Research Papers

arXiv:2512.20063v3 Announce Type: replace Abstract: We introduce $\texttt{PairFlow}$, a lightweight preprocessing step for training Discrete Flow Models (DFMs) to achieve few-step sampling without requiring a pretrained teacher. DFMs have recently emerged as a new class of generative models for discrete data, offering strong performance. However, they suffer from slow sampling due to their iterative nature. Existing acceleration methods largely depend on finetuning, which introduces substantial additional training overhead. $\texttt{PairFlow}$ addresses this issue with a lightweight preprocessing step. Inspired by ReFlow and its extension to DFMs, we train DFMs from coupled samples of source and target distributions, without requiring any pretrained teacher. At the core of our approach is a closed-form inversion for DFMs, which allows efficient construction of paired source-target samples. Despite its extremely low cost, taking only up to 1.7% of the compute needed for full model train

arXiv:2512.21208v3 Announce Type: replace Abstract: We develop a finite-dimensional sensitivity framework for studying stability in learning systems whose states include representations, parameters, and update variables. The central object is the \emph{Learning Stability Profile}, a collection of directional sensitivity operators that records how perturbations in inputs, parameter initialization, and update mechanisms propagate along a specified learning trajectory. The main result is a Lyapunov criterion for controlling this profile. Under explicit regularity, coercivity, and dissipation assumptions, an incremental Lyapunov energy yields uniform or exponentially decaying bounds on the associated linearized transition operators. The result is stated as a sufficient stability criterion, not as an unconditional converse theorem. The framework also distinguishes terminal decay, profile-wise boundedness, and subexponential growth, avoiding the identification of nonpositive growth exponents

arXiv:2512.24075v5 Announce Type: replace Abstract: Early lane-change intention prediction is essential for autonomous driving and ADAS, but it remains challenging because lane-changing behavior depends on evolving traffic risk, surrounding-vehicle interactions, and target-lane feasibility rather than only instantaneous vehicle states. This study proposes an evolutionary physics-informed temporal fusion framework for three-class lane-change intention prediction, including left lane change, right lane change, and no lane change. Instead of using static physics-informed variables alone, the proposed method derives temporal descriptors from conventional traffic signals, including risk evolution, gap persistence, counterfactual lane utility, interaction pressure gradient, maneuver feasibility, and intent consistency. These descriptors are fused with temporal embeddings learned from raw trajectory sequences through a sequence encoder, and the fused representation is used for final classific

arXiv:2601.10012v2 Announce Type: replace Abstract: Multimodal decentralized federated learning (DFL) must support collaboration among agents that hold different modality subsets and often different model components, while operating over peer-to-peer (P2P) overlays without a coordinating server or a global network view. A key obstacle is that conventional multimodal training often relies on a single shared representation, which implicitly assumes that heterogeneous peers can exchange and aggregate the same model components over the same communication links. In multimodal DFL, this assumption breaks down: uni- and multimodal agents may push incompatible updates through shared overlays, weakening both inter-agent transfer and cross-modal interaction. We present PARSE, a server-free framework that brings partial information decomposition (PID) into multimodal DFL. Each agent splits its latent features into redundant, unique, and synergistic slices ("feature fission"), and performs slice-a

arXiv:2601.14653v2 Announce Type: replace Abstract: Missing data in single-cell sequencing datasets poses significant challenges for extracting meaningful biological insights. However, existing imputation approaches, which often assume uniformity and data completeness, struggle to address cases with large patches of missing data. In this paper, we present CROT (Cluster-Regularized Optimal Transport), an optimal transport-based imputation algorithm designed to handle patch-based missing data in tabular formats. Our approach effectively captures the underlying data structure in the presence of significant missingness. Notably, it achieves superior imputation accuracy while significantly reducing runtime, demonstrating its scalability and efficiency for large-scale datasets. This work introduces a robust solution for imputation in heterogeneous, high-dimensional datasets with structured data absence, addressing critical challenges in both biological and clinical data analysis. Our code is

arXiv:2601.19070v2 Announce Type: replace Abstract: We rigorously study the thermodynamic limit of deep neural networks (DNNS) and recurrent neural networks (RNNs), assuming that the activation functions are sigmoids. A thermodynamic limit is a continuous neural network, where the neurons form a continuous space with infinitely many points. We show that such a network admits a unique state in a certain region of the parameter space, which depends continuously on the parameters. This state breaks into an infinite number of states outside the mentioned region of parameter space. Then, the critical organization is a bifurcation in the parameter space, where a network transitions from a unique state to infinitely many states. We use p-adic integers to codify hierarchical structures. Indeed, we present an algorithm that recasts the hierarchical topologies used in DNNs and RNNs as p-adic tree-like structures. In this framework, the hierarchical and the critical organizations are connected. W

arXiv:2601.19597v5 Announce Type: replace Abstract: While InfoNCE underlies modern contrastive learning, its geometric mechanisms remain under-characterized beyond the canonical alignment--uniformity decomposition. We develop a measure-theoretic framework in which representation measures evolve on a fixed embedding manifold. In the large-batch limit, we prove value and gradient consistency, linking the stochastic objective to explicit deterministic energy landscapes and revealing a geometric bifurcation between unimodal and symmetric multimodal regimes. In the unimodal case, the intrinsic energy is strictly convex and admits a unique Gibbs equilibrium, showing that entropy acts as a tie-breaker within the aligned basin. In the multimodal case, the intrinsic geometry becomes cross-coupled and contains a persistent negative symmetric divergence term: each modality's marginal reshapes the effective landscape of the other, allowing strong pairwise alignment to coexist with a persistent mod

arXiv:2601.21924v2 Announce Type: replace 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 correct abstraction for transfer in online RL and propose re-weighted targeting (RWT), an operator-level correction that retargets continuation values and compensates for transition mismatch via a change of measure. RWT reduces task mismatch to a fixed one-step correction and enables statistically sound reuse of source data. This alignment yields a two-stage RWT $Q$-learning framework that separates variance reduction from bias

arXiv:2601.22466v2 Announce Type: replace Abstract: Structure-Based Drug Design (SBDD) aims to discover bioactive ligands. Conventional approaches construct probability paths separately in Euclidean and probabilistic spaces for continuous atomic coordinates and discrete chemical categories, leading to a mismatch with the underlying statistical manifolds. We address this issue by representing molecules using composite exponential-family distributions, where coordinates and categories are represented within a unified natural parameter space to evolve synchronously along exponential geodesics under the Fisher-Rao metric. To avoid the instantaneous trajectory collapse induced by geodesics directly targeting Dirac distributions, we propose Evolving Exponential Geodesic Flow for SBDD (EvoEGF-Mol), which replaces static Dirac targets with dynamically concentrating distributions and is trained with a progressive-parameter-refinement architecture. Our model approaches a reference-level PoseBust

arXiv:2601.23164v2 Announce Type: replace Abstract: We study the stochastic linear bandits with parameter noise model, in which the reward of action $a$ is $a^\top \theta$ where $\theta$ is sampled i.i.d. We show a regret upper bound of $\widetilde{O} (\sqrt{d T \log (K/\delta) \sigma^2_{\max})}$ for a horizon $T$, general action set of size $K$ of dimension $d$, and where $\sigma^2_{\max}$ is the maximal variance of the reward for any action. We further provide a lower bound of $\widetilde{\Omega} (d \sqrt{T \sigma^2_{\max}})$ which is tight (up to logarithmic factors) whenever $\log (K) \approx d$. For more specific action sets, $\ell_p$ unit balls with $p \leq 2$ and dual norm $q$, we show that the minimax regret is $\widetilde{\Theta} (\sqrt{dT \sigma^2_q)}$, where $\sigma^2_q$ is a variance-dependent quantity that is always at most $4$. This is in contrast to the minimax regret attainable for such sets in the classic additive noise model, where the regret is of order $d \sqrt{T}$.

arXiv:2602.00511v2 Announce Type: replace Abstract: Despite their empirical success, neural network classifiers remain difficult to interpret. In softmax-based models, class regions are defined implicitly as solutions to systems of inequalities among logits, making them difficult to extract and visualize. We introduce Partition of Unity Neural Networks (PUNN), an architecture in which class probabilities arise directly from a learned partition of unity, without requiring a softmax layer. PUNN constructs $k$ nonnegative functions $h_1, \ldots, h_k$ satisfying $\sum_i h_i(x) = 1$, where each $h_i(x)$ directly represents $P(\text{class } i \mid x)$. Unlike softmax, where class regions are defined implicitly through coupled inequalities among logits, each PUNN partition function $h_i$ directly defines the probability of class $i$ as a standalone function of $x$. We prove that PUNN is dense in the space of continuous probability maps on compact domains. The gate functions $g_i$ that define

arXiv:2602.00545v3 Announce Type: replace Abstract: The eigenvalue distribution of the Hessian matrix plays a crucial role in understanding the optimization landscape of deep neural networks. Prior work has attributed the well-documented ``bulk-and-spike'' spectral structure, where a few dominant eigenvalues are separated from a bulk of smaller ones, to the imbalance in the data covariance matrix. In this work, we challenge this view by demonstrating that such spectral Bifurcation can arise purely from the network architecture, independent of data imbalance. Specifically, we analyze a deep linear network setup and prove that, even when the data covariance is perfectly balanced, the Hessian still exhibits a Bifurcation eigenvalue structure: a dominant cluster and a bulk cluster. Crucially, we establish that the ratio between dominant and bulk eigenvalues scales linearly with the network depth. This reveals that the spectral gap is strongly affected by the network architecture rather tha

arXiv:2602.01322v2 Announce Type: replace Abstract: Sparse autoencoders (SAEs) interpret neural network representations by decomposing activations into sparse combinations of dictionary atoms. However, SAEs assume features combine additively through linear reconstruction, an assumption that cannot capture compositional structure: linear models cannot distinguish whether ''Starbucks'' arises from the composition of ''star'' and ''coffee'' features or merely their co-occurrence. This forces SAEs to allocate monolithic features for compound concepts rather than decomposing them into interpretable constituents. We introduce PolySAE, which extends the SAE decoder with higher-order terms to model feature interactions while preserving the linear encoder essential for interpretability. Through low-rank tensor factorization on a shared projection subspace, PolySAE captures pairwise and triple feature interactions with small parameter overhead (3% on GPT2). Across four language models and three

arXiv:2602.02009v2 Announce Type: replace Abstract: Neuro-symbolic systems aim to combine the expressive structure of symbolic logic with the flexibility of neural learning; yet, generative models typically lack mechanisms to enforce declarative constraints at generation time. We propose Logic-Guided Vector Fields (LGVF), a neuro-symbolic framework that injects symbolic knowledge, specified as differentiable relaxations of logical constraints, into flow matching generative models. LGVF couples two complementary mechanisms: (1) a training-time logic loss that penalizes constraint violations along continuous flow trajectories, with weights that emphasize correctness near the target distribution; and (2) an inference-time adjustment that steers sampling using constraint gradients, acting as a lightweight, logic-informed correction to the learned dynamics. We evaluate LGVF on three constrained generation case studies spanning linear, nonlinear, and multi-region feasibility constraints. Acr

arXiv:2602.04139v2 Announce Type: replace Abstract: Neural operators provide a powerful framework for learning discretization invariant mappings between function spaces, but standard deterministic models do not capture predictive uncertainty. We introduce diffusion last layer (DLL), a modular probabilistic output head for neural operator backbones. DLL represents target fields through an input dependent low rank expansion inspired by the Karhunen-Lo\'eve expansion and learns a conditional diffusion model over the corresponding coefficient space. This design enables efficient distributional modeling while preserving the structural advantages of operator learning. On stochastic PDE benchmarks with random forcing, DLL achieves strong distributional fidelity and performs competitively with pixel space and conventional latent diffusion baselines. In deterministic long horizon rollout tasks, DLL improves rollout stability over the underlying backbone and provides useful estimates of predicti