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

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arXiv2026

Discrete Edge Multiscale Space based Hybrid Schwarz Preconditioner for High-Frequency Helmholtz Problems

In this work, we develop a novel hybrid Schwarz method, termed as edge multiscale space based hybrid Schwarz (EMs-HS), for solving the Helmholtz problem with large wavenumbers. The problem is discretized using $H^1$-conforming nodal finite element methods on meshes of size $h$ decreasing faster than $k^{-3/2}$ such that the discretization error can be bounded by the data uniformly with respect to $k$. EMs-HS consists of a one-level Schwarz preconditioner (RAS-imp) and a coarse solver in a multiplicative way. The RAS-imp preconditioner solves local problems on overlapping subdomains with impedance boundary conditions in parallel, and combines the local solutions using partition of unity. On the PDE level, this coarse space corresponds to an edge multiscale space proposed in {[S. Fu, G. Li, R. Craster, and S. Guenneau, \emph{Multiscale Model. Simul.}, 19(4):1684-1709, 2021]}. The approximation properties of this coarse space to the discrete solutions from the primal and adjoint problems are derived by a novel conforming Galerkin finite element method based upon a nonstandard variational formulation. This work represents the first theoretical analysis of an edge multiscale space at the discrete level. We prove that the EMs-HS preconditioner leads to a convergent fixed-point iteration uniformly for large wavenumbers, by rigorously analyzing the approximation properties of the coarse space to the global Helmholtz harmonic extension part and to the solution of the adjoint problem. We provide extensive numerical results on the sharpness of the theoretical findings and also demonstrate the method on challenging heterogeneous models.

math.NA↗

arXiv2026

Two non-semisimple quantum invariants of lens spaces

We calculate the chromatic spherical invariant $\mathscr{K}_{\mathrm{Rep}(H)}(L(p,q))$ of lens spaces $L(p, q)$ for arbitrary finite-dimensional unibalanced, unimodular Hopf algebras $H$. In the case of the index-2 Nichols Hopf algebra $\mathcal{K}_2$ and $q=1$, we find that the invariant of $L(p, 1)$ depends only on the parity of $p$ for $p\geq 1$. We also describe the duals $\mathcal{S_I}(M)^*$ of the admissible skein modules of handlebodies $M=H_g$ and of $M=L(p, q)$ for arbitrary tensor ideals $\mathcal{I}$ of a ribbon tensor category. In particular, $\mathcal{S_I}(L(p, q))^*$ corresponds with cyclic traces on $\mathcal{I}$ satisfying a property reminiscent of the modified trace condition.

math.GT↗

arXiv2026

Fluctuations in the Potts spin glass model at high temperature

We study the fluctuations of the free energy of the Potts spin glass with $κ$ colors at high temperature. The disorder is symmetric with unit variance and finite fourth moment. For configurations with a balanced, or nearly balanced, color profile, the log-partition function satisfies a central limit theorem whenever $β^2<α_c(κ)$. Here $κα_c(κ)$ is the critical inverse temperature of the Curie-Weiss-Potts model. A comparison of color profiles transfers this limit to the unconstrained model for $β<β_{\max}(κ)$, an explicit threshold. In the same range, the magnetizations of two replicas and their overlap matrix satisfy a joint quenched central limit theorem with independent Gaussian limits. The fourth cumulant of the disorder enters the limiting mean and variance explicitly.

math.PR↗

arXiv2026

On the Arnold corank, the Zariski multiplicity, and the tangent Milnor fiber problems

In this article, we approach the Arnold corank problem posed by Arnold himself in 1975, which asks whether the corank of a holomorphic function is a topological invariant. Here, the corank of a holomorphic function is the corank of its Hessian matrix at 0, which is one of the most basic and fundamental invariants of a holomorphic function. Here, we prove the topological invariance of the corank mod 2. Consequently, we obtain another proof of the Arnold corank problem in dimension 3, which was recently proved by Fernandes, Jelonek, and the author of this article. We also prove that the corank is constant in a continuous family of holomorphic functions with isolated singularities and constant Milnor number. We also approach a conjecture recently posed by Budur, Fernández de Bobadilla, Lê, and Nguyen (2022), which states that if two germs of holomorphic functions are right topologically equivalent, then the Milnor fibers of their initial forms are homotopy equivalent. We prove that a (much) weaker version of this conjecture, which states that if two holomorphic functions are right topologically equivalent, then the Milnor fibers of their initial forms have the same Euler characteristic, is equivalent to the Zariski multiplicity conjecture for right topological equivalence. Some other results are also presented here. For instance, the multiplicity $> 2$ of generalized semi-Bireskorn-Pham hypersurfaces is an invariant for the right topological equivalence.

math.AG↗

arXiv2026

Asymptotic Behavior of Transformers

In this paper we study the behavior of transformer networks generating text over long periods of time. We show that even a three-token, single-layer attention-only transformer can fail to converge. We then study a rich class of transformers with arbitrary finite depth, layer normalization, MLPs, RoPE encodings, and an arbitrary mix of local and global layers. Every transformer in this class has a softmax temperature threshold above which its empirical cache distribution converges to a unique limit, independent of initial conditions. We show further that, while each transformer has a temperature threshold, the supremum of this set is infinite, so there is no global minimal temperature that forces all transformers to converge.

cs.LG↗

arXiv2026

Steering Vectors for Competing Ethical Frameworks Are Interchangeable: A Competing-Target Test for Activation Steering

Activation steering adds a vector to a model's hidden states to control a named behaviour. A gain on that behaviour, however, does not show that the vector controls it directly: it may act through a component shared with neighbouring behaviours, which unsteered and random baselines cannot separate. We introduce the competing-target test: a vector is compared with the vector built the same way for a competing target, and an equivalence test states when their difference is below a useful margin. We apply it in open-weight models to vectors for Kantian deontology, which judges an act by the rule it follows, and act utilitarianism, which judges it by the welfare it produces. On held-out situations, prompting a framework raises its score and lowers the other's, whereas vectors for either framework move both scores alike, and none reaches the margin. The two vectors share most of their direction, a request to apply some framework; the same construction separates an optimistic from a pessimistic tone, whose vectors share much less. What a vector shares with its competitors therefore sets what it controls: steering a perspective can deliver a mixture, and measuring a disposition can measure its neighbours, unless tested against the competing target.

cs.AI↗

arXiv2026

Poincaré compactifications of pullbacks of parallel vector fields under counterexamples to the real Jacobian conjecture

Let $F: \mathbb{R}^2 \to \mathbb{R}^2$ be a polynomial map with nowhere zero Jacobian determinant. It is known that the global invertibility of $F$ is equivalent to the pullback of a parallel vector field being parallel. In this paper, we construct the phase portraits on the Poincaré disc of the pullbacks of the canonical annular, radial, and strip vector fields under non-injective maps $F$ that have recently appeared in the literature. Our arguments use local and global properties of vector fields as well as local and global properties of functions, thereby connecting techniques from dynamical systems and singularity theory.

math.DS↗

arXiv2026

VLX-Go: Robust Embodied Tracking through Multi-Stage Learning and On-Policy Refinement

Embodied visual tracking requires a robot to identify a designated target from visual observations and control its own motion to follow that target through an environment. Following an isolated person is a comparatively simple demonstration of embodied visual tracking, but following the intended person among distractors remains challenging. Existing methods exhibit a substantial drop in success from single-target to distractor tracking, motivating a focus on the shared spaces that person-following robots must navigate. We present \method{}, a vision--language waypoint policy built around the hypothesis that visual and language representations should be aligned before tracking-specific motion is learned. The policy combines complementary frozen visual encoders, multiscale temporal context, a transformer backbone, and a lightweight head for robot-centric waypoint prediction. Its training progresses through vision--language alignment, multimodal reasoning mid-training, and tracking specialization on 19,532 oracle episodes. Compared with 41.54\% distractor-tracking success for our earlier OmTrackVLA model, the complete multi-stage recipe achieves 55.80\%. We then explore on-policy refinement using filtered oracle labels for states visited by the policy. This preliminary study adds 2.42 percentage points of distractor-tracking success, reaching 58.22\%, while reducing collision rate by 1.99 pts. The final policy records the highest distractor- and ambiguous-tracking success rates among the compared methods. These results support staged multimodal learning as a promising direction for tracking among distractors and motivate further study of on-policy refinement for person following in shared spaces.

cs.CV↗

arXiv2026

Tail Competition Explains Scaling in Best-of-N Sampling for Verifiable Problems

Best-of-N sampling is a simple inference-time scaling strategy for large language models, yet its behavior under incomplete reward models remains poorly understood. We study Best-of-N as a competition between the extreme reward tails of correct and incorrect responses. This view shows that success depends not only on the probability of sampling a correct response, but also on whether correct responses dominate incorrect ones in the upper tail. Using extreme value theory, we characterize three asymptotic regimes: correct-tail-dominant, incorrect-tail-dominant, and critical explaining both monotonic gains and reward-hacking-induced degradation. We further derive finite-sample scaling laws for representative reward distributions, showing that, under Gaussian rewards, incorrect responses with sufficiently large variance can dominate selection even when their mean reward is lower. Unlike oracle selection, convergence with an incomplete selector can be polynomial rather than exponential. Finally, we propose a lightweight tail-tension criterion to estimate when additional sampling may become harmful. Experiments on synthetic data and real reward model scores are consistent with the theoretically predicted regimes, scaling laws, and diagnostic behavior, suggesting that tail competition provides a unified lens on Best-of-N sampling for verifiable problems.

cs.CL↗

arXiv2026

Bicolored Eulerian quasisymmetric functions, affine lengths, and Theta operators

We introduce a $q$-analogue of the bicolored Eulerian quasisymmetric functions by incorporating an additional grading arising from affine length, obtained by interpreting bicolored permutations as affine permutations. We also provide an intrinsic description of this refinement in terms of bicolored permutations by introducing notions of alignments and crossings, together with an explicit bijection identifying these statistics with the alignments and crossings in the existing literature. Finally, we prove that our refinement is symmetric by expressing it in terms of the Theta operators appearing in the Theta coinvariant Conjecture and the modified Macdonald symmetric functions. Assuming the Theta coinvariant conjecture implies the Schur-positivity of our refinement.

math.CO↗

arXiv2026

Dynamic Graph World Modelling: Learning Future Dynamics from Temporal Context

Dynamic graph learning models how entities and their relations evolve from historical observations to predict future graph states. Existing methods do not fully address dynamic graph world modelling, which requires learning transitions from temporal context to future latent graph states. This is difficult for three reasons: nodes and relations rely on different historical evidence, structural evolution is path-dependent, and future snapshots provide sparse and realization-specific targets. We propose Dynamic Graph World Modelling (DyG-WM), the first framework to jointly predict future node and relation representations from temporal context by answering three questions: what has evolved, how it evolved, and what will evolve next. To capture what has evolved, a historical node-relation context encoder summarizes node-neighborhood trajectories and pair-specific histories. To characterize how it evolved, a node-relation path-signature encoder captures ordered structural changes. To predict what will evolve next, a dual-level joint-embedding objective predicts target-snapshot node and relation representations without reconstructing the raw graph. Experiments on 12 link-prediction and two node-classification datasets demonstrate the effectiveness of DyG-WM across both tasks.

cs.LG↗

arXiv2026

DANGERLENS: Probing Dangerous Representations Hidden by Safety Alignment

Safety alignment teaches language models to refuse harmful requests, yet the internal accessibility of hazardous concepts can retain traces of earlier training. Can checkpoints with equally safe behavior differ in what remains accessible behind their refusals? In this work, we investigate this question through paired training histories and a direct audit of intermediate representations. We introduce DANGERLENS, a probe that maps hidden states into vocabulary space and uses blinded semantic judgments to distinguish harmful goals and operational means from hazard recognition and safety control. Experiments on three Qwen1.5 scales show that checkpoints with prior harmful exposure generally retain greater hazardous concept accessibility after the same safety alignment, with the strongest separation in intermediate and later layers. The same harmful update also produces different behavioral trajectories from closely matched starting points. Human relevance validation and readout ablations reinforce the measured accessibility contrast. Our findings show that training history remains visible inside behaviorally matched models and motivate internal accessibility audits alongside output safety evaluations.

cs.AI↗

arXiv2026

Seeing, Maintaining, and Learning: The Evolution of Multimodal Agent Memory

Multimodal models and agents have emerged to enable AI systems to learn from and interact with the real world more like humans by integrating information across multiple modalities. However, enabling multimodal agents to continually acquire useful information from complex, heterogeneous multimodal data remains a significant challenge as they move toward long-horizon tasks and lifelong settings. Addressing this challenge requires effective memory mechanisms that can maintain continuity across sessions, adapt to changing users and environments, and refine memory-management policies through accumulated experience. We introduce a two-axis analytical framework for multimodal agent memory structured around two key questions: how multimodal information is formed and represented (Axis I, Formation and Representation), and how its management adapts with accumulated experience (Axis II, Memory Management). Axis I, Formation and Representation, characterizes what information is retained and how it is encoded (e.g., modality-specific embeddings, textual and structured records, latent and parametric representations) to support subsequent reasoning and action. Axis II, Memory Management, distinguishes three tiers: T1 Static Memory reuses fixed memory; T2 Dynamic Memory updates memory through a stable policy; and T3 Self-Evolving Memory updates memory through an evolving policy. Based on this framework, we synthesize recurring design patterns and derive principles for balancing source fidelity with abstraction, maintaining temporal validity and provenance, grounding memory use in recoverable evidence, and evolving memory policies over time. Furthermore, we discuss the challenges and potential future directions for the memory mechanism of multimodal agents.

cs.AI↗

arXiv2026

Beyond Corrected Actions: Training LLM Agents on Textual Critiques

Large language models (LLMs) are increasingly used for multi-turn agentic tasks that require interactions with users and environments over extended sequences of actions. A common approach to improving LLM agents is to use more capable expert models to provide training supervision, either by behavior cloning the expert's trajectories or by using the expert to correct the actions in trajectories generated by the weaker student model. However, expert LLMs can provide richer supervision than actions alone: they can directly generate textual critique that explain why specific actions are incorrect. We study whether training on such feedback benefits LLM agents and propose Critique-Augmented Agentic Fine-Tuning (CAFT), a framework that elicits textual expert feedback on student-generated trajectories. For each incorrect action, the expert yields both a corrected action and a textual critique explaining the student's mistake--which we then use as the training target for fine-tuning. Across four student models from the Nemotron 3 and Gemma 4 families on the agentic domains $τ^2$-Bench Airline+Retail and WebShop, adding critiques to action-level supervision improves performance by 8% on average over action-only distillation. Additionally, CAFT checkpoints can also provide a better warm start for reinforcement learning than expert-trajectory distillation. Our results demonstrate that textual critiques can strengthen supervision for multi-turn LLM agents.

cs.CL↗

arXiv2026

OS-Bench: Evaluating SWE Agents on Cross-OS Code Migration

Language-model (LM) agents are increasingly evaluated on repository-level software engineering (SWE) benchmarks derived from GitHub issues and pull requests. Although these benchmarks cover a broad range of development tasks, they provide limited insight into a common yet technically distinct challenge: migrating an existing implementation from one operating system (OS) to another while preserving behavior on both. We introduce OS-Bench, an executable benchmark for cross-OS code migration between Linux and Windows. Motivated by case studies showing that cross-platform features are frequently implemented on one OS before support is added for another, OS-Bench identifies migration opportunities by comparing execution coverage collected from the same repository on both systems. Platform-specific regions are then verified, organized into five migration scenarios, and transformed into repository-level tasks with target-platform tests and source-platform regression tests. The resulting benchmark contains 140 validated tasks from 111 repositories across C, C++, C#, Go, and Rust, comprising 91 Windows-to-Linux and 49 Linux-to-Windows migrations. We evaluate six models with SWE-agent, Claude Code, OpenHands, and Win-agent. The best configurations achieve only 26.4% success on Linux-target tasks and 20.4% on Windows-target tasks while preserving correctness across both systems. These results indicate that cross-OS migration is a challenging and underexplored capability, and OS-Bench is a testbed for improving platform-aware SWE agents.

cs.SE↗

arXiv2026

The Impact of Detector Architecture, Model Scale, and Scene Density on Multi-Pedestrian Tracking

Pedestrian tracking in video is important for applications such as surveillance and scene analysis, but it becomes more challenging in crowded scenarios with frequent occlusions and rapid motion. This paper analyzes how detector architecture, model scale, scene density, and inference regime affect the tracking of multiple pedestrians. We compare the YOLO11, RT-DETR, and YOLO26 detector families with the ByteTrack and BoT-SORT trackers on sequences from the MOT17, MOT20, and SOMPT22 benchmarks. For YOLO26, we also compare traditional overlap filtering via Non-Maximum Suppression (NMS) with end-to-end inference. The RT-DETR family achieved the highest mean scores on the HOTA tracking quality metric across all three benchmarks with both trackers, with a more pronounced advantage on MOT20, albeit at a higher computational cost. On MOT17 and SOMPT22, YOLO26 variants, especially YOLO26-L with NMS, offered favorable combinations of quality and speed compared with RT-DETR. In the YOLO26 inference comparison, the end-to-end mode did not yield consistent tracking gains over the NMS-based regime. Taken together, these results provide a practical guide for selecting detectors and trackers for this task based on application priorities.

cs.CV↗

arXiv2026

Odd-to-Even-Layer Switch of Spontaneous Excitonic State in $\rm{TiSe_{2}}$ Thin Films

$\rm{TiSe_{2}}$ is a candidate of high temperature excitonic condensates with spontaneous exciton formation in addition to its charge density wave (CDW). However, direct observation and manipulation of this electron-hole paring state formation is still lacking. Here, using varying-temperature angle-resolved photoemission spectroscopy (VT-ARPES), we observe a distinct odd-to-even-layer switch of spontaneous exciton state formation with the evident correlated band structure in $\rm{TiSe_{2}}$ thin films. While the odd-layer $\rm{TiSe_{2}}$ films show a sharp band structure in single-particle picture superimposed by CDW renormalization, in the even-layer $\rm{TiSe_{2}}$ films, the full-filling valence band (VB) opens a distinct notch at the top, and the conductive band (CB) shows a significant extra signal extending above Fermi level with spectra broadening. These features indicate that the extra holes (notched VB) and electrons (broadening CB above Fermi level) form spontaneous excitons in even-layer $\rm{TiSe_{2}}$. Based on a correlated electron-hole model extracted from the tight-binding description, we reproduce the characterized band structures with spontaneous exciton formation, where the interlayer inter-band coupling in $\rm{TiSe_{2}}$ plays a key role, which leads to an odd-to-even-layer switch of the excitonic state formation. Our results provide direct evidences of the spontaneous exciton formation, promising an excitonic condensate as versatile platform for realizing Bose-Einstein condensate (BEC) and investigating novel correlated phenomena.

cond-mat.str-el↗

arXiv2026

Analytically Optimal Sample Allocations for Nested Multivariate Multifidelity Control Variate Estimators

Monte Carlo estimation, an essential tool for quantifying uncertainty in complex scientific and engineering applications, often has unacceptably large errors when computing resources are limited and each sample requires evaluating an expensive high-fidelity model. Multifidelity control variate methods seek to increase the accuracy of Monte Carlo estimation by combining a limited number of expensive high-fidelity samples with a larger number of cheaper lower-fidelity samples. Many different multifidelity estimators have been proposed, including multilevel Monte Carlo (MLMC), multifidelity Monte Carlo (MFMC), approximate control variates (ACVs), and multilevel best linear unbiased estimators (MLBLUEs). An important design choice in multifidelity estimation is the allocation of a limited computational budget among the available models to minimize estimator error. The state of the art in solving this budget allocation problem relies on numerical optimization; to date, closed form solutions have only been derived for estimator forms known to be suboptimal. In this work, we provide closed form expressions for optimal fractional sample allocations for a large class of nested multifidelity control variate estimators, in which higher-fidelity models are evaluated on a subset of the inputs that lower-fidelity models are evaluated on. Our analysis is based on reformulating nested MLBLUEs as an extended version of the MFMC estimator, and is applicable to general multivariate Monte Carlo estimation. We additionally propose a new approach for integer-valued budget allocation based on a greedy strategy used in combinatorial optimization, as well as a method for robust approximation of control variate coefficients from limited pilot samples. Two numerical examples illustrate our theoretical results and demonstrate the increased accuracy of our extended MFMC formulation relative to existing estimators.

stat.CO↗