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arXiv:2603.01157v1 Announce Type: cross Abstract: Risk forecasts in financial regulation and internal management are calculated through historical data. The unknown structural changes of financial data poses a substantial challenge in selecting an appropriate look-back window for risk modeling and forecasting. We develop a data-driven online learning method, called the bootstrap-based adaptive window selection (BAWS), that adaptively determines the window size in a sequential manner. A central component of BAWS is to compare the realized scores against a data-dependent […]

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arXiv:2603.01077v1 Announce Type: cross Abstract: We extend the unified kernel framework for transport equations and Koopman eigenfunctions, developed in previous work by the authors for deterministic systems, to stochastic differential equations (SDEs). In the deterministic setting, three analytically grounded constructions-Lions-type variational principles, Green’s function convolution, and resolvent operators along characteristic flows–were shown to yield identical reproducing kernels. For stochastic systems, the Koopman generator includes a second-order diffusion term, transforming the first-order hyperbolic transport equation into a second-order elliptic-parabolic […]

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arXiv:2603.01047v1 Announce Type: cross Abstract: Generative Flow Networks (GFlowNets) were developed to learn policies for efficiently sampling combinatorial candidates by interpreting their generative processes as trajectories in directed acyclic graphs. In the value-based training workflow, the objective is to enforce the balance over partial episodes between the flows of the learned policy and the estimated flows of the desired policy, implicitly encouraging policy divergence minimization. The policy-based strategy alternates between estimating the policy divergence and updating the policy, […]

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arXiv:2603.00945v1 Announce Type: cross Abstract: We study non-rectangular robust Markov decision processes under the average-reward criterion, where the ambiguity set couples transition probabilities across states and the adversary commits to a stationary kernel for the entire horizon. We show that any history-dependent policy achieving sublinear expected regret uniformly over the ambiguity set is robust-optimal, and that the robust value admits a minimax representation as the infimum over the ambiguity set of the classical optimal gains, without requiring any […]

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arXiv:2603.00888v1 Announce Type: cross Abstract: Despite exceptional predictive performance of Deep sequence models (DSMs), the main concern of their deployment centers around the lack of uncertainty awareness. In contrast, probabilistic models quantify the uncertainty associated with unobserved variables with rules of probability. Notably, Bayesian methods leverage Bayes’ rule to express our belief of unobserved variables in a principled way. Since exact Bayesian inference is computationally infeasible at scale, approximate inference is required in practice. Two major bottlenecks of […]

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arXiv:2603.00716v1 Announce Type: cross Abstract: We study computationally and statistically efficient reinforcement learning under the linear $Q^{pi}$ realizability assumption, where any policy’s $Q$-function is linear in a given state-action feature representation. Prior methods in this setting are either computationally intractable, or require (local) access to a simulator. In this paper, we propose a computationally efficient online RL algorithm, named Frozen Policy Iteration, under the linear $Q^{pi}$ realizability setting that works for Markov Decision Processes (MDPs) with stochastic initial […]

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arXiv:2603.00636v1 Announce Type: cross Abstract: We propose a retrodictive forecasting paradigm for time series: instead of predicting the future from the past, we identify the future that best explains the observed present via inverse MAP optimization over a Conditional Variational Autoencoder (CVAE). This conditioning is a statistical modeling choice for Bayesian inversion; it does not assert that future events cause past observations. The approach is theoretically grounded in an information-theoretic arrow-of-time measure: the symmetrized Kullback-Leibler divergence between forward […]

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arXiv:2603.00541v1 Announce Type: cross Abstract: Generative foundation models are increasingly scaled in both width and depth, posing significant challenges for stable feature learning and reliable hyperparameter (HP) transfer across model sizes. While maximal update parameterization ($mu$P) has provided a principled solution to both problems for width scaling, existing extensions to the joint width-depth scaling regime remain fragmented, architecture- and optimizer-specific, and often rely on technically involved theories. In this work, we develop a simple and unified spectral framework […]

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arXiv:2603.00393v1 Announce Type: cross Abstract: Inverse problems constrained by partial differential equations are often ill-conditioned due to noisy and incomplete data or inherent non-uniqueness. A prominent example is full waveform inversion, which estimates Earth’s subsurface properties by fitting seismic measurements subject to the wave equation, where ill-conditioning is inherent to noisy, band-limited, finite-aperture data and shadow zones. Casting the inverse problem into a Bayesian framework allows for a more comprehensive description of its solution, where instead of a […]

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arXiv:2603.00333v1 Announce Type: cross Abstract: This paper investigates numerical solution methods for the Schatten-$p$ quasi-norm regularized problem with $p in [0,1]$, which has been widely studied for finding low-rank solutions of linear inverse problems and gained successful applications in various mathematics and applied science fields. We propose a dynamic proximal gradient algorithm that, through the use of the Cayley transformation, avoids computationally expensive singular value decompositions at each iteration, thereby significantly reducing the computational complexity. The algorithm incorporates […]

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