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General Machine Learning · Everything Else

Baptiste Ferrere, Nicolas Bousquet, Gamboa Fabrice, Jean-Michel Loubes, Joseph Muré

Functional ANOVA offers a principled framework for interpretability by decomposing a model’s prediction into main effects and higher-order interactions. For independent features, this decomposition is well-defined, strongly linked with SHAP values, and serves as a cornerstone of additive explainability. However, the lack of an explicit closed-form expression for general dependent distributions has forced practitioners to rely on costly sampling-based approximations. We completely resolve this limitation for categorical inputs. By bridging functional analysis with the extension of discrete Fourier analysis, we derive a closed-form decomposition without any assumption. Our formulation is computationally very efficient. It seamlessly recovers the classical independent case and extends to arbitrary dependence structures, including distributions with non-rectangular support. Furthermore, leveraging the intrinsic link between SHAP and ANOVA under independence, our framework yields a natural generalization of SHAP values for the general categorical setting.

Deep Learning · Robustness

Yao Ni, Jeremie Houssineau, Yew Soon ONG, Piotr Koniusz

Deep neural networks achieve impressive results across diverse applications, yet their overconfidence on unseen inputs necessitates reliable epistemic uncertainty modelling. Existing methods for uncertainty modelling face a fundamental dilemma: Bayesian approaches provide principled estimates but remain computationally prohibitive, while efficient second-order predictors lack rigorous derivations connecting their specific objectives to epistemic uncertainty quantification. To resolve this dilemma, we introduce **D**irichlet-**a**pproximated **p**ossibilistic **p**osterior p**r**edictions (DAPPr), a principled framework leveraging possibility theory. We define a possibilistic posterior over parameters, projects this posterior to the prediction space via supremum operators, and approximates the projected posterior using learnable Dirichlet possibility functions. This projection-and-approximation strategy yields a simple training objective with closed-form solutions. Extensive experiments across diverse benchmarks demonstrate that our approach achieves competitive or superior uncertainty quantification performance compared to state-of-the-art evidential deep learning methods while maintaining both principled derivation and computational efficiency. Code will be available upon acceptance.

Applications · Computer Vision

Guangze Shi, Yingjie Mi, Jia Shen, Feixue Shao, Jiarui Cao, Yexin Lai, Xueyu Liu, Rui Wang, Yongfei Wu, Mingqiang Wei

Optimizing prompts for foundation models like SAM represents a challenging high-dimensional black-box optimization problem, fundamentally plagued by the credit assignment ambiguity. To address this, we introduce PromptPilot, a task-agnostic reinforcement learning framework that structurally decomposes the search space into orthogonal semantic and spatial subspaces. Specifically, a centralized manager orchestrates two specialized agents, a feature agent ensuring semantic coherence and a physical agent maximizing spatial coverage, to navigate conflicting optimization objectives. Crucially, our reward mechanism synergizes global segmentation feedback with an efficient approximation of Shapley values, enabling fine-grained attribution of performance gains to individual prompt actions. PromptPilot functions as an inference-time optimization strategy without parameter updates. Extensive experiments demonstrate that our game-theoretic approach significantly improves segmentation performance and generalization, offering a principled solution for automated prompt engineering.

Deep Learning · Large Language Models

Hen Davidov, Nachshon Cohen, Oren Kalinsky, Yaron Fairstein, Guy Kushilevitz, Ram Yazdi, Patrick Rebeschini

Large language models (LLMs) using chain-of-thought reasoning often waste substantial compute by producing long, incorrect responses. Abstention can mitigate this by withholding outputs unlikely to be correct. While most abstention methods decide to withhold outputs before or after generation, dynamic mid-generation abstention considers early termination of unpromising reasoning traces at each token position. Prior work has explored empirical variants of this idea, but principled guidance for the abstention rule remains lacking. We present a formal analysis of dynamic abstention for LLMs, modeling abstention as an explicit action within a regularized reinforcement learning framework. An abstention reward parameter controls the trade-off between compute and information. We show that abstaining when the value function falls below this reward strictly outperforms natural baselines under general conditions. We further derive a principled and efficient method to approximate the value function. Empirical results on mathematical reasoning tasks support our theory and demonstrate improved selective accuracy over existing methods.

Social Aspects · Accountability, Transparency, and Interpretability

Yixin Wang, Yucheng Dong

Local post-hoc explanations are widely used to understand black-box models on tabular data, with Local Interpretable Model-agnostic Explanations (LIME) being a popular approach. LIME approximates a black-box model using a sparse linear surrogate in a local neighborhood, implicitly assuming feature-wise linear homogeneity. However, this assumption often fails when local feature effects exhibit heterogeneous or nonlinear behaviors, resulting in unfaithful and unstable explanations. Moreover, LIME relies on a decoupled feature selection procedure that is not aligned with the surrogate modeling objective, further exacerbating instability under local sampling. To address these limitations, we propose PL-LIME, a two-stage sparse local explanation framework that ensures objective consistency across stages. PL-LIME models feature-wise local effects using instance-anchored piecewise linear functions, providing a minimal yet principled extension beyond linear surrogates under a fixed explanation budget. Sparsity is enforced through a decoupled nonnegative shrinkage procedure that directly scales the estimated local effects, improving stability while preserving interpretability. Experiments on synthetic and real-world datasets demonstrate that PL-LIME achieves higher local fidelity and stability, and provides more reliable local explanations that capture finer-grained local effect structures than LIME.

Deep Learning · Everything Else

Vincent Bürgin, Daniel Herbst, Ya-Wei Eileen Lin, Stefanie Jegelka

Many striking phenomena in deep learning, such as linear mode connectivity and the structured behavior of training dynamics, are closely tied to parameter symmetries: transformations that leave the realized function unchanged. Despite growing attention to structural parameter symmetries, the exact interplay between parameters, data, and representations remains underexplored. To investigate this, we develop a theoretical framework of effective function classes defined by the neurons' induced functions restricted to the representation subspace. We then formalize *effective symmetry breaking* via neuron identifiability across independent training runs. Our analysis shows that neural networks can admit large families of approximately equivalent solutions even in *structurally asymmetric* models. This allows us to disentangle the effects of data-specific and architectural symmetries. We further show that neuron identifiability enables representation merging *without prior alignment*, and characterize when such merging admits a linear low-loss connecting path. These findings highlight the role of effective function classes in affecting the loss landscape.

Deep Learning · Theory

Akshay Kumar, Jarvis Haupt

This paper studies the gradient flow dynamics that arise when training deep homogeneous neural networks assumed to have locally Lipschitz gradients and an order of homogeneity strictly greater than two. It is shown here that for sufficiently small initializations, during the early stages of training, the weights of the neural network remain small in (Euclidean) norm and approximately converge in direction to the Karush-Kuhn-Tucker (KKT) points of the recently introduced neural correlation function. Additionally, this paper also studies the KKT points of the neural correlation function for feed-forward networks with (Leaky) ReLU and polynomial (Leaky) ReLU activations, deriving necessary and sufficient conditions for rank-one KKT points.

General Machine Learning · Online Learning, Active Learning and Bandits

Mengtong Hu, Ziyang Gong, Xu Shi, Ling Zhou, Peter Song

Online learning for the Cox model is challenging because its partial likelihood is non-decomposable, with each risk set requiring a summation over all samples. We propose Collaborative Operation of Linked Survival Analysis (COLSA), an online learning framework that replaces the partial likelihood with the full likelihood using sieve approximation of the baseline hazard. The proposed likelihood function is decomposable and eliminates the need to store historical data in memory, enabling efficient online updates. Moreover, COLSA maintains sufficient statistics for a higher-order basis and employs data-driven basis projection to adaptively scale model complexity to the effective sample size. Unlike existing online Cox methods, COLSA achieves asymptotic normality and attains the same statistical efficiency as the pooled-data partial likelihood estimator, without accessing full data and only requiring constant memory. Simulation studies and application to kidney transplant data demonstrate that COLSA outperforms existing online methods and matches the performance of full-data estimation.

Deep Learning · Theory

Fares Mehouachi, Saif Jabari

Neural operators learn mappings between function spaces, enabling fast PDE surrogates. Despite architectural diversity, these methods often share a common input representation: raw coordinate-value pairs. This ignores the differential structure that defines the underlying physics. We study whether derivative features can improve neural operator learning. Through Picard iteration on mild solutions, we show that derivatives of the input naturally enter PDE solution operators, and we prove that providing them improves approximation rates substantially. But the optimal derivative order is not what one might expect. We show that the statistically optimal order is strictly less than the PDE order, for any finite sample size. This gap arises from a bias-variance tradeoff: higher-order derivatives carry more information but amplify noise. We characterize this tradeoff in closed form and show that learning the derivative order from data achieves automatic spectral regularization. We introduce $\partial$-NO (derivative-augmented neural operators), a simple augmentation that provides learnable fractional derivative features to any neural operator backbone. Across benchmarks, this consistently improves accuracy. Learned orders reflect dominant PDE structure while adapting to finite-sample constraints, confirming the theory.

Social Aspects · Alignment

Natalie Collina, Surbhi Goel, Aaron Roth, Emily Ryu, Mirah Shi

Aligning AI systems with human values remains a fundamental challenge, but does our inability to create perfectly aligned models preclude obtaining the benefits of alignment? We study a strategic setting where a human user interacts with multiple differently misaligned AI agents, none of which are individually well-aligned. Our key insight is that when the user’s utility lies approximately within the convex hull of the agents’ utilities, a condition that becomes easier to satisfy as model diversity increases, strategic competition can yield outcomes comparable to interacting with a perfectly aligned model. We model this as a multi-leader Stackelberg game, extending Bayesian persuasion to multi-round conversations between differently informed parties, and prove three results: (1) when perfect alignment would allow the user to learn her Bayes-optimal action, she can also do so in all equilibria under the convex hull condition; (2) under weaker assumptions requiring only approximate utility learning, a non-strategic user employing quantal response achieves near-optimal utility in all equilibria; and (3) when the user selects the best single AI after an evaluation period, equilibrium guarantees remain near-optimal without further distributional assumptions. We complement the theory with two forms of empirical evidence: First, we perform simulations of the best-AI selection game using best response dynamics, which show that competition among individually misaligned agents reliably improves user utility when the approximate convex hull assumption is satisfied, but does not always when it fails. Second, we show that synthetically generated AI utility functions (produced via perturbations of the same prompt to evaluate instances on a movie recommendation (MovieLens) and ethical judgement (ETHICS) dataset) quickly produce a convex hull that contains a good approximation of a given utility function even when none of the individual LLM utility functions is well aligned. We show that this phenomenon extends to human and LLM responses on real-world polling data (OpinionQA): a convex hull of LLM opinions can approximate human opinions more accurately than any individual LLM across a wide range of survey questions.

Social Aspects · Privacy

Yvonne Zhou, Mingyu Liang, Ivan Brugere, Danial Dervovic, Yue Guo, Antigoni Polychroniadou, Min Wu, Dana Dachman-Soled

We present the first theoretical convergence analysis of machine learning training under fully homomorphic encryption (FHE), combined with a differentially private (DP) training algorithm tailored to encrypted computation. Our approach improves computational efficiency over standard differentially private gradient descent (DP-GD) while achieving comparable utility. In particular, we prove convergence of approximate gradient descent using polynomial approximations of activation and loss functions, which are required for FHE compatibility. To preserve privacy in downstream tasks, we integrate differential privacy without relying on costly per-sample gradient clipping, enabling scalable encrypted learning. We also provide data-independent hyperparameter selection and theoretically grounded strategies for polynomial approximation which can be of independent interest. Together, these contributions advance the feasibility of efficient, private, and secure machine learning on sensitive data.

Social Aspects · Privacy

Ron Zadicario, Tova Milo

Submodular maximization subject to a knapsack constraint (SMK) is a fundamental problem in discrete optimization, with wide-ranging applications in machine learning and related fields. As these applications increasingly involve sensitive individual data, there is a growing need for high-utility algorithms that provide formal privacy guarantees. In this work, we study the SMK problem under differential privacy, considering both monotone and non-monotone objective functions. For monotone objectives, we propose a differentially private algorithm that achieves the optimal $(1-1/e)$-approximation ratio while significantly improving both additive error and query complexity over prior work. We also present a more efficient variant attaining a $1/2$-approximation. For non-monotone objectives, we introduce, to our knowledge, the first differentially private algorithm with provable guarantees, achieving a $1/4$-approximation in expectation and an additive error comparable to the best known for monotone objectives.

Deep Learning · Generative Models and Autoencoders

Rouzoumka Yadang Alexis, Jean Pinsolle, Eugénie TERREAUX, christele morisseau, Jean-Philippe Ovarlez, Chengfang Ren

Diffusion models learn a time-indexed score field $\mathbf{s}_\theta(\mathbf{x}_t,t)$ that often inherits approximate equivariances (flips, rotations, circular shifts) from in-distribution (ID) data and convolutional backbones. Most diffusion-based out-of-distribution (OOD) detectors exploit score magnitude or local geometry (energies, curvature, covariance spectra) and largely ignore equivariances. We introduce Group-Equivariant Posterior Consistency (GEPC), a training-free probe that measures how consistently the learned score transforms under a finite group $G$, detecting equivariance breaking even when score magnitude remains unchanged. At the population level, we propose the ideal GEPC residual which averages an equivariance-residual functional over $G$, and we derive ID upper bounds and OOD lower bounds under mild assumptions. GEPC requires only score evaluations and produces interpretable equivariance-breaking maps. On OOD image benchmark datasets, we show that GEPC achieves competitive or improved AUROC compared to recent diffusion-based baselines while remaining computationally lightweight. On high-resolution synthetic aperture radar imagery where OOD corresponds to targets or anomalies in clutter, GEPC yields strong target-background separation and visually interpretable equivariance-breaking maps.

Deep Learning · Everything Else

Ozan Candogan, Ayoub Foussoul

We introduce Deep Flow Networks (DFNs), a new class of discrete function approximators. DFNs are inspired by and generalize minimum-cost flow value functions that map node imbalances on a subset of nodes to the optimal flow cost. Such functions are known to be M-convex (Murota2003) and admit efficient optimization. On the theoretical side, we prove that DFNs are universal approximators for discrete functions on $\mathbb{Z}^d$ that admit convex extensions to $\mathbb{R}^d$, and characterize their optimization complexity in terms of their deviation from the M-convex regime. Guided by these results, we develop a practical DFN implementation for learning from data. Finally, we evaluate our implementation empirically on data from different ground-truth functions, showing that DFNs achieve strong approximation accuracy while being substantially faster to optimize than benchmark approaches.

Deep Learning · Large Language Models

Jeffrey T. H. Wong, Cheng Zhang, Xinye Cao, Pedro Gimenes, Christos-Savvas Bouganis, George Constantinides, Wayne Luk, Aaron Zhao

Large language models have demonstrated remarkable performance; however, their massive parameter counts make deployment highly expensive. Low-rank approximation offers a promising compression solution, yet existing approaches have two main limitations: (1) They focus on minimizing the output error of individual linear layers, without considering the architectural characteristics of Transformers, and (2) they decompose a large weight matrix into two small low-rank matrices. Consequently, these methods often fall short compared to other compression techniques like pruning and quantization, and introduce runtime overhead such as the extra GEMM kernel launches and memory operations for decomposed small matrices. To address these limitations, we propose $A^3$, a post-training low-rank approximation framework. $A^3$ splits a Transformer layer into three functional components, namely $\texttt{QK}$, $\texttt{OV}$, and $\texttt{MLP}$ and provides analytical solutions that reduces the hidden dimension size inside each component while minimizing the component's functional loss. This approach directly reduces model sizes, KV cache sizes, and FLOPs without introducing any runtime overheads. Through extensive experiments, we show that $A^3$ maintains superior performance compared to SoTAs. For example, under the same reduction budget in computation and memory, our low-rank approximated LLaMA 3.1-70B achieves a perplexity of 4.69 on WikiText-2, outperforming the previous SoTA's 7.87 by 3.18. We also show versatile applications of $A^3$ in KV cache compression, integration with quantization, fine-tuning and mixed-rank assignments.

Theory · Reinforcement Learning and Planning

Onno Eberhard, Claire Vernade, Michael Muehlebach

Theoretical properties of reinforcement learning algorithms are most commonly studied under the Markov assumption. This is unrealistic, as most environments encountered in practice are either partially observable, or require function approximation that restricts the agent to access non-Markovian state features. We consider the problem of learning an optimal reactive policy in a finite environment under deterministic observations (or equivalently, hard state aggregation). We introduce a new algorithm, _Committed Q-learning_, and prove almost sure convergence to the optimal reactive policy under an intuitive assumption we call _rewire-robustness_. This assumption is strictly weaker than the $q_\star$-realizability condition used in prior work. Our algorithm is a variant of classical Q-learning in which the behavior policy commits to a single action upon entering a feature, and only resamples actions when the observed feature changes.

Theory · Online Learning and Bandits

Dhruv Sarkar, Abhishek Sinha

We propose an anytime online algorithm for learning a sequence of convex cost functions while approximately satisfying a sequence of convex constraints, without prior knowledge of the time horizon. Both the cost and constraint functions may be chosen adversarially over time. While this problem has recently been resolved in the setting where the time horizon is known, extending these guarantees to the anytime setting, without resorting to inefficient doubling tricks, has remained technically challenging. Our main contribution is the introduction of a time-varying yet horizon-oblivious Lyapunov function to track constraint violations. The use of such a time-varying Lyapunov function introduces new technical difficulties, as a key monotonicity property underlying prior analyses no longer holds. By developing a novel analytical technique, we show that our algorithm achieves $O(\sqrt{t})$ \regret~ and $\tilde{O}(\sqrt{t})$ cumulative constraint violation (\CCV) for all $t \geq 1$. We further extend our framework to the dynamic regret setting, obtaining bounds that adapt to the unknown path length of the comparator sequence. Finally, we present an adaptive algorithm for the optimistic setting, whose performance scales gracefully with the cumulative prediction error. We validate the practical effectiveness of our approach through numerical experiments on the online shortest path problem.

Deep Learning · Algorithms

Hong-Kun Zhang, Xin Li, Sikun Yang, Zhihong Xia

A novel neural network inspired by Cauchy's integral formula, is proposed for function approximation tasks that include time series forecasting, missing data imputation, etc. Hence, the novel neural network is named CauchyNet. By embedding real-valued data into the complex plane, CauchyNet efficiently captures complex temporal dependencies, surpassing traditional real-valued models in both predictive performance and computational efficiency. Grounded in Cauchy's integral formula and supported by the universal approximation theorem, CauchyNet offers strong theoretical guarantees for function approximation. The architecture incorporates complex-valued activation functions, enabling robust learning from incomplete data while maintaining a compact parameter footprint and reducing computational overhead. Through extensive experiments in diverse domains, including transportation, energy consumption, and epidemiological data, CauchyNet consistently outperforms state-of-the-art models in predictive accuracy, often achieving a lower mean absolute error with fewer parameters. These findings highlight CauchyNet’s potential as an effective and efficient tool for data-driven predictive modeling, particularly in resource-constrained and data-scarce environments. The code used to reproduce the results will be released upon the publication.

Reinforcement Learning · Online

Debamita Ghosh, George Atia, Yue Wang

Reinforcement learning (RL) in real-world tasks often suffers from the performance degradation due to the distribution shift between training and deployment environments. Distributionally Robust RL (DR-RL) addresses this issue by optimizing the worst-case performance over an uncertainty set of transition dynamics, providing an optimized baseline performance upon deployment. However, existing methods typically require strong data access assumptions (e.g., a generative model or comprehensive offline datasets) and mostly focus on tabular settings. In this paper, we introduce a purely online DR-RL algorithm with general function approximation that learns a robust policy directly from interaction, without any prior knowledge or pre-collected data. Our method uses a dual-based fitted robust Bellman update to jointly learn the value function and the robust backup operator. We establish the first regret guarantee for online DR-RL in terms of an intrinsic complexity measure—the robust Bellman–Eluder (BE) dimension, for general $\phi$-divergence uncertainty sets. Our regret bound is sublinear and independent of $|\mathcal{S}|$ and $|\mathcal{A}|$, and recovers sharp rates in structured regimes, providing a scalable method for practical DR-RL.

Social Aspects · Accountability, Transparency, and Interpretability

Fabian Fumagalli, Landon Butler, Justin S. Kang, Kannan Ramchandran, R. Teal Witter

The Shapley value is a ubiquitous framework for attribution in machine learning, encompassing feature importance, data valuation, and causal inference. However, its exact computation is generally intractable, necessitating efficient approximation methods. While the most effective and popular estimators leverage the *paired sampling* heuristic to reduce estimation error, the theoretical mechanism driving this improvement has remained opaque. In this work, we provide an elegant and fundamental justification for paired sampling: we prove that the Shapley value depends *exclusively* on the odd component of the set function, and that paired sampling orthogonalizes the regression objective to filter out the irrelevant even component. Leveraging this insight, we propose OddSHAP, a novel consistent estimator that performs polynomial regression solely on the odd subspace. By utilizing the Fourier basis to isolate this subspace and employing a proxy model to identify high-impact interactions, OddSHAP overcomes the combinatorial explosion of higher-order approximations. Through an extensive benchmark evaluation, we find that OddSHAP achieves state-of-the-art estimation accuracy.