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arXiv:2603.02753v1 Announce Type: cross Abstract: Designing novel proteins with desired characteristics remains a significant challenge due to the large sequence space and the complexity of sequence-function relationships. Efficient exploration of this space to identify sequences that meet specific design criteria is crucial for advancing therapeutics and biotechnology. Here, we present BoGA (Bayesian Optimization Genetic Algorithm), a framework that combines evolutionary search with Bayesian optimization to efficiently navigate the sequence space. By integrating a genetic algorithm as a stochastic […]

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arXiv:2603.02729v1 Announce Type: cross Abstract: We study the problem of recovering a low-tubal-rank tensor $mathcal{X}_starin mathbb{R}^{n times n times k}$ from noisy linear measurements under the t-product framework. A widely adopted strategy involves factorizing the optimization variable as $mathcal{U} * mathcal{U}^top$, where $mathcal{U} in mathbb{R}^{n times R times k}$, followed by applying factorized gradient descent (FGD) to solve the resulting optimization problem. Since the tubal-rank $r$ of the underlying tensor $mathcal{X}_star$ is typically unknown, this method often assumes […]

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arXiv:2603.02649v1 Announce Type: cross Abstract: Adam and AdamW are a class of default optimizers for training deep learning models in machine learning. These adaptive algorithms converge faster but generalize worse compared to SGD. In fact, their proved generalization error $O(frac{1}{sqrt{N}})$ also is larger than $O(frac{1}{N})$ of SGD, where $N$ denotes training sample size. Recently, although some variants of Adam have been proposed to improve its generalization, their improved generalizations are still unexplored in theory. To fill this gap, […]

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arXiv:2603.02622v1 Announce Type: cross Abstract: While the Implicit Bias(or Implicit Regularization) of standard loss functions has been studied, the optimization geometry induced by discriminative metric-learning objectives remains largely unexplored.To the best of our knowledge, this paper presents an initial theoretical analysis of the implicit regularization induced by the Deep LDA,a scale invariant objective designed to minimize intraclass variance and maximize interclass distance. By analyzing the gradient flow of the loss on a L-layer diagonal linear network, we prove […]

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arXiv:2603.02616v1 Announce Type: cross Abstract: Structural heart disease (SHD) is a prevalent condition with many undiagnosed cases, and early detection is often limited by the high cost and accessibility constraints of echocardiography (ECHO). Recent studies show that artificial intelligence (AI)-based analysis of electrocardiograms (ECGs) can detect SHD, offering a scalable alternative. However, existing methods are fully black-box models, limiting interpretability and clinical adoption. To address these challenges, we propose an interpretable and effective framework that integrates clinically meaningful […]

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arXiv:2603.02533v1 Announce Type: cross Abstract: The focal-loss has become a widely used alternative to cross-entropy in class-imbalanced classification problems, particularly in computer vision. Despite its empirical success, a systematic information-theoretic study of the focal-loss remains incomplete. In this work, we adopt a distributional viewpoint and study the focal-entropy, a focal-loss analogue of the cross-entropy. Our analysis establishes conditions for finiteness, convexity, and continuity of the focal-entropy, and provides various asymptotic characterizations. We prove the existence and uniqueness of […]

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arXiv:2603.02491v1 Announce Type: cross Abstract: As artificial agents become increasingly capable, what internal structure is *necessary* for an agent to act competently under uncertainty? Classical results show that optimal control can be *implemented* using belief states or world models, but not that such representations are required. We prove quantitative “selection theorems” showing that low *average-case regret* on structured families of action-conditioned prediction tasks forces an agent to implement a predictive, structured internal state. Our results cover stochastic policies, […]

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arXiv:2603.02452v1 Announce Type: cross Abstract: A major focus in designing methods for learning distributions defined on manifolds is to alleviate the need to implicitly learn the manifold so that learning can concentrate on the data distribution within the manifold. However, accomplishing this often leads to compute-intensive solutions. In this work, we propose a simple modification to denoising score-matching in the ambient space to implicitly account for the manifold, thereby reducing the burden of learning the manifold while maintaining […]

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arXiv:2603.02429v1 Announce Type: cross Abstract: Underdamped Langevin dynamics (ULD) is a widely-used sampler for Gibbs distributions $pipropto e^{-V}$, and is often empirically effective in high dimensions. However, existing non-asymptotic convergence guarantees for discretized ULD typically scale polynomially with the ambient dimension $d$, leading to vacuous bounds when $d$ is large. The main known dimension-free result concerns the randomized midpoint discretization in Wasserstein-2 distance (Liu et al.,2023), while dimension-independent guarantees for ULD discretizations in KL divergence have remained open. […]

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arXiv:2603.02289v1 Announce Type: cross Abstract: Estimating causal effects is particularly challenging when outcomes arise in complex, non-Euclidean spaces, where conventional methods often fail to capture meaningful structural variation. We develop a framework for topological causal inference that defines treatment effects through differences in the topological structure of potential outcomes, summarized by power-weighted silhouette functions of persistence diagrams. We develop an efficient, doubly robust estimator in a fully nonparametric model, establish functional weak convergence, and construct a formal test […]

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