February 2026

arXiv:2602.20646v1 Announce Type: cross Abstract: We study stochastic gradient descent (SGD) for composite optimization problems with $N$ sequential operators subject to perturbations in both the forward and backward passes. Unlike classical analyses that treat gradient noise as additive and localized, perturbations to intermediate outputs and gradients cascade through the computational graph, compounding geometrically with the number of operators. We present the first comprehensive theoretical analysis of this setting. Specifically, we characterize how forward and backward perturbations propagate and […]

Ver mais

arXiv:2602.20578v1 Announce Type: cross Abstract: We study online maximization of non-monotone Diminishing-Return(DR)-submodular functions over down-closed convex sets, a regime where existing projection-free online methods suffer from suboptimal regret and limited feedback guarantees. Our main contribution is a new structural result showing that this class is $1/e$-linearizable under carefully designed exponential reparametrization, scaling parameter, and surrogate potential, enabling a reduction to online linear optimization. As a result, we obtain $O(T^{1/2})$ static regret with a single gradient query per round […]

Ver mais

arXiv:2602.20404v1 Announce Type: new Abstract: In tabular Markov decision processes (MDPs) with perfect state observability, each trajectory provides active samples from the transition distributions conditioned on state-action pairs. Consequently, accurate model estimation depends on how the exploration policy allocates visitation frequencies in accordance with the intrinsic complexity of each transition distribution. Building on recent work on coverage-based exploration, we introduce a parameterized family of decomposable and concave objective functions $U_kappa$ that explicitly incorporate both intrinsic estimation complexity and […]

Ver mais

arXiv:2602.20400v1 Announce Type: new Abstract: To steer language models towards truthful outputs on tasks which are beyond human capability, previous work has suggested training models on easy tasks to steer them on harder ones (easy-to-hard generalization), or using unsupervised training algorithms to steer models with no external labels at all (unsupervised elicitation). Although techniques from both paradigms have been shown to improve model accuracy on a wide variety of tasks, we argue that the datasets used for these […]

Ver mais

arXiv:2602.20399v1 Announce Type: new Abstract: Neural simulators promise efficient surrogates for physics simulation, but scaling them is bottlenecked by the prohibitive cost of generating high-fidelity training data. Pre-training on abundant off-the-shelf geometries offers a natural alternative, yet faces a fundamental gap: supervision on static geometry alone ignores dynamics and can lead to negative transfer on physics tasks. We present GeoPT, a unified pre-trained model for general physics simulation based on lifted geometric pre-training. The core idea is to […]

Ver mais

arXiv:2602.20398v1 Announce Type: new Abstract: Competition complexity formalizes a compelling intuition: rather than refining the mechanism, how much additional competition is sufficient for a simple mechanism to compete with an optimal one? We begin the study of this question in multi-unit pricing for welfare maximization using prophet inequalities. An online decision-maker observes $m geq k$ nonnegative values drawn independently from a known distribution, may select up to $k$ of them, and aims to maximize the expected sum of […]

Ver mais

arXiv:2602.20396v1 Announce Type: new Abstract: Explainable artificial intelligence promises to yield insights into relevant features, thereby enabling humans to examine and scrutinize machine learning models or even facilitating scientific discovery. Considering the widespread technique of Shapley values, we find that purely data-driven operationalization of multivariate feature importance is unsuitable for such purposes. Even for simple problems with two features, spurious associations due to collider bias and suppression arise from considering one feature only in the observational context of […]

Ver mais

arXiv:2602.20395v1 Announce Type: new Abstract: We introduce an integral equation formulation of the surface Stokes equations, constructed using two-dimensional Stokeslets. The resulting integral equations are Fredholm integral equations of the second kind and can be discretized to high order using standard tools. Since the resulting discrete linear systems are dense, we describe and analyze a proxy shell method to construct fast direct solvers for these systems. The properties of our integral equation, and the performance of the resulting […]

Ver mais

arXiv:2602.20390v1 Announce Type: new Abstract: This paper introduces a number of new techniques in the study of the famous question from numerical linear algebra: what is the largest possible growth factor when performing Gaussian elimination with complete pivoting? This question is highly complex, due to a complicated set of polynomial inequalities that need to be simultaneously satisfied. This paper introduces the JuMP + Groebner basis + discriminant polynomial approach as well as the use of interval arithmetic computations. […]

Ver mais

arXiv:2602.20379v1 Announce Type: new Abstract: Enterprise Retrieval-Augmented Generation (RAG) assistants operate in multi-turn, case-based workflows such as technical support and IT operations, where evaluation must reflect operational constraints, structured identifiers (e.g., error codes, versions), and resolution workflows. Existing RAG evaluation frameworks are primarily designed for benchmark-style or single-turn settings and often fail to capture enterprise-specific failure modes such as case misidentification, workflow misalignment, and partial resolution across turns. We present a case-aware LLM-as-a-Judge evaluation framework for enterprise multi-turn […]

Ver mais