arXiv daily

Machine Learning (cs.LG)

Fri, 23 Jun 2023

Other arXiv digests in this category:Thu, 14 Sep 2023; Wed, 13 Sep 2023; Tue, 12 Sep 2023; Mon, 11 Sep 2023; Fri, 08 Sep 2023; Tue, 05 Sep 2023; Fri, 01 Sep 2023; Thu, 31 Aug 2023; Wed, 30 Aug 2023; Tue, 29 Aug 2023; Mon, 28 Aug 2023; Fri, 25 Aug 2023; Thu, 24 Aug 2023; Wed, 23 Aug 2023; Tue, 22 Aug 2023; Mon, 21 Aug 2023; Fri, 18 Aug 2023; Thu, 17 Aug 2023; Wed, 16 Aug 2023; Tue, 15 Aug 2023; Mon, 14 Aug 2023; Fri, 11 Aug 2023; Thu, 10 Aug 2023; Wed, 09 Aug 2023; Tue, 08 Aug 2023; Mon, 07 Aug 2023; Fri, 04 Aug 2023; Thu, 03 Aug 2023; Wed, 02 Aug 2023; Tue, 01 Aug 2023; Mon, 31 Jul 2023; Fri, 28 Jul 2023; Thu, 27 Jul 2023; Wed, 26 Jul 2023; Tue, 25 Jul 2023; Mon, 24 Jul 2023; Fri, 21 Jul 2023; Thu, 20 Jul 2023; Wed, 19 Jul 2023; Tue, 18 Jul 2023; Mon, 17 Jul 2023; Fri, 14 Jul 2023; Thu, 13 Jul 2023; Wed, 12 Jul 2023; Tue, 11 Jul 2023; Mon, 10 Jul 2023; Fri, 07 Jul 2023; Thu, 06 Jul 2023; Wed, 05 Jul 2023; Tue, 04 Jul 2023; Mon, 03 Jul 2023; Fri, 30 Jun 2023; Thu, 29 Jun 2023; Wed, 28 Jun 2023; Tue, 27 Jun 2023; Mon, 26 Jun 2023; Thu, 22 Jun 2023; Wed, 21 Jun 2023; Tue, 20 Jun 2023; Fri, 16 Jun 2023; Thu, 15 Jun 2023; Tue, 13 Jun 2023; Mon, 12 Jun 2023; Fri, 09 Jun 2023; Thu, 08 Jun 2023; Wed, 07 Jun 2023; Tue, 06 Jun 2023; Mon, 05 Jun 2023; Fri, 02 Jun 2023; Thu, 01 Jun 2023; Wed, 31 May 2023; Tue, 30 May 2023; Mon, 29 May 2023; Fri, 26 May 2023; Thu, 25 May 2023; Wed, 24 May 2023; Tue, 23 May 2023; Mon, 22 May 2023; Fri, 19 May 2023; Thu, 18 May 2023; Wed, 17 May 2023; Tue, 16 May 2023; Mon, 15 May 2023; Fri, 12 May 2023; Thu, 11 May 2023; Wed, 10 May 2023; Tue, 09 May 2023; Mon, 08 May 2023; Fri, 05 May 2023; Thu, 04 May 2023; Wed, 03 May 2023; Tue, 02 May 2023; Mon, 01 May 2023; Fri, 28 Apr 2023; Thu, 27 Apr 2023; Wed, 26 Apr 2023; Tue, 25 Apr 2023; Mon, 24 Apr 2023; Fri, 21 Apr 2023; Thu, 20 Apr 2023; Wed, 19 Apr 2023; Tue, 18 Apr 2023; Mon, 17 Apr 2023; Fri, 14 Apr 2023; Thu, 13 Apr 2023; Wed, 12 Apr 2023; Tue, 11 Apr 2023; Mon, 10 Apr 2023
1.Variance-Covariance Regularization Improves Representation Learning

Authors:Jiachen Zhu, Ravid Shwartz-Ziv, Yubei Chen, Yann LeCun

Abstract: Transfer learning has emerged as a key approach in the machine learning domain, enabling the application of knowledge derived from one domain to improve performance on subsequent tasks. Given the often limited information about these subsequent tasks, a strong transfer learning approach calls for the model to capture a diverse range of features during the initial pretraining stage. However, recent research suggests that, without sufficient regularization, the network tends to concentrate on features that primarily reduce the pretraining loss function. This tendency can result in inadequate feature learning and impaired generalization capability for target tasks. To address this issue, we propose Variance-Covariance Regularization (VCR), a regularization technique aimed at fostering diversity in the learned network features. Drawing inspiration from recent advancements in the self-supervised learning approach, our approach promotes learned representations that exhibit high variance and minimal covariance, thus preventing the network from focusing solely on loss-reducing features. We empirically validate the efficacy of our method through comprehensive experiments coupled with in-depth analytical studies on the learned representations. In addition, we develop an efficient implementation strategy that assures minimal computational overhead associated with our method. Our results indicate that VCR is a powerful and efficient method for enhancing transfer learning performance for both supervised learning and self-supervised learning, opening new possibilities for future research in this domain.

2.TrustGuard: GNN-based Robust and Explainable Trust Evaluation with Dynamicity Support

Authors:Jie Wang, Zheng Yan, Jiahe Lan, Elisa Bertino, Witold Pedrycz

Abstract: Trust evaluation assesses trust relationships between entities and facilitates decision-making. Machine Learning (ML) shows great potential for trust evaluation owing to its learning capabilities. In recent years, Graph Neural Networks (GNNs), as a new ML paradigm, have demonstrated superiority in dealing with graph data. This has motivated researchers to explore their use in trust evaluation, as trust relationships among entities can be modeled as a graph. However, current trust evaluation methods that employ GNNs fail to fully satisfy the dynamicity nature of trust, overlook the adverse effects of attacks on trust evaluation, and cannot provide convincing explanations on evaluation results. To address these problems, in this paper, we propose TrustGuard, a GNN-based accurate trust evaluation model that supports trust dynamicity, is robust against typical attacks, and provides explanations through visualization. Specifically, TrustGuard is designed with a layered architecture that contains a snapshot input layer, a spatial aggregation layer, a temporal aggregation layer, and a prediction layer. Among them, the spatial aggregation layer can be plugged into a defense mechanism for a robust aggregation of local trust relationships, and the temporal aggregation layer applies an attention mechanism for effective learning of temporal patterns. Extensive experiments on two real-world datasets show that TrustGuard outperforms state-of-the-art GNN-based trust evaluation models with respect to trust prediction across single-timeslot and multi-timeslot, even in the presence of attacks. In particular, TrustGuard can explain its evaluation results by visualizing both spatial and temporal views.

3.Catching Image Retrieval Generalization

Authors:Maksim Zhdanov, Ivan Karpukhin

Abstract: The concepts of overfitting and generalization are vital for evaluating machine learning models. In this work, we show that the popular Recall@K metric depends on the number of classes in the dataset, which limits its ability to estimate generalization. To fix this issue, we propose a new metric, which measures retrieval performance, and, unlike Recall@K, estimates generalization. We apply the proposed metric to popular image retrieval methods and provide new insights about deep metric learning generalization.

4.Physics-constrained Random Forests for Turbulence Model Uncertainty Estimation

Authors:Marcel Matha, Christian Morsbach

Abstract: To achieve virtual certification for industrial design, quantifying the uncertainties in simulation-driven processes is crucial. We discuss a physics-constrained approach to account for epistemic uncertainty of turbulence models. In order to eliminate user input, we incorporate a data-driven machine learning strategy. In addition to it, our study focuses on developing an a priori estimation of prediction confidence when accurate data is scarce.

5.Higher-order Motif-based Time Series Classification for Forced Oscillation Source Location in Power Grids

Authors:Long Huo, Xin Chen

Abstract: Time series motifs are used for discovering higher-order structures of time series data. Based on time series motifs, the motif embedding correlation field (MECF) is proposed to characterize higher-order temporal structures of dynamical system time series. A MECF-based unsupervised learning approach is applied in locating the source of the forced oscillation (FO), a periodic disturbance that detrimentally impacts power grids. Locating the FO source is imperative for system stability. Compared with the Fourier analysis, the MECF-based unsupervised learning is applicable under various FO situations, including the single FO, FO with resonance, and multiple sources FOs. The MECF-based unsupervised learning is a data-driven approach without any prior knowledge requirement of system models or typologies. Tests on the UK high-voltage transmission grid illustrate the effectiveness of MECF-based unsupervised learning. In addition, the impacts of coupling strength and measurement noise on locating the FO source by the MECF-based unsupervised learning are investigated.

6.Explainable Lifelong Stream Learning Based on "Glocal" Pairwise Fusion

Authors:Chu Kiong Loo, Wei Shiung Liew, Stefan Wermter

Abstract: Real-time on-device continual learning applications are used on mobile phones, consumer robots, and smart appliances. Such devices have limited processing and memory storage capabilities, whereas continual learning acquires data over a long period of time. By necessity, lifelong learning algorithms have to be able to operate under such constraints while delivering good performance. This study presents the Explainable Lifelong Learning (ExLL) model, which incorporates several important traits: 1) learning to learn, in a single pass, from streaming data with scarce examples and resources; 2) a self-organizing prototype-based architecture that expands as needed and clusters streaming data into separable groups by similarity and preserves data against catastrophic forgetting; 3) an interpretable architecture to convert the clusters into explainable IF-THEN rules as well as to justify model predictions in terms of what is similar and dissimilar to the inference; and 4) inferences at the global and local level using a pairwise decision fusion process to enhance the accuracy of the inference, hence ``Glocal Pairwise Fusion.'' We compare ExLL against contemporary online learning algorithms for image recognition, using OpenLoris, F-SIOL-310, and Places datasets to evaluate several continual learning scenarios for video streams, low-sample learning, ability to scale, and imbalanced data streams. The algorithms are evaluated for their performance in accuracy, number of parameters, and experiment runtime requirements. ExLL outperforms all algorithms for accuracy in the majority of the tested scenarios.

7.Neural Algorithmic Reasoning Without Intermediate Supervision

Authors:Gleb Rodionov, Liudmila Prokhorenkova

Abstract: Neural Algorithmic Reasoning is an emerging area of machine learning focusing on building models which can imitate the execution of classic algorithms, such as sorting, shortest paths, etc. One of the main challenges is to learn algorithms that are able to generalize to out-of-distribution data, in particular with significantly larger input sizes. Recent work on this problem has demonstrated the advantages of learning algorithms step-by-step, giving models access to all intermediate steps of the original algorithm. In this work, we instead focus on learning neural algorithmic reasoning only from the input-output pairs without appealing to the intermediate supervision. We propose simple but effective architectural improvements and also build a self-supervised objective that can regularise intermediate computations of the model without access to the algorithm trajectory. We demonstrate that our approach is competitive to its trajectory-supervised counterpart on tasks from the CLRS Algorithmic Reasoning Benchmark and achieves new state-of-the-art results for several problems, including sorting, where we obtain significant improvements. Thus, learning without intermediate supervision is a promising direction for further research on neural reasoners.

8.CLUE: Calibrated Latent Guidance for Offline Reinforcement Learning

Authors:Jinxin Liu, Lipeng Zu, Li He, Donglin Wang

Abstract: Offline reinforcement learning (RL) aims to learn an optimal policy from pre-collected and labeled datasets, which eliminates the time-consuming data collection in online RL. However, offline RL still bears a large burden of specifying/handcrafting extrinsic rewards for each transition in the offline data. As a remedy for the labor-intensive labeling, we propose to endow offline RL tasks with a few expert data and utilize the limited expert data to drive intrinsic rewards, thus eliminating the need for extrinsic rewards. To achieve that, we introduce \textbf{C}alibrated \textbf{L}atent g\textbf{U}idanc\textbf{E} (CLUE), which utilizes a conditional variational auto-encoder to learn a latent space such that intrinsic rewards can be directly qualified over the latent space. CLUE's key idea is to align the intrinsic rewards consistent with the expert intention via enforcing the embeddings of expert data to a calibrated contextual representation. We instantiate the expert-driven intrinsic rewards in sparse-reward offline RL tasks, offline imitation learning (IL) tasks, and unsupervised offline RL tasks. Empirically, we find that CLUE can effectively improve the sparse-reward offline RL performance, outperform the state-of-the-art offline IL baselines, and discover diverse skills from static reward-free offline data.

9.Trading-off price for data quality to achieve fair online allocation

Authors:Mathieu Molina, Nicolas Gast, Patrick Loiseau, Vianney Perchet

Abstract: We consider the problem of online allocation subject to a long-term fairness penalty. Contrary to existing works, however, we do not assume that the decision-maker observes the protected attributes -- which is often unrealistic in practice. Instead they can purchase data that help estimate them from sources of different quality; and hence reduce the fairness penalty at some cost. We model this problem as a multi-armed bandit problem where each arm corresponds to the choice of a data source, coupled with the online allocation problem. We propose an algorithm that jointly solves both problems and show that it has a regret bounded by $\mathcal{O}(\sqrt{T})$. A key difficulty is that the rewards received by selecting a source are correlated by the fairness penalty, which leads to a need for randomization (despite a stochastic setting). Our algorithm takes into account contextual information available before the source selection, and can adapt to many different fairness notions. We also show that in some instances, the estimates used can be learned on the fly.

10.Enhanced Dengue Outbreak Prediction in Tamilnadu using Meteorological and Entomological data

Authors:Varalakshmi M VIT Vellore, India, Daphne Lopez VIT Vellore, India

Abstract: This paper focuses on studying the impact of climate data and vector larval indices on dengue outbreak. After a comparative study of the various LSTM models, Bidirectional Stacked LSTM network is selected to analyze the time series climate data and health data collected for the state of Tamil Nadu (India), for the period 2014 to 2020. Prediction accuracy of the model is significantly improved by including the mosquito larval index, an indication of VBD control measure.

11.Efficient Online Processing with Deep Neural Networks

Authors:Lukas Hedegaard

Abstract: The capabilities and adoption of deep neural networks (DNNs) grow at an exhilarating pace: Vision models accurately classify human actions in videos and identify cancerous tissue in medical scans as precisely than human experts; large language models answer wide-ranging questions, generate code, and write prose, becoming the topic of everyday dinner-table conversations. Even though their uses are exhilarating, the continually increasing model sizes and computational complexities have a dark side. The economic cost and negative environmental externalities of training and serving models is in evident disharmony with financial viability and climate action goals. Instead of pursuing yet another increase in predictive performance, this dissertation is dedicated to the improvement of neural network efficiency. Specifically, a core contribution addresses the efficiency aspects during online inference. Here, the concept of Continual Inference Networks (CINs) is proposed and explored across four publications. CINs extend prior state-of-the-art methods developed for offline processing of spatio-temporal data and reuse their pre-trained weights, improving their online processing efficiency by an order of magnitude. These advances are attained through a bottom-up computational reorganization and judicious architectural modifications. The benefit to online inference is demonstrated by reformulating several widely used network architectures into CINs, including 3D CNNs, ST-GCNs, and Transformer Encoders. An orthogonal contribution tackles the concurrent adaptation and computational acceleration of a large source model into multiple lightweight derived models. Drawing on fusible adapter networks and structured pruning, Structured Pruning Adapters achieve superior predictive accuracy under aggressive pruning using significantly fewer learned weights compared to fine-tuning with pruning.

12.Binary domain generalization for sparsifying binary neural networks

Authors:Riccardo Schiavone, Francesco Galati, Maria A. Zuluaga

Abstract: Binary neural networks (BNNs) are an attractive solution for developing and deploying deep neural network (DNN)-based applications in resource constrained devices. Despite their success, BNNs still suffer from a fixed and limited compression factor that may be explained by the fact that existing pruning methods for full-precision DNNs cannot be directly applied to BNNs. In fact, weight pruning of BNNs leads to performance degradation, which suggests that the standard binarization domain of BNNs is not well adapted for the task. This work proposes a novel more general binary domain that extends the standard binary one that is more robust to pruning techniques, thus guaranteeing improved compression and avoiding severe performance losses. We demonstrate a closed-form solution for quantizing the weights of a full-precision network into the proposed binary domain. Finally, we show the flexibility of our method, which can be combined with other pruning strategies. Experiments over CIFAR-10 and CIFAR-100 demonstrate that the novel approach is able to generate efficient sparse networks with reduced memory usage and run-time latency, while maintaining performance.

13.On the Convergence Rate of Gaussianization with Random Rotations

Authors:Felix Draxler, Lars Kühmichel, Armand Rousselot, Jens Müller, Christoph Schnörr, Ullrich Köthe

Abstract: Gaussianization is a simple generative model that can be trained without backpropagation. It has shown compelling performance on low dimensional data. As the dimension increases, however, it has been observed that the convergence speed slows down. We show analytically that the number of required layers scales linearly with the dimension for Gaussian input. We argue that this is because the model is unable to capture dependencies between dimensions. Empirically, we find the same linear increase in cost for arbitrary input $p(x)$, but observe favorable scaling for some distributions. We explore potential speed-ups and formulate challenges for further research.

14.PathMLP: Smooth Path Towards High-order Homophily

Authors:Chenxuan Xie, Jiajun Zhou, Shengbo Gong, Jiacheng Wan, Jiaxu Qian, Shanqing Yu, Qi Xuan, Xiaoniu Yang

Abstract: Real-world graphs exhibit increasing heterophily, where nodes no longer tend to be connected to nodes with the same label, challenging the homophily assumption of classical graph neural networks (GNNs) and impeding their performance. Intriguingly, we observe that certain high-order information on heterophilous data exhibits high homophily, which motivates us to involve high-order information in node representation learning. However, common practices in GNNs to acquire high-order information mainly through increasing model depth and altering message-passing mechanisms, which, albeit effective to a certain extent, suffer from three shortcomings: 1) over-smoothing due to excessive model depth and propagation times; 2) high-order information is not fully utilized; 3) low computational efficiency. In this regard, we design a similarity-based path sampling strategy to capture smooth paths containing high-order homophily. Then we propose a lightweight model based on multi-layer perceptrons (MLP), named PathMLP, which can encode messages carried by paths via simple transformation and concatenation operations, and effectively learn node representations in heterophilous graphs through adaptive path aggregation. Extensive experiments demonstrate that our method outperforms baselines on 16 out of 20 datasets, underlining its effectiveness and superiority in alleviating the heterophily problem. In addition, our method is immune to over-smoothing and has high computational efficiency.

15.Torsion Graph Neural Networks

Authors:Cong Shen, Xiang Liu, Jiawei Luo, Kelin Xia

Abstract: Geometric deep learning (GDL) models have demonstrated a great potential for the analysis of non-Euclidian data. They are developed to incorporate the geometric and topological information of non-Euclidian data into the end-to-end deep learning architectures. Motivated by the recent success of discrete Ricci curvature in graph neural network (GNNs), we propose TorGNN, an analytic Torsion enhanced Graph Neural Network model. The essential idea is to characterize graph local structures with an analytic torsion based weight formula. Mathematically, analytic torsion is a topological invariant that can distinguish spaces which are homotopy equivalent but not homeomorphic. In our TorGNN, for each edge, a corresponding local simplicial complex is identified, then the analytic torsion (for this local simplicial complex) is calculated, and further used as a weight (for this edge) in message-passing process. Our TorGNN model is validated on link prediction tasks from sixteen different types of networks and node classification tasks from three types of networks. It has been found that our TorGNN can achieve superior performance on both tasks, and outperform various state-of-the-art models. This demonstrates that analytic torsion is a highly efficient topological invariant in the characterization of graph structures and can significantly boost the performance of GNNs.

16.Manifold Contrastive Learning with Variational Lie Group Operators

Authors:Kion Fallah, Alec Helbling, Kyle A. Johnsen, Christopher J. Rozell

Abstract: Self-supervised learning of deep neural networks has become a prevalent paradigm for learning representations that transfer to a variety of downstream tasks. Similar to proposed models of the ventral stream of biological vision, it is observed that these networks lead to a separation of category manifolds in the representations of the penultimate layer. Although this observation matches the manifold hypothesis of representation learning, current self-supervised approaches are limited in their ability to explicitly model this manifold. Indeed, current approaches often only apply augmentations from a pre-specified set of "positive pairs" during learning. In this work, we propose a contrastive learning approach that directly models the latent manifold using Lie group operators parameterized by coefficients with a sparsity-promoting prior. A variational distribution over these coefficients provides a generative model of the manifold, with samples which provide feature augmentations applicable both during contrastive training and downstream tasks. Additionally, learned coefficient distributions provide a quantification of which transformations are most likely at each point on the manifold while preserving identity. We demonstrate benefits in self-supervised benchmarks for image datasets, as well as a downstream semi-supervised task. In the former case, we demonstrate that the proposed methods can effectively apply manifold feature augmentations and improve learning both with and without a projection head. In the latter case, we demonstrate that feature augmentations sampled from learned Lie group operators can improve classification performance when using few labels.

17.Comparing the Efficacy of Fine-Tuning and Meta-Learning for Few-Shot Policy Imitation

Authors:Massimiliano Patacchiola, Mingfei Sun, Katja Hofmann, Richard E. Turner

Abstract: In this paper we explore few-shot imitation learning for control problems, which involves learning to imitate a target policy by accessing a limited set of offline rollouts. This setting has been relatively under-explored despite its relevance to robotics and control applications. State-of-the-art methods developed to tackle few-shot imitation rely on meta-learning, which is expensive to train as it requires access to a distribution over tasks (rollouts from many target policies and variations of the base environment). Given this limitation we investigate an alternative approach, fine-tuning, a family of methods that pretrain on a single dataset and then fine-tune on unseen domain-specific data. Recent work has shown that fine-tuners outperform meta-learners in few-shot image classification tasks, especially when the data is out-of-domain. Here we evaluate to what extent this is true for control problems, proposing a simple yet effective baseline which relies on two stages: (i) training a base policy online via reinforcement learning (e.g. Soft Actor-Critic) on a single base environment, (ii) fine-tuning the base policy via behavioral cloning on a few offline rollouts of the target policy. Despite its simplicity this baseline is competitive with meta-learning methods on a variety of conditions and is able to imitate target policies trained on unseen variations of the original environment. Importantly, the proposed approach is practical and easy to implement, as it does not need any complex meta-training protocol. As a further contribution, we release an open source dataset called iMuJoCo (iMitation MuJoCo) consisting of 154 variants of popular OpenAI-Gym MuJoCo environments with associated pretrained target policies and rollouts, which can be used by the community to study few-shot imitation learning and offline reinforcement learning.

18.Scaling MLPs: A Tale of Inductive Bias

Authors:Gregor Bachmann, Sotiris Anagnostidis, Thomas Hofmann

Abstract: In this work we revisit the most fundamental building block in deep learning, the multi-layer perceptron (MLP), and study the limits of its performance on vision tasks. Empirical insights into MLPs are important for multiple reasons. (1) Given the recent narrative "less inductive bias is better", popularized due to transformers eclipsing convolutional models, it is natural to explore the limits of this hypothesis. To that end, MLPs offer an ideal test bed, being completely free of any inductive bias. (2) MLPs have almost exclusively been the main protagonist in the deep learning theory literature due to their mathematical simplicity, serving as a proxy to explain empirical phenomena observed for more complex architectures. Surprisingly, experimental datapoints for MLPs are very difficult to find in the literature, especially when coupled with large pre-training protocols. This discrepancy between practice and theory is worrying: Do MLPs reflect the empirical advances exhibited by practical models? Or do theorists need to rethink the role of MLPs as a proxy? We provide insights into both these aspects. We show that the performance of MLPs drastically improves with scale (93% on CIFAR10, 79% on CIFAR100, 69% on TinyImageNet), highlighting that lack of inductive bias can indeed be compensated. We observe that MLPs mimic the behaviour of their modern counterparts faithfully, with some components in the learning setting however surprisingly exhibiting stronger or unexpected behaviours. Due to their inherent computational efficiency, large pre-training experiments become more accessible for academic researchers. All of our experiments were run on a single GPU.

19.NetBooster: Empowering Tiny Deep Learning By Standing on the Shoulders of Deep Giants

Authors:Zhongzhi Yu, Yonggan Fu, Jiayi Yuan, Haoran You, Yingyan Lin

Abstract: Tiny deep learning has attracted increasing attention driven by the substantial demand for deploying deep learning on numerous intelligent Internet-of-Things devices. However, it is still challenging to unleash tiny deep learning's full potential on both large-scale datasets and downstream tasks due to the under-fitting issues caused by the limited model capacity of tiny neural networks (TNNs). To this end, we propose a framework called NetBooster to empower tiny deep learning by augmenting the architectures of TNNs via an expansion-then-contraction strategy. Extensive experiments show that NetBooster consistently outperforms state-of-the-art tiny deep learning solutions.

20.Margin Maximization in Attention Mechanism

Authors:Davoud Ataee Tarzanagh, Yingcong Li, Xuechen Zhang, Samet Oymak

Abstract: Attention mechanism is a central component of the transformer architecture which led to the phenomenal success of large language models. However, the theoretical principles underlying the attention mechanism are poorly understood, especially its nonconvex optimization dynamics. In this work, we explore the seminal softmax-attention model $f(\boldsymbol{X})=\langle \boldsymbol{Xv}, \texttt{softmax}(\boldsymbol{XWp})\rangle$, where, $\boldsymbol{X}$ is the token sequence and $(\boldsymbol{v},\boldsymbol{W},\boldsymbol{p})$ are tunable parameters. We prove that running gradient descent on $\boldsymbol{p}$, or equivalently $\boldsymbol{W}$, converges in direction to a max-margin solution that separates $\textit{locally-optimal}$ tokens from non-optimal ones. This clearly formalizes attention as a token separation mechanism. Remarkably, our results are applicable to general data and precisely characterize $\textit{optimality}$ of tokens in terms of the value embeddings $\boldsymbol{Xv}$ and problem geometry. We also provide a broader regularization path analysis that establishes the margin maximizing nature of attention even for nonlinear prediction heads. When optimizing $\boldsymbol{v}$ and $\boldsymbol{p}$ simultaneously with logistic loss, we identify conditions under which the regularization paths directionally converge to their respective hard-margin SVM solutions where $\boldsymbol{v}$ separates the input features based on their labels. Interestingly, the SVM formulation of $\boldsymbol{p}$ is influenced by the support vector geometry of $\boldsymbol{v}$. Finally, we verify our theoretical findings via numerical experiments and provide insights.

21.Active Coverage for PAC Reinforcement Learning

Authors:Aymen Al-Marjani, Andrea Tirinzoni, Emilie Kaufmann

Abstract: Collecting and leveraging data with good coverage properties plays a crucial role in different aspects of reinforcement learning (RL), including reward-free exploration and offline learning. However, the notion of "good coverage" really depends on the application at hand, as data suitable for one context may not be so for another. In this paper, we formalize the problem of active coverage in episodic Markov decision processes (MDPs), where the goal is to interact with the environment so as to fulfill given sampling requirements. This framework is sufficiently flexible to specify any desired coverage property, making it applicable to any problem that involves online exploration. Our main contribution is an instance-dependent lower bound on the sample complexity of active coverage and a simple game-theoretic algorithm, CovGame, that nearly matches it. We then show that CovGame can be used as a building block to solve different PAC RL tasks. In particular, we obtain a simple algorithm for PAC reward-free exploration with an instance-dependent sample complexity that, in certain MDPs which are "easy to explore", is lower than the minimax one. By further coupling this exploration algorithm with a new technique to do implicit eliminations in policy space, we obtain a computationally-efficient algorithm for best-policy identification whose instance-dependent sample complexity scales with gaps between policy values.

22.Adversarial Robustness Certification for Bayesian Neural Networks

Authors:Matthew Wicker, Andrea Patane, Luca Laurenti, Marta Kwiatkowska

Abstract: We study the problem of certifying the robustness of Bayesian neural networks (BNNs) to adversarial input perturbations. Given a compact set of input points $T \subseteq \mathbb{R}^m$ and a set of output points $S \subseteq \mathbb{R}^n$, we define two notions of robustness for BNNs in an adversarial setting: probabilistic robustness and decision robustness. Probabilistic robustness is the probability that for all points in $T$ the output of a BNN sampled from the posterior is in $S$. On the other hand, decision robustness considers the optimal decision of a BNN and checks if for all points in $T$ the optimal decision of the BNN for a given loss function lies within the output set $S$. Although exact computation of these robustness properties is challenging due to the probabilistic and non-convex nature of BNNs, we present a unified computational framework for efficiently and formally bounding them. Our approach is based on weight interval sampling, integration, and bound propagation techniques, and can be applied to BNNs with a large number of parameters, and independently of the (approximate) inference method employed to train the BNN. We evaluate the effectiveness of our methods on various regression and classification tasks, including an industrial regression benchmark, MNIST, traffic sign recognition, and airborne collision avoidance, and demonstrate that our approach enables certification of robustness and uncertainty of BNN predictions.

23.GKD: Generalized Knowledge Distillation for Auto-regressive Sequence Models

Authors:Rishabh Agarwal, Nino Vieillard, Piotr Stanczyk, Sabela Ramos, Matthieu Geist, Olivier Bachem

Abstract: Knowledge distillation is commonly used for compressing neural networks to reduce their inference cost and memory footprint. However, current distillation methods for auto-regressive models, such as generative language models (LMs), suffer from two key issues: (1) distribution mismatch between output sequences during training and the sequences generated by the student during its deployment, and (2) model under-specification, where the student model may not be expressive enough to fit the teacher's distribution. To address these issues, we propose Generalized Knowledge Distillation (GKD). GKD mitigates distribution mismatch by sampling output sequences from the student during training. Furthermore, GKD handles model under-specification by optimizing alternative divergences, such as reverse KL, that focus on generating samples from the student that are likely under the teacher's distribution. We demonstrate that GKD outperforms commonly-used approaches for distilling LLMs on summarization, machine translation, and arithmetic reasoning tasks.