mtybilly/Instruct2DS huggingface dataset:
On the detrimental effect of invariances in the likelihood for variational inference
Authors: Ralf Herbrich, Tim Januschowski, Yuyang (Bernie) Wang, Jan Gasthaus Richard Kurle
Published in: Advances in Neural Information Processing Systems 35  (NeurIPS 2022) (Main Conference Track), 2022

Abstract: Variational Bayesian posterior inference often requires simplifying approximations such as mean-field parametrisation to ensure tractability. However, prior work has associated the variational mean-field approximation for Bayesian neural networks with underfitting in the case of small datasets or large model sizes. In this work, we show that invariances in the likelihood function of over-parametrised models contribute to this phenomenon because these invariances complicate the structure of the posterior by introducing discrete and/or continuous modes which cannot be well approximated by Gaussian mean-field distributions. In particular, we show that the mean-field approximation has an additional gap in the evidence lower bound compared to a purpose-built posterior that takes into account the known invariances. Importantly, this invariance gap is not constant; it vanishes as the approximation reverts to the prior. We proceed by first considering translation invariances in a linear model with a single data point in detail. We show that, while the true posterior can be constructed from a mean-field parametrisation, this is achieved only if the objective function takes into account the invariance gap. Then, we transfer our analysis of the linear model to neural networks. Our analysis provides a framework for future work to explore solutions to the invariance problem.
Self-Supervised Learning Through Efference Copies
Authors: Qinghai Guo, Timoleon Moraitis Franz Scherr
Published in: Advances in Neural Information Processing Systems 35  (NeurIPS 2022) (Main Conference Track), 2022

Abstract: Self-supervised learning (SSL) methods aim to exploit the abundance of unlabelled data for machine learning (ML), however the underlying principles are often method-specific. An SSL framework derived from biological first principles of embodied learning could unify the various SSL methods, help elucidate learning in the brain, and possibly improve ML. SSL commonly transforms each training datapoint into a pair of views, uses the knowledge of this pairing as a positive (i.e. non-contrastive) self-supervisory sign, and potentially opposes it to unrelated, (i.e. contrastive) negative examples. Here, we show that this type of self-supervision is an incomplete implementation of a concept from neuroscience, the Efference Copy (EC). Specifically, the brain also transforms the environment through efference, i.e. motor commands, however it sends to itself an EC of the full commands, i.e. more than a mere SSL sign. In addition, its action representations are likely egocentric. From such a principled foundation we formally recover and extend SSL methods such as SimCLR, BYOL, and ReLIC under a common theoretical framework, i.e. Self-supervision Through Efference Copies (S-TEC). Empirically, S-TEC restructures meaningfully the within- and between-class representations. This manifests as improvement in recent strong SSL baselines in image classification, segmentation, object detection, and in audio. These results hypothesize a testable positive influence from the brain's motor outputs onto its sensory representations.
Precise Learning Curves and Higher-Order Scalings for Dot-product Kernel Regression
Authors: Hong Hu, Theodor Misiakiewicz, Yue Lu, Jeffrey Pennington Lechao Xiao
Published in: Advances in Neural Information Processing Systems 35  (NeurIPS 2022) (Main Conference Track), 2022

Abstract: As modern machine learning models continue to advance the computational frontier, it has become increasingly important to develop precise estimates for expected performance improvements under different model and data scaling regimes. Currently, theoretical understanding of the learning curves that characterize how the prediction error depends on the number of samples is restricted to either large-sample asymptotics ($m\to\infty$) or, for certain simple data distributions, to the high-dimensional asymptotics in which the number of samples scales linearly with the dimension ($m\propto d$). There is a wide gulf between these two regimes, including all higher-order scaling relations $m\propto d^r$, which are the subject of the present paper. We focus on the problem of kernel ridge regression for dot-product kernels and present precise formulas for the mean of the test error, bias, and variance, for data drawn uniformly from the sphere with isotropic random labels in the $r$th-order asymptotic scaling regime $m\to\infty$ with $m/d^r$ held constant. We observe a peak in the learning curve whenever $m \approx d^r/r!$ for any integer $r$, leading to multiple sample-wise descent and nontrivial behavior at multiple scales. We include a colab notebook that reproduces the essential results of the paper.
A Unified Model for Multi-class Anomaly Detection
Authors: Lei Cui, Yujun Shen, Kai Yang, Xin Lu, Yu Zheng, Xinyi Le Zhiyuan You
Published in: Advances in Neural Information Processing Systems 35  (NeurIPS 2022) (Main Conference Track), 2022

Abstract: Despite the rapid advance of unsupervised anomaly detection, existing methods require to train separate models for different objects. In this work, we present UniAD that accomplishes anomaly detection for multiple classes with a unified framework. Under such a challenging setting, popular reconstruction networks may fall into an "identical shortcut", where both normal and anomalous samples can be well recovered, and hence fail to spot outliers. To tackle this obstacle, we make three improvements. First, we revisit the formulations of fully-connected layer, convolutional layer, as well as attention layer, and confirm the important role of query embedding (i.e., within attention layer) in preventing the network from learning the shortcut. We therefore come up with a layer-wise query decoder to help model the multi-class distribution. Second, we employ a neighbor masked attention module to further avoid the information leak from the input feature to the reconstructed output feature. Third, we propose a feature jittering strategy that urges the model to recover the correct message even with noisy inputs. We evaluate our algorithm on MVTec-AD and CIFAR-10 datasets, where we surpass the state-of-the-art alternatives by a sufficiently large margin. For example, when learning a unified model for 15 categories in MVTec-AD, we surpass the second competitor on the tasks of both anomaly detection (from 88.1% to 96.5%) and anomaly localization (from 89.5% to 96.8%). Code is available at https://github.com/zhiyuanyou/UniAD.
Constrained GPI for Zero-Shot Transfer in Reinforcement Learning
Authors: Seohong Park, Gunhee Kim Jaekyeom Kim
Published in: Advances in Neural Information Processing Systems 35  (NeurIPS 2022) (Main Conference Track), 2022

Abstract: For zero-shot transfer in reinforcement learning where the reward function varies between different tasks, the successor features framework has been one of the popular approaches. However, in this framework, the transfer to new target tasks with generalized policy improvement (GPI) relies on only the source successor features [5] or additional successor features obtained from the function approximators’ generalization to novel inputs [11]. The goal of this work is to improve the transfer by more tightly bounding the value approximation errors of successor features on the new target tasks. Given a set of source tasks with their successor features, we present lower and upper bounds on the optimal values for novel task vectors that are expressible as linear combinations of source task vectors. Based on the bounds, we propose constrained GPI as a simple test-time approach that can improve transfer by constraining action-value approximation errors on new target tasks. Through experiments in the Scavenger and Reacher environment with state observations as well as the DeepMind Lab environment with visual observations, we show that the proposed constrained GPI significantly outperforms the prior GPI’s transfer performance. Our code and additional information are available at https://jaekyeom.github.io/projects/cgpi/.
UnfoldML: Cost-Aware and Uncertainty-Based Dynamic 2D Prediction for Multi-Stage Classification
Authors: Alind Khare, Glenn Matlin, Monish Ramadoss, Rishikesan Kamaleswaran, Chao Zhang, Alexey Tumanov Yanbo Xu
Published in: Advances in Neural Information Processing Systems 35  (NeurIPS 2022) (Main Conference Track), 2022

Abstract: Machine Learning (ML) research has focused on maximizing the accuracy of predictive tasks. ML models, however, are increasingly more complex, resource intensive, and costlier to deploy in resource-constrained environments. These issues are exacerbated for prediction tasks with sequential classification on progressively transitioned stages with “happens-before” relation between them.We argue that it is possible to “unfold” a monolithic single multi-class classifier, typically trained for all stages using all data, into a series of single-stage classifiers. Each single- stage classifier can be cascaded gradually from cheaper to more expensive binary classifiers that are trained using only the necessary data modalities or features required for that stage. UnfoldML is a cost-aware and uncertainty-based dynamic 2D prediction pipeline for multi-stage classification that enables (1) navigation of the accuracy/cost tradeoff space, (2) reducing the spatio-temporal cost of inference by orders of magnitude, and (3) early prediction on proceeding stages. UnfoldML achieves orders of magnitude better cost in clinical settings, while detecting multi- stage disease development in real time. It achieves within 0.1% accuracy from the highest-performing multi-class baseline, while saving close to 20X on spatio- temporal cost of inference and earlier (3.5hrs) disease onset prediction. We also show that UnfoldML generalizes to image classification, where it can predict different level of labels (from coarse to fine) given different level of abstractions of a image, saving close to 5X cost with as little as 0.4% accuracy reduction.
Generative Status Estimation and Information Decoupling for Image Rain Removal
Authors: Xin WANG, Jia Shen, Renjie Zhang, Ruonan Liu, Miaohui Wang, Wuyuan Xie, Qing Guo, Ping Li Di Lin
Published in: Advances in Neural Information Processing Systems 35  (NeurIPS 2022) (Main Conference Track), 2022

Abstract: Image rain removal requires the accurate separation between the pixels of the rain streaks and object textures. But the confusing appearances of rains and objects lead to the misunderstanding of pixels, thus remaining the rain streaks or missing the object details in the result. In this paper, we propose SEIDNet equipped with the generative Status Estimation and Information Decoupling for rain removal. In the status estimation, we embed the pixel-wise statuses into the status space, where each status indicates a pixel of the rain or object. The status space allows sampling multiple statuses for a pixel, thus capturing the confusing rain or object. In the information decoupling, we respect the pixel-wise statuses, decoupling the appearance information of rain and object from the pixel. Based on the decoupled information, we construct the kernel space, where multiple kernels are sampled for the pixel to remove the rain and recover the object appearance. We evaluate SEIDNet on the public datasets, achieving state-of-the-art performances of image rain removal. The experimental results also demonstrate the generalization of SEIDNet, which can be easily extended to achieve state-of-the-art performances on other image restoration tasks (e.g., snow, haze, and shadow removal).
Learning with little mixing
Authors: Stephen Tu Ingvar Ziemann
Published in: Advances in Neural Information Processing Systems 35  (NeurIPS 2022) (Main Conference Track), 2022

Abstract: We study square loss in a realizable time-series framework with martingale difference noise. Our main result is a fast rate excess risk bound which shows that whenever a trajectory hypercontractivity condition holds, the risk of the least-squares estimator on dependent data matches the iid rate order-wise after a burn-in time. In comparison, many existing results in learning from dependent data have rates where the effective sample size is deflated by a factor of the mixing-time of the underlying process, even after the burn-in time. Furthermore, our results allow the covariate process to exhibit long range correlations which are substantially weaker than geometric ergodicity. We call this phenomenon learning with little mixing, and present several examples for when it occurs: bounded function classes for which the $L^2$ and $L^{2+\epsilon}$ norms are equivalent, finite state irreducible and aperiodic Markov chains, various parametric models, and a broad family of infinite dimensional $\ell^2(\mathbb{N})$ ellipsoids. By instantiating our main result to system identification of nonlinear dynamics with generalized linear model  transitions, we obtain a nearly minimax optimal  excess risk bound after only a polynomial burn-in time.
ComGAN: Unsupervised Disentanglement and Segmentation via Image Composition
Authors: Kehua Guo, Xiangyuan Zhu, Zheng Wu, Liwei Wang Rui Ding
Published in: Advances in Neural Information Processing Systems 35  (NeurIPS 2022) (Main Conference Track), 2022

Abstract: We propose ComGAN, a simple unsupervised generative model, which simultaneously generates realistic images and high semantic masks under an adversarial loss and a binary regularization. In this paper, we first investigate two kinds of trivial solutions in the compositional generation process, and demonstrate their source is vanishing gradients on the mask. Then, we solve trivial solutions from the perspective of architecture. Furthermore, we redesign two fully unsupervised modules based on ComGAN (DS-ComGAN), where the disentanglement module associates the foreground, background and mask with three independent variables, and the segmentation module learns object segmentation. Experimental results show that (i) ComGAN's network architecture effectively avoids trivial solutions without any supervised information and regularization; (ii) DS-ComGAN achieves remarkable results and outperforms existing semi-supervised and weakly supervised methods by a large margin in both the image disentanglement and unsupervised segmentation tasks. It implies that the redesign of ComGAN is a possible direction for future unsupervised work.
Sparse Winning Tickets are Data-Efficient Image Recognizers
Authors: Xuxi Chen, Zhenyu Zhang, Tianlong Chen, Subhashini Venugopalan, Zhangyang Wang Mukund Varma T
Published in: Advances in Neural Information Processing Systems 35  (NeurIPS 2022) (Main Conference Track), 2022

Abstract: Improving the performance of deep networks in data-limited regimes has warranted much attention. In this work, we empirically show that “winning tickets” (small sub-networks) obtained via magnitude pruning based on the lottery ticket hypothesis, apart from being sparse are also effective recognizers in data-limited regimes. Based on extensive experiments, we find that in low data regimes (datasets of 50-100 examples per class), sparse winning tickets substantially outperform the original dense networks. This approach, when combined with augmentations or fine-tuning from a self-supervised backbone network, shows further improvements in performance by as much as 16% (absolute) on low-sample datasets and long-tailed classification. Further, sparse winning tickets are more robust to synthetic noise and distribution shifts compared to their dense counterparts. Our analysis of winning tickets on small datasets indicates that, though sparse, the networks retain density in the initial layers and their representations are more generalizable. Code is available at https://github.com/VITA-Group/DataEfficientLTH.
VAEL: Bridging Variational Autoencoders and Probabilistic Logic Programming
Authors: Giuseppe Marra, Emanuele Sansone Eleonora Misino
Published in: Advances in Neural Information Processing Systems 35  (NeurIPS 2022) (Main Conference Track), 2022

Abstract: We present VAEL, a neuro-symbolic generative model integrating variational autoencoders (VAE) with the reasoning capabilities of probabilistic logic (L) programming.  Besides standard latent subsymbolic variables, our model exploits a probabilistic logic program to define a further structured representation, which is used for logical reasoning. The entire process is end-to-end differentiable. Once trained, VAEL can solve new unseen generation tasks by (i) leveraging the previously acquired knowledge encoded in the neural component and (ii) exploiting new logical programs on the structured latent space. Our experiments provide support on the benefits of this neuro-symbolic integration both in terms of task generalization and data efficiency. To the best of our knowledge, this work is the first to propose a general-purpose end-to-end framework integrating probabilistic logic programming into a deep generative model.
The alignment property of SGD noise and how it helps select flat minima: A stability analysis
Authors: Mingze Wang, Weijie Su Lei Wu
Published in: Advances in Neural Information Processing Systems 35  (NeurIPS 2022) (Main Conference Track), 2022

Abstract: The phenomenon that stochastic gradient descent (SGD) favors flat minima has played a critical role in   understanding the implicit regularization of SGD. In this paper, we provide an explanation of this striking phenomenon by relating the particular noise structure  of SGD to its \emph{linear stability}  (Wu et al., 2018). Specifically, we consider training over-parameterized models with square loss. We prove that if a global minimum $\theta^*$ is linearly stable for SGD, then it must satisfy $\|H(\theta^*)\|_F\leq O(\sqrt{B}/\eta)$, where $\|H(\theta^*)\|_F, B,\eta$ denote the Frobenius norm of Hessian at $\theta^*$, batch size, and learning rate, respectively. Otherwise, SGD will escape from that minimum \emph{exponentially} fast. Hence, for minima accessible to SGD, the sharpness---as measured by the Frobenius norm of the Hessian---is bounded \emph{independently} of the model size and sample size.   The key to obtaining these results is exploiting the particular structure of SGD noise: The noise concentrates in sharp directions of local landscape and  the magnitude is proportional to loss value. This alignment property of SGD noise provably holds for linear networks and random feature models (RFMs), and is empirically verified for nonlinear networks. Moreover, the validity and practical relevance of our theoretical findings are also justified by extensive experiments on CIFAR-10 dataset.
EvenNet: Ignoring Odd-Hop Neighbors Improves Robustness of Graph Neural Networks
Authors: Zhen Wang, Yaliang Li, Bolin Ding, Zhewei Wei Runlin Lei
Published in: Advances in Neural Information Processing Systems 35  (NeurIPS 2022) (Main Conference Track), 2022

Abstract: Graph Neural Networks (GNNs) have received extensive research attention for their promising performance in graph machine learning. Despite their extraordinary predictive accuracy, existing approaches, such as GCN and GPRGNN, are not robust in the face of homophily changes on test graphs, rendering these models vulnerable to graph structural attacks and with limited capacity in generalizing to graphs of varied homophily levels. Although many methods have been proposed to improve the robustness of GNN models, most of these techniques are restricted to the spatial domain and employ complicated defense mechanisms, such as learning new graph structures or calculating edge attentions. In this paper, we study the problem of designing simple and robust GNN models in the spectral domain. We propose EvenNet, a spectral GNN corresponding to an even-polynomial graph filter. Based on our theoretical analysis in both spatial and spectral domains, we demonstrate that EvenNet outperforms full-order models in generalizing across homophilic and heterophilic graphs, implying that ignoring odd-hop neighbors improves the robustness of GNNs.  We conduct experiments on both synthetic and real-world datasets to demonstrate the effectiveness of EvenNet. Notably, EvenNet outperforms existing defense models against structural attacks without introducing additional computational costs and maintains competitiveness in traditional node classification tasks on homophilic and heterophilic graphs.
Differentiable Analog Quantum Computing for Optimization and Control
Authors: Yuxiang Peng, Yi-Ling Qiao, Ming Lin, Xiaodi Wu Jiaqi Leng
Published in: Advances in Neural Information Processing Systems 35  (NeurIPS 2022) (Main Conference Track), 2022

Abstract: We formulate the first differentiable analog quantum computing framework with specific parameterization design at the analog signal (pulse) level to better exploit near-term quantum devices via variational methods. We further propose a scalable approach to estimate the gradients of quantum dynamics using a forward pass with Monte Carlo sampling, which leads to a quantum stochastic gradient descent algorithm for scalable gradient-based training in our framework. Applying our framework to quantum optimization and control, we observe a significant advantage of differentiable analog quantum computing against SOTAs based on parameterized digital quantum circuits by {\em orders of magnitude}.
Promising or Elusive? Unsupervised Object Segmentation from Real-world Single Images
Authors: Bo Yang Yafei YANG
Published in: Advances in Neural Information Processing Systems 35  (NeurIPS 2022) (Main Conference Track), 2022

Abstract: In this paper, we study the problem of unsupervised object segmentation from single images. We do not introduce a new algorithm, but systematically investigate the effectiveness of existing unsupervised models on challenging real-world images. We firstly introduce four complexity factors to quantitatively measure the distributions of object- and scene-level biases in appearance and geometry for datasets with human annotations. With the aid of these factors, we empirically find that, not surprisingly, existing unsupervised models catastrophically fail to segment generic objects in real-world images, although they can easily achieve excellent performance on numerous simple synthetic datasets, due to the vast gap in objectness biases between synthetic and real images. By conducting extensive experiments on multiple groups of ablated real-world datasets, we ultimately find that the key factors underlying the colossal failure of existing unsupervised models on real-world images are the challenging distributions of object- and scene-level biases in appearance and geometry. Because of this, the inductive biases introduced in existing unsupervised models can hardly capture the diverse object distributions. Our research results suggest that future work should exploit more explicit objectness biases in the network design.
Efficiently Factorizing Boolean Matrices using Proximal Gradient Descent
Authors: Jilles Vreeken Sebastian Dalleiger
Published in: Advances in Neural Information Processing Systems 35  (NeurIPS 2022) (Main Conference Track), 2022

Abstract: Addressing the interpretability problem of NMF on Boolean data, Boolean Matrix Factorization (BMF) uses Boolean algebra to decompose the input into low-rank Boolean factor matrices. These matrices are highly interpretable and very useful in practice, but they come at the high computational cost of solving an NP-hard combinatorial optimization problem. To reduce the computational burden, we propose to relax BMF continuously using a novel elastic-binary regularizer, from which we derive a proximal gradient algorithm. Through an extensive set of experiments, we demonstrate that our method works well in practice: On synthetic data, we show that it converges quickly, recovers the ground truth precisely, and estimates the simulated rank exactly. On real-world data, we improve upon the state of the art in recall, loss, and runtime, and a case study from the medical domain confirms that our results are easily interpretable and semantically meaningful.
Learning from Future: A Novel Self-Training Framework for Semantic Segmentation
Authors: Yujun Shen, Haochen Wang, Jingjing Fei, Wei Li, Liwei Wu, Rui Zhao, Zehua Fu, Qingjie LIU Ye Du
Published in: Advances in Neural Information Processing Systems 35  (NeurIPS 2022) (Main Conference Track), 2022

Abstract: Self-training has shown great potential in semi-supervised learning. Its core idea is to use the model learned on labeled data to generate pseudo-labels for unlabeled samples, and in turn teach itself. To obtain valid supervision, active attempts typically employ a momentum teacher for pseudo-label prediction yet observe the confirmation bias issue, where the incorrect predictions may provide wrong supervision signals and get accumulated in the training process. The primary cause of such a drawback is that the prevailing self-training framework acts as guiding the current state with previous knowledge because the teacher is updated with the past student only. To alleviate this problem, we propose a novel self-training strategy, which allows the model to learn from the future. Concretely, at each training step, we first virtually optimize the student (i.e., caching the gradients without applying them to the model weights), then update the teacher with the virtual future student, and finally ask the teacher to produce pseudo-labels for the current student as the guidance. In this way, we manage to improve the quality of pseudo-labels and thus boost the performance. We also develop two variants of our future-self-training (FST) framework through peeping at the future both deeply (FST-D) and widely (FST-W). Taking the tasks of unsupervised domain adaptive semantic segmentation and semi-supervised semantic segmentation as the instances, we experimentally demonstrate the effectiveness and superiority of our approach under a wide range of settings. Code is available at https://github.com/usr922/FST.
A Simple and Provably Efficient Algorithm for Asynchronous Federated Contextual Linear Bandits
Authors: Tianhao Wang, Yifei Min, Quanquan Gu Jiafan He
Published in: Advances in Neural Information Processing Systems 35  (NeurIPS 2022) (Main Conference Track), 2022

Abstract: We study federated contextual linear bandits, where $M$ agents cooperate with each other to solve a global contextual linear bandit problem with the help of a central server. We consider the asynchronous setting, where all agents work independently and the communication between one agent and the server will not trigger other agents' communication. We propose a simple algorithm named FedLinUCB based on the principle of optimism. We prove that the regret of FedLinUCB is bounded by $\widetilde{\mathcal{O}}(d\sqrt{\sum_{m=1}^M T_m})$ and the communication complexity is $\widetilde{O}(dM^2)$, where $d$ is the dimension of the contextual vector and $T_m$ is the total number of interactions with the environment by agent $m$. To the best of our knowledge, this is the first provably efficient algorithm that allows fully asynchronous communication for federated linear bandits, while achieving the same regret guarantee as in the single-agent setting.
How Powerful are K-hop Message Passing Graph Neural Networks
Authors: Yixin Chen, Fuhai Li, Anindya Sarkar, Muhan Zhang Jiarui Feng
Published in: Advances in Neural Information Processing Systems 35  (NeurIPS 2022) (Main Conference Track), 2022

Abstract: The most popular design paradigm for Graph Neural Networks (GNNs) is 1-hop message passing---aggregating information from 1-hop neighbors repeatedly. However, the expressive power of 1-hop message passing is bounded by the Weisfeiler-Lehman (1-WL) test. Recently, researchers extended 1-hop message passing to $K$-hop message passing by aggregating information from $K$-hop neighbors of nodes simultaneously. However, there is no work on analyzing the expressive power of $K$-hop message passing. In this work, we theoretically characterize the expressive power of $K$-hop message passing. Specifically, we first formally differentiate two different kernels of $K$-hop message passing which are often misused in previous works. We then characterize the expressive power of $K$-hop message passing by showing that it is more powerful than 1-WL and can distinguish almost all regular graphs. Despite the higher expressive power, we show that $K$-hop message passing still cannot distinguish some simple regular graphs and its expressive power is bounded by 3-WL. To further enhance its expressive power, we introduce a KP-GNN framework, which improves $K$-hop message passing by leveraging the peripheral subgraph information in each hop. We show that KP-GNN can distinguish many distance regular graphs which could not be distinguished by previous distance encoding or 3-WL methods. Experimental results verify the expressive power and effectiveness of KP-GNN. KP-GNN achieves competitive results across all benchmark datasets.
Dynamic Tensor Product Regression
Authors: Zhao Song, Lichen Zhang Aravind Reddy
Published in: Advances in Neural Information Processing Systems 35  (NeurIPS 2022) (Main Conference Track), 2022

Abstract: In this work, we initiate the study of \emph{Dynamic Tensor Product Regression}. One has matrices $A_1\in \mathbb{R}^{n_1\times d_1},\ldots,A_q\in \mathbb{R}^{n_q\times d_q}$ and a label vector $b\in \mathbb{R}^{n_1\ldots n_q}$, and the goal is to solve the regression problem with the design matrix $A$ being the tensor product of the matrices $A_1, A_2, \dots, A_q$ i.e. $\min_{x\in \mathbb{R}^{d_1\ldots d_q}}~\|(A_1\otimes \ldots\otimes A_q)x-b\|_2$. At each time step, one matrix $A_i$ receives a sparse change, and the goal is to maintain a sketch of the tensor product $A_1\otimes\ldots \otimes A_q$ so that the regression solution can be updated quickly. Recomputing the solution from scratch for each round is extremely expensive so it is important to develop algorithms which can quickly update the solution with the new design matrix. Our main result is a dynamic tree data structure where any update to a single matrix can be propagated quickly throughout the tree. We show that our data structure can be used to solve dynamic versions of not only Tensor Product Regression, but also Tensor Product Spline regression (which is a generalization of ridge regression) and for maintaining Low Rank Approximations for the tensor product.
Generalization Analysis of Message Passing Neural Networks on Large Random Graphs
Authors: Ron Levie, Yunseok Lee, Gitta Kutyniok Sohir Maskey
Published in: Advances in Neural Information Processing Systems 35  (NeurIPS 2022) (Main Conference Track), 2022

Abstract: Message passing neural networks (MPNN) have seen a steep rise in popularity since their introduction as generalizations of convolutional neural networks to graph-structured data, and are now considered state-of-the-art tools for solving a large variety of graph-focused problems. We study the generalization error of MPNNs in graph classification and regression. We assume that graphs of different classes are sampled from different random graph models. We show that, when training a MPNN on a dataset sampled from such a distribution, the generalization gap increases in the complexity of the MPNN, and decreases, not only with respect to the number of training samples, but also with the average number of nodes in the graphs. This shows how a MPNN with high complexity can generalize from a small dataset of graphs, as long as the graphs are large. The generalization bound is derived from a uniform convergence result, that shows that any MPNN, applied on a graph, approximates the MPNN applied on the geometric model that the graph discretizes.
On Infinite Separations Between Simple and Optimal Mechanisms
Authors: Ariel Schvartzman Cohenca, S. Weinberg Alexandros Psomas
Published in: Advances in Neural Information Processing Systems 35  (NeurIPS 2022) (Main Conference Track), 2022

Abstract: We consider a revenue-maximizing seller with $k$ heterogeneous items for sale to a single additive buyer, whose values are drawn from a known, possibly correlated prior $\mathcal{D}$. It is known that there exist priors $\mathcal{D}$ such that simple mechanisms --- those with bounded menu complexity --- extract an arbitrarily small fraction of the optimal revenue~(Briest et al. 2015, Hart and Nisan 2019). This paper considers the opposite direction: given a correlated distribution $\mathcal{D}$ witnessing an infinite separation between simple and optimal mechanisms, what can be said about $\mathcal{D}$?\citet{hart2019selling} provides a framework for constructing such $\mathcal{D}$: it takes as input a sequence of $k$-dimensional vectors satisfying some geometric property, and produces a $\mathcal{D}$ witnessing an infinite gap. Our first main result establishes that this framework is without loss: every $\mathcal{D}$ witnessing an infinite separation could have resulted from this framework. An earlier version of their work provided a more streamlined framework (Hart and Nisan 2013). Our second main result establishes that this restrictive framework is not tight. That is, we provide an instance $\mathcal{D}$ witnessing an infinite gap, but which provably could not have resulted from the restrictive framework. As a corollary, we discover a new kind of mechanism which can witness these infinite separations on instances where the previous ``aligned'' mechanisms do not.
Online Learning and Pricing for Network Revenue Management with Reusable Resources
Authors: Cong Shi, Siqian Shen Huiwen Jia
Published in: Advances in Neural Information Processing Systems 35  (NeurIPS 2022) (Main Conference Track), 2022

Abstract: We consider a price-based network revenue management problem with multiple products and multiple reusable resources. Each randomly arriving customer requests a product (service) that needs to occupy a sequence of reusable resources (servers). We adopt an incomplete information setting where the firm does not know the price-demand function for each product and the goal is to dynamically set prices of all products to maximize the total expected revenue of serving customers. We propose novel batched bandit learning algorithms for finding near-optimal pricing policies, and show that they admit a near-optimal cumulative regret bound of $\tilde{O}(J\sqrt{XT})$, where $J$, $X$, and $T$ are the numbers of products, candidate prices, and service periods, respectively. As part of our regret analysis, we develop the first finite-time mixing time analysis of an open network queueing system (i.e., the celebrated Jackson Network), which could be of independent interest. Our numerical studies show that the proposed approaches perform consistently well.
Learning to Find Proofs and Theorems by Learning to Refine Search Strategies: The Case of Loop Invariant Synthesis
Authors: André Platzer Jonathan Laurent
Published in: Advances in Neural Information Processing Systems 35  (NeurIPS 2022) (Main Conference Track), 2022

Abstract: We propose a new approach to automated theorem proving where an AlphaZero-style agent is self-training to refine a generic high-level expert strategy expressed as a nondeterministic program. An analogous teacher agent is self-training to generate tasks of suitable relevance and difficulty for the learner. This allows leveraging minimal amounts of domain knowledge to tackle problems for which training data is unavailable or hard to synthesize. As a specific illustration, we consider loop invariant synthesis for imperative programs and use neural networks to refine both the teacher and solver strategies.
Exploitability Minimization in Games and Beyond
Authors: Amy Greenwald Denizalp Goktas
Published in: Advances in Neural Information Processing Systems 35  (NeurIPS 2022) (Main Conference Track), 2022

Abstract: Pseudo-games are a natural and well-known generalization of normal-form games, in which the actions taken by each player affect not only the other players' payoffs, as in games, but also the other players' strategy sets. The solution concept par excellence for pseudo-games is the generalized Nash equilibrium (GNE), i.e., a strategy profile at which each player's strategy is feasible and no player can improve their payoffs by unilaterally deviating to another strategy in the strategy set determined by the other players' strategies. The computation of GNE in pseudo-games has long been a problem of interest, due to applications in a wide variety of fields, from environmental protection to logistics to telecommunications. Although computing GNE is PPAD-hard in general, it is still of interest to try to compute them in restricted classes of pseudo-games. One approach is to search for a strategy profile that minimizes exploitability, i.e., the sum of the regrets across all players. As exploitability is nondifferentiable in general, developing efficient first-order methods that minimize it might not seem possible at first glance. We observe, however, that the exploitability-minimization problem can be recast as a min-max optimization problem, and thereby obtain polynomial-time first-order methods to compute a refinement of GNE, namely the variational equilibria (VE), in convex-concave cumulative regret pseudo-games with jointly convex constraints. More generally, we also show that our methods find the stationary points of the exploitability  in polynomial time in Lipschitz-smooth pseudo-games with jointly convex constraints. Finally, we demonstrate in experiments that our methods not only outperform known algorithms, but that even in pseudo-games where they are not guaranteed to converge to a GNE, they may do so nonetheless, with proper initialization.
Where2comm: Communication-Efficient Collaborative Perception via Spatial Confidence Maps
Authors: Shaoheng Fang, Zixing Lei, Yiqi Zhong, Siheng Chen Yue Hu
Published in: Advances in Neural Information Processing Systems 35  (NeurIPS 2022) (Main Conference Track), 2022

Abstract: Multi-agent collaborative perception could significantly upgrade the perception performance by enabling agents to share complementary information with each other through communication. It inevitably results in a fundamental trade-off between perception performance and communication bandwidth. To tackle this bottleneck issue, we propose a spatial confidence map, which reflects the spatial heterogeneity of perceptual information. It empowers agents to only share spatially sparse, yet perceptually critical information, contributing to where to communicate. Based on this novel spatial confidence map, we propose Where2comm, a communication-efficient collaborative perception framework. Where2comm has two distinct advantages: i) it considers pragmatic compression and uses less communication to achieve higher perception performance by focusing on perceptually critical areas; and ii) it can handle varying communication bandwidth by dynamically adjusting spatial areas involved in communication. To evaluate Where2comm, we consider 3D object detection in both real-world and simulation scenarios with two modalities (camera/LiDAR) and two agent types (cars/drones) on four datasets: OPV2V, V2X-Sim, DAIR-V2X, and our original CoPerception-UAVs. Where2comm consistently outperforms previous methods; for example, it achieves more than $100,000 \times$ lower communication volume and still outperforms DiscoNet and V2X-ViT on OPV2V. Our code is available at~\url{https://github.com/MediaBrain-SJTU/where2comm}.
Your Out-of-Distribution Detection Method is Not Robust!
Authors: Arshia Soltani Moakhar, Arman Zarei, Reihaneh Zohrabi, Mohammad Manzuri, Mohammad Hossein Rohban Mohammad Azizmalayeri
Published in: Advances in Neural Information Processing Systems 35  (NeurIPS 2022) (Main Conference Track), 2022

Abstract: Out-of-distribution (OOD) detection has recently gained substantial attention due to the importance of identifying out-of-domain samples in reliability and safety. Although OOD detection methods have advanced by a great deal, they are still susceptible to adversarial examples, which is a violation of their purpose. To mitigate this issue, several defenses have recently been proposed. Nevertheless, these efforts remained ineffective, as their evaluations are based on either small perturbation sizes, or weak attacks. In this work, we re-examine these defenses against an end-to-end PGD attack on in/out data with larger perturbation sizes, e.g. up to commonly used $\epsilon=8/255$ for the CIFAR-10 dataset. Surprisingly, almost all of these defenses perform worse than a random detection under the adversarial setting. Next, we aim to provide a robust OOD detection method. In an ideal defense, the training should expose the model to almost all possible adversarial perturbations, which can be achieved through adversarial training. That is, such training perturbations should based on both in- and out-of-distribution samples. Therefore, unlike OOD detection in the standard setting, access to OOD, as well as in-distribution, samples sounds necessary in the adversarial training setup. These tips lead us to adopt generative OOD detection methods, such as OpenGAN, as a baseline. We subsequently propose the Adversarially Trained Discriminator (ATD), which utilizes a pre-trained robust model to extract robust features, and a generator model to create OOD samples. We noted that, for the sake of training stability, in the adversarial training of the discriminator, one should attack real in-distribution as well as real outliers, but not generated outliers. Using ATD with CIFAR-10 and CIFAR-100 as the in-distribution data, we could significantly outperform all previous methods in the robust AUROC while maintaining high standard AUROC and classification accuracy. The code repository is available at https://github.com/rohban-lab/ATD.
Discovering and Overcoming Limitations of Noise-engineered Data-free Knowledge Distillation
Authors: Deepak Mishra Piyush Raikwar
Published in: Advances in Neural Information Processing Systems 35  (NeurIPS 2022) (Main Conference Track), 2022

Abstract: Distillation in neural networks using only the samples randomly drawn from a Gaussian distribution is possibly the most straightforward solution one can think of for the complex problem of knowledge transfer from one network (teacher) to the other (student). If successfully done, it can eliminate the requirement of teacher's training data for knowledge distillation and avoid often arising privacy concerns in sensitive applications such as healthcare. There have been some recent attempts at Gaussian noise-based data-free knowledge distillation, however, none of them offer a consistent or reliable solution. We identify the shift in the distribution of hidden layer activation as the key limiting factor, which occurs when Gaussian noise is fed to the teacher network instead of the accustomed training data. We propose a simple solution to mitigate this shift and show that for vision tasks, such as classification, it is possible to achieve a performance close to the teacher by just using the samples randomly drawn from a Gaussian distribution. We validate our approach on CIFAR10, CIFAR100, SVHN, and Food101 datasets. We further show that in situations of sparsely available original data for distillation, the proposed Gaussian noise-based knowledge distillation method can outperform the distillation using the available data with a large margin. Our work lays the foundation for further research in the direction of noise-engineered knowledge distillation using random samples.
NaturalProver: Grounded Mathematical Proof Generation with Language Models
Authors: Jiacheng Liu, Ximing Lu, Hannaneh Hajishirzi, Yejin Choi Sean Welleck
Published in: Advances in Neural Information Processing Systems 35  (NeurIPS 2022) (Main Conference Track), 2022

Abstract: Theorem proving in natural mathematical language – the mixture of symbolic and natural language used by humans – plays a central role in mathematical advances and education, and tests aspects of reasoning that are core to intelligence. Yet it has remained underexplored with modern generative models. We study large-scale language models on two new generation tasks: suggesting the next step in a mathematical proof, and full proof generation. We develop NaturalProver, a language model that generates proofs by conditioning on background references (e.g. theorems and definitions that are either retrieved or human-provided), and optionally enforces their presence with constrained decoding. On theorems from the NaturalProofs benchmark, NaturalProver improves the quality of next-step suggestions and generated proofs over fine-tuned GPT-3, according to human evaluations from university-level mathematics students. NaturalProver is capable of proving some theorems that require short (2-6 step) proofs, and providing next-step suggestions that are rated as correct and useful over 40% of the time, which is to our knowledge the first demonstration of these capabilities using neural language models.
Smoothed Online Convex Optimization Based on Discounted-Normal-Predictor
Authors: Wei Jiang, Jinfeng Yi, Tianbao Yang Lijun Zhang
Published in: Advances in Neural Information Processing Systems 35  (NeurIPS 2022) (Main Conference Track), 2022

Abstract: In this paper, we investigate an online prediction strategy named as Discounted-Normal-Predictor [Kapralov and Panigrahy, 2010] for smoothed online convex optimization (SOCO), in which the learner needs to minimize not only the hitting cost but also the switching cost. In the setting of learning with expert advice, Daniely and Mansour [2019] demonstrate that Discounted-Normal-Predictor can be utilized to yield nearly optimal regret bounds over any interval, even in the presence of switching costs. Inspired by their results, we develop a simple algorithm for SOCO: Combining online gradient descent (OGD) with different step sizes sequentially by Discounted-Normal-Predictor. Despite its simplicity, we prove that it is able to minimize the adaptive regret with switching cost, i.e., attaining nearly optimal regret with switching cost on every interval. By exploiting the theoretical guarantee of OGD for dynamic regret, we further show that the proposed algorithm can minimize the dynamic regret with switching cost in every interval.
One for All: Simultaneous Metric and Preference Learning over Multiple Users
Authors: Blake Mason, Ramya Korlakai Vinayak, Robert Nowak Gregory Canal
Published in: Advances in Neural Information Processing Systems 35  (NeurIPS 2022) (Main Conference Track), 2022

Abstract: This paper investigates simultaneous preference and metric learning from a crowd of respondents. A set of items represented by $d$-dimensional feature vectors and paired comparisons of the form ``item $i$ is preferable to item $j$'' made by each user is given. Our model jointly learns a distance metric that characterizes the crowd's general measure of item similarities along with a latent ideal point for each user reflecting their individual preferences. This model has the flexibility to capture individual preferences, while enjoying a metric learning sample cost that is amortized over the crowd. We first study this problem in a noiseless, continuous response setting (i.e., responses equal to differences of item distances) to understand the fundamental limits of learning. Next, we establish prediction error guarantees for noisy, binary measurements such as may be collected from human respondents, and show how the sample complexity improves when the underlying metric is low-rank. Finally, we establish recovery guarantees under assumptions on the response distribution. We demonstrate the performance of our model on both simulated data and on a dataset of color preference judgements across a large number of users.