NeurIPS 2025 论文列表

Solving bilevel optimization (BLO) problems to global optimality is generally intractable. A common surrogate is to compute a hyper-stationary point—a stationary point of the hyper-objective function obtained by minimizing or maximizing the upper-level objective over the lower-level solution set. Existing methods, however, either provide weak notions of stationarity or require restrictive assumptions to guarantee the smoothness of hyper-objective functions. In this paper, we eliminate these impractical assumptions and show that strong (Clarke) hyper-stationarity remains computable even when the hyper-objective is nonsmooth. Our key ingredient is a new structural property, called set smoothness, which captures the variational dependence of the lower-level solution set on the upper-level variable. We prove that this property holds for a broad class of BLO problems and ensures weak convexity (resp. concavity) of pessimistic (resp. optimistic) hyper-objective functions. Building on this foundation, we show that a zeroth-order algorithm that computes approximate Clarke hyper-stationary points with non-asymptotic convergence guarantees. To the best of our knowledge, this is the first computational guarantee for Clarke-type stationarity in nonsmooth BLO. Beyond this specific application, the set smoothness property emerges as a structural concept of independent interest, with potential to inform the analysis of broader classes of optimization and variational problems.

We propose KOALA++, a scalable Kalman-based optimization algorithm that explicitly models structured gradient uncertainty in neural network training. Unlike second-order methods, which rely on expensive second order gradient calculation, our method directly estimates the parameter covariance matrix by recursively updating compact gradient covariance products. This design improves upon the original KOALA framework that assumed diagonal covariance by implicitly capturing richer uncertainty structure without storing the full covariance matrix and avoiding large matrix inversions. Across diverse tasks, including image classification and language modeling, KOALA++ achieves accuracy on par or better than state-of-the-art second-order optimizers while maintaining the efficiency of first-order methods.

Recently, optimization on the Riemannian manifold have provided valuable insights to the optimization community. In this regard, extending these methods to to the Wasserstein space is of particular interest, since optimization on Wasserstein space is closely connected to practical sampling processes. Generally, the standard (continuous) optimization method on Wasserstein space is Riemannian gradient flow (i.e., Langevin dynamics when minimizing KL divergence). In this paper, we aim to enrich the family of continuous optimization methods in the Wasserstein space, by extending the gradient flow on it into the stochastic gradient descent (SGD) flow and stochastic variance reduction gradient (SVRG) flow. By leveraging the property of Wasserstein space, we construct stochastic differential equations (SDEs) to approximate the corresponding discrete Euclidean dynamics of the desired Riemannian stochastic methods. Then, we obtain the flows in Wasserstein space by Fokker-Planck equation. Finally, we establish convergence rates of the proposed stochastic flows, which align with those known in the Euclidean setting.

Speech signal analysis poses significant challenges, particularly in tasks such as speech quality evaluation and profiling, where the goal is to predict multiple perceptual and objective metrics. For instance, metrics like PESQ (Perceptual Evaluation of Speech Quality), STOI (Short-Time Objective Intelligibility), and MOS (Mean Opinion Score) each capture different aspects of speech quality. However, these metrics often have different scales, assumptions, and dependencies, making joint estimation non-trivial. To address these issues, we introduce ARECHO (Autoregressive Evaluation via Chain-based Hypothesis Optimization), a chain-based, versatile evaluation system for speech assessment grounded in autoregressive dependency modeling. ARECHO is distinguished by three key innovations: (1) a comprehensive speech information tokenization pipeline; (2) a dynamic classifier chain that explicitly captures inter-metric dependencies; and (3) a two-step confidence-oriented decoding algorithm that enhances inference reliability. Experiments demonstrate that ARECHO significantly outperforms the baseline framework across diverse evaluation scenarios, including enhanced speech analysis, speech generation evaluation, and noisy speech evaluation. Furthermore, its dynamic dependency modeling improves interpretability by capturing inter-metric relationships. Across tasks, ARECHO offers reference-free evaluation using its dynamic classifier chain to support subset queries (single or multiple metrics) and reduces error propagation via confidence-oriented decoding.

In this paper, we study an online strategic classification problem, where a principal aims to learn an accurate binary linear classifier from sequentially arriving agents. For each agent, the principal announces a classifier. The agent can strategically exercise costly manipulations on his features to be classified as the favorable positive class. The principal is unaware of the true feature-label distribution, but observes all reported features and only labels of positively classified agents. We assume that the true feature-label distribution is given by a halfspace model subject to arbitrary feature-dependent bounded noise (i.e., Massart Noise). This problem faces the combined challenges of agents' strategic feature manipulations, partial label observations, and label noises. We tackle these challenges by a novel learning algorithm. We show that the proposed algorithm yields classifiers that converge to the clairvoyant optimal one and attains a regret rate of $ O(\sqrt{T})$ up to poly-logarithmic and constant factors over $T$ cycles.

We analyze the global convergence of the single-timescale actor-critic (AC) algorithm for the infinite-horizon discounted Markov Decision Processes (MDPs) with finite state spaces. To this end, we introduce an elegant analytical framework for handling complex, coupled recursions inherent in the algorithm. Leveraging this framework, we establish that the algorithm converges to an $\epsilon$-close \textbf{globally optimal} policy with a sample complexity of $ O(\epsilon^{-3}) $. This significantly improves upon the existing complexity of $O(\epsilon^{-2})$ to achieve $\epsilon$-close \textbf{stationary policy}, which is equivalent to the complexity of $O(\epsilon^{-4})$ to achieve $\epsilon$-close \textbf{globally optimal} policy using gradient domination lemma. Furthermore, we demonstrate that to achieve this improvement, the step sizes for both the actor and critic must decay as $ O(k^{-\frac{2}{3}}) $ with iteration $k$, diverging from the conventional $O(k^{-\frac{1}{2}}) $ rates commonly used in (non)convex optimization.

The coordinated activity of neural populations underlies myriad brain functions. Manipulating this activity using brain stimulation techniques has great potential for scientific and clinical applications, as it provides a tool to causally influence brain function. To improve the accuracy by which one can manipulate neural activity, it is important to (1) take into account the pre-stimulation brain state, which can influence the brain’s response to stimulation, and (2) adaptively update stimulation parameters over time to compensate for changes in the brain’s response to stimulation. In this work, we propose Online MicroStimulation Optimization (OMiSO), a brain stimulation framework that leverages brain state information to find stimulation parameters that can drive neural population activity toward specified states. OMiSO includes two key advances: i) training a stimulation-response model that leverages the pre-stimulation brain state, and inverting this model to choose the stimulation parameters, and ii) updating this inverse model online using newly-observed responses to stimulation. We tested OMiSO using intracortical microstimulation with a ``Utah'' array and found that it outperformed competing methods that do not incorporate these advances. Taken together, OMiSO provides greater accuracy in achieving specified activity states, thereby advancing neuromodulation technologies for understanding the brain and for treating brain disorders.

Quantized training of Large Language Models (LLMs) remains an open challenge, as maintaining accuracy while performing all matrix multiplications in low precision has proven difficult. This is particularly the case when fine-tuning pre-trained models, which can have large weight, activation, and error (output gradient) outlier values that make lower-precision optimization difficult. To address this, we present HALO, a new quantization-aware training approach for Transformers that enables accurate and efficient low-precision training by combining 1) strategic placement of Hadamard rotations in both forward and backward passes, which mitigate outliers, 2) high-performance kernel support, and 3) FSDP integration for low-precision communication. Our approach ensures that all large matrix multiplications during the forward and backward passes are executed in lower precision. Applied to LLaMa models, HALO achieves near-full-precision-equivalent results during fine-tuning on various tasks, while delivering up to 1.41x end-to-end speedup for full fine-tuning on RTX 4090 GPUs. HALO efficiently supports both standard and parameter-efficient fine-tuning (PEFT). Our results demonstrate the first practical approach to fully quantized LLM fine-tuning that maintains accuracy in INT8 and FP6 precision, while delivering performance benefits.

Interpretable reinforcement learning policies are essential for high-stakes decision-making, yet optimizing decision tree policies in Markov Decision Processes (MDPs) remains challenging. We propose SPOT, a novel method for computing decision tree policies, which formulates the optimization problem as a mixed-integer linear program (MILP). To enhance efficiency, we employ a reduced-space branch-and-bound approach that decouples the MDP dynamics from tree-structure constraints, enabling efficient parallel search. This significantly improves runtime and scalability compared to previous methods. Our approach ensures that each iteration yields the optimal decision tree. Experimental results on standard benchmarks demonstrate that SPOT achieves substantial speedup and scales to larger MDPs with a significantly higher number of states. The resulting decision tree policies are interpretable and compact, maintaining transparency without compromising performance. These results demonstrate that our approach simultaneously achieves interpretability and scalability, delivering high-quality policies an order of magnitude faster than existing approaches.

As deep learning models continue to scale, the growing computational demands have amplified the need for effective coreset selection techniques. Coreset selection aims to accelerate training by identifying small, representative subsets of data that approximate the performance of the full dataset. Among various approaches, gradient-based methods stand out due to their strong theoretical underpinnings and practical benefits, particularly under limited data budgets. However, these methods face challenges such as naïve stochastic gradient descent (SGD) acting as a surprisingly strong baseline and the breakdown of representativeness due to loss curvature mismatches over time. In this work, we propose a novel framework that addresses these limitations. First, we establish a connection between posterior sampling and loss landscapes, enabling robust coreset selection even in high-data-corruption scenarios. Second, we introduce a smoothed loss function based on posterior sampling onto the model weights, enhancing stability and generalization while maintaining computational efficiency. We also present a novel convergence analysis for our sampling-based coreset selection method. Finally, through extensive experiments, we demonstrate how our approach achieves faster training and enhanced generalization across diverse datasets than the current state of the art.

We study the fundamental question of how informative a dataset is for solving a given decision-making task. In our setting, the dataset provides partial information about unknown parameters that influence task outcomes. Focusing on linear programs, we characterize when a dataset is sufficient to recover an optimal decision, given an uncertainty set on the cost vector. Our main contribution is a sharp geometric characterization that identifies the directions of the cost vector that matter for optimality, relative to the task constraints and uncertainty set. We further develop a practical algorithm that, for a given task, constructs a minimal or least-costly sufficient dataset. Our results reveal that small, well-chosen datasets can often fully determine optimal decisions---offering a principled foundation for task-aware data selection.

Transformers have emerged as a powerful neural network architecture capable of tackling a wide range of learning tasks. In this work, we provide a theoretical analysis of their ability to automatically extract structure from data in an unsupervised setting. In particular, we demonstrate their suitability for clustering when the input data is generated from a Gaussian mixture model. To this end, we study a simplified two-head attention layer and define a population risk whose minimization with unlabeled data drives the head parameters to align with the true mixture centroids.

Equivariant neural networks are designed to respect symmetries through their architecture, boosting generalization and sample efficiency when those symmetries are present in the data distribution. Real-world data, however, often departs from perfect symmetry because of noise, structural variation, measurement bias, or other symmetry-breaking effects. Strictly equivariant models may struggle to fit the data, while unconstrained models lack a principled way to leverage partial symmetries. Even when the data is fully symmetric, enforcing equivariance can hurt training by limiting the model to a restricted region of the parameter space. Guided by homotopy principles, where an optimization problem is solved by gradually transforming a simpler problem into a complex one, we introduce Adaptive Constrained Equivariance (ACE), a constrained optimization approach that starts with a flexible, non-equivariant model and gradually reduces its deviation from equivariance. This gradual tightening smooths training early on and settles the model at a data-driven equilibrium, balancing between equivariance and non-equivariance. Across multiple architectures and tasks, our method consistently improves performance metrics, sample efficiency, and robustness to input perturbations compared with strictly equivariant models and heuristic equivariance relaxations.

Deep learning models often struggle with distribution shifts between training and deployment environments. Distributionally Robust Optimization (DRO) offers a promising framework by optimizing worst-case performance over a set of candidate distributions, which is called as the \emph{uncertainty set}. However, the efficacy of DRO heavily depends on the design of uncertainty set, and existing methods often perform suboptimally due to inappropriate and inflexible uncertainty sets. In this work, we first propose a novel perspective that casts entropy-regularized Wasserstein DRO as a dynamic process of distributional exploration and semantic alignment, both driven by optimal transport (OT). This unified viewpoint yields two key new techniques: \emph{semantic calibration}, which bootstraps semantically meaningful transport costs via inverse OT, and \emph{adaptive refinement}, which adjusts uncertainty set using OT-driven feedback. Together, these components form an exploration-and-feedback system, where the transport costs and uncertainty set evolve jointly during training, enabling the model to better adapt to potential distribution shifts. Moreover, we provide an in-depth analysis on this adaptive process and prove the theoretical convergence guarantee. Finally, we present our experimental results across diverse distribution shift scenarios, which demonstrate that our approach significantly outperforms existing methods, achieving state-of-the-art robustness.

Classical optimisation theory guarantees monotonic objective decrease for gradient descent (GD) when employed in a small step size, or "stable", regime. In contrast, gradient descent on neural networks is frequently performed in a large step size regime called the "edge of stability", in which the objective decreases non-monotonically with an observed implicit bias towards flat minima. In this paper, we take a step toward quantifying this phenomenon by providing convergence rates for gradient descent with large learning rates in an overparametrised least squares setting. The key insight behind our analysis is that, as a consequence of overparametrisation, the set of global minimisers forms a Riemannian manifold $M$, which enables the decomposition of the GD dynamics into components parallel and orthogonal to $M$. The parallel component corresponds to Riemannian gradient descent on the objective sharpness, while the orthogonal component corresponds to a quadratic dynamical system. This insight allows us to derive convergence rates in three regimes characterised by the learning rate size: the subcritical regime, in which transient instability is overcome in finite time before linear convergence to a suboptimally flat global minimum; the critical regime, in which instability persists for all time with a power-law convergence toward the optimally flat global minimum; the supercritical regime, in which instability persists for all time with linear convergence to an oscillation of period two centred on the optimally flat global minimum.

Split Federated Learning (SFL) enables scalable training on edge devices by combining the parallelism of Federated Learning (FL) with the computational offloading of Split Learning (SL). Despite its great success, SFL suffers significantly from the well-known straggler issue in distributed learning systems. This problem is exacerbated by the dependency between Split Server and clients: the Split Server side model update relies on receiving activations from clients. Such synchronization requirement introduces significant time latency, making straggler a critical bottleneck to the scalability and efficiency of the system. To mitigate this problem, we propose *MU-SplitFed*, a straggler-resilient SFL algorithm that decouples training progress from straggler delays via a simple yet effective unbalanced update mechanism. By enabling the server to perform $\tau$ local updates per client round, *MU-SplitFed* achieves convergence rate $\mathcal{O}(\sqrt{d/(\tau T)})$, showing a linear reduction in communication round by a factor of $\tau$. Experiments demonstrate that *MU-SplitFed* consistently outperforms baseline methods with the presence of stragglers and effectively mitigates their impact through adaptive tuning of $\tau$.

Distribution shifts between training and test data undermine the reliability of deep neural networks, challenging real-world applications across domains and subpopulations. While distributionally robust optimization (DRO) methods like GroupDRO aim to improve robustness by optimizing worst-case performance over predefined groups, their use of a single global classifier can be restrictive when facing substantial inter-environment variability. We propose Multi-Expert Distributionally Robust Optimization (MEDRO), a novel extension of GroupDRO designed to address such complex shifts. MEDRO employs a shared feature extractor with $m$ environment-specific expert classifier heads, and introduces a min-max objective over all $m^{2}$ expert-environment pairings, explicitly modeling cross-environment risks. This expanded uncertainty set captures fine-grained distributional variations that a single classifier might overlook. Empirical evaluations on a range of standard distribution shift benchmarks demonstrate that MEDRO often achieves robust predictive performance compared to existing methods. Furthermore, MEDRO offers practical inference strategies, such as ensembling or gating mechanisms, for typical scenarios where environment labels are unavailable at test time. Our findings suggest MEDRO as a promising step toward resilient and generalizable machine learning under real-world distribution shifts.

In this paper, we investigate the necessity of traceability for accurate learning in stochastic convex optimization (SCO) under $\ell_p$ geometries. Informally, we say a learning algorithm is \emph{$m$-traceable} if, by analyzing its output, it is possible to identify at least $m$ of its training samples. Our main results uncover a fundamental tradeoff between traceability and excess risk in SCO. For every $p\in [1,\infty)$, we establish the existence of an excess risk threshold below which every sample-efficient learner is traceable with the number of samples which is a \emph{constant fraction} of its training sample. For $p\in [1,2]$, this threshold coincides with the best excess risk of differentially private (DP) algorithms, i.e., above this threshold, there exist algorithms that are not traceable, which corresponds to a sharp phase transition. For $p \in (2,\infty)$, this threshold instead gives novel lower bounds for DP learning, partially closing an open problem in this setup. En route to establishing these results, we prove a sparse variant of the fingerprinting lemma, which is of independent interest to the community.

Recent neural combinatorial optimization (NCO) methods have shown promising problem-solving ability without requiring domain-specific expertise. Most existing NCO methods use training and testing data with a fixed constraint value and lack research on the effect of constraint tightness on the performance of NCO methods. This paper takes the capacity-constrained vehicle routing problem (CVRP) as an example to empirically analyze the NCO performance under different tightness degrees of the capacity constraint. Our analysis reveals that existing NCO methods overfit the capacity constraint, and they can only perform satisfactorily on a small range of the constraint values but poorly on other values. To tackle this drawback of existing NCO methods, we develop an efficient training scheme that explicitly considers varying degrees of constraint tightness and propose a multi-expert module to learn a generally adaptable solving strategy. Experimental results show that the proposed method can effectively overcome the overfitting issue, demonstrating superior performance on the CVRP and CVRP with time windows (CVRPTW) with various constraint tightness degrees. The code is available at [https://github.com/CIAM-Group/Rethinking\_Constraint\_Tightness](https://github.com/CIAM-Group/Rethinking\_Constraint\_Tightness).