March 2026

arXiv:2603.20392v1 Announce Type: cross Abstract: Probabilistic circuit (PC) structure learning is hampered by greedy algorithms that make irreversible, locally optimal decisions. We propose SymCircuit, which replaces greedy search with a learned generative policy trained via entropy-regularized reinforcement learning. Instantiating the RL-as-inference framework in the PC domain, we show the optimal policy is a tempered Bayesian posterior, recovering the exact posterior when the regularization temperature is set inversely proportional to the dataset size. The policy is implemented as SymFormer, […]

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arXiv:2603.20388v1 Announce Type: cross Abstract: We derive the asymptotic risk function of regularized empirical risk minimization (ERM) estimators tuned by $n$-fold cross-validation (CV). The out-of-sample prediction loss of such estimators converges in distribution to the squared-error loss (risk function) of shrinkage estimators in the normal means model, tuned by Stein’s unbiased risk estimate (SURE). This risk function provides a more fine-grained picture of predictive performance than uniform bounds on worst-case regret, which are common in learning theory: it […]

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arXiv:2603.22050v1 Announce Type: new Abstract: Supervised machine learning describes the practice of fitting a parameterized model to labeled input-output data. Supervised machine learning methods have demonstrated promise in learning efficient surrogate models that can (partially) replace expensive high-fidelity models, making many-query analyses, such as optimization, uncertainty quantification, and inference, tractable. However, when training data must be obtained through the evaluation of an expensive model or experiment, the amount of training data that can be obtained is often limited, […]

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arXiv:2603.21918v1 Announce Type: new Abstract: This paper develops a unified framework for measuring concentration in weighted systems embedded in networks of interactions. While traditional indices such as the Herfindahl-Hirschman Index capture dispersion in weights, they neglect the topology of relationships among the elements receiving those weights. To address this limitation, we introduce a family of topology-aware concentration indices that jointly account for weight distributions and network structure. At the core of the framework lies a baseline Network Concentration […]

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arXiv:2603.21678v1 Announce Type: new Abstract: Time-dependent reliability analysis of nonlinear dynamical systems under stochastic excitations is a critical yet computationally demanding task. Conventional approaches, such as Monte Carlo simulation, necessitate repeated evaluations of computationally expensive numerical solvers, leading to significant computational bottlenecks. To address this challenge, we propose textit{CoNBONet}, a neuroscience-inspired surrogate model that enables fast, energy-efficient, and uncertainty-aware reliability analysis, providing a scalable alternative to techniques such as Monte Carlo simulations. CoNBONet, short for textbf{Co}nformalized textbf{N}euroscience-inspired textbf{B}ayesian […]

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arXiv:2603.21342v1 Announce Type: new Abstract: We introduce Generalized Discrete Diffusion from Snapshots (GDDS), a unified framework for discrete diffusion modeling that supports arbitrary noising processes over large discrete state spaces. Our formulation encompasses all existing discrete diffusion approaches, while allowing significantly greater flexibility in the choice of corruption dynamics. The forward noising process relies on uniformization and enables fast arbitrary corruption. For the reverse process, we derive a simple evidence lower bound (ELBO) based on snapshot latents, instead […]

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arXiv:2603.21247v1 Announce Type: new Abstract: We propose a landmark-constrained algorithm, LA-VDM (Landmark Accelerated Vector Diffusion Maps), to accelerate the Vector Diffusion Maps (VDM) framework built upon the Graph Connection Laplacian (GCL), which captures pairwise connection relationships within complex datasets. LA-VDM introduces a novel two-stage normalization that effectively address nonuniform sampling densities in both the data and the landmark sets. Under a manifold model with the frame bundle structure, we show that we can accurately recover the parallel transport […]

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arXiv:2603.21235v1 Announce Type: new Abstract: Nonrigid registration is conventionally divided into point set registration, which aligns sparse geometries, and image registration, which aligns continuous intensity fields on regular grids. However, this dichotomy creates a critical bottleneck for emerging scientific data, such as spatial transcriptomics, where high-dimensional vector-valued functions, e.g., gene expression, are defined on irregular, sparse manifolds. Consequently, researchers currently face a forced choice: either sacrifice single-cell resolution via voxelization to utilize image-based tools, or ignore the critical […]

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arXiv:2603.21144v1 Announce Type: new Abstract: This paper proposes a new formulation of functional Gaussian Process regression in manifolds, based on an Empirical Bayes approach, in the spatiotemporal random field context. We apply the machinery of tight Gaussian measures in separable Hilbert spaces, exploiting the invariance property of covariance kernels under the group of isometries of the manifold. The identification of these measures with infinite-product Gaussian measures is then obtained via the eigenfunctions of the Laplace-Beltrami operator on the […]

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arXiv:2603.21091v1 Announce Type: new Abstract: Based on some recent work of the author on stochastic approximation in non-markovian environments, the situation when the driving random process is non-ergodic in addition to being non-markovian is considered. Using this, we propose an analytic framework for understanding transformer based learning, specifically, the `attention’ mechanism, and continual learning, both of which depend on the entire past in principle.

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