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Social Aspects · Accountability, Transparency and Interpretability

Shuangqi Li, Hieu Le, Jingyi Xu, Mathieu Salzmann

We study gradient-based data attribution, aiming to identify which training examples most influence a given output. Existing methods for this task either treat network parameters uniformly or rely on implicit weighting derived from Hessian approximations, which do not fully model functional heterogeneity of network parameters. To address this, we propose a method to explicitly learn parameter importance weights directly from data, without requiring annotated labels. Our approach improves attribution accuracy across diverse tasks, including image classification, language modeling, and diffusion, and enables fine-grained attribution for concepts like subject and style.

Deep Learning · Generative Models and Autoencoders

Vaishnavi Patil, Siddhi Patil, Matthew Evanusa, Amit Kumar Kundu, Cornelia Fermuller, Joseph JaJa

Disentangled representation learning aims to identify and organize the underlying sources of variation in observed data. However, learning disentangled representations from observational data alone without any additional supervision necessitates inductive biases to solve the fundamental identifiability problem of uniquely recovering the true latent structure and parameters of the data-generating process. Existing methods address this by imposing heuristic inductive biases that typically lack these theoretical identifiability guarantees. Additionally, these methods rely on strong regularization to impose these inductive biases, creating an inherent trade-off in which stronger regularization improves disentanglement but limits the latent capacity to represent underlying variations. To address both challenges, we propose a principled generative model with a Bayesian nonparametric hierarchical mixture prior that embeds inductive biases within a provably identifiable framework for unsupervised disentanglement. Specifically, the hierarchical mixture prior imposes the structural constraints necessary for identifiability guarantees, while the nonparametric formulation allows the latent representation to scale with infinite capacity to faithfully represent the complete set of underlying variations without violating these structural constraints. To enable tractable inference under this nonparametric hierarchical prior, we develop a structured variational inference framework with a nested variational family that both preserves the hierarchical structure of the identifiable generative model and approximates the expressiveness of the nonparametric prior. We evaluate our proposed probabilistic model on standard disentanglement benchmarks, 3DShapes and MPI3D datasets characterized by diverse source variation distributions, to demonstrate that our method consistently outperforms strong baseline models through structural biases and a unified objective function, obviating the need for auxiliary regularization constraints or careful hyperparameter tuning.

Deep Learning · Algorithms

Mara Daniels, Philippe Rigollet

We introduce a highly expressive class of function approximators called *Splat Regression Models*. Model outputs are mixtures of heterogeneous and anisotropic bump functions, termed *splats*, each weighted by an output vector. The power of splat modeling lies in its ability to locally adjust the scale and direction of each splat, achieving both high interpretability and accuracy. Fitting splat models reduces to optimization over the space of mixing measures, which can be implemented using Wasserstein-Fisher-Rao gradient flows. As a byproduct, we recover the popular *Gaussian Splatting* methodology as a special case, providing a unified theoretical framework for this state-of-the-art technique that clearly disambiguates the inverse problem, the model, and the optimization algorithm. Through numerical experiments, we demonstrate that the resulting models and algorithms constitute a flexible and promising approach for solving diverse approximation, estimation, and inverse problems involving low-dimensional data.

Deep Learning · Generative Models and Autoencoders

Roman Tarasov, Petr Mokrov, Milena Gazdieva, Evgeny Burnaev, Aleksandr Korotin

Neural network-based optimal transport (OT) is a recent and fruitful direction in the generative modeling community. It finds its applications in various fields such as domain translation, image super-resolution, computational biology and others. Among the existing OT approaches, of considerable interest are adversarial minimax solvers based on semi-dual formulations of OT problems. While promising, these methods lack theoretical investigation from a statistical learning perspective. Our work fills this gap by establishing upper bounds on the generalization error of an approximate OT map recovered by the minimax quadratic OT solver. Importantly, the bounds we derive depend solely on some standard statistical and mathematical properties of the considered functional classes (neural nets). While our analysis focuses on the quadratic OT, we believe that similar bounds could be derived for general OT case, paving the promising direction for future research. Our experimental illustrations are available online https://github.com/milenagazdieva/StatOT.

Deep Learning · Algorithms

Sergey Pozdnyakov, Philippe Schwaller

High-dimensional linear mappings, or linear layers, dominate both the parameter count and the computational cost of most modern deep-learning models. We introduce a general-purpose drop-in replacement, lookup multivariate Kolmogorov-Arnold Networks (lmKANs), which deliver a substantially better trade-off between capacity and inference cost. Our construction expresses a general high-dimensional mapping through trainable low-dimensional multivariate functions. These functions can carry dozens or hundreds of trainable parameters each, and yet it takes only a few multiplications to compute them because they are implemented as spline lookup tables. Empirically, lmKANs reduce inference FLOPs by up to 6.0× while matching the flexibility of MLPs in general high-dimensional function approximation. In another feedforward fully connected benchmark, on the tabular-like dataset of randomly displaced methane configurations, lmKANs enable more than 10× higher H100 throughput at equal accuracy. Within the framework of Convolutional Neural Networks, lmKAN-based CNNs cut inference FLOPs at matched accuracy by 1.6–2.1× and by 1.7× on the CIFAR-10 and ImageNet-1k datasets, respectively. Our code, including dedicated CUDA kernels, is available online at https://github.com/schwallergroup/lmkan.

Social Aspects · Accountability, Transparency and Interpretability

Fabian Fumagalli, R. Teal Witter, Christopher Musco

Shapley values have emerged as a central game-theoretic tool in explainable AI (XAI). However, computing Shapley values exactly requires $2^d$ game evaluations for a model with $d$ features. Lundberg and Lee's KernelSHAP algorithm has emerged as a leading method for avoiding this exponential cost. KernelSHAP approximates Shapley values by approximating the game as a linear function, which is fit using a small number of game evaluations for random feature subsets. In this work, we extend KernelSHAP by approximating the game via higher degree polynomials, which capture non-linear interactions between features. Our resulting PolySHAP method yields empirically better Shapley value estimates for various benchmark datasets, and we prove that these estimates are consistent. Moreover, we connect our approach to paired sampling (antithetic sampling), a ubiquitous modification to KernelSHAP that improves empirical accuracy. We prove that paired sampling outputs exactly the same Shapley value approximations as second-order PolySHAP, without ever fitting a degree 2 polynomial. To the best of our knowledge, this finding provides the first strong theoretical justification for the excellent practical performance of the paired sampling heuristic.

Social Aspects · Fairness, Equity, Justice and Safety

Jihu Lee, Kunwoong Kim, Sehyun Park, Insung Kong, Dongyoon Yang, Yongdai Kim

With the growing importance of trustworthy AI, algorithmic fairness has emerged as a critical concern. Among various fairness notions, group fairness - which measures the model bias between sensitive groups - has received significant attention. While many group-fair models have focused on satisfying group fairness constraints, model uncertainty has received relatively little attention, despite its importance for robust and trustworthy decision-making. To address this, we adopt a Bayesian framework to capture model uncertainty in fair model training. We first define group-fair posterior distributions and then introduce a fair variational Bayesian inference. Then we propose a novel distribution termed matched Gibbs posterior, as a proxy distribution for the fair variational Bayesian inference by employing a new group fairness measure, the matched deviation. A notable feature of matched Gibbs posterior is that it approximates the posterior distribution well under the fairness constraint without requiring heavy computation. Theoretically, we show that the matched deviation has a strong relation to existing group fairness measures, highlighting desirable fairness guarantees. Computationally, by treating the matching function in the matched deviation as a learnable parameter, we develop an efficient MCMC algorithm. Experiments on real-world datasets demonstrates that matched Gibbs posterior outperforms other methods in balancing uncertainty–fairness and utility–fairness trade-offs, while also offering additional desirable properties.

Deep Learning · Graph Neural Networks

Jinwoo Kim, Xingyue Huang, Krzysztof Olejniczak, Kyungbin Min, Michael Bronstein, Seunghoon Hong, Ismail I Ceylan

We study the problem of zero-shot link prediction on knowledge graphs (KGs), which requires models to generalize to novel entities and novel relations. Knowledge graph foundation models (KGFMs) address this task by enforcing equivariance over both nodes and relations, which enables them to learn structural properties of nodes and relations that transfer to novel KGs with similar structure. However, the conventional notion of deterministic equivariance inherently limits the expressive power of KGFMs, as it prevents them from distinguishing relations that are structurally similar but semantically distinct. To overcome this limitation, we propose to leverage probabilistic node-relation equivariance, which preserves equivariance in distribution while using structured randomness to break symmetries at inference time. Building on this principle, we present Flock, a KGFM that iteratively samples random walks, encodes them into sequences, embeds them with a sequence model, and aggregates node and relation representations through learned pooling. Flock respects probabilistic node-relation equivariance and, crucially, is a universal approximator for isomorphism-invariant link-level functions over KGs. Empirically, Flock perfectly solves our new diagnostic dataset Petals on which current KGFMs fail, and achieves state-of-the-art performance on entity and relation prediction tasks across 54 KGs from diverse domains. Code is available at https://github.com/jw9730/flock.

Theory · Reinforcement Learning and Planning

Donghwan Lee, Hyukjun Yang, Bumgeun Park

There are two primary approaches to solving Markov decision problems (MDPs): dynamic programming based on the Bellman equation and linear programming (LP). Dynamic programming methods are the most widely used and form the foundation of both classical and modern reinforcement learning (RL). By contrast, LP-based methods have been less commonly employed, although they have recently gained attention in contexts such as offline RL. The relative underuse of the LP-based methods stems from the fact that it leads to an inequality-constrained optimization problem, which is generally more challenging to solve effectively compared with Bellman-equation-based methods. The purpose of this paper is to establish a theoretical foundation for solving LP-based MDPs in a more effective and practical manner. Our key idea is to leverage the log-barrier function, widely used in inequality-constrained optimization, to transform the LP formulation of the MDP into an unconstrained optimization problem. This reformulation enables approximate solutions to be obtained easily via gradient descent. While the method may appear naive, to the best of our knowledge, a thorough theoretical interpretation of this approach has not yet been developed. This paper aims to bridge this gap.

General Machine Learning · Transfer, Multitask and Meta-learning

Geonwoo Cho, Jaegyun Im, Jihwan Lee, Hojun Yi, Sejin Kim, Sundong Kim

Generalizing deep reinforcement learning agents to unseen environments remains a significant challenge. One promising solution is Unsupervised Environment Design (UED), a co‑evolutionary framework in which a teacher adaptively generates tasks with high learning potential, while a student learns a robust policy from this evolving curriculum. Existing UED methods typically measure learning potential via regret, the gap between optimal and current performance, approximated solely by value‑function loss. Building on these approaches, we introduce the transition-prediction error as an additional term in our regret approximation. To capture how training on one task affects performance on others, we further propose a lightweight metric called Co-Learnability. By combining these two measures, we present Transition‑aware Regret Approximation with Co‑learnability for Environment Design (TRACED). Empirical evaluations show that TRACED produces curricula that improve zero-shot generalization over strong baselines across multiple benchmarks. Ablation studies confirm that the transition-prediction error drives rapid complexity ramp‑up and that Co‑Learnability delivers additional gains when paired with the transition-prediction error. These results demonstrate how refined regret approximation and explicit modeling of task relationships can be leveraged for sample-efficient curriculum design in UED. https://geonwoo.me/traced

Theory · Reinforcement Learning and Planning

Denis Zorba, David Siska, Lukasz Szpruch

We prove the stability and global convergence of a coupled actor-critic gradient flow for infinite-horizon and entropy-regularised Markov decision processes (MDPs) in continuous state and action space with linear function approximation under Q-function realisability. We consider a version of the actor critic gradient flow where the critic is updated using temporal difference (TD) learning while the policy is updated using a policy mirror descent method on a separate timescale. For general action spaces, the relative entropy regularizer is unbounded and thus it is not clear a priori that the actor-critc flow does not suffer from finite-time blow-up. Therefore we first demonstrate stability which in turn enables us obtain a convergence rate of the actor critic flow to the optimal regularised value function. The arguments presented show that timescale separation is crucial for stability and convergence in this setting.

Alexandros Hollender, Sonja Kraiczy

Recent alignment methods for large language models, most notably reinforcement learning from human feedback (RLHF), often train an auxiliary reward model to minimize a loss function on binary preference data over model responses. We study a theoretical setting inspired by principle-guided methods such as Constitutional AI, in which a small set of principles (e.g., helpfulness, toxicity) act as “voters” that guide binary comparisons---such as preferring the less toxic response. We model these principles as linear directions in an embedding space of responses, a simplifying assumption motivated by the Linear Representation Hypothesis---concepts are linear directions in representation-space---a useful first-order approximation in practice. In this \emph{linear social choice model}, Ge et al. (2024) showed that an optimal linear reward model can violate Pareto optimality (PO): From the principles-as-voters lens, this means a response A can be less helpful and more toxic than B, yet still receive a higher reward. We analyze axiomatic violations in the linear social choice setting and probe the robustness of negative results under realistic assumptions. We show that added expressivity does not resolve the issue: polynomial reward models can still fail PO. We then offer a pragmatic alternative showing that when the data uniformly covers the embedding space, broad classes of loss-based rules in the limit exactly recover the axiomatic guarantees. This yields a recipe for constitutional-style alignment with provable guarantees: enforce balanced coverage \emph{via dataset design} to restore axiomatic guarantees without abandoning standard training pipelines.

General Machine Learning · Causality

Xiangkun Wu, Qianglin Wen, Yingying Zhang, Hongtu Zhu, Ting Li, Chengchun Shi

A/B testing has become a gold standard for modern technological companies to conduct policy evaluation. Yet, its application to time series experiments, where treatments are sequentially assigned over time, remains challenging. Existing designs suffer from two limitations: (i) they do not fully leverage the entire history for treatment allocation; (ii) they rely on strong assumptions to approximate the objective function (e.g., the mean squared error of the estimated treatment effect) for optimizing the design. We first establish an impossibility theorem showing that failure to condition on the full history leads to suboptimal designs, due to the dynamic dependencies in time series experiments. To address both limitations simultaneously, we next propose a transformer reinforcement learning (RL) approach which leverages transformers to condition treatment allocation on the entire history and employs RL to directly optimize the MSE without relying on restrictive assumptions. Empirical evaluations on synthetic data, a publicly available dispatch simulator, and a real-world ridesharing dataset demonstrate that our proposal consistently outperforms existing designs.

Deep Learning · Theory

Themistoklis Haris, Zihan Zhang, Yuichi Yoshida

Understanding simplicity biases in deep learning offers a promising path toward developing reliable AI. A common metric for this, inspired by Boolean function analysis, is average sensitivity, which captures a model's robustness to single-token perturbations. We argue that average sensitivity has two key limitations: it lacks a natural generalization to real-valued domains and fails to explain the "junta-like" input dependence we empirically observe in modern LLMs. To address these limitations, we propose *noise stability* as a more comprehensive simplicity metric. Noise stability expresses a model's robustness to correlated noise applied to *all* input coordinates simultaneously. We provide a theoretical analysis of noise stability for single-layer attention and ReLU MLP layers and tackle the multi-layer propagation problem with a covariance interval propagation approach. Building on this theory, we develop a practical *noise stability regularization* method. Experiments on algorithmic and next-token-prediction tasks show that our regularizer consistently catalyzes grokking and accelerates training by approximately $35$\% and $75$\% respectively. Our results establish noise stability as a powerful tool for understanding and improving modern Transformers.

Applications · Language, Speech and Dialog

Hongjue Zhao, Haosen Sun, Jiangtao Kong, Xiaochang Li, Qineng Wang, Liwei Jiang, Qi Zhu, Tarek Abdelzaher, Yejin Choi, Manling Li 等

Activation steering, or representation engineering, offers a lightweight approach to align large language models (LLMs) by manipulating their internal activations at inference time. However, current methods suffer from two key limitations: \textit{(i)} the lack of a unified theoretical framework for guiding the design of steering directions, and \textit{(ii)} an over-reliance on \textit{one-step steering} that fail to capture complex patterns of activation distributions. In this work, we propose a unified ordinary differential equations (ODEs)-based \textit{theoretical} framework for activation steering in LLM alignment. We show that conventional activation addition can be interpreted as a first-order approximation to the solution of an ODE. Based on this ODE perspective, identifying a steering direction becomes equivalent to designing a \textit{barrier function} from control theory. Derived from this framework, we introduce ODESteer, a kind of ODE-based steering guided by barrier functions, which shows \textit{empirical} advancement in LLM alignment. ODESteer identifies steering directions by defining the barrier function as the log-density ratio between positive and negative activations, and employs it to construct an ODE for \textit{multi-step and adaptive} steering. Compared to state-of-the-art activation steering methods, ODESteer achieves consistent empirical improvements on diverse LLM alignment benchmarks, a notable $5.7\%$ improvement over TruthfulQA, $2.5\%$ over UltraFeedback, and $2.4\%$ over RealToxicityPrompts. Our work establishes a principled new view of activation steering in LLM alignment by unifying its theoretical foundations via ODEs, and validating it empirically through the proposed ODESteer method.

Deep Learning · Algorithms

Sudong Cai, Shuyuan Zheng, Bingzhi Chen, Shuai Yuan, Chuan Xiao, Jianbin Qin, Bing WANG

Neural networks necessitate nonlinearities to achieve universal approximability. Traditional activation functions introduce nonlinearities through rigid feature rectifications. Recent self-gated variants improve traditional methods in fitting flexibility by incorporating learnable content-aware factors and non-local dependencies, enabling dynamic adjustments to activation curves via adaptive translation and scaling. While SOTA approaches achieve notable gains in conventional CNN layers, they struggle to enhance Transformer layers, where fine-grained context is inherently modeled, severely reducing the effectiveness of non-local dependencies leveraged in activation processes. We refer to this critical yet unexplored challenge as the **non-local tension** of activation. Drawing on a decision-making perspective, we systematically analyze the origins of the non-local tension problem and explore the initial solution to foster a more discriminative and generalizable neural activation methodology. This is achieved by rethinking how non-local cues are encoded and transformed into adaptive scaling coefficients, which in turn recalibrate the contributions of features to filter updates through neural activation. Grounded in these insights, we present **FleS**, a novel self-gated activation model for discriminative pattern recognition. Extensive experiments on various popular benchmarks validate our interpretable methodology for improving neural activation modeling.

Deep Learning · Generative Models and Autoencoders

Zeqi Ye, Qijie Zhu, Molei Tao, Minshuo Chen

Diffusion models have achieved remarkable success across diverse domains, but they remain vulnerable to memorization---reproducing training data rather than generating novel outputs. This not only limits their creative potential but also raises concerns about privacy and safety. While empirical studies have explored mitigation strategies, theoretical understanding of memorization remains limited. We address this gap through developing a dual-separation result via two complementary perspectives: statistical estimation and network approximation. From the estimation side, we show that the ground-truth score function does not minimize the empirical denoising loss, creating a separation that drives memorization. From the approximation side, we prove that implementing the empirical score function requires network size to scale with sample size, spelling a separation compared to the more compact network representation of the ground-truth score function. Guided by these insights, we develop a pruning-based method that reduces memorization while maintaining generation quality in diffusion transformers.

Reinforcement Learning · Function Approximation

Théo Vincent, Yogesh Tripathi, Tim Faust, Abdullah Akgül, Yaniv Oren, Melih Kandemir, Jan Peters, Carlo D Eramo

The use of target networks in deep reinforcement learning is a widely popular solution to mitigate the brittleness of semi-gradient approaches and stabilize learning. However, target networks notoriously require additional memory and delay the propagation of Bellman updates compared to an ideal target-free approach. In this work, we step out of the binary choice between target-free and target-based algorithms. We introduce a new method that uses a copy of the last linear layer of the online network as a target network, while sharing the remaining parameters with the up-to-date online network. This simple modification enables us to keep the target-free's low-memory footprint while leveraging the target-based literature. We find that combining our approach with the concept of iterated $Q$-learning, which consists of learning consecutive Bellman updates in parallel, helps improve the sample-efficiency of target-free approaches. Our proposed method, iterated Shared $Q$-Learning (iS-QL), bridges the performance gap between target-free and target-based approaches across various problems while using a single $Q$-network, thus stepping towards resource-efficient reinforcement learning algorithms.

Dhruva Karkada, Joseph Turnbull, Yuxi Liu, James Simon

We study kernel regression with common rotation-invariant kernels on real datasets including CIFAR-5m, SVHN, and ImageNet. We give a theoretical framework that predicts learning curves (test risk vs. sample size) from only two measurements: the empirical data covariance matrix and an empirical polynomial decomposition of the target function $f_*$. The key new idea is an analytical approximation of a kernel’s eigenvalues and eigenfunctions with respect to an anisotropic data distribution. The eigenfunctions resemble Hermite polynomials of the data, so we call this approximation the \textit{Hermite eigenstructure ansatz} (HEA). We prove the HEA for Gaussian data, but we find that real image data is often ``Gaussian enough’’ for the HEA to hold well in practice, enabling us to predict learning curves by applying prior results relating kernel eigenstructure to test risk. Extending beyond kernel regression, we empirically find that MLPs in the feature-learning regime learn Hermite polynomials in the order predicted by the HEA. Our HEA framework is a proof of concept that an end-to-end theory of learning which maps dataset structure all the way to model performance is possible for nontrivial learning algorithms on real datasets.

Reinforcement Learning · Deep RL

Théo Vincent, Daniel Palenicek, Boris Belousov, Jan Peters, Carlo D Eramo, Théo Vincent

The vast majority of Reinforcement Learning methods is largely impacted by the computation effort and data requirements needed to obtain effective estimates of action-value functions, which in turn determine the quality of the overall performance and the sample-efficiency of the learning procedure. Typically, action-value functions are estimated through an iterative scheme that alternates the application of an empirical approximation of the Bellman operator and a subsequent projection step onto a considered function space. It has been observed that this scheme can be potentially generalized to carry out multiple iterations of the Bellman operator at once, benefiting the underlying learning algorithm. However, until now, it has been challenging to effectively implement this idea, especially in high-dimensional problems. In this paper, we introduce iterated $Q$-Network (i-QN), a novel principled approach that enables multiple consecutive Bellman updates by learning a tailored sequence of action-value functions where each serves as the target for the next. We show that i-QN is theoretically grounded and that it can be seamlessly used in value-based and actor-critic methods. We empirically demonstrate the advantages of i-QN in Atari $2600$ games and MuJoCo continuous control problems.