-Aware Weighted Training (TAWT), a weighted training algorithm for cross-task learning based on minimizing a representation-based task distance between the source and target tasks. We show that TAWT is easy to implement, is computationally efficient, requires little hyperparameter tuning, and enjoys non-asymptotic learning-theoretic guarantees. The effectiveness of TAWT is corroborated through extensive experiments with BERT on four sequence tagging tasks in natural language processing (NLP), including part-of-speech (PoS) tagging, chunking, predicate detection, and named entity recognition (NER). As a byproduct, the proposed representation-based task distance allows one to reason in a theoretically principled way about several critical aspects of cross-task learning, such as the choice of the source data and the impact of fine-tuning.
Galerkin Neural Networks: A Framework for Approximating Variational Equations with Error Control
Authors: Mark Ainsworth, Justin Dong
Date: 2021-05-28 00:00:00

We present a new approach to using neural networks to approximate the solutions of variational equations, based on the adaptive construction of a sequence of finite-dimensional subspaces whose basis functions are realizations of a sequence of neural networks. The finite-dimensional subspaces are then used to define a standard Galerkin approximation of the variational equation. This approach enjoys a number of advantages, including: the sequential nature of the algorithm offers a systematic approach to enhancing the accuracy of a given approximation; the sequential enhancements provide a useful indicator for the error that can be used as a criterion for terminating the sequential updates; the basic approach is largely oblivious to the nature of the partial differential equation under consideration; and, some basic theoretical results are presented regarding the convergence (or otherwise) of the method which are used to formulate basic guidelines for applying the method.
Support vector machines and linear regression coincide with very high-dimensional features
Authors: Navid Ardeshir, Clayton Sanford, Daniel Hsu
Date: 2021-05-28 00:00:00
Proceeding: NeurIPS 2021 12
Tasks: regression

The support vector machine (SVM) and minimum Euclidean norm least squares regression are two fundamentally different approaches to fitting linear models, but they have recently been connected in models for very high-dimensional data through a phenomenon of support vector proliferation, where every training example used to fit an SVM becomes a support vector. In this paper, we explore the generality of this phenomenon and make the following contributions. First, we prove a super-linear lower bound on the dimension (in terms of sample size) required for support vector proliferation in independent feature models, matching the upper bounds from previous works. We further identify a sharp phase transition in Gaussian feature models, bound the width of this transition, and give experimental support for its universality. Finally, we hypothesize that this phase transition occurs only in much higher-dimensional settings in the $\ell_1$ variant of the SVM, and we present a new geometric characterization of the problem that may elucidate this phenomenon for the general $\ell_p$ case.
Accelerating Neural ODEs Using Model Order Reduction
Authors: Mikko Lehtimäki, Lassi Paunonen, Marja-Leena Linne
Date: 2021-05-28 00:00:00
Tasks: model, Time Series, Time Series Analysis, Time Series Classification

Embedding nonlinear dynamical systems into artificial neural networks is a powerful new formalism for machine learning. By parameterizing ordinary differential equations (ODEs) as neural network layers, these Neural ODEs are memory-efficient to train, process time-series naturally and incorporate knowledge of physical systems into deep learning models. However, the practical applications of Neural ODEs are limited due to long inference times, because the outputs of the embedded ODE layers are computed numerically with differential equation solvers that can be computationally demanding. Here we show that mathematical model order reduction methods can be used for compressing and accelerating Neural ODEs by accurately simulating the continuous nonlinear dynamics in low-dimensional subspaces. We implement our novel compression method by developing Neural ODEs that integrate the necessary subspace-projection and interpolation operations as layers of the neural network. We validate our approach by comparing it to neuron pruning and SVD-based weight truncation methods from the literature in image and time-series classification tasks. The methods are evaluated by acceleration versus accuracy when adjusting the level of compression. On this spectrum, we achieve a favourable balance over existing methods by using model order reduction when compressing a convolutional Neural ODE. In compressing a recurrent Neural ODE, SVD-based weight truncation yields good performance. Based on our results, our integration of model order reduction with Neural ODEs can facilitate efficient, dynamical system-driven deep learning in resource-constrained applications.
Symmetry-driven graph neural networks
Authors: Francesco Farina, Emma Slade
Date: 2021-05-28 00:00:00
Tasks: Inductive Bias

Exploiting symmetries and invariance in data is a powerful, yet not fully exploited, way to achieve better generalisation with more efficiency. In this paper, we introduce two graph network architectures that are equivariant to several types of transformations affecting the node coordinates. First, we build equivariance to any transformation in the coordinate embeddings that preserves the distance between neighbouring nodes, allowing for equivariance to the Euclidean group. Then, we introduce angle attributes to build equivariance to any angle preserving transformation - thus, to the conformal group. Thanks to their equivariance properties, the proposed models can be vastly more data efficient with respect to classical graph architectures, intrinsically equipped with a better inductive bias and better at generalising. We demonstrate these capabilities on a synthetic dataset composed of $n$-dimensional geometric objects. Additionally, we provide examples of their limitations when (the right) symmetries are not present in the data.
Targeted Deep Learning: Framework, Methods, and Applications
Authors: Shih-Ting Huang, Johannes Lederer
Date: 2021-05-28 00:00:00
Tasks: Deep Learning

Deep learning systems are typically designed to perform for a wide range of test inputs. For example, deep learning systems in autonomous cars are supposed to deal with traffic situations for which they were not specifically trained. In general, the ability to cope with a broad spectrum of unseen test inputs is called generalization. Generalization is definitely important in applications where the possible test inputs are known but plentiful or simply unknown, but there are also cases where the possible inputs are few and unlabeled but known beforehand. For example, medicine is currently interested in targeting treatments to individual patients; the number of patients at any given time is usually small (typically one), their diagnoses/responses/... are still unknown, but their general characteristics (such as genome information, protein levels in the blood, and so forth) are known before the treatment. We propose to call deep learning in such applications targeted deep learning. In this paper, we introduce a framework for targeted deep learning, and we devise and test an approach for adapting standard pipelines to the requirements of targeted deep learning. The approach is very general yet easy to use: it can be implemented as a simple data-preprocessing step. We demonstrate on a variety of real-world data that our approach can indeed render standard deep learning faster and more accurate when the test inputs are known beforehand.
Fair Representations by Compression
Authors: Xavier Gitiaux, Huzefa Rangwala
Date: 2021-05-28 00:00:00
Tasks: Decoder, Fairness

Organizations that collect and sell data face increasing scrutiny for the discriminatory use of data. We propose a novel unsupervised approach to transform data into a compressed binary representation independent of sensitive attributes. We show that in an information bottleneck framework, a parsimonious representation should filter out information related to sensitive attributes if they are provided directly to the decoder. Empirical results show that the proposed method, \textbf{FBC}, achieves state-of-the-art accuracy-fairness trade-off. Explicit control of the entropy of the representation bit stream allows the user to move smoothly and simultaneously along both rate-distortion and rate-fairness curves. \end{abstract}