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arXiv2025

Provably Efficient Reward Transfer in Reinforcement Learning with Discrete Markov Decision Processes

In this paper, we propose a new solution to reward adaptation (RA) in reinforcement learning, where the agent adapts to a target reward function based on one or more existing source behaviors learned a priori under the same domain dynamics but different reward functions. While learning the target behavior from scratch is possible, it is often inefficient given the available source behaviors. Our work introduces a new approach to RA through the manipulation of Q-functions. Assuming the target reward function is a known function of the source reward functions, we compute bounds on the Q-function and present an iterative process (akin to value iteration) to tighten these bounds. Such bounds enable action pruning in the target domain before learning even starts. We refer to this method as "Q-Manipulation" (Q-M). The iteration process assumes access to a lite-model, which is easy to provide or learn. We formally prove that Q-M, under discrete domains, does not affect the optimality of the returned policy and show that it is provably efficient in terms of sample complexity in a probabilistic sense. Q-M is evaluated in a variety of synthetic and simulation domains to demonstrate its effectiveness, generalizability, and practicality.

cs.LG↗
arXiv2026

Step Back to Move Forward: Reflection-Aware Preference Optimization for Visual Generation

Diffusion models have become the mainstream paradigm for modern visual generation and have substantially advanced multimedia content synthesis, especially in text-to-image and text-to-video tasks. To further align such generative models with human preferences, reinforcement learning (RL) has recently shown strong potential as a post-training strategy. Nevertheless, existing policy gradient-based methods often explore inefficiently, making them vulnerable to local optima that may degrade semantic faithfulness and visual realism. To address these challenges, we present Reflection-Aware GRPO (RA-GRPO), a new RL-based preference alignment framework for diffusion generative models. The core idea is to improve "forward" generation by incorporating "backward" reflection during optimization. We first introduce Diffusion Reflection, which rectifies intermediate sampling trajectories by inverting the diffusion process with a weak estimator, guiding latent states toward higher-probability regions of the true data manifold. Furthermore, we introduce Counterfactual Path Synthesis to implicitly distill these rectified trajectories into the policy, enabling the model to internalize the benefits of search-based exploration without incurring inference-time overhead. Extensive experiments on T2I and T2V models demonstrate that RA-GRPO significantly outperforms existing methods, particularly in mitigating reward hacking and improving generalization. The method remains architecture-agnostic and integrates seamlessly with standard pipelines, suggesting a promising direction for stable preference alignment.

cs.CV↗
arXiv2026

Are Economists Open to AI? A Text-as-Data-as-Survey Approach via Language Models

Traditional surveys yield comparable measures but are costly to field, difficult to reconstruct retrospectively, and often ill-suited to fast-moving or sensitive topics. While large-scale internet text is often noisy and weakly structured. To bridge this gap, we introduce Text-as-Data-as-Survey (TaDaS). TaDaS employs Reference-Anchored Semantic Reparameterization (RAS) to project unstructured main text into survey-like evidence, leveraging structured auxiliary text as semantic anchors. Applying TaDaS to 1.25 million Economics Job Market Rumors posts linked with 53,585 top economics and finance publications, we track economists' evolving research sentiment toward AI. Cross-sectionally, AI-related research discussions are less open, with openness and curiosity declining rapidly at first years. Over time, however, economists have become increasingly open and curious, with a notable shift around 2018. Ultimately, TaDaS provides a scalable, non-reactive method to extract longitudinal insights from digital archives, unlocking diverse applications across industry and academia.

cs.CE↗
arXiv2026

A Tri-Agent Framework for Evaluating and Aligning Question Clarification Capabilities of Large Language Models

Large Language Models (LLMs) are increasingly deployed in interactive systems where understanding user intent precisely is paramount. A key capability for such systems is effective question clarification, especially when user queries are ambiguous or underspecified. This paper introduces a novel tri-agent framework for the robust evaluation of an LLM's ability to engage in clarifying dialogue. Our framework comprises three distinct LLM-based agents: (1) a Question Clarifying Agent (QCA), the system under evaluation, tasked with identifying ambiguities and posing clarifying questions; (2) a Respondent Agent (RA), designed to simulate human user responses, potentially including irrelevant or challenging replies; and (3) an Evaluator Agent (EA), an LLM-as-a-judge, which assesses the quality of the dialogue based on a comprehensive set of metrics. We detail a methodology for synthetic data generation in the supply chain domain as an example. We propose metrics evaluating ambiguity handling, question quality, dialogue efficiency, language appropriateness, and final intent alignment. We also briefly discuss the validation of the EA against human judgments. This work provides a structured approach to benchmark, validate, and improve the clarification capabilities of conversational LLM applications.

cs.CL↗
arXiv2026

ScoreMix: Synthetic Data Generation by Score Composition in Diffusion Models Improves Recognition

Synthetic data generation is increasingly used in machine learning for training and data augmentation. Yet, current strategies often rely on external foundation models or datasets, whose usage is restricted in many scenarios due to policy or legal constraints. We propose ScoreMix, a self-contained synthetic generation method to produce hard synthetic samples for recognition tasks by leveraging the score compositionality of diffusion models. The approach mixes class-conditioned scores along reverse diffusion trajectories, yielding domain-specific data augmentation without external resources. We systematically study class-selection strategies and find that mixing classes distant in the discriminator's embedding space yields larger gains, providing up to 3% additional average improvement, compared to selection based on proximity. Interestingly, we observe that condition and embedding spaces are largely uncorrelated under standard alignment metrics, and the generator's condition space has a negligible effect on downstream performance. Across 8 public face recognition benchmarks, ScoreMix improves accuracy by up to 7 percentage points, without hyperparameter search, highlighting both robustness and practicality. Our method provides a simple yet effective way to maximize discriminator performance using only the available dataset, without reliance on third-party resources. Paper website: https://parsa-ra.github.io/scoremix/.

cs.CV↗
arXiv2026

Star-Fusion: A Multi-modal Transformer Architecture for Discrete Celestial Orientation via Spherical Topology

Reliable celestial attitude determination is a critical requirement for autonomous spacecraft navigation, yet traditional "Lost-in-Space" (LIS) algorithms often suffer from high computational overhead and sensitivity to sensor-induced noise. While deep learning has emerged as a promising alternative, standard regression models are often confounded by the non-Euclidean topology of the celestial sphere and by the periodic boundary conditions of Right Ascension (RA) and Declination (Dec). In this paper, we present Star-Fusion, a multi-modal architecture that reformulates orientation estimation as a discrete topological classification task. Our approach leverages spherical K-Means clustering to partition the celestial sphere into K topologically consistent regions, effectively mitigating coordinate wrapping artifacts. The proposed architecture employs a tripartite fusion strategy: a SwinV2-Tiny transformer backbone for photometric feature extraction, a convolutional heatmap branch for spatial grounding, and a coordinate-based MLP for geometric anchoring. Experimental evaluations on a synthetic Hipparcos-derived dataset demonstrate that Star-Fusion achieves a Top-1 accuracy of 93.4% and a Top-3 accuracy of 97.8%. Furthermore, the model exhibits high computational efficiency, maintaining an inference latency of 18.4 ms on resource-constrained COTS hardware, making it a viable candidate for real-time onboard deployment in next-generation satellite constellations.

cs.CV↗
arXiv2026

CMRVision: A Foundation Model for Cardiac MR Image Analysis

Cardiac magnetic resonance (CMR) imaging provides complementary information on cardiac anatomy, function, and tissue characterization across multiple sequences and views. In this work, we investigate foundation model pretraining for 2D CMR and introduce CMRVision, a CMR-specific foundation model trained using DINOv3-style self-supervised learning on a multi-center, multi-sequence cohort of 36 million CMR images. We systematically evaluate architectural and training design choices for domain-specific pretraining. CMRVision is evaluated on two downstream tasks: multi-task segmentation across cine, late gadolinium enhancement (LGE), and mapping sequences, and cine view classification. Our experiments show that CMR-specific pretraining, smaller patch sizes, and patch-level objectives consistently improve downstream performance. Across a multi-task segmentation benchmark, CMRVision achieved the strongest overall performance, outperforming prior natural-image (NI), medical-image, supervised, and CMR foundation model baselines. Improvements were modest but consistent across structures and sequences, with Dice scores ranging from 0.940-0.967 for LV and 0.855-0.905 for myocardium, and reaching 0.929 for RV, 0.920 for LA, and 0.931 for RA. The largest gains were observed for myocardium segmentation in LGE and mapping images. In a zero-shot segmentation task on unseen LGE long-axis views, the model achieved an average Dice score of 0.692, demonstrating cross-view generalization. For cine view classification, CMRVision achieved the highest average accuracy (0.906), compared to prior methods reported in the literature. These results highlight the potential of CMRVision to support robust and generalizable cardiac MRI analysis across multiple sequences and views.

cs.CV↗
arXiv2026

AlcaTRAz - Anchored Tree-Rule Defense Against Jailbreaks

Large language models (LLMs) are vulnerable to jailbreak attacks that bypass safety alignment through carefully crafted prompts. Many existing defenses require access to model weights or internals, making them difficult to apply to black-box deployments. We propose AlcaTRAz (Anchored Tree-Rule defense Against jailbreaks), a prompt-level defense based on rule trees that operates exclusively on the input text and requires no modification or retraining of the target model. The method automatically learns a transferable transformation rule that inserts controlled character-level perturbations at selected positions, thereby disrupting structural regularities exploited by jailbreak attacks while largely preserving the model's utility on benign queries. We evaluate the proposed method across 33 open-weight models, 22 jailbreak attack types, and a benchmark of short, single-turn benign questions, comparing against three representative prompt-level baselines (Llama Guard, RA-LLM, Goal Prioritization). Among the compared defenses, AlcaTRAz achieves the best composite security and functionality score in 73.4 % of model-attack combinations and shifts the aggregate score from a modal value of 10 (maximal-severity response to the malicious request) in the undefended setting to a modal value of 2 (near-refusal) after defense, while keeping the mean benign score within 0.27 points of the undefended baseline (8.35 vs. 8.62 on a 0-10 scale). AlcaTRAz substantially reduces but does not eliminate jailbreak success: a high-severity tail remains, and we do not consider adaptive attackers, so we position it as one layer within a defense-in-depth strategy rather than a standalone guarantee.

cs.CR↗
arXiv2005

The maximum entropy state

We give an algorithm for calculating the maximum entropy state as the least fixed point of a Scott continuous mapping on the domain of classical states in their Bayesian order.

math.PR↗
arXiv2026

Eigenvalues and eigenfunctions of the fractional Laplacian on the interval

We prove a three-term asymptotic formula for the eigenvalues of the fractional Laplacian on the bounded interval $(-1,1)$. This improves the eigenvalue asymptotics of Kulczycki--Kwaśnicki--Małecki--Stós and Kwaśnicki, and confirms the conjectural $O_α(n^{-2})$ remainder suggested by the numerical simulations of Kaleta--Kwaśnicki--Małecki. Moreover, we prove that the normalized eigenfunctions are bounded uniformly in the eigenvalue index $n$ and the fractional order $α$. This settles the conjecture proposed by Kwaśnicki through numerical experiments. Furthermore, we prove that the $n$-th eigenfunction has exactly $n-1$ zeros in the interval $(-1,1)$ and every zero is simple, and hence there are exactly $n$ nodal domains. A key ingredient in the proof is an explicit representation of the eigenfunction.

math.CA↗
arXiv2025

Turing complete Navier-Stokes steady states via cosymplectic geometry

In this article, we construct stationary solutions to the Navier-Stokes equations on certain Riemannian $3$-manifolds that exhibit Turing completeness, in the sense that they are capable of performing universal computation. This universality arises on manifolds admitting nonvanishing harmonic 1-forms, thus showing that computational universality is not obstructed by viscosity, provided the underlying geometry satisfies a mild cohomological condition. The proof makes use of a correspondence between nonvanishing harmonic $1$-forms and cosymplectic geometry, which extends the classical correspondence between Beltrami fields and Reeb flows on contact manifolds.

math.DG↗
arXiv2026

Geometric mean and Lebesgue-type decomposition of completely positive maps

We introduce the geometric mean and the parallel sum of completely positive (CP) maps between von Neumann algebras, based on the Pusz--Woronowicz theory of positive sesquilinear forms. We provide a concrete characterization via a block matrix positivity condition and establish their fundamental properties, including the AM--GM--HM inequality with respect to the CP order. In finite-dimensional settings, our construction is compatible with the Choi--Jamiolkowski correspondence, under which the geometric mean of CP maps corresponds to the Kubo--Ando geometric mean of their Choi matrices. This yields a natural operator-theoretic framework for interpolating quantum channels. As an application, we obtain index-type inequalities for conditional expectations in subfactor theory. Finally, we establish a Lebesgue-type decomposition of CP maps via a parallel sum construction, thereby providing a unified framework that simultaneously generalizes Ando's decomposition of bounded positive operators and Kosaki's decomposition of normal positive functionals on von Neumann algebras.

math.OA↗
arXiv2026

An Inverse Problem for Determining the Piston Speed from a Given Lipschitz Leading Shock

We analyze an inverse problem for determining the piston speed and the associated flow field from a prescribed leading shock and the initial data in a shock tube. The gas flow is described by the isentropic Euler equations (i.e., the $p$-system), while the trajectory of the leading shock is prescribed as a given Lipschitz curve. Under an Oleĭnik-type entropy condition on the leading shock, we develop a modified wavefront tracking scheme to construct the flow field behind the shock. This construction enables us to determine the corresponding piston speed and the associated flow field.

math.AP↗
arXiv2026

Two Adjoint Perspectives on Fokker-Planck Optimization: A Microscopic-Macroscopic Correspondence

The Fokker-Planck equation admits both a macroscopic Eulerian description through probability densities and a microscopic Lagrangian description through stochastic trajectories. Consequently, optimization problems constrained by the Fokker-Planck equation can be formulated from either perspective. Surprisingly, the corresponding adjoint equations appear to be fundamentally different: the macroscopic adjoint is governed by the backward Kolmogorov equation, whereas the microscopic adjoint evolves pathwise along stochastic trajectories. In this note, we reconcile these two formulations by establishing their correspondence in the continuum setting. We further show that, although their discrete gradients no longer coincide after discretization, both provide consistent numerical approximations of the continuum gradient. Explicit convergence rates are established for both discretization strategies.

math.NA↗
arXiv2026

Multiplicative comparisons of Rényi entropies for weighted Bernoulli sums

We establish improved multiplicative bounds relating the Rényi entropies of different orders for weighted sums of independent Bernoulli random variables. In particular, we prove a logarithmic bound between the zeroth-order and infinity-order Rényi entropies, which yields a polynomial improvement over the square-root bound of Jain, Sah, and Sawhney. Additionally, we obtain explicit constant-factor bounds for comparisons among Rényi entropies of nonzero orders.

math.PR↗
arXiv2026

Set Theory in the Foundation of Math; Internal Classes and External Sets

Usual math sets have special types: countable, compact, open, occasionally Borel, rarely projective, etc. Each such set is described by a single set theory formula with parameters unrelated to formulas. Exotic expressions involving sets related to formulas of unbounded quantifier depth appear mostly in esoteric or foundational studies. Recognizing the internal to math (formula-specified) and external (parameter-based) aspects of math objects greatly simplifies foundations. I postulate that external sets (not internally specified, constituting the domain of quantifiable variables) are hereditarily countable and independent of purely formula-defined classes, i.e. with finite algorithmic information about them. Variables for classes are not explicitly quantified. This opens a way to eliminate all non-integer quantifiers in set theory sentences. The restrictions seem to require almost no changes in math papers, only reinterpreting some formalities.

cs.LO↗
arXiv2026

Harmonic higher weight distributions, Simonis' approach of MacWilliams identity and moments

We present a combinatorial proof of Simonis type MacWilliams identity for harmonic higher weight distributions of linear codes. Furthermore, we investigate the statistical moments of the harmonic higher weight enumerators for random linear codes. Defining the enumerators via rank functions of the generator matrices of linear codes, we prove that its expectation vanishes for all non-trivial harmonic functions due to the inherent symmetry of random matrices, and we also derive an explicit, non-trivial formula for the covariance.

math.CO↗