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Theory · Game Theory

Safwan Hossain, Evi Micha, Yiling Chen, Ariel Procaccia

We propose a new variant of the strategic classification problem: a principal reveals a classifier, and $n$ agents report their (possibly manipulated) features to be classified. Motivated by real-world applications, our model crucially allows the manipulation of one agent to affect another; that is, it explicitly captures inter-agent externalities. The principal-agent interactions are formally modeled as a Stackelberg game, with the resulting agent manipulation dynamics captured as a simultaneous game. We show that under certain assumptions, the pure Nash Equilibrium of this agent manipulation game is unique and can be efficiently computed. Leveraging this result, PAC learning guarantees are established for the learner: informally, we show that it is possible to learn classifiers that minimize loss on the distribution, even when a random number of agents are manipulating their way to a pure Nash Equilibrium. We also comment on the optimization of such classifiers through gradient-based approaches. This work sets the theoretical foundations for a more realistic analysis of classifiers that are robust against multiple strategic actors interacting in a common environment.

Theory · Game Theory

Boning Li, Longbo Huang

Efficiently computing approximate equilibrium strategies in large Imperfect Information Extensive-Form Games (IIEFGs) poses significant challenges due to the game tree's exponential growth. While pruning and abstraction techniques are essential for complexity reduction, existing methods face two key limitations: (i) Seamless integration of pruning with Counterfactual Regret Minimization (CFR) is nontrivial, and (ii) Pruning and abstraction approaches incur prohibitive computational costs, hindering real-world deployment. We propose Expected-Value Pruning and Abstraction (EVPA), a novel online framework that addresses these challenges through three synergistic components: (i) Expected value estimation using approximate Nash equilibrium strategies to quantify information set utilities, (ii) Minimax pruning before CFR to eliminate a large number of sub-optimal actions permanently, and (iii) Dynamic online information abstraction merging information sets based on their current and future expected values in subgames. Experiments on Heads-up No-Limit Texas Hold'em (HUNL) show EVPA outperforms DeepStack's replication and Slumbot with significant win-rate margins in multiple settings. Remarkably, EVPA requires only $1$\%-$2$\% of the solving time to reach an approximate Nash equilibrium compared to DeepStack's replication.

Theory · Deep Learning

Tokio Kajitsuka, Issei Sato

Recent research in the field of machine learning has increasingly focused on the memorization capacity of Transformers, but how efficient they are is not yet well understood.We demonstrate that Transformers can memorize labels with $\tilde{O}(\sqrt{N})$ parameters in a next-token prediction setting for $N$ input sequences of length $n$, which is proved to be optimal up to logarithmic factors.This indicates that Transformers can efficiently perform memorization with little influence from the input length $n$ owing to the benefit of parameter sharing.We also analyze the memorization capacity in the sequence-to-sequence setting, and find that $\tilde{O}(\sqrt{nN})$ parameters are not only sufficient, but also necessary at least for Transformers with hardmax.These results suggest that while self-attention mechanisms can efficiently identify input sequences, the feed-forward network becomes a bottleneck when associating a label to each token.

Theory · Deep Learning

Robert Ganian, Mathis Rocton, Simon Wietheger

We initiate the study of the computational complexity of training graph neural networks (GNNs). We consider the classical node classification setting; there, the intractability of training multidimensonal GNNs immediately follows from known lower bounds for training classical neural networks (and holds even for trivial GNNs). However, one-dimensional GNNs form a crucial case of interest: the computational complexity of training such networks depends on both the graphical structure of the network and the properties of the involved activation and aggregation functions. As our main result, we establish the NP-hardness of training ReLU-activated one-dimensional GNNs via a highly non-trivial reduction. We complement this result with algorithmic upper bounds for the training problem in the ReLU-activated and linearly-activated settings.

Probabilistic Methods · Everything Else

Siddharth Swaroop, Mohammad Emtiyaz Khan, Finale Doshi-Velez

We provide new connections between two distinct federated learning approaches based on (i) ADMM and (ii) Variational Bayes (VB), and propose new variants by combining their complementary strengths. Specifically, we show that the dual variables in ADMM naturally emerge through the "site" parameters used in VB with isotropic Gaussian covariances. Using this, we derive two versions of ADMM from VB that use flexible covariances and functional regularisation, respectively. Through numerical experiments, we validate the improvements obtained in performance. The work shows connection between two fields that are believed to be fundamentally different and combines them to improve federated learning.

Probabilistic Methods · Monte Carlo and Sampling Methods

Denis Blessing, Xiaogang Jia, Gerhard Neumann

Diffusion models optimized via variational inference (VI) have emerged as a promising tool for generating samples from unnormalized target densities. These models create samples by simulating a stochastic differential equation, starting from a simple, tractable prior, typically a Gaussian distribution. However, when the support of this prior differs greatly from that of the target distribution, diffusion models often struggle to explore effectively or suffer from large discretization errors. Moreover, learning the prior distribution can lead to mode-collapse, exacerbated by the mode-seeking nature of reverse Kullback-Leibler divergence commonly used in VI.To address these challenges, we propose end-to-end learnable Gaussian mixture priors (GMPs). GMPs offer improved control over exploration, adaptability to target support, and increased expressiveness to counteract mode collapse. We further leverage the structure of mixture models by proposing a strategy to iteratively refine the model through the addition of mixture components during training. Our experimental results demonstrate significant performance improvements across a diverse range of real-world and synthetic benchmark problems when using GMPs without requiring additional target evaluations.

Probabilistic Methods · Bayesian Models and Methods

Pankaj Bhagwat, Linglong Kong, Bei Jiang

Conformal prediction has emerged as a popular technique for facilitating valid predictive inference across a spectrum of machine learning models, under minimal assumption of exchangeability. Recently, Hoff (2023) showed that full conformal Bayes provides the most efficient prediction sets (smallest by expected volume) among all prediction sets that are valid at the $(1 - \alpha)$ level if the model is correctly specified. However, a critical issue arises when the Bayesian model itself may be mis-specified, resulting in prediction interval that might be suboptimal, even though it still enjoys the frequentist coverage guarantee. To address this limitation, we propose an innovative solution that combines Bayesian model averaging (BMA) with conformal prediction. This hybrid not only leverages the strengths of Bayesian conformal prediction but also introduces a layer of robustness through model averaging. Theoretically, we prove that the resulting prediction interval will converge to the optimal level of efficiency, if the true model is included among the candidate models. This assurance of optimality, even under potential model uncertainty, provides a significant improvement over existing methods, ensuring more reliable and precise uncertainty quantification.

Reinforcement Learning · Planning

Jan Robine, Marc Höftmann, Stefan Harmeling

What are the essential components of world models? How far do we get with world models that are not employing RNNs, transformers, discrete representations, and image reconstructions? This paper introduces SGF, a Simple, Good, and Fast world model that uses self-supervised representation learning, captures short-time dependencies through frame and action stacking, and enhances robustness against model errors through data augmentation. We extensively discuss SGF’s connections to established world models, evaluate the building blocks in ablation studies, and demonstrate good performance through quantitative comparisons on the Atari 100k benchmark. The code is available at https://github.com/jrobine/sgf.

Reinforcement Learning · Deep RL

Zhenghai Xue, Bo An, Shuicheng YAN

We introduce AGSA, an Agent-Gated Shared Autonomy framework that learns from high-level human feedback to tackle the challenges of reward-free training, safe exploration, and imperfect low-level human control. Recent human-in-the loop learning methods enable human participants to intervene a learning agent’s control and provide online demonstrations. Nonetheless, these methods rely heavily on perfect human interactions, including accurate human-monitored intervention decisions and near-optimal human demonstrations. AGSA employs a dedicated gating agent to determine when to switch control, thereby reducing the need of constant human monitoring. To obtain a precise and foreseeable gating agent, AGSA trains a long-term gating value function from human evaluative feedback on the gating agent’s intervention requests and preference feedback on pairs of human intervention trajectories. Instead of relying on potentially suboptimal human demonstrations, the learning agent is trained using control-switching signals from the gating agent. We provide theoretical insights on performance bounds that respectively describe the ability of the two agents. Experiments are conducted with both simulated and real human participants at different skill levels in challenging continuous control environments. Comparative results highlight that AGSA achieves significant improvements over previous human-in-the-loop learning methods in terms of training safety, policy performance, and user-friendliness.

Optimization · Non-Convex

Sixin Zhang

We study min-max algorithms to solve zero-sum differential games onRiemannian manifold.Based on the notions ofdifferential Stackelberg equilibriumand differential Nash equilibrium on Riemannian manifold,we analyze the local convergence of two representative deterministic simultaneous algorithms $\tau$-GDA and $\tau$-SGAto such equilibria.Sufficient conditions are obtained to establish the linear convergence rateof $\tau$-GDA based on the Ostrowski theorem on manifold and spectral analysis. To avoid strong rotational dynamics in $\tau$-GDA, $\tau$-SGA is extended fromthe symplectic gradient-adjustment method in Euclidean space.We analyze an asymptotic approximation of $\tau$-SGA when the learning rate ratio $\tau$ is big. In some cases, it can achieve a faster convergence rate to differential Stackelberg equilibrium compared to $\tau$-GDA. We show numerically how the insights obtained from theconvergence analysis may improvethe training of orthogonal Wasserstein GANs using stochastic $\tau$-GDA and $\tau$-SGA on simple benchmarks.

Optimization · Non-Convex

Dimitris Oikonomou, Nicolas Loizou

Sharpness-Aware Minimization (SAM) has emerged as a powerful method for improving generalization in machine learning models by minimizing the sharpness of the loss landscape. However, despite its success, several important questions regarding the convergence properties of SAM in non-convex settings are still open, including the benefits of using normalization in the update rule, the dependence of the analysis on the restrictive bounded variance assumption, and the convergence guarantees under different sampling strategies. To address these questions, in this paper, we provide a unified analysis of SAM and its unnormalized variant (USAM) under one single flexible update rule (Unified SAM), and we present convergence results of the new algorithm under a relaxed and more natural assumption on the stochastic noise. Our analysis provides convergence guarantees for SAM under different step size selections for non-convex problems and functions that satisfy the Polyak-Lojasiewicz (PL) condition (a non-convex generalization of strongly convex functions). The proposed theory holds under the arbitrary sampling paradigm, which includes importance sampling as special case, allowing us to analyze variants of SAM that were never explicitly considered in the literature. Experiments validate the theoretical findings and further demonstrate the practical effectiveness of Unified SAM in training deep neural networks for image classification tasks.

Deep Learning · Everything Else

Ashish Kumar, Jaesik Park

In the era of vision Transformers, the recent success of VanillaNet shows the hugepotential of simple and concise convolutional neural networks (ConvNets). Wheresuch models mainly focus on runtime, it is also crucial to simultaneously focuson other aspects, e.g., FLOPs, parameters, etc, to strengthen their utility further.To this end, we introduce a refreshing ConvNet macro design called ColumnarStage Network (CoSNet). CoSNet has a systematically developed simple andconcise structure, smaller depth, low parameter count, low FLOPs, and attention-less operations, well suited for resource-constrained deployment. The key noveltyof CoSNet is deploying parallel convolutions with fewer kernels fed by inputreplication, using columnar stacking of these convolutions, and minimizing the useof 1×1 convolution layers. Our comprehensive evaluations show that CoSNet rivalsmany renowned ConvNets and Transformer designs under resource-constrainedscenarios. Pretrained models shall be open-sourced.

Deep Learning · Everything Else

Vladimir Boza, Vladimir Macko

Neural networks are often challenging to work with due to their large size and complexity. To address this, various methods aim to reduce model size by sparsifying or decomposing weight matrices, such as magnitude pruning and low-rank or block-diagonal factorization. In this work, we present Double Sparse Factorization (DSF), where we factorize each weight matrix into two sparse matrices. Although solving this problem exactly is computationally infeasible, we propose an efficient heuristic based on alternating minimization via ADMM that achieves state-of-the-art results, enabling unprecedented sparsification of neural networks. For instance, in a one-shot pruning setting, our method can reduce the size of the LLaMA2-13B model by 50% while maintaining better performance than the dense LLaMA2-7B model. We also compare favorably with Optimal Brain Compression, the state-of-the-art layer-wise pruning approach for convolutional neural networks. Furthermore, accuracy improvements of our method persist even after further model fine-tuning.Code available at: https://github.com/usamec/double_sparse

Deep Learning · Sequential Models, Time series

T. Konstantin Rusch, Daniela Rus

We propose Linear Oscillatory State-Space models (LinOSS) for efficiently learning on long sequences. Inspired by cortical dynamics of biological neural networks, we base our proposed LinOSS model on a system of forced harmonic oscillators. A stable discretization, integrated over time using fast associative parallel scans, yields the proposed state-space model. We prove that LinOSS produces stable dynamics only requiring nonnegative diagonal state matrix. This is in stark contrast to many previous state-space models relying heavily on restrictive parameterizations. Moreover, we rigorously show that LinOSS is universal, i.e., it can approximate any continuous and causal operator mapping between time-varying functions, to desired accuracy. In addition, we show that an implicit-explicit discretization of LinOSS perfectly conserves the symmetry of time reversibility of the underlying dynamics. Together, these properties enable efficient modeling of long-range interactions, while ensuring stable and accurate long-horizon forecasting. Finally, our empirical results, spanning a wide range of time-series tasks from mid-range to very long-range classification and regression, as well as long-horizon forecasting, demonstrate that our proposed LinOSS model consistently outperforms state-of-the-art sequence models. Notably, LinOSS outperforms Mamba and LRU by nearly 2x on a sequence modeling task with sequences of length 50k.

Deep Learning · Theory

Ouns El Harzli, Bernardo Grau

We study Bayesian neural networks (BNNs) in the theoretical limits of infinitely increasing number of training examples, network width and input space dimension. Our findings establish new bridges between kernel-theoretic approaches and techniques derived from statistical mechanics through the correspondence between Mercer's eigenvalues and limiting spectral distributions of covariance matrices studied in random matrix theory. Our theoretical contributions first consist in novel integral formulas that accurately describe the predictors of BNNs in the asymptotic linear-width and sublinear-width regimes. Moreover, we extend the recently developed renormalisation theory of deep linear neural networks, enabling a rigorous explanation of the mounting empirical evidence that hints at the theory's applicability to nonlinear BNNs with ReLU activations in the linear-width regime. From a practical standpoint, our results introduce a novel technique for estimating the predictor statistics of a trained BNN that is applicable to the sublinear-width regime where the predictions of the renormalisation theory are inaccurate.

Deep Learning · Self-Supervised Learning

Yongwei Che, Benjamin Eysenbach

While internet-scale data often come in pairs (e.g., audio+image, image+text), we often want to perform inferences over modalities unseen together in the training data (e.g., audio+text). Prior work has addressed this issue by learning multiple contrastive embedding spaces between existing modality pairs, implicitly hoping that unseen modality pairs will end up being aligned. This theoretical paper proves that this hope is well founded, under certain assumptions. Starting with the proper Bayesian approach of integrating out intermediate modalities, we show that directly comparing the representations of data from unpaired modalities can recover the same likelihood ratio. Our analysis builds on prior work on the geometry and probabilistic interpretation of contrastive representations, showing how these representations can answer many of the same inferences as probabilistic graphical models. Our analysis suggests two new ways of using contrastive representations: in settings with pre-trained contrastive models, and for handling language ambiguity in reinforcement learning. Our numerical experiments study the importance of our assumptions and demonstrate these new applications.

Deep Learning · Robustness

Yan Scholten, Stephan Günnemann

Conformal prediction provides model-agnostic and distribution-free uncertainty quantification through prediction sets that are guaranteed to include the ground truth with any user-specified probability. Yet, conformal prediction is not reliable under poisoning attacks where adversaries manipulate both training and calibration data, which can significantly alter prediction sets in practice. As a solution, we propose reliable prediction sets (RPS): the first efficient method for constructing conformal prediction sets with provable reliability guarantees under poisoning. To ensure reliability under training poisoning, we introduce smoothed score functions that reliably aggregate predictions of classifiers trained on distinct partitions of the training data. To ensure reliability under calibration poisoning, we construct multiple prediction sets, each calibrated on distinct subsets of the calibration data. We then aggregate them into a majority prediction set, which includes a class only if it appears in a majority of the individual sets. Both proposed aggregations mitigate the influence of datapoints in the training and calibration data on the final prediction set. We experimentally validate our approach on image classification tasks, achieving strong reliability while maintaining utility and preserving coverage on clean data. Overall, our approach represents an important step towards more trustworthy uncertainty quantification in the presence of data poisoning.

Deep Learning · Robustness

Varun Mulchandani, Jung-Eun Kim

Deep neural networks have been shown to learn and rely on spurious correlations present in the data that they are trained on. Reliance on such correlations can cause these networks to malfunction when deployed in the real world, where these correlations may no longer hold. To overcome the learning of and reliance on such correlations, recent studies propose approaches that yield promising results. These works, however, study settings where the strength of the spurious signal is significantly greater than that of the core, invariant signal, making it easier to detect the presence of spurious features in individual training samples and allow for further processing. In this paper, we identify new settings where the strength of the spurious signal is relatively weaker, making it difficult to detect any spurious information while continuing to have catastrophic consequences. We also discover that spurious correlations are learned primarily due to only a handful of all the samples containing the spurious feature and develop a novel data pruning technique that identifies and prunes small subsets of the training data that contain these samples. Our proposed technique does not require inferred domain knowledge, information regarding the sample-wise presence or nature of spurious information, or human intervention. Finally, we show that such data pruning attains state-of-the-art performance on previously studied settings where spurious information is identifiable.

Deep Learning · Robustness

Bing Sun, Jun Sun, Wei Zhao

Despite their advances and success, real-world deep neural networks are known to be vulnerable to adversarial attacks. Universal adversarial perturbation, an input-agnostic attack, poses a serious threat for them to be deployed in security-sensitive systems. In this case, a single universal adversarial perturbation deceives the model on a range of clean inputs without requiring input-specific optimization, which makes it particularly threatening. In this work, we observe that universal adversarial perturbations usually lead to abnormal entropy spectrum in hidden layers, which suggests that the prediction is dominated by a small number of ``feature'' in such cases (rather than democratically by many features). Inspired by this, we propose an efficient yet effective defense method for mitigating UAPs called \emph{Democratic Training} by performing entropy-based model enhancement to suppress the effect of the universal adversarial perturbations in a given model. \emph{Democratic Training} is evaluated with 7 neural networks trained on 5 benchmark datasets and 5 types of state-of-the-art universal adversarial attack methods. The results show that it effectively reduces the attack success rate, improves model robustness and preserves the model accuracy on clean samples.

Deep Learning · Other Representation Learning

Benjamin Vandersmissen, Lucas Deckers, Jose Oramas

Recently within Spiking Neural Networks, a method called Twin Network Augmentation (TNA) has been introduced. This technique claims to improve the validation accuracy of a Spiking Neural Network simply by training two networks in conjunction and matching the logits via the Mean Squared Error loss. In this paper, we validate the viability of this method on a wide range of popular Convolutional Neural Network (CNN) benchmarks and compare this approach to existing Knowledge Distillation schemes. Next, we conduct a in-depth study of the different components that make up TNA and determine that its effectiveness is not solely situated in an increase of trainable parameters, but rather the effect of the training methodology. Finally, we analyse the representations learned by networks trained with TNA and highlight their superiority in a number of tasks, thus proving empirically the applicability of Twin Network Augmentation on CNN models.