Reproducing kernel Hilbert spaces provide a foundational framework for kernel-based learning, where regularization and interpolation problems admit finite-dimensional solutions through classical representer theorems. Many modern learning models, however — including fixed-architecture neural networks equipped with non-quadratic norms — naturally give rise to non-Hilbertian geometries that fall outside this setting. In Banach spaces, continuity of point-evaluation functionals alone is insufficient to guarantee feature representations or kernel-based learning formulations. In this work, we develop a functional-analytic framework for learning in […]

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arXiv:2602.10326v1 Announce Type: new Abstract: Despite the remarkable success of sampling-based generative models such as flow matching, they can still produce samples of inconsistent or degraded quality. To assess sample reliability and generate higher-quality outputs, we propose uncertainty-aware flow matching (UA-Flow), a lightweight extension of flow matching that predicts the velocity field together with heteroscedastic uncertainty. UA-Flow estimates per-sample uncertainty by propagating velocity uncertainty through the flow dynamics. These uncertainty estimates act as a reliability signal for individual […]

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arXiv:2601.03330v1 Announce Type: new Abstract: We formalize a minimal setting in which a chronology (a strict partial order on events) is forced by consistency of distributed information under local composability. The system maintains distributed records interpreted as constraints over a global possibility space (Omega, Sigma), optionally with a measure mu. Events act locally by monotonically tightening records, and independent events commute (diamond/trace semantics), yielding schedule invariance. We define operational influence without assuming primitive time: e influences f if […]

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arXiv:2601.00160v1 Announce Type: new Abstract: End-to-end automatic speech recognition has become the dominant paradigm in both academia and industry. To enhance recognition performance, the Weighted Finite-State Transducer (WFST) is widely adopted to integrate acoustic and language models through static graph composition, providing robust decoding and effective error correction. However, WFST decoding relies on a frame-by-frame autoregressive search over CTC posterior probabilities, which severely limits inference efficiency. Motivated by establishing a more principled compatibility between WFST decoding and CTC […]

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arXiv:2601.14488v1 Announce Type: new Abstract: Fully symmetric positive interior (f-SPI) quadrature rules are key building blocks for high-order discretizations of partial differential equations, yet high-degree rules with few nodes remain scarce on reference elements commonly used in mesh generation. We construct new f-SPI rules on the square, cube, prism, and pyramid by coupling a variable parameterization that enforces positivity and interiority with an efficient Levenberg-Marquardt optimization and a symmetry-aware node-reduction strategy that eliminates and collapses orbits, allowing transitions […]

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Table of Links Abstract and 1. Introduction Related Works 2.1 Traditional Index Selection Approaches 2.2 RL-based Index Selection Approaches Index Selection Problem Methodology 4.1 Formulation of the DRL Problem 4.2 Instance-Aware Deep Reinforcement Learning for Efficient Index Selection System Framework of IA2 5.1 Preprocessing Phase 5.2 RL Training and Application Phase Experiments 6.1 Experimental Setting 6.2 Experimental Results 6.3 End-to-End Performance Comparison 6.4 Key Insights Conclusion and Future Work, and References 5.1 Preprocessing Phase The preprocessing phase is […]

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arXiv:2602.08862v1 Announce Type: cross Abstract: We give a randomized online algorithm that guarantees near-optimal $widetilde O(sqrt T)$ expected swap regret against any sequence of $T$ adaptively chosen Lipschitz convex losses on the unit interval. This improves the previous best bound of $widetilde O(T^{2/3})$ and answers an open question of Fishelson et al. [2025b]. In addition, our algorithm is efficient: it runs in $mathsf{poly}(T)$ time. A key technical idea we develop to obtain this result is to discretize the […]

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arXiv:2406.01552v2 Announce Type: replace Abstract: Tensors are a fundamental data structure for many scientific contexts, such as time series analysis, materials science, and physics, among many others. Improving our ability to produce and handle tensors is essential to efficiently address problems in these domains. In this paper, we show how to exploit the underlying symmetries of functions that map tensors to tensors. More concretely, we develop universally expressive equivariant machine learning architectures on tensors that exploit that, in […]

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We study a structured bi-level optimization problem where the upper-level objective is a smooth function and the lower-level problem is policy optimization in a Markov decision process (MDP). The upper-level decision variable parameterizes the reward of the lower-level MDP, and the upper-level objective depends on the optimal induced policy. Existing methods for bi-level optimization and RL often require second-order information, impose strong regularization at the lower level, or inefficiently use samples through nested-loop procedures. In this work, we […]

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arXiv:2601.21080v1 Announce Type: new Abstract: We propose a parametric hyperbolic conservation law (SymCLaw) for learning hyperbolic systems directly from data while ensuring conservation, entropy stability, and hyperbolicity by design. Unlike existing approaches that typically enforce only conservation or rely on prior knowledge of the governing equations, our method parameterizes the flux functions in a form that guarantees real eigenvalues and complete eigenvectors of the flux Jacobian, thereby preserving hyperbolicity. At the same time, we embed entropy-stable design principles […]

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