January 2026

arXiv:2601.22005v1 Announce Type: cross Abstract: Distance metrics are central to machine learning, yet distances between ensembles of quantum states remain poorly understood due to fundamental quantum measurement constraints. We introduce a hierarchy of integral probability metrics, termed MMD-$k$, which generalizes the maximum mean discrepancy to quantum ensembles and exhibit a strict trade-off between discriminative power and statistical efficiency as the moment order $k$ increases. For pure-state ensembles of size $N$, estimating MMD-$k$ using experimentally feasible SWAP-test-based estimators requires […]

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arXiv:2601.21924v1 Announce Type: cross Abstract: We study online transfer reinforcement learning (RL) in episodic Markov decision processes, where experience from related source tasks is available during learning on a target task. A fundamental difficulty is that task similarity is typically defined in terms of rewards or transitions, whereas online RL algorithms operate on Bellman regression targets. As a result, naively reusing source Bellman updates introduces systematic bias and invalidates regret guarantees. We identify one-step Bellman alignment as the […]

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arXiv:2601.21917v1 Announce Type: cross Abstract: We show that computing even very coarse approximations of critical points is intractable for simple classes of nonconvex functions. More concretely, we prove that if there exists a polynomial-time algorithm that takes as input a polynomial in $n$ variables of constant degree (as low as three) and outputs a point whose gradient has Euclidean norm at most $2^n$ whenever the polynomial has a critical point, then P=NP. The algorithm is permitted to return […]

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arXiv:2601.21895v1 Announce Type: cross Abstract: Modern large language models (LLMs) such as GPT, Claude, and Gemini have transformed the way we learn, work, and communicate. Yet, their ability to produce highly human-like text raises serious concerns about misinformation and academic integrity, making it an urgent need for reliable algorithms to detect LLM-generated content. In this paper, we start by presenting a geometric approach to demystify rewrite-based detection algorithms, revealing their underlying rationale and demonstrating their generalization ability. Building […]

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arXiv:2601.21887v1 Announce Type: cross Abstract: We design a variational state estimation (VSE) method that provides a closed-form Gaussian posterior of an underlying complex dynamical process from (noisy) nonlinear measurements. The complex process is model-free. That is, we do not have a suitable physics-based model characterizing the temporal evolution of the process state. The closed-form Gaussian posterior is provided by a recurrent neural network (RNN). The use of RNN is computationally simple in the inference phase. For learning the […]

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arXiv:2601.21873v1 Announce Type: cross Abstract: Learning systems often expand their ambient features or latent representations over time, embedding earlier representations into larger spaces with limited new latent structure. We study transfer learning for structured matrix estimation under simultaneous growth of the ambient dimension and the intrinsic representation, where a well-estimated source task is embedded as a subspace of a higher-dimensional target task. We propose a general transfer framework in which the target parameter decomposes into an embedded source […]

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arXiv:2601.21856v1 Announce Type: cross Abstract: Ultrasound (US) interpretation is hampered by multiplicative speckle, acquisition blur from the point-spread function (PSF), and scanner- and operator-dependent artifacts. Supervised enhancement methods assume access to clean targets or known degradations; conditions rarely met in practice. We present a blind, self-supervised enhancement framework that jointly deconvolves and denoises B-mode images using a Swin Convolutional U-Net trained with a emph{physics-guided} degradation model. From each training frame, we extract rotated/cropped patches and synthesize inputs by […]

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arXiv:2601.21789v1 Announce Type: cross Abstract: We introduce ECSEL, an explainable classification method that learns formal expressions in the form of signomial equations, motivated by the observation that many symbolic regression benchmarks admit compact signomial structure. ECSEL directly constructs a structural, closed-form expression that serves as both a classifier and an explanation. On standard symbolic regression benchmarks, our method recovers a larger fraction of target equations than competing state-of-the-art approaches while requiring substantially less computation. Leveraging this efficiency, ECSEL […]

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arXiv:2601.21765v1 Announce Type: cross Abstract: We consider Bayesian variable selection for binary outcomes under a probit link with a spike-and-slab prior on the regression coefficients. Motivated by the computational challenges encountered by Markov chain Monte Carlo (MCMC) samplers in high-dimensional regimes, we develop a mean-field variational Bayes approximation in which all variational factors admit closed-form updates, and the evidence lower bound is available in closed form. This, in turn, allows the development of an efficient coordinate ascent variational […]

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arXiv:2601.21739v1 Announce Type: cross Abstract: Adam has been at the core of large-scale training for almost a decade, yet a simple empirical fact remains unaccounted for: both validation scores and the qualitative behaviour of the training runs improve when the momentum parameters satisfy $beta_{1}=beta_{2}$. Some recent studies have reported this pattern, but there is still no explanation for why this choice helps. We show that this choice is closely tied to a structural property that we refer to […]

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