February 2026

arXiv:2504.08324v2 Announce Type: replace-cross Abstract: This paper provides an introduction to Double/Debiased Machine Learning (DML). DML is a general approach to performing inference about a target parameter in the presence of nuisance functions: objects that are needed to identify the target parameter but are not of primary interest. Nuisance functions arise naturally in many settings, such as when controlling for confounding variables or leveraging instruments. The paper describes two biases that arise from nuisance function estimation and explains […]

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arXiv:2411.04551v3 Announce Type: replace-cross Abstract: Transformers are deep neural network architectures that underpin the recent successes of large language models. Unlike more classical architectures that can be viewed as point-to-point maps, a Transformer acts as a measure-to-measure map implemented as specific interacting particle system on the unit sphere: the input is the empirical measure of tokens in a prompt and its evolution is governed by the continuity equation. In fact, Transformers are not limited to empirical measures and […]

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arXiv:2409.00730v4 Announce Type: replace-cross Abstract: Generating physically feasible dynamics in a data-driven context is challenging, especially when adhering to physical priors expressed in specific equations or formulas. Existing methodologies often overlook the integration of physical priors, resulting in violation of basic physical laws and suboptimal performance. In this paper, we introduce a novel framework that seamlessly incorporates physical priors into diffusion-based generative models to address this limitation. Our approach leverages two categories of priors: 1) distributional priors, such […]

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arXiv:2408.11773v2 Announce Type: replace-cross Abstract: The use of reinforcement learning algorithms in financial trading is becoming increasingly prevalent. However, the autonomous nature of these algorithms can lead to unexpected outcomes that deviate from traditional game-theoretical predictions and may even destabilize markets. In this study, we examine a scenario in which two autonomous agents, modelled with Double Deep Q-Learning, learn to liquidate the same asset optimally in the presence of market impact, under the Almgren-Chriss (2000) framework. We show […]

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arXiv:2406.04112v3 Announce Type: replace-cross Abstract: While overparameterization in machine learning models offers great benefits in terms of optimization and generalization, it also leads to increased computational requirements as model sizes grow. In this work, we show that by leveraging the inherent low-dimensional structures of data and compressible dynamics within the model parameters, we can reap the benefits of overparameterization without the computational burdens. In practice, we demonstrate the effectiveness of this approach for deep low-rank matrix completion as […]

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arXiv:2404.17592v3 Announce Type: replace-cross Abstract: As e-commerce expands, delivering real-time personalized recommendations from vast catalogs poses a critical challenge for retail platforms. Maximizing revenue requires careful consideration of both individual customer characteristics and available item features to continuously optimize assortments over time. In this paper, we consider the dynamic assortment problem with dual contexts — user and item features. In high-dimensional scenarios, the quadratic growth of dimensions complicates computation and estimation. To tackle this challenge, we introduce a […]

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arXiv:2011.07687v2 Announce Type: replace-cross Abstract: We consider the bandit problem of selecting $K$ out of $N$ arms at each time step. The reward can be a non-linear function of the rewards of the selected individual arms. The direct use of a multi-armed bandit algorithm requires choosing among $binom{N}{K}$ options, making the action space large. To simplify the problem, existing works on combinatorial bandits {typically} assume feedback as a linear function of individual rewards. In this paper, we prove […]

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arXiv:2602.12039v2 Announce Type: replace Abstract: Logit regularization, the addition of a convex penalty directly in logit space, is widely used in modern classifiers, with label smoothing as a prominent example. While such methods often improve calibration and generalization, their mechanism remains under-explored. In this work, we analyze a general class of such logit regularizers in the context of linear classification, and demonstrate that they induce an implicit bias of logit clustering around finite per-sample targets. For Gaussian data, […]

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arXiv:2602.10538v2 Announce Type: replace Abstract: Agentic theorem provers — pipelines that couple a mathematical reasoning model with library retrieval, subgoal-decomposition/search planner, and a proof assistant verifier — have recently achieved striking empirical success, yet it remains unclear which components drive performance and why such systems work at all despite classical hardness of proof search. We propose a distributional viewpoint and introduce textbf{statistical provability}, defined as the finite-horizon success probability of reaching a verified proof, averaged over an instance […]

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arXiv:2602.09394v2 Announce Type: replace Abstract: Manufacturing lines, service journeys, supply chains, and AI reasoning chains share a common challenge: attributing a terminal outcome to the intermediate stage that caused it. We establish an information-theoretic barrier to this credit assignment problem: the signal connecting early steps to final outcomes decays exponentially with depth, creating a critical horizon beyond which reliable learning from endpoint data alone requires exponentially many samples. We prove four results. First, a Signal Decay Bound: sample […]

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