SEARCH · Searcharxiv

Search Searcharxiv

Search indexed arXiv papers on artificial intelligence, large language models, computer vision and robotics. Read source abstracts and follow links to arXiv.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 37 records · Page 2Linked to original sources

arXiv2026

Sublinear Algorithms for Estimating Single-Linkage Clustering Costs

Single-linkage clustering (SLC) is a fundamental method for hierarchical data analysis. In the distance setting, a $k$-clustering produced by SLC can be obtained by computing a minimum spanning tree (MST) and deleting its $k-1$ heaviest edges. This naturally induces a cost profile for the SLC hierarchy: for each $k\in[n]$, we define $\mathrm{cost}_k$ to be the weight of the resulting $k$-component spanning forest, equivalently, the minimum total weight of any spanning forest with exactly $k$ connected components. The corresponding \emph{SLC cost profile} is $(\mathrm{cost}_1,\ldots,\mathrm{cost}_n)$, and the scalar quantity $\mathrm{cost}(G)=\sum_{k=1}^{n}\mathrm{cost}_k$ is the area under this profile. We study the problem of approximating these quantities in sublinear time. We assume that the input is a weighted graph $G$ of average degree $d$ with edge weights in $\{1,\dots,W\}$, accessed through adjacency-list queries; missing edges are treated as having infinite distance. Our main result is a sampling-based algorithm that outputs a succinct sketch of the entire SLC cost profile in the distance setting. The algorithm runs in $\widetilde{O}(d\sqrt{W}/\varepsilon^3)$ time and returns a sketch from which one can derive estimates $(\widehat{\mathrm{cost}}_1,\ldots,\widehat{\mathrm{cost}}_n)$ satisfying $\sum_{k=1}^{n}\bigl|\widehat{\mathrm{cost}}_k-\mathrm{cost}_k\bigr| \le \varepsilon\,\mathrm{cost}(G)$. Thus, we obtain an $\ell_1$ approximation to the full profile whose error is at most an $\varepsilon$-fraction of the area under the true profile. In particular, this yields a $(1\pm\varepsilon)$-approximation to $\mathrm{cost}(G)$ within the same running time. We also prove a nearly matching lower bound of $Ω(d\sqrt{W}/\varepsilon^2)$ queries for estimating $\mathrm{cost}(G)$.

cs.DS↗

arXiv2026

A sensitivity analysis for the average derivative effect

In observational studies, exposures are often continuous rather than binary or discrete. At the same time, sensitivity analysis is an important tool that can help determine the robustness of a causal conclusion to a certain level of unmeasured confounding, which can never be ruled out in an observational study. Sensitivity analysis approaches for continuous exposures have now been proposed for several causal estimands. In this article, we focus on the average derivative effect (ADE). We obtain closed-form bounds for the ADE under a sensitivity model that constrains the odds ratio (at any two dose levels) between the latent and observed generalized propensity score. We propose flexible, efficient estimators for the bounds that are compatible with machine learning algorithms as well as point-wise and simultaneous (over the sensitivity parameter) confidence intervals. We examine the finite sample performance of the methods through simulations and illustrate the methods on a study assessing the effect of parental income on educational attainment and a study assessing the price elasticity of petrol.

stat.ME↗

arXiv2026

Graphical Model-based Inference on Persistent Homology

Persistent homology is a cornerstone of topological data analysis, offering a multiscale summary of topology with robustness to nuisance transformations, such as rotations and small deformations. Persistent homology has seen broad use across domains such as computer vision and neuroscience. Most statistical treatments, however, use homology primarily as a feature extractor, relying on statistical distance-based tests or simple time-to-event models for inferential tasks. While these approaches can detect global differences, they rarely localize the source of those differences. We address this gap by taking a graphical model-based approach: we associate each vertex with a population latent position in a conic space and model each bar's key events (birth and death times) using an exponential distribution, whose rate is a transformation of the latent positions according to an event occurring on the graph. The low-dimensional bars have simple graph-event representations, such as the formation of a minimum spanning tree or the triangulation of a loop, and thus enjoy tractable likelihoods. Taking a Bayesian approach, we infer latent positions and enable model extensions such as hierarchical models that allow borrowing strength across groups. Applications to a neuroimaging study of Alzheimer's disease demonstrate that our method localizes sources of difference and provides interpretable, model-based analyses of topological structure in complex data. The code is provided and maintained at https://github.com/zitian-wu/graphPH.

stat.ME↗

arXiv2026

Positive Characteristic Sets for Relational Pattern Languages

In the context of learning formal languages, data about an unknown target language L is given in terms of a set of (word,label) pairs, where a binary label indicates whether or not the given word belongs to L. A (polynomial-size) characteristic set for L, with respect to a reference class L of languages, is a set of such pairs that satisfies certain conditions allowing a learning algorithm to (efficiently) identify L within L. In this paper, we introduce the notion of positive characteristic set, referring to characteristic sets of only positive examples. These are of importance in the context of learning from positive examples only. We study this notion for classes of relational pattern languages, which are of relevance to various applications in string processing.

cs.FL↗

arXiv2026

Quantum Orthogonal Separable Physics-Informed Neural Networks

We introduce Quantum Orthogonal Separable Physics-Informed Neural Networks (QO-SPINNs), which replace selected dense hidden transformations in physics-informed PDE models with quantum-compatible orthogonal maps. A pyramidal reconfigurable-beamsplitter circuit realizes these maps with $Θ(d)$ circuit depth. Under the stated signed-readout access model and fixed per-call failure probability, a width-$d$ map has sequential access-cost upper bound $\mathcal O(d\log d/ε^2)$, which is asymptotically smaller than the $Θ(d^2)$ cost of conventional direct dense multiplication when $ε(d)^{-2}\log d=o(d)$. Because unary state preparation discards magnitude, we retain each hidden-state norm classically and restore it after readout, yielding the exact map $Wh$ under ideal readout. We study this construction in two complementary settings: forward PDE regression and a norm-controlled residual model for representation geometry and uncertainty quantification. In the norm-controlled model, structural orthogonality yields explicit bi-Lipschitz bounds, while finite-readout analysis relates sufficient reconstruction precision to a prescribed physical-coordinate resolution through trained-model constants. This makes the access-cost condition assessable for trained checkpoints, although favorable fixed-resolution scaling across widths is not established. A post-hoc Bayesian-linear covariance provides uncertainty from the same frozen predictor, and cross-PDE transfer shows that strong distance-awareness can persist even when absolute coverage calibration fails. All Quantum Orthogonal (QO) layers are evaluated by classical simulation: the results therefore characterize a quantum-compatible structured neural primitive rather than demonstrating a practical quantum-hardware advantage.

quant-ph↗

arXiv2026

PepEVOLVE: Position-Aware Dynamic Peptide Optimization via Group-Relative Advantage

Macrocyclic peptides are an emerging modality that combines biologics-like affinity with small-molecule-like developability, yet their vast combinatorial space and multi-parameter objectives make lead optimization slow and challenging. Prior generative approaches for peptide lead optimization (e.g., PepINVENT) require chemists to pre-specify mutable positions for optimization, choices that are not always known a priori, and rely on static pretraining and optimization algorithms that limit the model's ability to generalize and effectively optimize peptide sequences. We introduce PepEVOLVE, a position-aware, dynamic framework that learns both where to edit and how to dynamically optimize peptides for multi-parameter improvement. PepEVOLVE (i) augments pretraining with dynamic masking and CHUCKLES shifting to improve generalization, (ii) uses a context-free multi-armed-bandit router that discovers high-reward residues, and (iii) couples a novel evolving optimization algorithm with group-relative advantage to stabilize reinforcement updates. During in silico evaluations, the router policy reliably learns and concentrates probability on chemically tractable sites that influence the desired peptide's properties. On a therapeutically motivated Rev-binding macrocycle benchmark, PepEVOLVE outperformed PepINVENT by reaching higher averaged permeability-weighted optimization scores of approximately 0.8 vs. 0.6, achieving best candidates with score of 0.97 (vs. 0.89), and converging in fewer steps under the task of optimizing permeability and lipophilicity with structure constraints. Overall, PepEVOLVE offers a practical, reproducible path to linear and macrocyclic peptide lead optimization when optimal edit sites are unknown, enabling more efficient chemical space exploration and improving design quality across multiple objectives to accelerate the design cycles.

cs.LG↗

arXiv2026

Magic Gems: Convex Hulls of Lifted Magic Squares

Given an arrangement of $\{1,\dots,n^2\}$ in an $n\times n$ grid, we lift each cell to $\mathbb{R}^3$ by centring its grid coordinates $(x,y)$ at the origin and taking its centred entry $z = s_{ij} - (n^2+1)/2$ as a vertical height. The convex hull of these $n^2$ points is the gem of the arrangement, whose lower and upper boundaries are the regular subdivisions of the grid induced by $\pm z$. While random arrangements and generic linear magic squares have gems whose vertex counts grow with $n$, our main theorem shows that the classical Siamese (de la Loubère) magic square of every odd order $n\ge5$ has $f$-vector $(12,26,16)$, isometry group $\{\pm\mathrm{id}\}$, and only the twelve vertices forced by the boundary of the grid. The proof shears the lift onto five horizontal terraces and reduces the hull calculation to a finite table of polynomials in $m=(n-1)/2$; the same method gives $f$-vector $(12,24,14)$ for the base-$n$ digit-exchanged square. Along any family of linear squares with fixed steps the $f$-vector is eventually periodic in $n$, whereas over all linear magic squares of prime order $n$ the maximum vertex count grows as $Θ(\ln n)$. Whenever the heights have vanishing first moments, a short principal-axes argument shows that the point set has a non-trivial isometry if and only if the arrangement is self-complementary up to dihedral symmetry. An exact census of the $880$ magic squares of order four yields $616$ congruence classes and $352$ combinatorial types of gems, and shows that while vertex and facet counts are nearly insensitive to the magic line-sum conditions, the volume and solid centroid shift systematically.

math.CO↗

arXiv2026

Complete Characterizations of Well-Posedness in Parametric Composite Optimization

This paper characterizes the well-posedness of Karush-Kuhn-Tucker system for perturbed composite optimization. Using the parabolic regularity, we introduce a novel second-order variational function, shown to be the pivotal object governing second-order behavior. This foundational result yields the strong second-order sufficient condition introduced here for the general class of composite optimization problems to naturally extend the classical second-order sufficient condition in nonlinear programming. Then we obtain several equivalent characterizations of the second-order qualification condition (SOQC) and highlight its relationship with the constraint nondegeneracy condition under the $\mathcal{C}^{2}$-cone reducibility assumption. These insights lead us to multiple equivalent conditions for the major Lipschitz-like/Aubin property of KKT systems, including SOQC combined with the new second-order subdifferential condition and SOQC combined with tilt stability of local minimizers. Under the $\mathcal{C}^{2}$-cone reducibility, we settle the long-standing question by proving the equivalence between the Aubin property of KKT systems around local minimizers and the classical notion of strong regularity. Finally, we demonstrate that the Lipschitz-like property is equivalent to the nonsingularity of the generalized Jacobian associated with the KKT system under a certain verifiable assumption. These results provide a unified and rigorous framework for analyzing stability and sensitivity of solutions to composite optimization problems, as well as for the design and justification of numerical algorithms.

math.OC↗

arXiv2026

Quasipolynomial behavior via constructibility in multigraded algebra

Piecewise quasipolynomial growth of Presburger counting functions combines with tame persistent homology module theory to conclude piecewise quasipolynomial behavior of constructible families of finely graded modules over constructible commutative semigroup rings. Functorial preservation of constructibility for families under local cohomology, $\operatorname{Tor}$, and $\operatorname{Ext}$ yield piecewise quasipolynomial, quasilinear, or quasiconstant growth statements for length of local cohomology, $a$-invariants, regularity, depth; length of $\operatorname{Tor}$ and Betti numbers; length of $\operatorname{Ext}$ and Bass numbers; associated primes via $v$-invariants; and extended degrees, including the usual degree, Hilbert-Samuel multiplicity, arithmetic degree, and homological degree.

math.AC↗

arXiv2026

A Lyapunov-Based Small-Gain Theorem for Fixed-Time ISS: Theory, Optimization, and Games

We develop a Lyapunov-based small-gain theorem for establishing fixed-time input-to-state stability (FxT-ISS) guarantees in interconnected nonlinear dynamical systems. The proposed framework considers interconnections in which each subsystem admits a FxT-ISS Lyapunov function, providing robustness with respect to external inputs. We show that, under an appropriate nonlinear small-gain condition, the overall interconnected system inherits the FxT-ISS property. In this sense, the proposed result complements existing Lyapunov-based smallgain theorems for asymptotic and finite-time stability, and enables a systematic analysis of interconnection structures exhibiting fixed-time stability. To illustrate the applicability of the theory, we study feedback-based optimization problems with time-varying cost functions, and Nash-equilibrium seeking for noncooperative games with nonlinear dynamical plants in the loop. For both problems, we present a class of non-smooth gradient or pseudogradient-based controllers that achieve fixed-time convergence without requiring time-scale separation and using real-time feedback. Numerical examples are provided to validate the theoretical findings.

eess.SY↗

arXiv2026

Global Well-Posedness of the Vacuum Free Boundary Problem for the Degenerate Compressible Navier-Stokes Equations With Large Data of Spherical Symmetry

The study of global-in-time dynamics of vacuum is crucial for understanding viscous flows. In particular, physical vacuum, which ensures a finite, nontrivial pressure-induced acceleration in the normal direction on the moving boundary, naturally arises in the motion of gaseous stars and shallow water. The corresponding large-data problems for spherically symmetric flows remain open, due to the combined difficulties of coordinate singularity at the origin and degeneracy on the moving boundary. In this paper, we analyze the free boundary problem for the barotropic compressible Navier-Stokes equations with density-dependent viscosity coefficients (as in the shallow water equations) in two and three spatial dimensions. For a general class of spherically symmetric initial densities: $ρ_0^β\in H^3$ with $β\in (\frac{1}{3},γ-1]$ ($γ$: adiabatic exponent), vanishing on the moving boundary in the form of a distance function, we establish the global existence of the unique classical solution with large data. Moreover, our solution is classical up to the moving boundary, and the physical vacuum is allowed for the data under consideration here when $β=γ-1$. The key ingredient of our analysis is to obtain the uniform control over the first-order spatial derivatives of the flow map $η(t,r)$ in spherically symmetric Lagrangian coordinates, which is achieved by some novel density-weighted estimates and flow-map-weighted estimates for the solutions.

math.AP↗

arXiv2026

Simultaneous determination of Hubble constant and cosmic baryon density: Forecasts for the synergy between FRBs and emerging probes

Two of the most pressing challenges in cosmology are the persistent discrepancy in measurements of the Hubble constant, referred to as the Hubble tension, and the deficit of baryons in the local Universe, known as the missing baryon problem. Fast radio bursts (FRBs) provide a unique probe of both the Hubble constant $H_0$ and the cosmic baryon density $Ω_{\rm b}$. However, constraints from FRBs alone suffer from a severe $H_0$-$Ω_{\rm b}$ degeneracy that prevents them from resolving either problem. We show that this degeneracy can be broken by combining FRBs with other emerging probes whose degeneracy directions differ in the $H_0$-$Ω_{\rm b}$ plane. Specifically, we quantify three multi-messenger approaches: FRBs paired with gravitational wave (GW) standard sirens, strong gravitational lensing (SGL) time delays, and 21 cm intensity mapping (IM) surveys. The combinations FRB+GW, FRB+SGL, and FRB+21 cm IM each deliver simultaneous constraints on $H_0$ and $Ω_{\rm b}$ better than (1%, 1.5%) in the $Λ$CDM model, and when dynamical dark energy is introduced, the constraining precision degrades gracefully as model complexity increases. Furthermore, within a model-independent framework, both FRB+GW and FRB+SGL constrain $H_0$ and $Ω_{\rm b}$ to precisions better than (1.5%, 3%). These precision levels are based on nominal observational expectations and would improve significantly under optimistic observational scenarios.

astro-ph.CO↗

arXiv2026

Beyond the Dirac Delta: Mitigating Diversity Collapse in Reinforcement Fine-Tuning for Versatile Image Generation

Reinforcement learning (RL) has emerged as a paradigm for fine-tuning large-scale generative models, such as diffusion and flow models, to align with complex human preferences and user-specified tasks. A fundamental limitation remains \textit{the curse of diversity collapse}, where the objective formulation and optimization landscape inherently collapse the policy to a Dirac delta distribution. To address this challenge, we propose \textbf{DRIFT} (\textbf{D}ive\textbf{R}sity-\textbf{I}ncentivized Reinforcement \textbf{F}ine-\textbf{T}uning for Versatile Image Generation), an innovative framework that systematically incentivizes output diversity throughout the on-policy fine-tuning process, reconciling strong task alignment with high generation diversity to enhance versatility essential for applications that demand diverse candidate generations. We approach the problem across three representative perspectives: i) \textbf{sampling} a reward-concentrated subset that filters out reward outliers to prevent premature collapse; ii) \textbf{prompting} with stochastic variations to expand the conditioning space, and iii) \textbf{optimization} of the intra-group diversity with a potential-based reward shaping mechanism. Experimental results show that DRIFT exhibits clear Pareto dominance in task alignment and generation diversity, achieving 3.88\%$\sim$81.42\% higher diversity at matched alignment and 14.38\%$\sim$56.45\% higher alignment at matched diversity. Our code is available at \textcolor{magenta}{\href{https://github.com/NJU-RL/DRIFT}{https://github.com/NJU-RL/DRIFT}}.

cs.LG↗

arXiv2026

RoSeViT: Role-Separated Vision Transformers for ARC Visual Reasoning

ARC tasks can be formulated as visual transformation problems, where a model must infer a high-level transformation rule from a small set of demonstrations and apply it consistently across a grid. While dense Vision Transformers (ViTs) perform well in this setting, they entangle local visual state and global transformation logic within a shared token representation, which can hinder consistent reasoning. In this paper, we introduce RoSeViT, a role-separated Vision Transformer that explicitly decouples high-level instruction inference from visual workspace computation. RoSeViT uses controller tokens to aggregate transformation-level information and workspace tokens to represent the visual grid, with a structured attention pass in which nonlocal workspace interactions are routed through the controller. This design is motivated by our formal analysis showing that enforcing a shared instruction representation can reduce the effective complexity of visual transformation modeling. RoSeViT outperforms dense ViT baselines under the standard VARC training and evaluation protocol for ARC. In a controlled backbone replacement setting, it improves ARC-1 accuracy from 54.5 to 56.6, and with recurrent refinement reaches 58.8. When integrated into the full system, RoSeViT-Ensemble improves performance from 60.4 to 62.6 on ARC-1. These results demonstrate that explicitly separating instruction and workspace representations leads to more effective visual reasoning on ARC tasks. GitHub repository: https://github.com/lz7fd/RoSeViT.

cs.AI↗

arXiv2026

Spectral-Aligned Pruning for Universal Error-Correcting Code Transformers

Universal channel decoders based on transformers-such as the Foundation Error Correction Code Transformer (FECCT)-achieve competitive decoding performance across diverse code families with a single shared backbone, optionally followed by code-specific finetuning. However, the high computational complexity and large parameter footprint of FECCT present substantial obstacles to practical deployment. To address these challenges, we investigate structured pruning for FECCT and propose Spectral-Aligned Pruning (SAP), a structure-aware framework that enables cross-code reuse of structured pruning masks by leveraging the spectrum of the corresponding bipartite graph. SAP is grounded in classical graph analysis of codes: the two algebraically largest adjacency eigenvalues provide compact spectral proxies for degree scale, expansion ratio, and minimum-distance lower bounds. These quantities are directly relevant to decoding performance: degree scale reflects how densely codeword bits and parity checks are connected; expansion ratio influences how information propagates across the bipartite graph; and minimum distance characterizes codeword separation. Based on this connection, SAP uses these two leading eigenvalues as a lightweight code signature for pruning-mask retrieval. Empirically, this two-dimensional signature yields stable library selection equivalent to higher-dimensional spectral signatures in our evaluation. After pruning, SAP uses parameter-efficient low-rank adaptation (LoRA) to recover decoding performance while storing only a small number of additional adapter parameters per code. Experiments across diverse codes show that SAP achieves decoding performance comparable to dedicated per-code pruning, while enabling substantial reductions in computational cost and model memory footprint through kernel-level structured pruning. Code is available at https://github.com/iil-postech/sap.

cs.IT↗

arXiv2026

STAPO: Stabilizing Reinforcement Learning for LLMs by Silencing Rare Spurious Tokens

Reinforcement Learning (RL) has significantly improved large language model reasoning, but existing RL fine-tuning methods rely heavily on heuristic techniques such as entropy regularization and reweighting to maintain stability. In practice, they often suffer from late-stage performance collapse, leading to degraded reasoning quality and unstable training. We identify a key factor behind this instability: a small fraction of tokens, termed spurious tokens (around 0.01%), which contribute little to the reasoning outcome but receive disproportionately amplified gradient updates due to inheriting the full sequence-level reward. We present a unified framework for evaluating token-level optimization impacts across spurious risk, gradient norms, and entropy changes. Building on the analysis of token characteristics that severely disrupt optimization, we propose the Silencing Spurious Tokens (S2T) mechanism to efficiently suppress their gradient perturbations. Incorporating this mechanism into a group-based objective, we propose Spurious-Token-Aware Policy Optimization (STAPO), which promotes stable and effective large-scale model refinement. Across six mathematical benchmarks and three model scales, STAPO consistently demonstrates superior entropy stability and achieves average accuracy improvements over baselines including GRPO, 20-Entropy, and JustRL under two widely-adopted evaluation settings.

cs.CL↗

arXiv2026

Decoding cell signaling via optimal transport and information theory

Cellular signal processing performs reliably despite molecular noise. Mutual information (MI) is widely used to quantify signaling fidelity, capturing how well outputs discriminate input states. However, it fails to capture whether the output preserves the statistical structure of the input, a property crucial in morphogen patterning and dose-dependent signaling. To address this gap, we introduce the 2-Wasserstein (2-WD) distance, which provides a geometric basis for comparing input and output distributions. We define MI as informational fidelity (INF) and the inverse of the 2-WD as geometric fidelity (GMF). Applying this dual-fidelity framework to canonical regulatory motifs under Gaussian channel approximation reveals topology-dependent trade-offs: coherent feed-forward loops can perform well in both dimensions, whereas feedback architectures reduce INF to enhance GMF. Experimental analysis of tumor necrosis factor signaling reveals dual-fidelity behavior qualitatively consistent with feedback regulation. RAS-MAPK data analysis further shows that jointly considering INF and GMF better characterizes intracellular signal relay than INF alone. Our results thus indicate that these signaling behaviors are not fully characterized by MI alone; instead, distributional correspondence provides a complementary dimension of signaling fidelity. Our study provides a practical framework for analyzing natural networks and guiding the design of task-specific synthetic circuits.

physics.bio-ph↗

arXiv2026

SGNO: Spectral Generator Neural Operator for Long-Horizon PDE Prediction

Neural operators efficiently simulate dynamical systems by repeatedly predicting the next state. However, small errors at each step can accumulate, causing long-term predictions to drift from the true trajectory. Long-term error reflects both the propagation of earlier prediction errors and new errors introduced at each step. How to reduce these errors is therefore a critical question. We propose the Spectral Generator Neural Operator (SGNO), which combines a linear estimate of the next state with a learned correction. The linear component uses consecutive states in the training data to fit a map from the current state to the next. A neural network corrects this prediction by learning changes that the linear model does not capture, including nonlinear interactions. Both components are trained jointly toward the same next-state target. Experiments across 13 periodic PDE configurations in one to three dimensions show that SGNO accurately learns state evolution on linear tasks and reduces 100-step rollout error by 13-74% over the strongest baseline under the main comparison protocol on each nonlinear task. Longer-horizon extrapolation tests show lower late-window prediction errors on several nonlinear tasks. These results show that combining fitted propagation with learned state-dependent correction can improve long-horizon autoregressive prediction on the evaluated PDE tasks. Code is available at https://github.com/cruiseresearchgroup/SGNO.

cs.LG↗