nils-herrmann/clean_scirepeval huggingface dataset:
Optimal Policies Tend To Seek Power
Authors: Alexander Matt Turner, Logan Riggs Smith, Rohin Shah, Andrew Critch, Prasad Tadepalli

Some researchers speculate that intelligent reinforcement learning (RL) agents would be incentivized to seek resources and power in pursuit of the objectives we specify for them. Other researchers point out that RL agents need not have human-like power-seeking instincts. To clarify this discussion, we develop the first formal theory of the statistical tendencies of optimal policies. In the context of Markov decision processes, we prove that certain environmental symmetries are sufficient for optimal policies to tend to seek power over the environment. These symmetries exist in many environments in which the agent can be shut down or destroyed. We prove that in these environments, most reward functions make it optimal to seek power by keeping a range of options available and, when maximizing average reward, by navigating towards larger sets of potential terminal states.
Fast Tucker Rank Reduction for Non-Negative Tensors Using Mean-Field Approximation
Authors: Kazu Ghalamkari, Mahito Sugiyama

We present an efficient low-rank approximation algorithm for non-negative tensors. The algorithm is derived from our two findings: First,  we show that rank-1 approximation for tensors can be viewed as a mean-field approximation by treating each tensor as a probability distribution. Second, we theoretically provide a sufficient condition for distribution parameters to reduce Tucker ranks of tensors; interestingly, this sufficient condition can be achieved by iterative application of the mean-field approximation. Since the mean-field approximation is always given as a closed formula, our findings lead to a fast low-rank approximation algorithm without using a gradient method. We empirically demonstrate that our algorithm is faster than the existing non-negative Tucker rank reduction methods and achieves competitive or better approximation of given tensors.
Provable Guarantees for Self-Supervised Deep Learning with Spectral Contrastive Loss
Authors: Jeff Z. HaoChen, Colin Wei, Adrien Gaidon, Tengyu Ma

Recent works in self-supervised learning have advanced the state-of-the-art by relying on the contrastive learning paradigm, which learns representations by pushing positive pairs, or similar examples from the same class, closer together while keeping negative pairs far apart. Despite the empirical successes, theoretical foundations are limited -- prior analyses assume conditional independence of the positive pairs given the same class label, but recent empirical applications use heavily correlated positive pairs (i.e., data augmentations of the same image). Our work analyzes contrastive learning without assuming conditional independence of positive pairs using a novel concept of the augmentation graph on data.  Edges in this graph connect augmentations of the same data, and ground-truth classes naturally form connected sub-graphs. We propose a loss that performs spectral decomposition on the population augmentation graph and can be succinctly written as a contrastive learning objective on neural net representations. Minimizing this objective leads to features with provable accuracy guarantees under linear probe evaluation. By standard generalization bounds, these accuracy guarantees also hold when minimizing the training contrastive loss. In all, this work provides the first provable analysis for contrastive learning where the guarantees can apply to realistic empirical settings.
Differentiable Unsupervised Feature Selection based on a Gated Laplacian
Authors: Ofir Lindenbaum, Uri Shaham, Erez Peterfreund, Jonathan Svirsky, Nicolas Aidan Casey, Yuval Kluger

Scientific observations may consist of a large number of variables (features). Selecting a subset of meaningful features is often crucial for identifying patterns hidden in the ambient space. In this paper, we present a method for unsupervised feature selection, and we demonstrate its advantage in clustering, a common unsupervised task. We propose a differentiable loss that combines a graph Laplacian-based score that favors low-frequency features with a gating mechanism for removing nuisance features. Our method improves upon the naive graph Laplacian score by replacing it with a gated variant computed on a subset of low-frequency features. We identify this subset by learning the parameters of continuously relaxed Bernoulli variables, which gate the entire feature space. We mathematically motivate the proposed approach and demonstrate that it is crucial to compute the graph Laplacian on the gated inputs rather than on the full feature set in the high noise regime. Using several real-world examples, we demonstrate the efficacy and advantage of the proposed approach over leading baselines.
Bandits with many optimal arms
Authors: Rianne de Heide, James Cheshire, Pierre MENARD, Alexandra Carpentier

We consider a stochastic bandit problem with a possibly infinite number of arms. We write $p^*$ for the proportion of optimal arms and $\Delta$ for the minimal mean-gap between optimal and sub-optimal arms. We characterize the optimal learning rates both in the cumulative regret setting, and in the best-arm identification setting in terms of the problem parameters $T$ (the budget), $p^*$ and $\Delta$. For the objective of minimizing the cumulative regret, we provide a lower bound of order $\Omega(\log(T)/(p^*\Delta))$ and a UCB-style algorithm with matching upper bound up to a factor of $\log(1/\Delta)$. Our algorithm needs $p^*$ to calibrate its parameters, and we prove that this knowledge is necessary, since adapting to $p^*$ in this setting is impossible. For best-arm identification we also provide a lower bound of order $\Omega(\exp(-cT\Delta^2p^*))$ on the probability of outputting a sub-optimal arm where $c>0$ is an absolute constant. We also provide an elimination algorithm with an upper bound matching the lower bound up to a factor of order $\log(T)$ in the exponential, and that does not need $p^*$ or $\Delta$ as parameter. Our results apply directly to the three related problems of competing against the $j$-th best arm, identifying an $\epsilon$ good arm, and finding an arm with mean larger than a quantile of a known order.
Stability and Deviation Optimal Risk Bounds with Convergence Rate $O(1/n)$
Authors: Yegor Klochkov, Nikita Zhivotovskiy

The sharpest known high probability generalization bounds for uniformly stable algorithms (Feldman, Vondrak, NeurIPS 2018,  2019), (Bousquet, Klochkov, Zhivotovskiy, COLT, 2020) contain a generally inevitable sampling error term of order $\Theta(1/\sqrt{n})$. When applied to excess risk bounds, this leads to suboptimal results in several standard stochastic convex optimization problems. We show that if the so-called Bernstein condition is satisfied, the term $\Theta(1/\sqrt{n})$ can be avoided, and high probability excess risk bounds of order up to $O(1/n)$ are possible via uniform stability. Using this result, we show a high probability excess risk bound with the rate $O(\log n/n)$ for strongly convex and Lipschitz losses valid for \emph{any} empirical risk minimization method. This resolves a question of Shalev-Shwartz, Shamir, Srebro, and Sridharan ( 2009). We discuss how $O(\log n/n)$ high probability excess risk bounds are possible for projected gradient descent in the case of strongly convex and Lipschitz losses without the usual smoothness assumption.
Do Vision Transformers See Like Convolutional Neural Networks?
Authors: Maithra Raghu, Thomas Unterthiner, Simon Kornblith, Chiyuan Zhang, Alexey Dosovitskiy

Convolutional neural networks (CNNs) have so far been the de-facto model for visual data. Recent work has shown that (Vision) Transformer models (ViT) can achieve comparable or even superior performance on image classification tasks. This raises a central question: how are Vision Transformers solving these tasks? Are they acting like convolutional networks, or learning entirely different visual representations? Analyzing the internal representation structure of ViTs and CNNs on image classification benchmarks, we find striking differences between the two architectures, such as ViT having more uniform representations across all layers. We explore how these differences arise, finding crucial roles played by self-attention, which enables early aggregation of global information, and ViT residual connections, which strongly propagate features from lower to higher layers. We study the ramifications for spatial localization, demonstrating ViTs successfully preserve input spatial information, with noticeable effects from different classification methods. Finally, we study the effect of (pretraining) dataset scale on intermediate features and transfer learning, and conclude with a discussion on connections to new architectures such as the MLP-Mixer.
Dynamic COVID risk assessment accounting for community virus exposure from a spatial-temporal transmission model
Authors: Yuan Chen, Wenbo Fei, Qinxia Wang, Donglin Zeng, Yuanjia Wang

COVID-19 pandemic has caused unprecedented negative impacts on our society, including further exposing inequity and disparity in public health. To study the impact of socioeconomic factors on COVID transmission, we first propose a spatial-temporal model to examine the socioeconomic heterogeneity and spatial correlation of COVID-19 transmission at the community level. Second, to assess the individual risk of severe COVID-19 outcomes after a positive diagnosis, we propose a dynamic, varying-coefficient model that integrates individual-level risk factors from electronic health records (EHRs) with community-level risk factors. The underlying neighborhood prevalence of infections (both symptomatic and pre-symptomatic) predicted from the previous spatial-temporal model is included in the individual risk assessment so as to better capture the background risk of virus exposure for each individual. We design a weighting scheme to mitigate multiple selection biases inherited in EHRs of COVID patients. We analyze COVID transmission data in New York City (NYC, the epicenter of the first surge in the United States) and EHRs from NYC hospitals, where time-varying effects of community risk factors and significant interactions between individual- and community-level risk factors are detected. By examining the socioeconomic disparity of infection risks and interaction among the risk factors, our methods can assist public health decision-making and facilitate better clinical management of COVID patients.
Matrix encoding networks for neural combinatorial optimization
Authors: Yeong-Dae Kwon, Jinho Choo, Iljoo Yoon, Minah Park, Duwon Park, Youngjune Gwon

Machine Learning (ML) can help solve combinatorial optimization (CO) problems better. A popular approach is to use a neural net to compute on the parameters of a given CO problem and extract useful information that guides the search for good solutions. Many CO problems of practical importance can be specified in a matrix form of parameters quantifying the relationship between two groups of items. There is currently no neural net model, however, that takes in such matrix-style relationship data as an input. Consequently, these types of CO problems have been out of reach for ML engineers. In this paper, we introduce Matrix Encoding Network (MatNet) and show how conveniently it takes in and processes parameters of such complex CO problems. Using an end-to-end model based on MatNet, we solve asymmetric traveling salesman (ATSP) and flexible flow shop (FFSP) problems as the earliest neural approach. In particular, for a class of FFSP we have tested MatNet on, we demonstrate a far superior empirical performance to any methods (neural or not) known to date.
Sharp Impossibility Results for Hyper-graph Testing
Authors: Jiashun Jin, Tracy Ke, Jiajun Liang

In a broad Degree-Corrected Mixed-Membership (DCMM) setting, we test whether a non-uniform hypergraph has only one community or has multiple communities. Since both the null and alternative hypotheses have many unknown parameters, 
the challenge is, given an alternative, how to identify the null that is hardest to separate from the alternative. We approach this by proposing a degree matching strategy where the main idea is leveraging the theory for tensor scaling to create a least favorable pair of hypotheses. We present a  result on standard  minimax lower bound theory and a result on Region of Impossibility (which is more informative than the minimax lower bound). We show that our lower bounds are tight by introducing a new test that attains the lower bound up to a logarithmic factor. We also discuss the case where the hypergraphs may have mixed-memberships.
Information-theoretic generalization bounds for black-box learning algorithms
Authors: Hrayr Harutyunyan, Maxim Raginsky, Greg Ver Steeg, Aram Galstyan

We derive information-theoretic generalization bounds for supervised learning algorithms based on the information contained in predictions rather than in the output of the training algorithm. These bounds improve over the existing information-theoretic bounds, are applicable to a wider range of algorithms, and solve two key challenges: (a) they give meaningful results for deterministic algorithms and (b) they are significantly easier to estimate. We show experimentally that the proposed bounds closely follow the generalization gap in practical scenarios for deep learning.
Deceive D: Adaptive Pseudo Augmentation for GAN Training with Limited Data
Authors: Liming Jiang, Bo Dai, Wayne Wu, Chen Change Loy

Generative adversarial networks (GANs) typically require ample data for training in order to synthesize high-fidelity images. Recent studies have shown that training GANs with limited data remains formidable due to discriminator overfitting, the underlying cause that impedes the generator's convergence. This paper introduces a novel strategy called Adaptive Pseudo Augmentation (APA) to encourage healthy competition between the generator and the discriminator. As an alternative method to existing approaches that rely on standard data augmentations or model regularization, APA alleviates overfitting by employing the generator itself to augment the real data distribution with generated images, which deceives the discriminator adaptively. Extensive experiments demonstrate the effectiveness of APA in improving synthesis quality in the low-data regime. We provide a theoretical analysis to examine the convergence and rationality of our new training strategy. APA is simple and effective. It can be added seamlessly to powerful contemporary GANs, such as StyleGAN2, with negligible computational cost.  https://github.com/EndlessSora/DeceiveD.
Robust Predictable Control
Authors: Benjamin Eysenbach, Ruslan Salakhutdinov, Sergey Levine

Many of the challenges facing today's reinforcement learning (RL) algorithms, such as robustness, generalization, transfer, and computational efficiency are closely related to compression.  Prior work has convincingly argued why minimizing information is useful in the supervised learning setting, but standard RL algorithms lack an explicit mechanism for compression. The RL setting is unique because (1) its sequential nature allows an agent to use past information to avoid looking at future observations and (2) the agent can optimize its behavior to prefer states where decision making requires few bits. We take advantage of these properties to propose a method (RPC) for learning simple policies. This method brings together ideas from information bottlenecks, model-based RL, and bits-back coding into a simple and theoretically-justified algorithm. Our method jointly optimizes a latent-space model and policy to be self-consistent, such that the policy avoids states where the model is inaccurate. We demonstrate that our method achieves much tighter compression than prior methods, achieving up to 5$\times$ higher reward than a standard information bottleneck when constrained to use just 0.3 bits per observation. We also demonstrate that our method learns policies that are more robust and generalize better to new tasks.
How Tight Can PAC-Bayes be in the Small Data Regime?
Authors: Andrew Y. K. Foong, Wessel Bruinsma, David R. Burt, Richard E Turner

In this paper, we investigate the question: _Given a small number of datapoints, for example $N = 30$, how tight can PAC-Bayes and test set bounds be made?_ For such small datasets, test set bounds adversely affect generalisation performance by withholding data from the training procedure. In this setting, PAC-Bayes bounds are especially attractive, due to their ability to use all the data to simultaneously learn a posterior and bound its generalisation risk. We focus on the case of i.i.d. data with a bounded loss and consider the generic PAC-Bayes theorem of Germain et al. While their theorem is known to recover many existing PAC-Bayes bounds, it is unclear what the tightest bound derivable from their framework is. For a fixed learning algorithm and dataset, we show that the tightest possible bound coincides with a bound considered by Catoni; and, in the more natural case of distributions over datasets, we establish a lower bound on the best bound achievable in expectation. Interestingly, this lower bound recovers the Chernoff test set bound if the posterior is equal to the prior. Moreover, to illustrate how tight these bounds can be, we study synthetic one-dimensional classification tasks in which it is feasible to meta-learn both the prior and the form of the bound to numerically optimise for the tightest bounds possible. We find that in this simple, controlled scenario, PAC-Bayes bounds are competitive with comparable, commonly used Chernoff test set bounds. However, the sharpest test set bounds still lead to better guarantees on the generalisation error than the PAC-Bayes bounds we consider.
A Bi-Level Framework for Learning to Solve Combinatorial Optimization on Graphs
Authors: Runzhong Wang, Zhigang Hua, Gan Liu, Jiayi Zhang, Junchi Yan, Feng Qi, Shuang Yang, JUN ZHOU, Xiaokang Yang

Combinatorial Optimization (CO) has been a long-standing challenging research topic featured by its NP-hard nature. Traditionally such problems are approximately solved with heuristic algorithms which are usually fast but may sacrifice the solution quality. Currently, machine learning for combinatorial optimization (MLCO) has become a trending research topic, but most existing MLCO methods treat CO as a single-level optimization by directly learning the end-to-end solutions, which are hard to scale up and mostly limited by the capacity of ML models given the high complexity of CO. In this paper, we propose a hybrid approach to combine the best of the two worlds, in which a bi-level framework is developed with an upper-level learning method to optimize the graph (e.g. add, delete or modify edges in a graph), fused with a lower-level heuristic algorithm solving on the optimized graph. Such a bi-level approach simplifies the learning on the original hard CO and can effectively mitigate the demand for model capacity. The experiments and results on several popular CO problems like Directed Acyclic Graph scheduling, Graph Edit Distance and Hamiltonian Cycle Problem show its effectiveness over manually designed heuristics and single-level learning methods.
Uniform Concentration Bounds toward a Unified  Framework for Robust Clustering
Authors: Debolina Paul, Saptarshi Chakraborty, Swagatam Das, Jason Xu

Recent advances in center-based clustering continue to improve upon the drawbacks of Lloyd's celebrated $k$-means algorithm over $60$ years after its introduction. Various methods seek to address poor local minima, sensitivity to outliers, and data that are not well-suited to Euclidean measures of fit, but many are supported largely empirically. Moreover, combining such approaches in a piecemeal manner can result in ad hoc methods, and the limited theoretical results supporting each individual contribution may no longer hold. Toward addressing these issues in a principled way, this paper proposes a cohesive robust framework for center-based clustering under a general class of dissimilarity measures. In particular, we present a rigorous theoretical treatment within a Median-of-Means (MoM) estimation framework, showing that it subsumes several popular $k$-means variants. In addition to unifying existing methods, we derive uniform concentration bounds that complete their analyses, and bridge these results to the MoM framework via Dudley's chaining arguments. Importantly, we neither require any assumptions on the distribution of the outlying observations nor on the relative number of observations $n$ to features $p$. We establish strong consistency and an error rate of $O(n^{-1/2})$ under mild conditions, surpassing the best-known results in the literature. The methods are empirically validated thoroughly on real and synthetic datasets.
Differential Privacy Over Riemannian Manifolds
Authors: Matthew Reimherr, Karthik Bharath, Carlos J Soto

In this work we consider the problem of releasing a differentially private statistical summary that resides on a Riemannian manifold.  We present an extension of the Laplace or K-norm mechanism that utilizes intrinsic distances and volumes on the manifold.  We also consider in detail the specific case where the summary is the Fr\'echet mean of data residing on a manifold.  We demonstrate that our mechanism is rate optimal and depends only on the dimension of the manifold, not on the dimension of any ambient space, while also showing how ignoring the manifold structure can decrease the utility of the sanitized summary.  We illustrate our framework in two examples of particular interest in statistics: the space of symmetric positive definite matrices, which is used for covariance matrices, and the sphere, which can be used as a space for modeling discrete distributions.
Topological Relational Learning on Graphs
Authors: Yuzhou Chen, Baris Coskunuzer, Yulia Gel

Graph neural networks (GNNs) have emerged as a powerful tool for graph classification and representation learning. However, GNNs tend to suffer from over-smoothing problems and are vulnerable to graph perturbations. To address these challenges, we propose a novel topological neural framework of topological relational inference (TRI) which allows for integrating higher-order graph information to GNNs and for systematically learning a local graph structure. The key idea is to rewire the original graph by using the persistent homology of the small neighborhoods of the nodes and then to incorporate the extracted topological summaries as the side information into the local algorithm. As a result, the new framework enables us to harness both the conventional information on the graph structure and information on higher order topological properties of the graph. We derive theoretical properties on stability of the new local topological representation of the graph and discuss its implications on the graph algebraic connectivity. The experimental results on node classification tasks demonstrate that the new TRI-GNN outperforms all 14 state-of-the-art baselines on 6 out 7 graphs and exhibit higher robustness to perturbations, yielding up to 10\% better performance under noisy scenarios.