nils-herrmann/clean_scirepeval huggingface dataset:
Locality defeats the curse of dimensionality in convolutional teacher-student scenarios
Authors: Alessandro Favero, Francesco Cagnetta, Matthieu Wyart

Convolutional neural networks perform a local and translationally-invariant treatment of the data: quantifying which of these two aspects is central to their success remains a challenge. We study this problem within a teacher-student framework for kernel regression, using 'convolutional' kernels inspired by the neural tangent kernel of simple convolutional architectures of given filter size. Using heuristic methods from physics, we find in the ridgeless case that locality is key in determining the learning curve exponent $\beta$ (that relates the test error $\epsilon_t\sim P^{-\beta}$ to the size of the training set $P$), whereas translational invariance is not. In particular, if the filter size of the teacher $t$ is smaller than that of the student $s$, $\beta$ is a function of $s$ only and does not depend on the input dimension. We confirm our predictions on $\beta$ empirically. We conclude by proving, under a natural universality assumption, that performing kernel regression with a ridge that decreases with the size of the training set leads to similar learning curve exponents to those we obtain in the ridgeless case.
Optimization-Based Algebraic Multigrid Coarsening Using Reinforcement Learning
Authors: Ali Taghibakhshi, Scott MacLachlan, Luke Olson, Matthew West

Large sparse linear systems of equations are ubiquitous in science and engineering, such as those arising from discretizations of partial differential equations. Algebraic multigrid (AMG) methods are one of the most common methods of solving such linear systems, with an extensive body of underlying mathematical theory. A system of linear equations defines a graph on the set of unknowns and each level of a multigrid solver requires the selection of an appropriate coarse graph along with restriction and interpolation operators that map to and from the coarse representation. The efficiency of the multigrid solver depends critically on this selection and many selection methods have been developed over the years. Recently, it has been demonstrated that it is possible to directly learn the AMG interpolation and restriction operators, given a coarse graph selection. In this paper, we consider the complementary problem of learning to coarsen graphs for a multigrid solver, a necessary step in developing fully learnable AMG methods. We propose a method using a reinforcement learning (RL) agent based on graph neural networks (GNNs), which can learn to perform graph coarsening on small planar training graphs and then be applied to unstructured large planar graphs, assuming bounded node degree. We demonstrate that this method can produce better coarse graphs than existing algorithms, even as the graph size increases and other properties of the graph are varied. We also propose an efficient inference procedure for performing graph coarsening that results in linear time complexity in graph size.
The Complexity of Sparse Tensor PCA
Authors: Davin Choo, Tommaso d'Orsi

We study the problem of sparse tensor principal component analysis: given a tensor $\pmb Y = \pmb W + \lambda x^{\otimes p}$ with $\pmb W \in \otimes^p \mathbb{R}^n$ having i.i.d. Gaussian entries, the goal is to recover the $k$-sparse unit vector $x \in \mathbb{R}^n$. The model captures both sparse PCA (in its Wigner form)  and tensor PCA.

For the highly sparse regime of $k \leq \sqrt{n}$, we present a family of algorithms that smoothly interpolates between a simple polynomial-time algorithm and the exponential-time exhaustive search algorithm. For any $1 \leq t \leq k$, our algorithms recovers the sparse vector for signal-to-noise ratio $\lambda \geq \tilde{\mathcal{O}} (\sqrt{t} \cdot (k/t)^{p/2})$ in time $\tilde{\mathcal{O}}(n^{p+t})$, capturing the state-of-the-art guarantees for the matrix settings (in both the polynomial-time and sub-exponential time regimes).

Our results naturally extend to the case of $r$ distinct $k$-sparse signals with disjoint supports, with guarantees that are independent of the number of spikes. Even in the restricted case of sparse PCA, known algorithms only recover the sparse vectors for $\lambda \geq \tilde{\mathcal{O}}(k \cdot r)$ while our algorithms require $\lambda \geq \tilde{\mathcal{O}}(k)$.

Finally, by analyzing the low-degree likelihood ratio, we complement these algorithmic results with rigorous evidence illustrating the trade-offs between signal-to-noise ratio and running time. This lower bound captures the known lower bounds for both sparse  PCA and tensor PCA. In this general model, we observe a more intricate three-way trade-off between the number of samples $n$, the sparsity $k$, and the tensor power $p$.
Tractable Regularization of Probabilistic Circuits
Authors: Anji Liu, Guy Van den Broeck

Probabilistic Circuits (PCs) are a promising avenue for probabilistic modeling. They combine advantages of probabilistic graphical models (PGMs) with those of neural networks (NNs). Crucially, however, they are tractable probabilistic models, supporting efficient and exact computation of many probabilistic inference queries, such as marginals and MAP. Further, since PCs are structured computation graphs, they can take advantage of deep-learning-style parameter updates, which greatly improves their scalability. However, this innovation also makes PCs prone to overfitting, which has been observed in many standard benchmarks. Despite the existence of abundant regularization techniques for both PGMs and NNs, they are not effective enough when applied to PCs. Instead, we re-think regularization for PCs and propose two intuitive techniques, data softening and entropy regularization, that both take advantage of PCs' tractability and still have an efficient implementation as a computation graph. Specifically, data softening provides a principled way to add uncertainty in datasets in closed form, which implicitly regularizes PC parameters. To learn parameters from a softened dataset, PCs only need linear time by virtue of their tractability. In entropy regularization, the exact entropy of the distribution encoded by a PC can be regularized directly, which is again infeasible for most other density estimation models. We show that both methods consistently improve the generalization performance of a wide variety of PCs. Moreover, when paired with a simple PC structure, we achieved state-of-the-art results on 10 out of 20 standard discrete density estimation benchmarks. Open-source code and experiments are available at https://github.com/UCLA-StarAI/Tractable-PC-Regularization.
Overcoming the curse of dimensionality with Laplacian regularization in semi-supervised learning
Authors: Vivien Cabannes, Loucas Pillaud-Vivien, Francis Bach, Alessandro Rudi

As annotations of data can be scarce in large-scale practical problems, leveraging unlabelled examples is one of the most important aspects of machine learning. This is the aim of semi-supervised learning. To benefit from the access to unlabelled data, it is natural to diffuse smoothly knowledge of labelled data to unlabelled one. This induces to the use of Laplacian regularization. Yet, current implementations of Laplacian regularization suffer from several drawbacks, notably the well-known curse of dimensionality. In this paper, we design a new class of algorithms overcoming this issue, unveiling a large body of spectral filtering methods. Additionally, we provide a statistical analysis showing that our estimators exhibit desirable behaviors. They are implemented through (reproducing) kernel methods, for which we provide realistic computational guidelines in order to make our method usable with large amounts of data.
Who Leads and Who Follows in Strategic Classification?
Authors: Tijana Zrnic, Eric Mazumdar, Shankar Sastry, Michael Jordan

As predictive models are deployed into the real world, they must increasingly contend with strategic behavior. A growing body of work on strategic classification treats this problem as a Stackelberg game: the decision-maker "leads" in the game by deploying a model, and the strategic agents "follow" by playing their best response to the deployed model. Importantly, in this framing, the burden of learning is placed solely on the decision-maker, while the agents’ best responses are implicitly treated as instantaneous. In this work, we argue that the order of play in strategic classification is fundamentally determined by the relative frequencies at which the decision-maker and the agents adapt to each other’s actions. In particular, by generalizing the standard model to allow both players to learn over time, we show that a decision-maker that makes updates faster than the agents can reverse the order of play, meaning that the agents lead and the decision-maker follows. We observe in standard learning settings that such a role reversal can be desirable for both the decision-maker and the strategic agents. Finally, we show that a decision-maker with the freedom to choose their update frequency can induce learning dynamics that converge to Stackelberg equilibria with either order of play.
On the Generative Utility of Cyclic Conditionals
Authors: Chang Liu, Haoyue Tang, Tao Qin, Jintao Wang, Tie-Yan Liu

We study whether and how can we model a joint distribution $p(x,z)$ using two conditional models $p(x|z)$ and $q(z|x)$ that form a cycle. This is motivated by the observation that deep generative models, in addition to a likelihood model $p(x|z)$, often also use an inference model $q(z|x)$ for extracting representation, but they rely on a usually uninformative prior distribution $p(z)$ to define a joint distribution, which may render problems like posterior collapse and manifold mismatch. To explore the possibility to model a joint distribution using only $p(x|z)$ and $q(z|x)$, we study their compatibility and determinacy, corresponding to the existence and uniqueness of a joint distribution whose conditional distributions coincide with them. We develop a general theory for operable equivalence criteria for compatibility, and sufficient conditions for determinacy. Based on the theory, we propose a novel generative modeling framework CyGen that only uses the two cyclic conditional models. We develop methods to achieve compatibility and determinacy, and to use the conditional models to fit and generate data. With the prior constraint removed, CyGen better fits data and captures more representative features, supported by both synthetic and real-world experiments.
Indicators of Attack Failure: Debugging and Improving Optimization of Adversarial Examples
Authors: Maura Pintor, Luca Demetrio, Angelo Sotgiu, Giovanni Manca, Ambra Demontis, Nicholas Carlini, Battista Biggio, Fabio Roli

Evaluating robustness of machine-learning models to adversarial examples is a challenging problem. Many defenses have been shown to provide a false sense of security by causing gradient-based attacks to fail, and they have been broken under more rigorous evaluations. Although guidelines and best practices have been suggested to improve current adversarial robustness evaluations, the lack of automatic testing and debugging tools makes it difficult to apply these recommendations in a systematic manner. In this work, we overcome these limitations by (i) defining a set of quantitative indicators which unveil common failures in the optimization of gradient-based attacks, and (ii) proposing specific mitigation strategies within a systematic evaluation protocol. Our extensive experimental analysis shows that the proposed indicators of failure can be used to visualize, debug and improve current adversarial robustness evaluations, providing a first concrete step towards automatizing and systematizing current adversarial robustness evaluations.
Fair Scheduling for Time-dependent Resources
Authors: Bo Li, Minming Li, Ruilong Zhang

We study a fair resource scheduling problem, where a set of interval jobs are to be allocated to heterogeneous machines controlled by intellectual agents.
Each job is associated with release time, deadline, and processing time such that it can be processed if its complete processing period is between its release time and deadline. 
The machines gain possibly different utilities by processing different jobs, and all jobs assigned to the same machine should be processed without overlap.
We consider two widely studied solution concepts, namely, maximin share fairness and envy-freeness.
For both criteria, we discuss the extent to which fair allocations exist and present constant approximation algorithms for various settings.
Learned Robust PCA: A Scalable Deep Unfolding Approach for High-Dimensional Outlier Detection
Authors: HanQin Cai, Jialin Liu, Wotao Yin

Robust principal component analysis (RPCA) is a critical tool in modern machine learning, which detects outliers in the task of low-rank matrix reconstruction. In this paper, we propose a scalable and learnable non-convex approach for high-dimensional RPCA problems, which we call Learned Robust PCA (LRPCA). LRPCA is highly efficient, and its free parameters can be effectively learned to optimize via deep unfolding. Moreover, we extend deep unfolding from finite iterations to infinite iterations via a novel feedforward-recurrent-mixed neural network model. We establish the recovery guarantee of LRPCA under mild assumptions for RPCA. Numerical experiments show that LRPCA outperforms the state-of-the-art RPCA algorithms, such as ScaledGD and AltProj, on both synthetic datasets and real-world applications.
Interactive Label Cleaning with Example-based Explanations
Authors: Stefano Teso, Andrea Bontempelli, Fausto Giunchiglia, Andrea Passerini

We tackle sequential learning under label noise in applications where a human supervisor can be queried to relabel suspicious examples. Existing approaches are flawed, in that they only relabel incoming examples that look "suspicious" to the model. As a consequence, those mislabeled examples that elude (or don't undergo) this cleaning step end up tainting the training data and the model with no further chance of being cleaned. We propose CINCER, a novel approach that cleans both new and past data by identifying \emph{pairs of mutually incompatible examples}. Whenever it detects a suspicious example, CINCER identifies a counter-example in the training set that - according to the model - is maximally incompatible with the suspicious example, and asks the annotator to relabel either or both examples, resolving this possible inconsistency. The counter-examples are chosen to be maximally incompatible, so to serve as \emph{explanations} of the model's suspicion, and highly influential, so to convey as much information as possible if relabeled. CINCER achieves this by leveraging an efficient and robust approximation of influence functions based on the Fisher information matrix (FIM). Our extensive empirical evaluation shows that clarifying the reasons behind the model's suspicions by cleaning the counter-examples helps in acquiring substantially better data and models, especially when paired with our FIM approximation.
Distilling Object Detectors with Feature Richness
Authors: Zhixing Du, Rui Zhang, Ming Chang, Xishan Zhang, Shaoli Liu, Tianshi Chen, Yunji Chen

In recent years, large-scale deep models have achieved great success, but the huge computational complexity and massive storage requirements make it a great challenge to deploy them in resource-limited devices. As a model compression and acceleration method, knowledge distillation effectively improves the performance of small models by transferring the dark knowledge from the teacher detector. However, most of the existing distillation-based detection methods mainly imitating features near bounding boxes, which suffer from two limitations. First, they ignore the beneficial features outside the bounding boxes. Second, these methods imitate some features which are mistakenly regarded as the background by the teacher detector. To address the above issues, we propose a novel Feature-Richness Score (FRS) method to choose important features that improve generalized detectability during distilling. The proposed method effectively retrieves the important features outside the bounding boxes and removes the detrimental features within the bounding boxes. Extensive experiments show that our methods achieve excellent performance on both anchor-based and anchor-free detectors. For example, RetinaNet with ResNet-50 achieves 39.7% in mAP on the COCO2017 dataset, which even surpasses the ResNet-101 based teacher detector 38.9% by 0.8%. Our implementation is available at https://github.com/duzhixing/FRS.
Why Lottery Ticket Wins? A Theoretical Perspective of Sample Complexity on Sparse Neural Networks
Authors: Shuai Zhang, Meng Wang, Sijia Liu, Pin-Yu Chen, Jinjun Xiong

The lottery ticket hypothesis (LTH) states that learning on a properly pruned network (the winning ticket) has improved test accuracy over the original unpruned network. Although LTH has been justified empirically in a broad range of deep neural network (DNN) involved applications like computer vision and natural language processing, the theoretical validation of the improved generalization of a winning ticket remains elusive. To the best of our knowledge, our work, for the first time, characterizes the performance of training a pruned neural network by analyzing the geometric structure of the objective function and the sample complexity to achieve zero generalization error. We show that the convex region near a desirable model with guaranteed generalization enlarges as the neural network model is pruned, indicating the structural importance of a winning ticket. Moreover, as the algorithm for training a pruned neural network is specified as an (accelerated) stochastic gradient descent algorithm, we theoretically show that the number of samples required for achieving zero generalization error is proportional to the number of the non-pruned weights in the hidden layer. With a fixed number of samples, training a pruned neural network enjoys a faster convergence rate to the desired model than training the original unpruned one, providing a formal justification of the improved generalization of the winning ticket. Our theoretical results are acquired from learning a pruned neural network of one hidden layer, while experimental results are further provided to justify the implications in pruning multi-layer neural networks.
On the interplay between data structure and loss function in classification problems
Authors: Stéphane d'Ascoli, Marylou Gabrié, Levent Sagun, Giulio Biroli

One of the central features of modern machine learning models, including deep neural networks, is their generalization ability on structured data in the over-parametrized regime. 
In this work, we consider an analytically solvable setup to investigate how properties of data impact learning in classification problems, and compare the results obtained for quadratic loss and logistic loss. 
Using methods from statistical physics, we obtain a precise asymptotic expression for the train and test errors of random feature models trained on a simple model of structured data. The input covariance is built from independent blocks allowing us to tune the saliency of low-dimensional structures and their alignment with respect to the target function.
Our results show in particular that in the over-parametrized regime, the impact of data structure on both train and test error curves is greater for logistic loss than for mean-squared loss: the easier the task, the wider the gap in performance between the two losses at the advantage of the logistic. 
Numerical experiments on MNIST and CIFAR10 confirm our insights.
A Contrastive Learning Approach for Training Variational Autoencoder Priors
Authors: Jyoti Aneja, Alex Schwing, Jan Kautz, Arash Vahdat

Variational autoencoders (VAEs) are one of the powerful likelihood-based generative models with applications in many domains. However, they struggle to generate high-quality images, especially when samples are obtained from the prior without any tempering. One explanation for VAEs' poor generative quality is the prior hole problem: the prior distribution fails to match the aggregate approximate posterior. Due to this mismatch, there exist areas in the latent space with high density under the prior that do not correspond to any encoded image. Samples from those areas are decoded to corrupted images. To tackle this issue, we propose an energy-based prior defined by the product of a base prior distribution and a reweighting factor, designed to bring the base closer to the aggregate posterior. We train the reweighting factor by noise contrastive estimation, and we generalize it to hierarchical VAEs with many latent variable groups. Our experiments confirm that the proposed noise contrastive priors improve the generative performance of state-of-the-art VAEs by a large margin on the MNIST, CIFAR-10, CelebA 64, and CelebA HQ 256 datasets. Our method is simple and can be applied to a wide variety of VAEs to improve the expressivity of their prior distribution.
Robustifying Algorithms of Learning Latent Trees with Vector Variables
Authors: Fengzhuo Zhang, Vincent Tan

We consider learning the structures of Gaussian latent tree models with vector observations when a subset of them are arbitrarily corrupted. First, we present the sample complexities of Recursive Grouping (RG) and Chow-Liu Recursive Grouping (CLRG) without the assumption that the effective depth is bounded in the number of observed nodes, significantly generalizing the results in Choi et al. (2011). We show that Chow-Liu initialization in CLRG greatly reduces the sample complexity of RG from being exponential in the diameter of the tree to only logarithmic in the diameter for the hidden Markov model (HMM). Second, we robustify RG, CLRG, Neighbor Joining (NJ) and Spectral NJ (SNJ) by using the truncated inner product. These robustified algorithms can tolerate a number of corruptions up to the square root of the number of clean samples. Finally, we derive the first known instance-dependent impossibility result for structure learning of latent trees. The optimalities of the robust version of CLRG and NJ are verified by comparing their sample complexities and the impossibility result.
Self-Supervised Bug Detection and Repair
Authors: Miltiadis Allamanis, Henry Richard Jackson-Flux, Marc Brockschmidt

Machine learning-based program analyses have recently shown the promise of integrating formal and probabilistic reasoning towards aiding software development. However, in the absence of large annotated corpora, training these analyses is challenging. Towards addressing this, we present BugLab, an approach for self-supervised learning of bug detection and repair.  BugLab co-trains two models: (1) a detector model that learns to detect and repair bugs in code, (2) a selector model that learns to create buggy code for the detector to use as training data. A Python implementation of BugLab improves by 30% upon baseline methods on a test dataset of 2374 real-life bugs and finds 19 previously unknown bugs in open-source software.