March 2026

arXiv:2510.08382v3 Announce Type: replace-cross Abstract: In this paper we will give a characterization of the learnability of forgiving 0-1 loss functions in the multiclass setting with effectively finite cardinality of the output and label space. To do this, we create a new combinatorial dimension that is based off of the Natarajan Dimension and we show that a hypothesis class is learnable in our setting if and only if this Generalized Natarajan Dimension is finite. We also show how […]

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arXiv:2509.22613v2 Announce Type: replace-cross Abstract: Recent reinforcement learning (RL) methods have substantially enhanced the planning capabilities of Large Language Models (LLMs), yet the theoretical basis for their effectiveness remains elusive. In this work, we investigate RL’s benefits and limitations through a tractable graph-based abstraction, focusing on policy gradient (PG) and Q-learning methods. Our theoretical analyses reveal that supervised fine-tuning (SFT) may introduce co-occurrence-based spurious solutions, whereas RL achieves correct planning primarily through exploration, underscoring exploration’s role in enabling […]

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arXiv:2507.08965v2 Announce Type: replace-cross Abstract: Classifier-Free Guidance (CFG) is a widely used technique for conditional generation and improving sample quality in continuous diffusion models, and its extensions to discrete diffusion has recently started to be investigated. In order to improve the algorithms in a principled way, this paper starts by analyzing the exact effect of CFG in the context of a low-dimensional masked diffusion model, with a special emphasis on the guidance schedule. Our analysis shows that high […]

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arXiv:2506.05668v5 Announce Type: replace-cross Abstract: Diffusion models generate data by removing noise gradually, which corresponds to the time-reversal of a noising process. However, access to only the denoising kernels is often insufficient. In many applications, we need the knowledge of the marginal densities along the generation trajectory, which enables tasks such as inference-time control. To address this gap, in this paper, we introduce the Radon-Nikodym Estimator (RNE). Based on the concept of the textit{density ratio} between path distributions, […]

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arXiv:2506.01502v3 Announce Type: replace-cross Abstract: Learning population dynamics involves recovering the underlying process that governs particle evolution, given evolutionary snapshots of samples at discrete time points. Recent methods frame this as an energy minimization problem in probability space and leverage the celebrated JKO scheme for efficient time discretization. In this work, we introduce $texttt{iJKOnet}$, an approach that combines the JKO framework with inverse optimization techniques to learn population dynamics. Our method relies on a conventional $textit{end-to-end}$ adversarial training […]

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arXiv:2505.21813v2 Announce Type: replace-cross Abstract: Data Augmentation (DA) has become an essential tool to improve robustness and generalization of modern machine learning. However, when deciding on DA strategies it is critical to choose parameters carefully, and this can be a daunting task which is traditionally left to trial-and-error or expensive optimization based on validation performance. In this paper, we counter these limitations by proposing a novel framework for optimizing DA. In particular, we take a probabilistic view of […]

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arXiv:2505.18996v3 Announce Type: replace-cross Abstract: Hybrid neural ordinary differential equations (neural ODEs) integrate mechanistic models with neural ODEs, offering strong inductive bias and flexibility, and are particularly advantageous in data-scarce healthcare settings. However, excessive latent states and interactions from mechanistic models can lead to training inefficiency and over-fitting, limiting practical effectiveness of hybrid neural ODEs. In response, we propose a new hybrid pipeline for automatic state selection and structure optimization in mechanistic neural ODEs, combining domain-informed graph modifications […]

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arXiv:2505.15008v3 Announce Type: replace-cross Abstract: Selective classification enhances the reliability of predictive models by allowing them to abstain from making uncertain predictions. In this work, we revisit the design of optimal selection functions through the lens of the Neyman–Pearson lemma, a classical result in statistics that characterizes the optimal rejection rule as a likelihood ratio test. We show that this perspective not only unifies the behavior of several post-hoc selection baselines, but also motivates new approaches to selective […]

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arXiv:2505.13614v3 Announce Type: replace-cross Abstract: The high-dimensional parameter space of deep neural networks — the neuromanifold — is endowed with a unique metric tensor defined by the Fisher information. Reliable and scalable computation of this metric tensor is valuable for theorists and practitioners. Focusing on neural classifiers, we return to a low-dimensional space of probability distributions, which we call the core space, and examine the spectrum and envelopes of its Fisher information matrix. We extend our discoveries there […]

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arXiv:2502.13583v4 Announce Type: replace-cross Abstract: A substantial body of work in machine learning (ML) and randomized numerical linear algebra (RandNLA) has exploited various sorts of random sketching methodologies, including random sampling and random projection, with much of the analysis using Johnson–Lindenstrauss and subspace embedding techniques. Recent studies have identified the issue of inversion bias — the phenomenon that inverses of random sketches are not unbiased, despite the unbiasedness of the sketches themselves. This bias presents challenges for the […]

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