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arXiv2026

"More Is Different'' in Neural Circuits: Algebraic Emergence of Effective Theories in Canonical Recurrent Motifs of Biological Neuronal Networks

Canonical neural circuit motifs are usually described functionally: divisive normalization rescales population activity by a pooled signal, and winner-take-all competition selects one pattern through recurrent excitation and shared inhibition. We represent them, and their compositions, algebraically as finite transformation systems and analyze the transition monoids generated by their input-conditioned updates, distinguishing structure already present in a generator from structure that appears only through composition, and, on a joint state space, structure inherited from one factor from structure that lives on a joint configuration. Individually aperiodic updates can generate non-aperiodic monoids. In the WTA, every frozen-drive generator collapses to fixed points, yet short input sequences create local cycles of winner-dependent inhibitory gating: globally dissipative dynamics with a reversible action. The strongest result arises in WTA-to-DN composition. The composed monoid then contains a genuinely composite local cycle in which normalization state and the winner's gating state change together, although every primitive generator is aperiodic. Holonomy analysis certifies this as a group component of the Krohn-Rhodes cascade rather than an incidental cycle, and finds most group-carrying image sets on joint configurations, whereas the uncoupled product has none. An exhaustive interface sweep shows that the composite cycle is a property of the coupling rather than of a chosen map. If motifs are building blocks of neural computation, composing them is a form of programming: one chooses primitives and interfaces so that the generated algebra has the intended repertoire. The transition monoid is that repertoire - what a primitive presents to any later construction. Recurrent circuits are compositional transformation systems; their algebra constrains what they can be programmed to compute.

q-bio.NC↗

arXiv2026

Axonal delay dispersion decides whether a neuron detects an event or a sequence, and predicts cortical column diameter

Cortical neurons fire sparsely -- often fewer than one spike per sensory window -- making rate coding insufficient and temporal coding a necessity. That conduction delays convert firing order into synchrony is long established. What governs which class of temporal feature a neuron detects -- one volley of coincident input, or two in a particular order -- has not been examined. We propose a delay-signature framework in which the axonal conduction delays converging on a dendritic branch constitute a physical key: only input sequences whose spike-time differences the delays compensate arrive synchronously, and coincidence detection, via calcium plateau thresholds, converts that synchrony into an all-or-none output. In simulations of an integrator-neuron model we report three results. First, a single physical scalar -- the dispersion of the delay set -- moves a population from event detection to order-selective sequence detection. The transition is emergent under random delays and connectivity: at narrow dispersion sequence detectors do not exist, and the dispersion at which they overtake event detectors tracks the inter-event interval with a slope statistically indistinguishable from one. This maps a computational distinction onto the anatomical one between myelinated and unmyelinated projections, making myelination a switch on what a neuron computes, not only a regulator of speed. Second, the same dispersion sets the code's limits: it bounds the longest codable interval and fixes an absolute timing tolerance of about a millisecond, with slowing better tolerated than speeding. Third, that millisecond window and horizontal conduction velocity together predict cortical column diameter, and the two areas with direct measurements fall where the relation puts them. One anatomically measurable parameter thus sets what a neuron detects and the limits of what it can represent.

q-bio.NC↗

arXiv2026

Diffusion models for eye-gaze trajectory generation using position and velocity representations

Eye-tracking data are expensive to collect, requiring specialized hardware and controlled laboratory conditions, and difficult to share because of privacy constraints. We address this using two complementary denoising diffusion probabilistic models (DDPMs) for unconditional generation of eye-gaze dynamics from visual-search data. Both use an identical FiLM-conditioned one-dimensional U-Net with self-attention (19.35,M parameters), trained on 8,s sliding-window sequences from 28 participants. One model generates raw two-dimensional gaze-position sequences, while the other generates two-component velocity sequences; each uses representation-specific preprocessing, training settings, data partitions, and evaluation protocols. Both are evaluated across three independent training seeds, with aggregated metrics reported as mean,$\pm$,SD. The position-space model achieves a mean Jensen-Shannon (JS) divergence of $0.016\pm0.004$ across nine kinematic features, with the highest feature-wise mean below $0.030$, fixation duration within 2% of real data, and a Fr'echet Gaze Distance more than an order of magnitude below statistical and Markovian baselines. Under a Train-on-Synthetic-Test-on-Real protocol, synthetic-only training achieves $R^2=0.66\pm0.02$, or 82.7% of the real-data $R^2$ point estimate. The velocity-space model achieves a mean JS divergence of $0.0065$ across velocity components, speed, log-speed, and turning angle, with a maximum of $0.015\pm0.005$. Reconstructed path length is less accurate ($0.21\pm0.02$ versus $0.03\pm0.01$ in position space), although the protocols differ. Overall, unconditional diffusion captures local gaze kinematics and short-range temporal and directional structure, while long-range properties such as saccade counts and cumulative path geometry remain targets for future conditioned models.

cs.CV↗

arXiv2026

A Systematic Approach to Mechanism Design with Stochastic Dynamic Stability

We consider a resource allocation problem with strategic agents that have private stochastic satisfaction functions and local constraints. To achieve a global optimal solution, we propose an incentive mechanism that induces a game among the agents. For the payment function of the mechanism, we construct a family of quadratic functions using the linear matrix inequality (LMI) approach that implements the social welfare maximizing outcome on the unique Nash equilibrium (NE) of the induced game while ensuring budget balance and individual rationality. Moreover, we propose a decentralized variable sample-size proximal best-response (VS-PBR) algorithm with Krasnoselskij iteration where only aggregate information is available to the agents. The algorithm is dynamically stable, as it is proven to converge in the mean-square sense to the NE of the game. The efficiency of the mechanism is then investigated on the Sioux Falls City transportation network, where electric vehicle (EV) users jointly select their destination and route.

eess.SY↗

arXiv2026

On the Structure of $(\min,+)$ Convolution

The $(\min,+)$ convolution is a central problem in fine-grained complexity, and it remains open whether it can be computed in truly subquadratic time. We study it through tropical polynomials, where $(\min,+)$ convolution is exactly tropical polynomial multiplication. We introduce the tropical decomposition width, $\operatorname{tdw}(A)$, which measures how finely a tropical polynomial can be decomposed into factors of small degree. We prove two modular convexity theorems showing that bounded tropical decomposition width forces convexity on arithmetic progression subpolynomials. This yields deterministic algorithms for computing $a\otimes b$ in $$O\left(n\max(\operatorname{tdw}(a),\operatorname{tdw}(b))^2\right)$$ when $\max(\operatorname{tdw}(a),\operatorname{tdw}(b))$ is given, and in $$O\left(ne^{\min(\operatorname{tdw}(a),\operatorname{tdw}(b))(1+o(1))}\right)$$ without prior knowledge of the width. Neither algorithm requires a decomposition of the input sequences. The same structural ideas give a randomized algorithm for Multiple-Sequence $(\min,+)$ Convolution: given $k$ sequences of length at most $n$, their convolution can be computed in $$O\left(kn^2\sqrt{\min(k,n)}\log^{1.5}(kn)\right)$$ time, improving the natural $O(k^2n^2)$ bound. Finally, we introduce interpolation algebras for tropical polynomials and show that classes with bounded tropical decomposition width admit interpolation algebras of finite generating rank, whereas distinguishing all tropical polynomials of degree at most $n$ requires generating rank $\lfloor n/2\rfloor+1$. We also prove that tropical decomposition width cannot decrease under any flat $\mathbb T$-algebra extension. Together, these results connect the tractability of $(\min,+)$ convolution with structural rigidity in tropical polynomial multiplication.

cs.CC↗

arXiv2026

A Sharp Unitarily Invariant Norm Bound for the Off-Diagonal Block Perturbation of a Hermitian Matrix

Let $$ A=\begin{bmatrix} H_1 & E^* \\ E & H_2 \end{bmatrix} \quad\text{and}\quad \widetilde A=\begin{bmatrix} H_1 & 0 \\ 0 & H_2 \end{bmatrix} $$ be two partitioned Hermitian matrices, where $\widetilde A$ is obtained from $A$ by simply dropping the off-diagonal blocks, and let $η$ be the gap between the spectra ${\rm eig}(H_1)$ of $H_1$ and ${\rm eig}(H_2)$ of $H_2$. Define, for $δ\ge 0$ and $ε\ge 0$, $$ ϕ(δ,ε)= \begin{cases} 2ε/(δ+\sqrt{δ^2+4ε^2}), &\quad\mbox{if $(δ,ε)\ne (0,0)$}, 1, &\quad\mbox{if $(δ,ε) = (0,0)$}, \end{cases} $$ and let $V=A-\widetilde A$ and $ε_2=\|E\|_2=\|V\|_2$, the matrix spectral norm. Li and Li [{\em Linear Algebra Appl.}, 395:183--190, 2005] established a sharp spectral-norm bound on the changes in the eigenvalues of $A$: $$ \big\|{\rm diag}\big(\pmbλ(A)-\pmbλ(\widetilde A)\big)\big\|_2 \le ϕ(η,ε_2)\,\|E\|_2, $$ where $\pmbλ(A)$ is the vector whose components are the eigenvalues of $A$ in descending order and similarly for $\pmbλ(\widetilde A)$. The goal of this paper is to resolve the question: how far an extension of this result in the form $$ \big\|{\rm diag}\big(\pmbλ(A)-\pmbλ(\widetilde A)\big)\big\|_{\rm UI} \le ϕ(η,ε_2)\,\|A-\widetilde A\|_{\rm UI} $$ remains valid for some or all unitarily invariant norms $\|\cdot\|_{\rm UI}$? Two results are obtained: (a) the extension holds for any $Q$-norm, a subclass of unitarily invariant norms that encompasses the Schatten $p$-norm for $2\le p\le\infty$ (particularly, the Frobenius norm and the spectral norm included), and (b) the extension holds for any unitarily invariant norm if ${\rm rank}(E)\le 1$. It is demonstrated that the equality is attained on the $2\times 2$ matrix $A$.

math.NA↗

arXiv2025

Security Science (SecSci), Basic Concepts and Mathematical Foundations

This textbook compiles the lecture notes from security courses taught at Oxford in the 2000s, at Royal Holloway in the 2010s, and currently in Hawaii. The early chapters are suitable for a first course in security. The middle chapters have been used in advanced courses. Towards the end there are also some research problems.

cs.CR↗

arXiv2026

Fully Distributed GNE Algorithms for Multi-Robot Placement without Consensus on Multipliers

Recent machine learning research has increasingly focused on equilibrium analysis in non-cooperative games rather than solely on optimal solutions. Many such problems involve shared constraints and can be formulated as Generalized Nash Equilibrium Problems (GNEPs). For strongly monotone games, existing methods compute consensus-based variational GNEs (v-GNEs) by exchanging Lagrange multipliers. We propose a fully distributed continuous-time algorithm for shared linear equality constraints that converges without multiplier exchange and reaches any GNE, reducing communication overhead and improving privacy. Discrete-time schemes are also provided, and the method is validated on a multi-robot placement task.

cs.LG↗

arXiv2026

TSExplorer: An interactive data annotation and exploration tool for time-series data

We present TSExplorer, a cross-platform tool for interactive annotation and exploration of time-series data. The tool enables users to inspect high-dimensional datasets through multiple complementary 2D visualizations derived from high-dimensional feature representations. TSExplorer is designed as a general-purpose research tool supporting a wide range of workflows, including exploratory data analysis, annotation of unlabeled or partially-labeled datasets, comparison of feature representations, and post-hoc inspection and refinement of existing labels with interactive visual feedback.

cs.HC↗

arXiv2026

Towards a universal language of concepts: A survey

Humans can learn and generalize novel concepts from sparse data because they express knowledge in rich structural formats. In this paper, we propose that programs are a strong candidate for universal representation of concepts. We review computational models of concept learning that use programs as their concept representation and evaluate their contribution toward a universal representational language.

cs.AI↗

arXiv2026

VIBE: Video Instruction-aligned Background music gEneration

Current video-to-music (V2M) models lack semantic control and fail to penalize instruction violations, largely due to their reliance on reconstruction objectives and the representational bottleneck of static cross-modal conditioning in Diffusion Autoregressive (DAR) architectures. To resolve this, we introduce VIBE, a novel text-and-video-to-music (T+V2M) generation model that leverages: (1) Conditioning Connection, a depth-wise cross-layer conditioning mechanism that dynamically bridges the planning and diffusion refinement heads and (2) a comprehensive reward modeling taxonomy, optimizing for both hard, verifiable constraints (e.g., tempo, key) and soft, subjective qualities (e.g., musicality, multimodal alignment) with a structured 5-stage training curriculum. Upon evaluation using audio-visual alignment, instruction following, and audio quality metrics, along with a subjective human evaluation study, we observe that VIBE demonstrates enhanced controllability and instruction adherence while performing comparably to most evaluated baselines on generation fidelity and multimodal alignment.

cs.SD↗

arXiv2026

MultiGhostBench: A Multilingual Benchmark for Long-Form LLM-Generated Text Attribution under Distribution Shifts

While existing work on LLM authorship attribution (AA) has made progress, available benchmarks remain limited, often focusing on English, controlled settings, or relatively outdated models, with the few multilingual studies considering only relatively short texts. We introduce MultiGhostBench, a multilingual benchmark comprising 928 books generated by five recent LLMs across six languages and three scripts, with an average length of approximately 59K words per book. The benchmark supports evaluation under domain, author, and language shifts. Evaluation of representative AA methods shows that no single method consistently performs best across settings, and performance generally degrades under distribution shifts. Transformer-based detectors can retain generator-related information across languages, although transfer effectiveness varies by language pair, whereas statistical and fingerprint-based detectors are more language-dependent. We envision MultiGhostBench as a valuable resource for the development and evaluation of robust AA methods. The dataset and code can be found at https://github.com/GrecoMT/MultiGhostBench.

cs.CL↗

arXiv2026

Aligning Agentic World Models via Knowledgeable Experience Learning

Current Large Language Models (LLMs) exhibit a critical modal disconnect: they possess vast semantic knowledge but lack the procedural grounding to respect the immutable laws of the physical world. Consequently, while these agents implicitly function as world models, their simulations often suffer from physical hallucinations-generating plans that are logically sound but physically unexecutable. Existing alignment strategies predominantly rely on resource-intensive training or fine-tuning, which attempt to compress dynamic environmental rules into static model parameters. However, such parametric encapsulation is inherently rigid, struggling to adapt to the open-ended variability of physical dynamics without continuous, costly retraining. To bridge this gap, we introduce WorldMind, a framework that autonomously constructs a symbolic World Knowledge Repository by synthesizing environmental feedback. Specifically, it unifies Process Experience to enforce physical feasibility via prediction errors and Goal Experience to guide task optimality through successful trajectories. Experiments on EB-ALFRED and EB-Habitat demonstrate that WorldMind achieves superior performance compared to baselines with remarkable cross-model and cross-environment transferability.

cs.CL↗

arXiv2026

CyrillicQA: The Influence of Phonetically Encoded Secret Language on LLM Performance

Due to the selection of their training data, large language models (LLMs) perform best on standard-language inputs from languages using the Latin alphabet with large speaker populations, while disadvantaging other language varieties. Nevertheless, they can also be a versatile tool for preserving precisely such endangered languages. But do they also possess the necessary creativity and capacity for abstraction to decode phonetically encoded language the same way humans do?

cs.CL↗

arXiv2026

A Non-Formulable Theorem: A Fundamental Limit of Finite Syntactic Systems and Its Consequences for Security and AI

For every coherent and sufficiently expressive finite syntactic system S, we prove the existence of at least one theorem that S cannot produce autonomously. The result is a metatheorem: it proves the existence of a theorem, and applies to every finite syntactic system - security mechanisms, AI systems, formal verifiers, legal systems, economic models, and the formal system in which it is itself proved.

cs.CR↗

arXiv2026

Visual Framing for News Stance Detection via Image Generation

Article-level news stance detection aims to identify the perspective of news articles toward social issues. Despite advances in stance detection and its importance for trustworthy media environments, news articles pose distinct challenges because their stances are often implicit, subtly conveyed through journalistic framing, and embedded in long, structurally complex texts. To address these challenges, we introduce VFStance, which leverages visual framing to make implicit stance cues more explicit via image generation. In evaluation experiments, we demonstrate the effectiveness of VFStance over existing methods and the contribution of visual framing to its performance. Finally, a controlled user study (N=200) in a snippet-based news consumption setting further demonstrates that VFStance can make stance signals visually salient and highlights its potential use beyond automated stance detection.

cs.CL↗

arXiv2026

Decentralized Vision-Based Autonomous Aerial Wildlife Monitoring

Wildlife field operations demand efficient parallel deployment methods to identify and interact with specific individuals, enabling simultaneous collective behavioral analysis, and health and safety interventions. Previous robotics solutions approach the problem from the herd perspective, or are manually operated and limited in scale. We propose a decentralized vision-based multi-quadrotor system for wildlife monitoring that is scalable, low-bandwidth, and sensor-minimal (single onboard RGB camera). Our approach enables robust identification and tracking of large species in their natural habitat. We develop novel vision-based coordination and tracking algorithms designed for dynamic, unstructured environments without reliance on centralized communication or control. We validate our system through real-world experiments, demonstrating reliable deployment in diverse field conditions.

cs.RO↗

arXiv2026

Transformer-Based Autonomous Driving Models and Deployment-Oriented Compression: A Survey

Transformer-based models are becoming a central paradigm in autonomous driving because they can capture long-range spatial dependencies, multi-agent interactions, and multimodal context across perception, prediction, and planning. At the same time, their deployment in real vehicles remains difficult because high-capacity attention-based architectures impose substantial latency, memory, and energy overhead. This survey reviews representative Transformer-based autonomous driving models and organizes them by task role, sensing configuration, and architectural design. More importantly, it examines these models from a deployment-oriented perspective and analyzes how efficiency constraints reshape model design choices in practice. We further review compression and acceleration strategies relevant to Transformer-based driving systems, including quantization, pruning, knowledge distillation, low-rank approximation, and efficient attention, and discuss their benefits, limitations, and task-dependent applicability. Rather than treating compression as an isolated post-processing step, we highlight it as a system-level design consideration that directly affects deployability, robustness, and safety. Finally, we identify open challenges and future research directions toward standardized, safety-aware, and hardware-conscious evaluation of efficient autonomous driving systems.

cs.LG↗