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arXiv2026

Robust Tangent Space Estimation via Laplacian Eigenvector Gradient Orthogonalization

Estimating the tangent spaces of a data manifold is a fundamental problem in geometric data analysis. The standard approach, Local Principal Component Analysis (LPCA), struggles in high-noise settings due to a critical trade-off in choosing the neighborhood size. Selecting an optimal size requires prior knowledge of the geometric and noise characteristics of the data that are often unavailable. In this paper, we propose a spectral method, Laplacian Eigenvector Gradient Orthogonalization (LEGO), that utilizes the global structure of the data to guide local tangent space estimation. Instead of relying solely on local neighborhoods, LEGO estimates the tangent space at each data point by orthogonalizing the gradients of low-frequency eigenvectors of the graph Laplacian. We provide two theoretical justifications of our method. First, a differential geometric analysis on the tubular neighborhood of a manifold shows that gradients of the low-frequency Neumann eigenfunctions of the tube align closely with the manifold's tangent bundle, while an eigenfunction with high gradient in directions orthogonal to the manifold lies deeper in the spectrum. Second, a random matrix theoretic analysis also demonstrates that low-frequency eigenvectors are robust to sub-Gaussian noise. These results allow us to derive the asymptotic scaling and stability of the estimated eigenvector gradients. Numerical experiments demonstrate that LEGO yields tangent space estimates that are significantly more robust to noise than those from LPCA, resulting in marked improvements in downstream tasks such as manifold learning, boundary detection, and local intrinsic dimension estimation.

cs.LG↗

arXiv2026

To Distill or Decide? Understanding the Algorithmic Trade-off in Partially Observable Reinforcement Learning

Partial observability is a notorious challenge in reinforcement learning (RL), due to the need to learn complex, history-dependent policies. Recent empirical successes have used privileged expert distillation--which leverages availability of latent state information during training (e.g., from a simulator) to learn and imitate the optimal latent, Markovian policy--to disentangle the task of "learning to see" from "learning to act". While expert distillation is more computationally efficient than RL without latent state information, it also has well-documented failure modes. In this paper--through a simple but instructive theoretical model called the perturbed Block MDP, and controlled experiments on challenging simulated locomotion tasks--we investigate the algorithmic trade-off between privileged expert distillation and standard RL without privileged information. Our main findings are: (1) The trade-off empirically hinges on the stochasticity of the latent dynamics, as theoretically predicted by contrasting approximate decodability with belief contraction in the perturbed Block MDP; and (2) The optimal latent policy is not always the best latent policy to distill. Our results suggest new guidelines for effectively exploiting privileged information, potentially advancing the efficiency of policy learning across many practical partially observable domains.

cs.LG↗

arXiv2026

Gamma Convergence and Smooth Exact-segregation Approximation for Partially Segregated Systems

We study three-component Dirichlet energies subject to the partial segregation constraint $u_1u_2u_3=0$. Our main result is a smooth approximation theorem on bounded Lipschitz domains in arbitrary dimension. For compatible nonnegative Lipschitz boundary data, every admissible $H^1$ configuration can be approximated strongly in $H^1$ by globally Lipschitz maps that are smooth in the interior and preserve both the prescribed boundary trace and the segregation constraint exactly. The construction combines a Lipschitz retraction, variable-radius mollification, and smooth truncation preserving existing zeros, without assumptions on interfaces or junctions. Under the weaker assumption of compatible nonnegative $H^{1/2}$ boundary data, we establish existence of minimizers and $Γ$-convergence in $L^2$ for the energies with product penalization $\varepsilon^{-1}\int_Ω(u_1u_2u_3)^2\,dx$. We also identify the exact $L^2$ distance to the constrained class and construct segregated corrections with controlled Dirichlet energy. The resulting correction estimate has order $\varepsilon^{1/6}$ for bounded-energy configurations; this exponent is sharp in general and improves to $o(\varepsilon^{1/6})$ for almost-minimizers.

math.AP↗

arXiv2026

DynamiQ: Unlocking the Potential of Dynamic Task Allocation in Parallel Fuzzing

We present DynamiQ, a full-fledged and optimized successor to AFLTeam that supports dynamic and adaptive parallel fuzzing. Unlike most existing approaches that treat individual seeds as tasks, DynamiQ leverages structural information from the program's call graph to define tasks and continuously refines task allocation using runtime feedback. This design significantly reduces redundant exploration and enhances fuzzing efficiency at scale. Built on top of the state-of-the-art LibAFL framework, DynamiQ incorporates several practical optimizations in both task allocation and task-aware fuzzing. We evaluate DynamiQ on eighteen targets from Magma and FuzzBench with a total budget of over 40 CPU years. It achieves the highest mean branch coverage on fourteen targets, with average relative gains ranging from 8.37% to 19.53% over five baseline fuzzers. Across our experiments, DynamiQ identifies nine previously unknown bugs.

cs.SE↗

arXiv2026

Global non-equilibrium thermodynamics of stationary states applied to the Rayleigh-Bénard convection

Classical thermodynamics describes physical systems in thermodynamic equilibrium, characterized in particular by the absence of macroscopic motion. Global non-equilibrium thermodynamics extends this framework to include physical systems in stationary states (Hołyst et al., EPL 149, 30001 (2025)). Here, we demonstrate that this extended theory captures macroscopic motion in stationary states, thereby providing a unified framework for global thermodynamics and fluid mechanics. We apply the theory to stationary Rayleigh-Bénard convection and show how the second law of global non-equilibrium thermodynamics determines the direction of changes in fluid motion.

physics.flu-dyn↗

arXiv2026

Group Contrastive Policy Optimization: Learning Beyond the Self-Exploration Limit with Golden Answers

Reinforcement learning with verifiable rewards (RLVR) has become a powerful paradigm for improving the reasoning abilities of large language models, yet group-based methods lose their learning signal when every sampled response receives zero reward. We propose Group Contrastive Policy Optimization (GCPO), a hybrid objective that preserves standard on-policy optimization for informative rollout groups and activates a proximal contrastive objective only when exploration completely fails. The auxiliary objective pairs an offline golden reasoning trajectory with the current policy's failed responses, thereby providing a reliable positive reference and prompt-specific hard negatives without treating the golden trajectory as an on-policy rollout. Its old-policy token probabilities are evaluated through teacher forcing and used solely to constrain the update, rather than as an importance-sampling correction for the teacher distribution. A first-order analysis shows that the resulting update increases a length-normalized likelihood margin between reliable reasoning and observed failures. Experiments across two model scales and 10 core mathematical reasoning benchmarks demonstrate that GCPO improves training efficiency and final reasoning performance over competitive supervised and RLVR baselines.

cs.AI↗

arXiv2026

How to Teach Large Multimodal Models New Skills

How can we teach large multimodal models (LMMs) new skills without erasing prior abilities? We study sequential fine-tuning on five target skills while monitoring general ability on eight held-out benchmarks across three model families. Surprisingly, we find that performance lost on held-out tasks after fine-tuning on one skill can partly recover when the model is subsequently tuned on a different skill. We trace this behavior to a measurable shift in the output token distribution, manifested through a simple counting-bias probe that shows the shift co-varies with forgetting. Guided by this insight, we identify two simple, robust tuning recipes that learn strongly while limiting drift: (i) updating only the self-attention projection layers (SA Proj., $Δ$ learning +24.9 / $Δ$ held-out forgetting -0.6), and (ii) updating only the MLP Gate&Up while freezing the Down projection (+30.5 / -2.1). Both substantially outperform full-LLM tuning (+31.8 / -23.3) in the learning-forgetting trade-off. We also compare against common forgetting mitigation methods: Learning without Forgetting (LwF), LoRA, Mixture-of-Experts, and weight-space interpolation (WiSE-FT), and find that our selective tuning recipes match or exceed their learning-stability balance while remaining simpler, requiring no replay, auxiliary parameters, or per-stage tuning. These results hold across LLaVA-OneVision, LLaVA-NeXT, and Qwen2.5-VL, confirming that the key to teaching LMMs new skills without forgetting lies in controlling output distribution shift by choosing which components to tune. Code will be made available.

cs.AI↗

arXiv2026

Probing the Dependence of Partonic Energy Loss on the Initial Energy Density of the Quark Gluon Plasma

Considerable evidence now exists for partonic energy loss due to interaction with the hot, dense medium created in ultra-relativistic heavy-ion collisions. A primary signal of this energy loss is the suppression of high transverse momentum $p_{\mathrm{T}}$ hadron yields in A-A collisions relative to appropriately scaled $pp$ collisions at the same energy. Measuring the collision energy dependence of this energy loss is vital to understanding the medium, but it is difficult to disentangle the medium-driven energy loss from the natural kinematic variance of the steeply-falling $p_{\mathrm{T}}$ spectra across different $\sqrt{s_{\mathrm{NN}}}$. To decouple these effects, we utilize a phenomenologically motivated spectrum shift model to estimate the average transverse momentum loss $Δp_{\mathrm{T}}$ imparted on high $p_{\mathrm{T}}$ partons in A-A collisions, a proxy for the medium induced energy loss. We observe a striking correlation between $Δp_{\mathrm{T}}$ and Glauber-derived estimates of initial state energy density $\varepsilon_{\mathrm{Bj}}$, consistent across two orders of magnitude in collision energy for a variety of nuclear species. To access the path-length dependence of energy loss, we couple our model to geometric event shape estimates extracted from Glauber calculations to produce predictions for high-$p_{\mathrm{T}}$ hadron elliptic flow $v_2$ that agree reasonably with data.

nucl-th↗

arXiv2026

Cut elimination for the alternation-free modal mu-calculus

We present a syntactic cut-elimination procedure for the alternation-free fragment of the modal mu-calculus. Cut reduction is carried out within a cyclic proof system, where proofs are finitely branching but may be non-wellfounded. The structure of such proofs is exploited to directly transform a cyclic proof with cuts into a cut-free one, without detouring through other logics or relying on intermediate machinery for regularisation. Novel ingredients include the use of multicuts and results from the theory of well-quasi-orders, the later used in the termination argument.

cs.LO↗

arXiv2026

Computationally Efficient Neural Receiver via Axial Self-Attention

Deep learning-based neural receivers offer promising physical-layer solutions for next-generation wireless systems. We propose an axial self-attention transformer neural receiver that achieves state-of-the-art Block Error Rate (BLER) performance with significantly improved computational efficiency during inference and large-scale training. By factorizing attention operations along temporal and spectral axes, the proposed architecture reduces computational complexity from $O((TF)^2)$ to $O(T^2F+TF^2)$, yielding substantially fewer floating-point operations and attention matrix multiplications per transformer block. Experimental validation under 3GPP Clustered Delay Line (CDL) channels demonstrates consistent performance gains across varying mobility scenarios. Under non-line-of-sight conditions, our proposed axial neural receiver outperforms global self-attention and convolutional neural receiver baselines at 10% BLER and 1% BLER respectively, with reduced computational complexity.

eess.SP↗

arXiv2026

Nonhomogeneous elastic turbulence in the two-dimensional Taylor-Couette flow

Elastic turbulence is a spatially and temporally disordered flow state appearing in viscoelastic fluids at vanishing fluid inertia and large elasticity. The resulting flows have broad technological interest, particularly to enhance mixing and heat transfer in microdevices. Although its experimental characterization is now well established in different setups, its theoretical understanding and numerical reproducibility remain challenging, especially in wall-bounded geometries. By means of numerical simulations, we investigate the onset of elastic turbulence and the characteristics of the developed turbulent-like states in the two-dimensional, confined, Taylor-Couette system. First, we characterize the purely elastic instability, addressing previously contrasting evidences. We then show that the fully nonlinear dynamics are weakly anisotropic and strongly nonhomogeneous. Indeed, they are confined in a dynamically active region adjacent to the inner wall, akin to the elastic boundary layer from previous predictions. Within this region,in spite of some non-negligible deviations due to the nonhomeogeneity of our setup, the statistical and spectral turbulent properties are to reasonable extent not far from the theoretical expectations and experimental observations.

physics.flu-dyn↗

arXiv2026

Human-AI Interactions and the Psychological Triad: A Multi-Domain Survey of Cognitive, Behavioral, and Emotional Impacts

As human-AI interactions increasingly reshape social and research landscapes, the risks of overreliance, cognitive offloading, and the nuanced degradation of human agency have become more apparent. This paper addresses these challenges by introducing a novel conceptual framework based on the psychological triad: cognition, behavior, and emotion. Through a comprehensive survey of recent research, we observe that while AI can substantially enhance outcomes such as memory, creativity, and engagement, it simultaneously introduces systemic risks, including diminished critical thinking, skill erosion, and increased anxiety. Emotional outcomes are shown to be similarly mixed, with AI systems offering support and stress reduction while raising critical concerns regarding dependency, inappropriate attachments, and ethical oversight. By synthesizing these findings into the TRIAD model, a recursive framework of appraisal, execution, and regulation, this paper moves beyond isolated metrics toward a systems-level understanding of how AI shapes cognitive depth, behavioral patterns, and emotional development over time. The proposed model underscores the need for responsible, context-aware AI integration and establishes a grounded evaluation framework capable of capturing the complex, human-centered trade-offs inherent in modern technological advancement.

cs.HC↗

arXiv2026

Eventually periodic resolutions with applications to integral group rings

We present a general construction of eventually periodic projective resolutions for modules over the quotient of a ring by a regular central element. Our approach combines the iterated mapping cone technique with the higher homotopies of Shamash. The periodic part of each resolution comes from a matrix factorization of the central element. The construction is applied to the integral group rings of quotients of groups of finite cohomological dimension by infinite cyclic central subgroups. We give explicit calculations for several families of groups, including hyperbolic triangle groups and the mapping class group of the plane with four punctures.

math.GR↗

arXiv2026

Star operation, microscopic sets and porous sets

This paper explores the interplay between star operations, microscopic sets, and porous sets. The study focuses on the Galvin-Mycielski-Solovay theorem, which characterizes strongly measure zero sets and their interactions with meager sets. Results include the investigation of the star operation $\mathcal{F}^*$ and its properties. The paper also examines the relationship between porous sets and microscopic sets. Additionally, the work presents constructions of families $\mathcal{F}$ in $\mathcal{P}(\mathbb{Z}), \mathcal{P}(\mathbb{Z}^ω),$ and $\mathcal{P}(2^ω)$ that satisfy $\mathcal{F} = \mathcal{F}^*$. Theorems and lemmas are provided to establish conditions under which $\mathcal{F}^{**} = \mathcal{F}$ and to analyze the implications of the Borel Conjecture and its dual. The paper concludes with a discussion of microscopic sets and their properties, including their interactions with porous sets and the non-equivalence of certain classes of sets.

math.LO↗

arXiv2026

FlowCritic: Bridging Value Estimation with Flow Matching in Reinforcement Learning

Reliable value estimation serves as the cornerstone of reinforcement learning (RL) by evaluating long-term returns and guiding policy improvement, significantly influencing the convergence speed and final performance. Existing works improve the reliability of value function estimation via multi-critic ensembles and distributional RL, yet the former merely combines multi point estimation without capturing distributional information, whereas the latter relies on discretization or quantile regression, limiting the expressiveness of complex value distributions. Inspired by flow matching's success in generative modeling, we propose a generative paradigm for value estimation, named FlowCritic. Departing from conventional regression for deterministic value prediction, FlowCritic leverages flow matching to model value distributions and generate samples for value estimation.

cs.LG↗

arXiv2026

Universal Inference for Testing Calibration and Specification of Mean Estimates within the Exponential Dispersion Family

Calibration of mean estimates is a crucial property in many applications, particularly in actuarial decision-making. Tests of mean-calibration are often performed under the assumption that the estimated means correctly preserve the ordering of the corresponding population means. In this paper, we first consider the classical Likelihood Ratio Test (LRT) within the Exponential Dispersion Family (EDF), and we show that applying likelihood-based methods to test mean-calibration within the EDF requires a strong ordering assumption on the mean estimates. This assumption makes the null hypothesis of the mean-calibration test equivalent to the correct specification of the mean estimates. Next, we investigate the framework of universal inference for testing mean-calibration and mean-specification, and the relationship between the tests. We develop a sub-sampled split LRT within the EDF that provides finite-sample guarantees with universally valid critical values. We investigate type I error, power, and e-power of the sub-sampled split LRT and compare its performance with that of the classical LRT. We also propose a novel test statistic based on a sub-sampled split $L_q$-likelihood ratio test (L$q$RT) to enhance the performance of the statistical test. Numerical results demonstrate that universal inference based on the sub-sampled split LRT and sub-sampled split L$q$RT provides an attractive alternative to the classical LRT within the EDF, achieving high power for detecting miscalibration and misspecification in medium- and large-sized samples.

stat.AP↗

arXiv2026

Revisiting GAN with Bayes-Optimal Discrimination

We approach generative adversarial network (GAN) training from its original real-versus-fake classification viewpoint, replacing the cross-entropy discriminator objective with an upper bound on the Bayes error rate (BER). Using the Bayes optimal learning threshold (BOLT) loss, we formulate an adversarial game in which the discriminator tightens this bound and the generator maximizes it. We characterize the unrestricted optimal discriminator and show that, under balanced class priors, the population game is equivalent to minimizing total variation between the data and generator distributions. Restricting the bounded discriminator to be 1-Lipschitz yields BOLT-GAN. For balanced priors and the full discriminator class, we establish upper and lower bounds relating its population discrepancy to Wasserstein-1 distance on bounded domains. Controlled experiments on four image-generation benchmarks show improved sample quality and coverage over WGAN-GP under matched architectures, optimization settings, and gradient penalties. At a common 20-epoch budget, BOLT-GAN reduces Fréchet Inception Distance (FID) from 60.0 to 44.2 on CIFAR-10 and from 102.5 to 28.4 on LSUN Bedroom-64.

cs.LG↗

arXiv2026

Entropy-Guided Greedy Heuristic for Minimal Differential Set Construction

This paper addresses the challenge of identifying a minimal subset of discrete predictor variables that best explains a binary class. We propose a greedy heuristic for feature selection that sequentially constructs a differential set by iteratively adding the variable that yields the most significant reduction in conditional entropy. The method incorporates a confidence-guided acceptance criterion that accounts for finite-sample uncertainty, allowing the search to adaptively balance the risk of including spurious variables against the opportunity to capture meaningful predictors. Because the procedure yields a compact set of statistically validated predictors together with an explicit confidence level for each one, it is well suited to healthcare innovation and management applications such as biomarker and risk-factor identification, diagnostic panel design, and clinical decision support, where minimizing the number of tests or indicators collected is critical for cost, feasibility, and patient burden.

stat.CO↗