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General Machine Learning · Scalable Algorithms

Shuo Ji, Jie Hu, Zhouqiao He, Zijie Zhao, Tianrui Li, Jie Xu

Computation overhead has emerged as a critical bottleneck in Federated Learning (FL). Coreset selection tackles this challenge by constructing an informative subset to represent the full dataset. However, existing approaches optimize coreset construction solely at the data level and enforce a uniform retention ratio across all clients, ignoring client heterogeneity and introducing detrimental fragmented clients. In this paper, we first introduce a *gradient projection Shapley value* (GPSV) to evaluate client contributions. GPSV captures both the directional and magnitude information of client updates and enables exact Shapley value calculation with $\mathcal{O}(1)$ per-coalition evaluation. Building on GPSV, we then propose ShapCCS, the first client-level coreset selection strategy for FL. ShapCCS prioritizes clients with high GPSV scores while excluding fragmented clients with negligible or even negative GPSV. As a client-level coreset selection strategy, ShapCCS can be integrated with a data-level selection approach, and additionally reduces communication costs, an advantage unattainable by data-level methods alone. Extensive experiments demonstrate the superiority of ShapCCS on model performance and robustness to noise. The code is available at https://anonymous.4open.science/r/ShapCCS-5CBB.

Deep Learning · Algorithms

Hang Zhou, Haixu Wu, Haonan Shangguan, Yuezhou Ma, Huikun Weng, Jianmin Wang, Mingsheng Long

Deep learning has emerged as a transformative tool for the neural surrogate modeling of partial differential equations (PDEs), known as neural PDE solvers. However, scaling these solvers to industrial-scale geometries with over $10^8$ cells remains a fundamental challenge due to the prohibitive memory complexity of processing high-resolution meshes. We present Transolver-3, a new member of the Transolver family as a highly scalable framework designed for high-fidelity physics simulations. To bridge the gap between limited GPU capacity and the resolution requirements of complex engineering tasks, we introduce two key architectural optimizations: faster slice and deslice by exploiting matrix multiplication associative property and geometry slice tiling to partition the computation of physical states. Combined with an amortized training strategy by learning on random subsets of original high-resolution meshes and a physical state caching technique during inference, Transolver-3 enables high-fidelity field prediction on industrial-scale meshes. Extensive experiments demonstrate that Transolver-3 is capable of handling meshes with over 160 million cells, achieving impressive performance across three challenging simulation benchmarks, including aircraft and automotive design tasks.

Social Aspects · Fairness

Minh Phu Vuong, Jinyoung Lee, Young-Ju Lee, Chul-Ho Lee

Fair graph clustering has emerged as a critical research area for addressing algorithmic bias in machine learning. The objective is to ensure that the proportion of each protected group within a cluster is consistent with its representation in the entire dataset. However, most existing spectral solutions rely on computationally expensive eigendecompositions of the graph Laplacian, limiting their scalability. In this paper, we propose Riemannian Fair Spectral Clustering (R-FairSC), a novel method that formulates fair spectral clustering as a constrained optimization problem on a Riemannian manifold. We develop a Riemannian alternating direction method of multipliers employing a variable-splitting strategy to efficiently solve the associated subproblems. Numerical experiments on large synthetic and real-world graphs demonstrate that R-FairSC significantly improves computational efficiency over state-of-the-art methods while maintaining high clustering quality and fairness.

General Machine Learning · Scalable Algorithms

Khai Nguyen

Sliced optimal transport (SOT), or sliced Wasserstein (SW) distance, is widely recognized for its statistical and computational scalability. In this work, we further enhance computational scalability by proposing the first method for estimating SW from sample streams, called streaming sliced Wasserstein (Stream-SW). To define Stream-SW, we first introduce a streaming estimator of the one-dimensional Wasserstein distance (1DW). Since the 1DW has a closed-form expression, given by the absolute difference between the quantile functions of the compared distributions, we leverage quantile approximation techniques for sample streams to define a streaming 1DW estimator. By applying the streaming 1DW to all projections, we obtain Stream-SW. The key advantage of Stream-SW is its low memory complexity while providing theoretical guarantees on the approximation error. We demonstrate that Stream-SW achieves a more accurate approximation of SW than random subsampling, with lower memory consumption, when comparing Gaussian distributions and mixtures of Gaussians from streaming samples. Additionally, we conduct experiments on point cloud classification, point cloud gradient flows, and streaming change point detection to further highlight the favorable performance of the proposed Stream-SW.

Optimization · Non-Convex

Jingni Song, Jiawei Huang, Kangke Cheng, Bangxian Han, Hu Ding

The Gromov-Wasserstein (GW) distance provides a powerful framework for aligning structured data by comparing the intrinsic geometries of metric measure spaces, and has become a fundamental tool in machine learning. Most existing methods leverage entropy regularization to reduce the computational complexity to $\boldsymbol{\mathrm{O}}(n^3)$, where $n$ is the number of samples. However, this cubic time complexity remains a major bottleneck in large-scale applications, severely limiting the scalability. To address this challenge, we propose LoBCD-GW, an efficient GW optimization algorithm. Specifically, we reveal the data-dependent sparsity of large-magnitude updates to the coupling matrix and introduce a localized block coordinate selection strategy. This confines the optimization to a "selected set" of size $r$ (which is a parameter that depends on the given data set, and usually is much less than $n$), thereby reducing the complexity to $\boldsymbol{\mathrm{O}}(r^3)$. In addition, unlike prior acceleration methods often based on constraint relaxation, our method can guarantee the strict feasibility through a novel "marginal compensation mechanism" to synchronize local mass redistribution with global constraints. Finally, we conduct a set of experiments on various datasets, and the results demonstrate that our method achieves a $160\times$ speedup on large-scale graph alignment benchmarks, while maintaining state-of-the-art accuracy.

Probabilistic Methods · Monte Carlo and Sampling Methods

Youguang Chen, George Biros

Independent Metropolis–Hastings (IMH) algorithms are widely used in Bayesian inference, but their efficiency deteriorates when proposal distributions are constructed from inaccurate or approximate models. We introduce Proximal-IMH, an IMH method that enhances proposal distributions through a proximal posterior correction. Given an approximate posterior sample, each proposal is generated by minimizing a quadratically regularized surrogate objective, producing a local correction that balances fidelity to the exact model with stability around the approximate state. We analyze the resulting proposals from an optimization and probabilistic perspective, showing how the proximal correction improves alignment between approximate and exact posteriors and leads to improved acceptance and mixing behavior. The proposed framework applies to both linear and nonlinear forward operators, and is particularly well suited to Bayesian inverse problems where exact posterior sampling is computationally prohibitive. Numerical experiments on inverse problems with approximate forward models, including nonlinear operators, demonstrate that Proximal-IMH consistently outperforms existing IMH variants while retaining their simplicity and scalability.

Reinforcement Learning · Planning

Zergham Ahmed, Josh Tenenbaum, Chris Bates, Samuel Gershman

Modern reinforcement learning (RL) systems have demonstrated remarkable capabilities in complex environments, such as video games. However, they still fall short of achieving human-like sample efficiency and adaptability when learning new domains. Theory-based reinforcement learning (TBRL) is an algorithmic framework specifically designed to address this gap. Modeled on cognitive theories, TBRL leverages structured, causal world models---``theories''---as forward simulators for use in planning, generalization and exploration. Although current TBRL systems provide compelling explanations of how humans learn to play video games, they face several technical limitations: their theory languages are restrictive, and their planning algorithms are not scalable. To address these challenges, we introduce TheoryCoder, an instantiation of TBRL that exploits hierarchical representations of theories and efficient program synthesis methods for more powerful learning and planning. TheoryCoder equips agents with general-purpose abstractions (e.g., ``move to''), which are then grounded in a particular environment by learning a low-level transition model (a Python program synthesized from observations by a large language model). A bilevel planning algorithm can exploit this hierarchical structure to solve large domains. We demonstrate that this approach can be successfully applied to diverse and challenging grid-world games, where approaches based on directly synthesizing a policy perform poorly. Ablation studies demonstrate the benefits of using hierarchical abstractions.

Peter Potaptchik, Lee Kit, Michael Albergo

We propose a simple, scalable algorithm based on stochastic interpolants for sampling from unnormalized densities and for fine-tuning generative models. The approach, Tilt Matching, arises from a dynamical equation relating the flow matching velocity to one targeting the same distribution tilted by a reward, implicitly solving a stochastic optimal control problem. The resulting velocity inherits the regularity of stochastic interpolant transports while minimizing an objective with strictly lower variance than flow matching itself. The update to the velocity field can be interpreted as the sum of all joint cumulants between the interpolant velocity and the reward, and to first order is their covariance. The method requires neither reward gradients nor backpropagation through trajectories of the flow or diffusion. We empirically demonstrate that the approach is efficient and highly scalable, providing state-of-the-art results on sampling under Lennard-Jones systems and competitive performance for fine-tuning Stable Diffusion, without requiring reward multipliers. The framework also applies directly to tilting few-step flow map models.

Applications · Computer Vision

George Webber, Alexander Denker, Riccardo Barbano, Andrew Reader

Flow-based generative models provide strong unconditional priors for inverse problems, but guiding their dynamics for conditional generation remains challenging. Recent work casts training-free conditional generation in flow models as an optimal control problem; however, solving the resulting trajectory optimisation is computationally and memory intensive, requiring differentiation through the flow dynamics or adjoint solves. We propose MPC-Flow, a model predictive control framework that formulates inverse problem solving with flow-based generative models as a sequence of control sub-problems, enabling practical optimal control-based guidance at inference time. We provide theoretical guarantees linking MPC-Flow to the underlying optimal control objective and show how different algorithmic choices yield a spectrum of guidance algorithms, including regimes that avoid backpropagation through the generative model trajectory. We evaluate MPC-Flow on benchmark image restoration tasks, spanning linear and non-linear settings such as in-painting, deblurring, and super-resolution, and demonstrate strong performance and scalability to massive state-of-the-art architectures via training-free guidance of FLUX.2 (32B) in a quantised setting on consumer hardware.

Applications · Chemistry, Physics, and Earth Sciences

Jiwoong Kim, Jongwon Lee, Sungwoo Park

We introduce Euler–Poincaré Neural Dynamics (EPND), a geometric-mechanics–driven framework that redefines how Koopman-type neural models learn dynamical systems. Unlike conventional operator-learning methods that rely on function-space linearization, EPND places geometric mechanics at the core of its architecture the mathematical engine governing evolution through Lie-group flows. This foundation enables a principled treatment of curvature, symmetry, and conservation, that ensures both interpretability and physical consistency. Building on this foundation, we develop the Euler–Poincaré Parallel Scan, a parallel algorithm that leverages the associative algebra of Lie-group compositions to overcome the inefficiencies of sequential computation. By unifying geometric structure with scalable computation, EPND achieves high accuracy, strong stability, and significant parallel acceleration in modeling long-horizon dynamics of versatile scientific simulation.

Applications · Chemistry, Physics, and Earth Sciences

Jiwoong Kim, Jongwon Lee, Jungwoo Park, Sungwoo Park

We present a Lie-algebraic approach to model Koopman dynamics that integrates algebraic structure with computational scalability. The proposed formulation constrains the neural generators to evolve within prescribed Lie subalgebras and constructs finite-time flows through a neural Magnus expansion construction, thereby maintaining consistency with the associated Lie-group composition over each time segment. To address the computational burden inherent in sequential propagation, we exploit the associativity of Lie-group compositions and construct segmentwise propagators via a prefix-scan algorithm, which reduces the depth of temporal composition from linear to logarithmic. Consequently, the framework enables accurate long-horizon prediction while improving computational efficiency, and provides a principled foundation for scalable Koopman operator learning for nonlinear systems.

Deep Learning · Theory

Viktoriia Chekalina, Daniil Moskovskiy, Tatyana Matveeva, Andrey Kuznetsov, Evgeny Frolov

The Fisher Information Matrix (FIM) provides a principled geometric framework for parameter sensitivity in neural networks, but directly computing and using the full FIM is infeasible in high-dimensional models. As a result, most existing methods rely on diagonal approximations that discard important correlation structure. We introduce Matrix-free Fisher Factorization (MFF), a GPU-tractable algorithm that captures both diagonal and off-diagonal dependencies without materializing the full matrix. For post-training neural network layer compression, we prove that under Matrix-Variate Normal assumptions, MFF yields GFWSVD, a unique closed-form linear layer decomposition that optimally minimizes the expected second-order loss increase. Experiments on controlled numerical benchmarks with large neural networks show that GFWSVD achieves up to 50\% compression while matching or exceeding state-of-the-art diagonal and activation-based baselines across most tasks, and it reliably avoids collapse in dense architectures such as Llama 3. Moreover, when used to initialize existing optimization pipelines (e.g., Dobi-SVD), GFWSVD better preserves accuracy at 40\% parameter reduction in regimes where standard methods substantially degrade. Together, these results position MFF and GFWSVD as foundational algorithmic primitives for scalable, second-order-aware neural network approximation and parameter sensitivity.

Deep Learning · Algorithms

Benhao Huang, Zhengyang Geng, Zico Kolter

Reasoning is central to building intelligent systems that can solve unseen problems beyond training. Yet we still lack a principled understanding of what internal mechanism enables neural networks to generalize reasoning beyond memorized patterns. We hypothesize that generalizable reasoning emerges through learning task-conditioned attractors. Concretely, the model learns a latent dynamical system whose fixed points correspond to valid solutions. We term models that reason by converging to such task-conditioned fixed points *Equilibrium Reasoners (EqR)*. This attractor view elucidates when and how to scale test-time compute. Empirically, improvements from scaling test-time compute are tightly coupled with convergence to attractors. By shaping a more favorable attractor landscape and leveraging stochasticity, EqR improves convergence and scales reliably at test time. Our models scale along two axes: *depth* by running more solver steps, and *width* by aggregating stochastic trajectories from multiple random initializations. As we scale test-time compute by $8192\times$, with max effective layers surpassing 300,000 layers when unrolled, reasoning accuracy rises from 8\% to over 99\% on Sudoku-Extreme. We hope our attractor perspective sheds light on scalable reasoning through test-time computation.

Optimization · Zero-order and Black-box Optimization

Yukun Du, Haiyue Yu, Jiang Jiang, Shuaiwen Tang, Xiaotong Xie, Haobo Liu, Chongshuang Hu, Shengkun Chang

Existing Meta-Black-Box Optimization (MetaBBO) methods focus on how to search when controlling optimizers, but largely overlook where to search. We propose MetaSG-SAEA, a bi-level MetaBBO framework for expensive constrained multi-objective optimization problems (ECMOPs), in which a meta-policy provides search guidance to the low-level Surrogate-Assisted Evolutionary Algorithm (SAEA). To achieve this, we introduce Max–Min Constraint-Calibrated Inequality (MM-CCI), a compact, problem-agnostic region abstraction that maps heterogeneous constraint evaluations to an ordered scalar level; we further provide a theoretical analysis of its fundamental properties. Building on this region abstraction, we adopt diffusion-based population initialization to translate the meta-policy’s region-level guidance into solution-level priors for the SAEA. To make MetaSG-SAEA scalable, we construct an attention-based state representation across varying problem dimensions, population sizes, and numbers of objectives and constraints. Experimental results demonstrate that MetaSG-SAEA outperforms state-of-the-art baselines across diverse benchmarks and exhibits the ability to generalize across problem distributions.

Theory · Optimization

Deyi Kong, Zaiwei Chen, Shuzhong Zhang, Shancong Mou

In this work, we propose *Natural Hypergradient Descent* (NHGD), a new method for solving bilevel optimization problems. To address the computational bottleneck in hypergradient estimation—namely, the need to compute or approximate Hessian inverses—we exploit the statistical structure of the inner optimization problem and use the empirical Fisher information matrix as an asymptotically consistent surrogate for the Hessian. This design enables a parallel *optimize-and-approximate* framework in which the Hessian-inverse approximation is updated *synchronously* with the stochastic inner optimization, reusing gradient information at negligible additional cost. Our main theoretical contribution establishes high-probability error bounds and sample complexity guarantees for NHGD that match those of state-of-the-art optimize-then-approximate methods, while significantly reducing computational time overhead. Empirical evaluations on representative bilevel learning tasks further demonstrate the practical advantages of NHGD, highlighting its scalability and effectiveness in large-scale machine learning settings.

Reinforcement Learning · Batch/Offline

Da Wang, Yi Ma, Ting Guo, Lin Li, Wei Wei, Jiye Liang

Generalization remains a central challenge in offline reinforcement learning (RL), where policies are trained solely from static datasets and must perform reliably under distribution shift. While most existing offline RL methods focus on reducing training loss using standard optimizers such as Adam, the role of loss landscape geometry $-$ particularly sharpness $-$ has received little attention. Sharpness-Aware Minimization (SAM) has recently shown strong generalization benefits in supervised learning by favoring flatter minima. However, directly applying SAM to offline RL is non-trivial: unlike supervised settings with ground-truth labels, offline RL relies on bootstrapped targets, making sharpness estimation noisy and often destabilizing optimization. In this paper, we revisit offline RL from an optimization perspective and investigate how sharpness-aware optimization can be made effective in this setting. We propose Q bound weighted SAM (Q-SAM), a robust and scalable framework that treats sharpness as a weighted objective and selectively prioritizes samples that are most suitable for sharpness-aware optimization based on Q bounds. By aligning the SAM objective with the characteristics of bootstrapped value estimation, Q-SAM amplifies the benefits of sharpness minimization while preserving training stability. Extensive experiments on standard offline RL benchmarks demonstrate that Q-SAM consistently improves generalization performance across diverse datasets and algorithms. Our results highlight the importance of loss sharpness in offline RL and suggest optimizer design as a promising direction for developing more robust offline RL methods.

Social Aspects · Accountability, Transparency, and Interpretability

Andrea Marzo, Alessio Ragno, Roberto Capobianco

Reinforcement learning (RL) has achieved remarkable success across complex decision-making tasks, especially with the advent of deep neural networks. However, the resulting models are often opaque, making their deployment in safety-critical domains challenging. Explainable AI aims to address this issue, but most specific efforts for deep RL remain limited either to post-hoc explanation methods or to imitation learning and distillation procedures. These latter approaches rely on pre-trained black-box agents and are typically restricted to environments with discrete action spaces, limiting their scalability and interpretability. In this paper, we introduce ProtoSAC, a novel deep RL architecture that integrates a prototype-based actor into the Soft Actor-Critic (SAC) algorithm, enabling intrinsic interpretability in continuous action spaces. Our method learns a set of prototypes that represent interpretable state clusters, each associated with a Gaussian action distribution. Actions are generated as a similarity-weighted mixture over these prototypes, providing transparent decision-making without sacrificing performance. We evaluate ProtoSAC on continuous action-space environments and show that it matches the performance of the original SAC while offering enhanced interpretability.

Optimization · Discrete and Combinatorial Optimization

Bin Chen, Shouliang Zhu, Beidan Liu, Yong Zhao, Tianle Pu, Huichun Li, Zhengqiu Zhu

Designing heuristics for combinatorial optimization problems (COPs) is a fundamental yet challenging task that traditionally requires extensive domain expertise. Recently, Large Language Model (LLM)-based Automated Heuristic Design (AHD) has shown promise in autonomously generating heuristic components with minimal human intervention. However, most existing LLM-based AHD methods enforce fixed algorithmic templates to ensure executability, which confines the search to component-level tuning and limits system-level algorithmic expressiveness. To enable open-ended solver synthesis beyond rigid templates, we propose Automated Algorithm Design via Evolutionary Program Trees (A$_2$DEPT), which treats LLMs as system-level algorithm architects. A$_2$DEPT explores the vast program space via a tree-structured evolutionary search with \textit{hybrid selection} and \textit{hierarchical operators}, enabling iterative refinement of complete algorithms. To make open-ended generation practical, we enforce executability with a lightweight program-maintenance loop that performs feedback-driven repair. In experiments, A$_2$DEPT consistently outperforms state-of-the-art baselines across standard and highly constrained benchmarks, reducing the optimality gap by an average of 9.8\%. Our work implies that system-level algorithm synthesis is a viable and scalable paradigm for LLM-driven optimization.

Social Aspects · Privacy

Toan Tran, Arturs Backurs, Zinan Lin, Victor Reis, Li Xiong, Sergey Yekhanin

This paper investigates the problem of generating synthetic tabular data with differential privacy (DP) guarantees, enabling data sharing in sensitive domains. Despite extensive study, state-of-the-art methods often focus on minimizing low-order marginal query errors and overlook the challenges posed by high-order correlations. To address this gap, we extend the Private Evolution (PE) framework, originally developed for DP-compliant image and text synthesis, to tabular data. We introduce Tab-PE -- an algorithm for synthetic tabular data generation under DP constraints. Tab-PE iteratively improves a candidate dataset via an evolutionary process that leverages tabular-specialized operators to produce variations, privately scores them, and selects the highest-quality samples to retain and propagate. In contrast to the original PE, which relies on large foundation models, Tab-PE employs heuristic operators with significantly lower computational costs, makes PE more practical and scalable for tabular data. Through extensive experiments on real-world and simulation datasets, we demonstrate that Tab-PE substantially outperforms prior baselines on datasets exhibiting high-order correlations. Compared to the best baseline -- AIM, Tab-PE improves classification accuracy by up to 10\% while running 28$\times$ faster.

Social Aspects · Privacy

Alireza Khayatian, Anil Vullikanti, Aritra Konar

Computing the principal component (PC) of the adjacency matrix of an undirected graph has several applications ranging from identifying key vertices for influence maximization and controlling diffusion processes, to discovering densely interconnected vertex subsets. However, many networked datasets are sensitive, which necessitates private computation of the PC for use in the aforementioned applications. Differential privacy has emerged as the gold standard in privacy-preserving data analysis, but existing DP algorithms for private PC suffer from low accuracy due to large noise injection or high complexity. Motivated by the large gap between the local and global sensitivities of the PC on real-graphs, we consider instance-specific mechanisms for privately computing the PC under edge-DP. These mechanisms guarantee privacy for all datasets, but provide good utility on ``well-behaved'' datasets by injecting smaller amounts of noise. More specifically, we consider the Propose-Test-Release (PTR) framework. Although computationally expensive in general, we design a novel approach for implementing a PTR variant in the same time as computation of a non-private PC, while offering good utility. Our framework tests in a differentially-private manner whether a given graph is ``well-behaved'' or not, and then tests whether its private to release a noisy PC with small noise. As a consequence, this also leads to the first DP algorithm for the Densest-$k$-subgraph problem, a key graph mining primitive. We run our method on diverse real-world networks, with the largest having 3 million vertices, and compare its utility to a pre-existing baseline based on the private power method (PPM). Although PTR requires a slightly larger privacy budget, on average, it achieves a 180-fold improvement in runtime over PPM.