Papers

In recent years, three initiatives have emerged to develop generative language models in Hungary. The motivation behind them is the same. For Hungarian, no model with the given capability existed, or existing English-centric models offered limited proficiency. A detailed examination of the corresponding studies, however, reveals several methodological limitations. First, the reliability of the evaluation protocols is questionable. Contrary to the findings of Csibi et al. [2026], evaluation under the recommended inference settings shows that Qwen3-4B achieves higher scores than Racka-4B, its Hungarian-adapted version. Data contamination is evident in the work of Yang et al. [2025d] and Szentmihályi et al. [2025], potentially biasing the reported results. Second, the training pipelines fall short of current best practices in corpus curation and data mixture, which risks wasting substantial compute on low-quality data. The lack of controlled ablations prevents reliable assessment of these choices. Third, none of the three papers assessed forgetting or capability loss. Testing the adapted models on a subset of the original benchmarks indicates performance decline in all three cases, especially Racka-4B. These observations emphasize the importance of rigorous experimental design in language model development, given the significant computational and financial costs involved.

As telecommunication networks evolve toward autonomous 5G-Advanced and 6G operations, agentic artificial intelligence (AI) workflows, where large language models (LLMs) execute multi-step reasoning, invoke diagnostic tools, retrieve domain knowledge, and coordinate across agent teams, are increasingly embedded across the edge-cloud continuum. While the biological brain accomplishes complex cognition on an exceptionally modest metabolic power budget of approximately 20W contemporary LLMs are profoundly energy- and memory-intensive, making sustainable lifecycle orchestration a critical operational priority. However, existing AI lifecycle metrics evaluate only isolated, single-model inferences or overlook multi-agent execution graphs entirely. Consequently, network operators lack foundational models to determine whether distributed agent communication incurs meaningful energy costs and where across edge-cloud tiers agent teams should physically reside. To address this gap, we introduce agentic-eCAL, generalizing the Energy Cost of AI Lifecycle (eCAL) metric to directed multi-agent workflows by coupling a closed-form two-rate single-call energy model (compute-bound prefill and memory-bound decode) with 7-layer OSI data transport. Grounded in hundreds of GPU benchmark configurations on NVIDIA A100 and H100, 16 open-weight models and 8 orchestration topologies, we validate components of the metric and study workflow placement implications. Our findings demonstrate that inter-agent text transport incurs 0.25% of workflow energy across 5G RAN, metro, and optical links. Therefore in edge-cloud agent placement the dominant energy cost of distribution is often not the transmission of inter-agent text itself, but the additional inference and context processing induced by that communication.

Large language models are increasingly used to generate and evaluate online content, yet it remains unclear whether the qualities they associate with higher engagement match what real users respond to. We study this question using 1.17 million answers to 25,978 questions from Zhihu, Quora, and Reddit, comparing real platform answers and AI-generated answers across four within-question engagement levels. We introduce Ontological Preference Measurement, which represents answers along three dimensions: logic, affect, and expression. We find a systematic gap between AI preference and real user engagement: as target engagement increases, LLMs add more explicit logical structure, while real user engagement is more strongly associated with affective and expressive salience. We call this tendency logic overbinding. Based on this diagnosis, we propose Ontology-Masked Reasoning Autoencoding (OMRA), a controlled intervention that masks and reconstructs over-explained spans while preserving stance, factual content, and coherence. Across four LLM families, OMRA reduces the measured gap by an average of 54.4%. In human evaluation, OMRA wins 62.4% of pairwise preference judgments against matched real platform answers, even though the real answers are more often judged to be human-written.

The availability and consistency of online services remain vulnerable due to Distributed Denial of Service (DDoS) attacks. These attacks are evolving by adopting more complex strategies to evade traditional network security systems. Despite the effectiveness of machine learning models in detecting DDoS traffic, targeted adversarial attacks can degrade their classification accuracy. This work proposes a robust detection framework that integrates generative adversarial modelling with advanced machine learning models. We trained Random Forests, Deep Neural Ensembles, and Transformer-based models using the CICDDoS2019 dataset to establish the frameworks baseline performance. To enhance the models defensive capacity, we generated synthetic adversarial flows that simulate potential evasion attempts and adversarial traffic using a Wasserstein Generative Adversarial Network with Gradient Penalty (WGAN-GP). Then, we combined the generated traffic with benign and malicious traffic to construct hybrid datasets to train the models to learn more generalizable decision boundaries. The experimental results indicate that the proposed methodology significantly enhances detection accuracy and resilience, especially against unseen adversarial traffic. We also tested the designed framework using real-world generated traffic, which demonstrates its capability in practical settings. The scalable and efficient solution against adversarial DDoS attacks, introduced in this work, paves the way towards more resilient and adaptive network defense systems that combine generative adversarial augmentation with recent advances in learning models.

We study the existence and vanishing viscosity limit of steady incompressible Navier-Stokes flows in a horizontally periodic strip with no slip boundary conditions and midline symmetric forcing. Taking a Poiseuille flow as the leading order Euler profile, we construct higher order symmetric approximate solutions and establish the existence of a symmetric solution to the associated nonlinear error equation. Under suitable compatibility conditions on the forcing, this construction yields a family of midline symmetric steady Navier-Stokes solutions that converges to the prescribed Poiseuille flow at the optimal rate.

Vision Transformers (ViTs) have achieved state-of-the-art performance across a range of computer vision tasks, mainly thanks to the self-attention mechanism. However, its complexity, increasing quadratically with the number of tokens, remains the major obstacle to ViT efficiency and deployment at scale. Token merging reduces this cost by aggregating redundant tokens. Yet existing methods are typically evaluated within a single architecture, leaving open whether their effectiveness stems from the merging mechanism itself or from the specific decoder they are paired with. We extend Graph-Guided Token Merging (G2TM), a single module inserted early in a ViT-based network, beyond its original Segmenter setting. We evaluate G2TM across three semantic segmentation frameworks (Segmenter, SETR, EoMT) and three decoder families (Linear, Transformer-, convolution-based), as well as standard ViT image classification. Our results show that G2TM's behavior and accuracy-efficiency trade-off are consistent across every tested architecture for a given backbone size, indicating that its effectiveness is a property of the encoder rather than the decoder. G2TM also generalizes well to image classification, achieving an even smaller degradation in accuracy compared to semantic segmentation. We further find that G2TM's optimal hyperparameters, resulting in a consistent drop in GFLOPs of 22-47% and an increase in throughput by up to 74% for segmentation models on ADE20K dataset, depend primarily on the backbone's pre-training recipe and on the target dataset, rather than on the decoder choice.

Artificial Intelligence (AI) is currently only applied to non-safety critical applications due to the strict standards and regulations for railway industries. We propose to review the three main fields necessary to increase trust in data science and AI algorithms and reach compliance: robustness, Operational Design Domain (ODD), and explainability. Robustness is the ability of an AI system to maintain its level of performance under any circumstances (ISO24029). ODDs allow the explicit definition of operating conditions under which a system is intended to operate, according to the recently published DIN DKE SPEC 99004. Explainability is the property of an AI system to express important factors influencing the AI system results in a way that humans can understand. Those 3 domains of research are already well investigated by nonrailway actors, with algorithms and methods ready to use for railway applications. A system view is necessary to ensure all trustworthy requirements interact continuously in a safe MLOps environment thereby fostering acceptance from regulators, operators and the public. Beyond safeguarding safety-critical applications, we aim to show that fostering deep trust in AI, as now required by regulatory frameworks worldwide, will unlock its full potential and transform the pace of adoption across mission-critical domains.

In this paper, we investigate the localization of various $q$-form fields on a codimension-two brane. In particular, the $0$-form scalar field, the $1$-form $U(1)$ gauge vector field, and the $2$-form Kalb-Ramond field are considered with gravitational coupling, where a coupling function $F(R)$ is introduced into the six-dimensional actions of these fields. The function $F(R)$ depends on the scalar curvature of the bulk. Within this framework, we find that the massless modes of different $q$-form fields can be localized on the thick brane for positive values of the coupling parameters $t_1$ and $t_2$. For the massive modes, the different $q$-form fields exhibit similar localization properties determined by the coupling parameter $t_2$. When $0<t_2<v^2/24$, the massive modes of these fields cannot be localized on the brane, while they may exist as the resonant modes. In the case $t_2=v^2/24$, a finite number of massive modes can be localized on the thick brane, and the number of localized modes increases with the coupling parameter $t_1$. Finally, when $t_2>v^2/24$, the effective potentials associated with the Kaluza-Klein modes of these $q$-form fields form infinitely deep potential wells, so that all massive modes can be localized on the brane. Moreover, the tachyonic massive modes can always be excluded for different $q$-form fields.

Traditional graph rigidity theory enforces structural constraints in the position space, effectively restricting a multi-agent formation to a static geometric shape. In this paper, we introduce a fundamental paradigm shift by applying rigidity constraints directly to the agents' continuous-time velocity space. We propose the concept of generalized velocity rigidity, demonstrating that the macroscopic physical motion patterns of a multi-agent network are entirely dictated by the underlying static graph topology. By strictly confining the network's acceleration profile to the null space of the velocity rigidity matrix, we mathematically map the trivial motions of this null space into exact physical trajectories. Specifically, we prove that translational, rotational, and scaling trivial motions seamlessly integrate into cohesive curved flocking, synchronized helical and circular $\mathrm{SO}(d)$ orbiting, and exponential spatial homothety, respectively. Furthermore, we analyze velocity-space singularities, showing that velocity consensus induces a valid topological contraction rather than a structural failure. Finally, we provide comprehensive numerical simulations to validate these theoretical mappings, demonstrating that complex macroscopic maneuvers can be orchestrated purely through algebraic constraints in the velocity space, unlocking unprecedented spatial shape flexibility for multi-agent swarms.

For every constant $c > 0$, we unconditionally construct witness encryption for NP in the classical generic cyclic group model with the following properties. For SAT instances of size $n$, encryption runs in time poly$(n)$, and any satisfying assignment can be used to decrypt in poly$(n)$ time with correctness error $2^{-n}$. If no satisfying assignment exists, every generic adversary making at most $n^{(\log n)^c}$ group queries has distinguishing advantage at most $n^{-(\log n)^c}$. Along the way, we give the first superconstant-factor NP-hardness of approximation result for homogeneous MinRank under randomized polynomial-time reductions. We obtain a gap of $(\log n)^c$ for any prescribed constant $c>0$, even when YES instances are required to have a rank-one matrix of the form $\mathbf u\mathbf v^T$ where $\mathbf v$ is a 0/1 vector. The main results of this paper were discovered by Codex / ChatGPT 6 Astra Ultra using harness components from the UCLA Moonshot Harness Project, in response to a general strategy for witness encryption suggested by the authors. See the end of the introduction for a discussion.

Classroom observations are widely recognized as a key tool for establishing benchmarks of education quality and guiding pedagogical improvement, yet they remain resource-intensive and dependent on trained observers. This study evaluated the feasibility of using a LLM (GPT-5 model) to score teacher-child interactions in early childhood classrooms, benchmarked against human raters. The study analyzed 87 video-recorded observations from 38 classrooms across 30 kindergartens in Hong Kong. Using observation transcripts, the AI model was configured to apply the full Classroom Assessment Scoring System (CLASS) framework. AI-rated scores were then compared with human ratings by examining correlations and differences in mean scores of the CLASS domains and dimensions. The results showed greater convergence between AI and raters for the Emotional Support domain and, in particular, the Quality of Feedback dimension, which captures how teachers use feedback to extend children's learning. Greater divergence emerged for interactions that were more procedural or context-dependent, particularly within the Classroom Organization and Instructional Support domains. These findings suggest that transcript-based AI scoring may capture some of the relative variation in teacher-child interactions but cannot yet reproduce calibrated human judgements consistently across the full CLASS framework. AI-assisted observation may therefore be more appropriate as a preliminary screening tool rather than as a replacement for trained observers, providing teachers with evidence for reflection rather than high-stakes evaluation. Future research should examine whether domain-specific training and incorporation of contextual and visual information can improve alignment between AI and human rated scores.

Web browsing often appears ephemeral: users visit a few websites, complete a task, and move on. However, even short fragments of browsing activity can contain rich and structured behavioral signals. In this work, we conduct a comparative empirical study of two complementary behavioral inference tasks: session-level user identification and next-domain prediction. Both tasks are derived from the same cleaned event stream and evaluated on large-scale anonymous browsing traces, with sessionization and splitting adapted to the temporal requirements of each task. For user identification, we evaluate classical and neural models operating on session-level behavioral and domain features. For next-domain prediction, we combine graph-based modeling with Large Language Models (LLMs). Experimental results show that short browsing sessions are highly identifiable, while future navigation actions are highly predictable from long-term interaction structure combined with recent behavioral context. Furthermore, LLM-derived semantic features yield only marginal gains over purely structural and sequential models, indicating that repeated interaction patterns remain the dominant predictive signal in the evaluated web-browsing setup. These findings highlight the extent to which interaction history substantially contributes to both user identifiability and navigation predictability in browsing traces.

Agentic AI systems plan, invoke tools, and act with limited supervision; they are now both the subject of audits and, increasingly, the auditor. Independence-the foundation of assurance-is still applied to them as a binary. We argue that it must be graded along three orthogonal axes: principal independence (who controls the auditor), substrate independence (an auditor that shares the auditee's foundation-model family, toolchain, or guardrails fails with the auditee), and evidence independence (whether evidence is attestable rather than self-reported). Each axis has precedent; the contribution is to grade all three on a single audit, aggregate them by the weakest link, and apply the same rubric when the auditor is itself an agent. We give the model a formal basis by transplanting the beta-factor model of common-cause failure from reliability engineering. We also provide a seven-step protocol whose outputs a third party can verify, a structural detectability analysis of a procurement-controls agent audited at three grades, and a closed-form study of the model in which, at a declared common-mode share of 0.90 for a same-family auditor and a declared reporting probability of 0.6 for an internal team, a conventional internal audit of an agent-a real audit team, a second agent, and provider logs-surfaces 5.9% of the faults it could in principle see and, independently of those two values, none at all in half of the fault classes. Because an evidence grade says who could have altered a record, not what the record covers, every load-bearing record also carries a declared-scope predicate, and reports carry a false-flag rate beside the detection floor wherever the auditor's own performance has been measured. We map the triple to the EU AI Act as amended, ISO-IEC 42006, UK public-sector risk-management guidance, and audit-regulator practice.

The Kaneko-Zagier conjecture predicts a correspondence between finite and symmetric multiple zeta values. Under this correspondence, $\zeta(3)$ corresponds to an element $Z(3)$ defined by Bernoulli numbers. We prove a conjecture of Tasaka relating $Z(3)$ to the quotient of two solutions of a recurrence. A two-index $q$-recurrence connects this quotient to a finite harmonic $q$-series. Using a method of the author, Takeyama, and Tasaka, we obtain the algebraic and analytic limits $3Z(3)/4$ and $3\zeta(3)/4$ at roots of unity.

Payment operations are a critical financial infrastructure, but the value of large language models in this domain remains unclear because payment rules change quickly, evidence is fragmented, and decisions depend on transaction state, participant role, region, and payment rail. Existing benchmarks do not isolate whether failures come from missing payment-rule knowledge, poor use of supplied evidence, or brittleness under imperfect harness inputs. We introduce BENCHCOMPASS, a payment-domain benchmark whose construction pipeline builds scenario-grounded tasks from typed evidence packs, applies LLM-based quality checks, creates task-input attack variants, and reserves final item admission for domain experts. The release contains an expert-reviewed Pro benchmark covering payment knowledge, context-grounded scenario reasoning, and Attacked Open robustness, plus a lower-assurance Normal pool for inspection and future curation. Across 16 model variants, BENCHCOMPASS shows qualitatively different failure modes: missing parametric payment knowledge, incomplete reasoning over supplied rules, and failure to reject plausible but invalid workflows. The benchmark remains unsaturated: the best frontier model reaches 89.6% on Open Context-Grounded Reasoning and 81.7% under attacked inputs, while a representative 32B open-weight model reaches 69.8% and 42.6%. Benchmark data and code are available at https://github.com/ant-intl/BenchCompass.

The BFKL equation describes how the density of gluons in a hadron grows with the collision energy. This evolution is often treated as a random walk in the logarithm of the gluon transverse momentum, but it has not been established that one set of positive step probabilities describes this walk in the size and the direction of the momentum, or that such probabilities exist beyond leading order. We show that one positive step density describes the evolution in the size and the direction of the momentum with no approximation at leading order, fixed coupling and zero momentum transfer, once the gluon density is rescaled by the size of its transverse momentum and its growth is divided out. The displacements of the resulting walk over separate, equal intervals of rapidity, the logarithm of the energy in units of a reference energy, are then independent and identically distributed, which makes the walk a Levy process. We also show that this description fails when the series in the coupling is cut at next-to-leading order, with the reference energy and the scale of the coupling both set by the product of the transverse momenta before and after an emission. The evolution averaged over directions then has no probability law at any fixed positive coupling and rapidity, because a negative correction growing as the squared logarithm of the momentum ratio outweighs the leading term when one momentum is much larger than the other. A positive step density for the averaged walk agrees with this truncated evolution to next-to-leading order and defines a random walk for every value of the strong coupling below one, so the failure comes from the truncation. The main message is that agreement with perturbation theory does not guarantee positive step probabilities, so an evolution equation summed to all orders and meant to describe a random walk must be tested for them.

The practical implementation of Control Barrier Functions (CBFs) for safety-critical control is often hindered by uncertainty in the knowledge of the state. While existing robust CBF methods address state uncertainty, they often lack recursive feasibility guarantees or fail when uncertainty levels are high, allowing the system to enter regions where no safe control input exists. To resolve this, we propose a novel framework of enforcing recursive CBFs. Rather than merely ensuring the invariance of the original safe set, this approach enforces the forward invariance of a subset of the safe region where a robustly safe control input is guaranteed to exist. This holistic framework ensures that the system never strays into ambiguous regions, providing continued feasibility and safety guarantees, regardless of the level of state uncertainty.

We characterize the bath resources needed to supply repeated uses of a fixed finite-dimensional quantum channel in a closed device. For each horizon $T$, one bath, one initial state and one repeated unitary are fixed before the user. Each output is returned before the next input arrives; no reset, discard, fresh ancilla or uncounted controller is available. Approximation error must vanish against arbitrary adaptive users with quantum memory and references. Writing $r=\lim \log_2(R_T)/T$ for the bath dimension rate and $s=\lim S(\omega_T)/T$ for the actual initial entropy rate, we prove that the achievable region is exactly $s\ge 0$, $r+s\ge h$ and $r-s\ge\kappa$. Here $h$ is maximum entropy exchange and $\kappa$ is a smoothed independent-reference extension cost, with the zero-error limit taken before the supremum over full-rank inputs. Its exact fixed-input form is an affine transform of the zero-leakage quantum privacy funnel. The minimum dimension rate is $(h+\kappa)/2$. The proof combines entropy converses, a bath-dimension-independent support repair, and a closed adaptive implementation of encoder-only fully quantum Slepian–Wolf recycling. All seeds, clocks, workspace and retained residues are counted. Worked examples include dephasing, pure replacement and a qubit channel with $0<\kappa<h$. No computability of $\kappa$ or efficient circuit synthesis is claimed.

We give exact polynomial-time algorithms in fixed dimension for mixed-integer quadratic programming over arbitrary rational polyhedra and for integer cubic programming over bounded rational polyhedra. The quadratic objective may be indefinite; the algorithm detects infeasibility, certifies unboundedness, or returns an exact minimizer. For an instance with N variables and m constraints, the running time is 2O(Nlog N) times (m+ 1)O(N) times a factor in which the binary encoding lengths of the coefficients are raised to a power O(N); for pure integer problems, and for mixed-integer problems with integral right-hand side and linear term, only the constraint and quadratic matrices enter this factor, while the right-hand side and linear term enter polynomially. This replaces the dependence on coefficient magnitudes in earlier fixed-parameter results by dependence on encoding length, and the exponent O(N) is optimal under the exponential time hypothesis. For cubic objectives, integer minimization over a bounded polyhedron was previously known to be polynomial only in dimension two. Our algorithm extends to any polynomial whose second directional derivatives are concave in position, which includes cubics with an added concave quartic form. Both algorithms rest on a hidden convexity of such objectives on bounded lattice sets, exposed by a cover of the feasible integer points by reflecting cells. For quadratics, a negative-curvature integer displacement excludes a cell, and otherwise supporting inequalities on its integer points permit exact optimization through an integer-query separation oracle. For cubics and the broader class, negative curvature at a query point yields a linear cut valid for every global minimizer in the cell, and supporting inequalities among the remaining admissible points play the same role.

We prove a Pogorelov interior estimate for strictly plurisubharmonic solutions of the complex Monge-Ampère equation $\det(u_{i\bar{j}})=1$ with homogeneous Dirichlet data under the condition that, for some constant $\kappa\geq 1$, $(\kappa u_{i\bar{j}}-u_{is}u^{s\bar{t}}u_{\overline{tj}})$ is non-negative definite. For $\kappa=1$, this gives the estimate for real convex solutions. The estimate depends only on the dimension, $\kappa$, and the $C^0$ and $C^1$ norms of the solution. As an application, every smooth entire convex solution of $\det(u_{i\bar{j}})=1$ on $\mathbb{C}^n$ is a real quadratic polynomial. The same conclusion holds if real convexity is assumed only outside a compact subset of $\mathbb{C}^n$.

As modern societies rely more on autonomous systems to facilitate daily life, assuring their safe operation is paramount. Naturally, there are many techniques available to predict and prevent system failures. However, the safety afforded by such schemes may become misaligned with the true system, which can change in unexpected ways - from partial faults to natural wear-and-tear - that subtly degrade its stability. The implications that such subtle changes have on autonomous system stability can be observed through generic indicators of resilience derived from critical slowing down, popular for anticipating catastrophic tipping points in natural systems. Here, we show how one can systematically design these generic indicators for nonlinear control systems and show how these can reflect loss of stability though simulations of canonical robotic systems wherein their proximity to instability is manipulated directly. These results are affirmed through real-world flight experiments of a quadrotor that is nudged towards instability by progressively damaging its propeller blades. Our results show that the implications of degraded resilience on closed-loop stability are evident well before they appear, for which the indicators of resilience derived here can provide an early warning.

We explore a class of Lorentz-violating scalar-field models where the effects of the scalar field on antimatter can be strongly enhanced compared to matter. Non-trivial differences in phenomenology arise for spectroscopy measurements depending on whether the scalar field changes slowly or rapidly on the atomic scale. We highlight opportunities for precision tests in the laboratory including dark matter searches, in particular with spectroscopy and interferometry measurements, as well as certain types of antimatter experiments.

Precise retrieval of scientific information is fundamentally constrained by long-tailed concepts and high fact-sensitivity of scientific corpora. These challenges often limit the effectiveness of dense retrievers and hallucination-prone LLM augmentation. To address this, we present REPAIR, a self-evolving data augmentation framework for scientific dense retrievers. REPAIR iteratively synthesizes training data to address knowledge gaps by cycling through diagnosis of long-tail concepts, API-guided evidence expansion, and differentiation via hard negative mining. This process effectively grounds retrieval in factual reality to resolve fine-grained distinctions. Extensive experiments demonstrate that REPAIR significantly outperforms 19 strong baselines on nine materials science and biomedical benchmarks. Our work highlights that diagnosing and factually augmenting data to long-tail deficits is essential for robust scientific retrieval.

We show that descriptive complexity can serve as a foundation for formalizing computational complexity results in a proof assistant, by constructing a Lean library centered around the following concepts: decision problems are isomorphism-invariant predicates on finite structures; complexity classes are defined by their logical characterization; membership is shown by definability witnesses; hardness is shown by first-order reductions from a known hard problem. We also establish bridges to traditional machine models such as (non)deterministic Turing machines. The library proves 73 completeness results, on 68 problems or problem families, over 14 different classes; relations between the classes established inside the logic and not by machine simulation, among them NL = coNL and the Abiteboul-Vianu theorem; and unconditional lower bounds, among them $\mathrm{FO}(\leq) \subsetneq \mathrm{FO}(\leq, \mathrm{TC})$ and the failure of order-free FO(IFP) to capture PTIME.

Recent advances in artificial intelligence and computer vision are reshaping sports performance analysis by enabling automated detection, tracking, and performance analysis. In hammer throw, performance is strongly determined by the kinematic conditions at release, particularly release speed, release angle, and release height. However, identifying the release instant from video typically requires manual frame-by-frame inspection, which is subjective and cumbersome in real-world training scenarios. In this paper, we present a fully automatic multi-signal release frame detection (MS-RFD) method for hammer throw using reconstructed 3D hammer trajectories. The proposed method integrates four complementary kinematic signals: speed dynamics, angular velocity transition, radial distance relative to the rotation center, and post-release trajectory linearity. These signals are fused to score and verify candidate release frames. MS-RFD is evaluated through the throwing-distance estimation error obtained from the release parameters estimated at the detected frame. An ablation study analyzes the contribution of each signal and compares alternative candidate selection strategies. The results show that speed dynamics and radial expansion provide the strongest signals for release frame detection, while angular velocity and post-release linearity provide smaller refinements.

Recent advancements have successfully adapted autoregressive language models to process multimodal signals, such as images and actions. Since raw action signals are continuous, effective tokenization is essential to map high-dimensional inputs into compact discrete tokens for autoregressive processing. However, existing discrete action tokenizers often suffer from high reconstruction loss, failing to preserve the fine-grained dynamics required for precise control. This "discretization bottleneck" significantly limits the performance ceiling of downstream Vision-Language-Action (VLA) models. To address this, we propose ${M}^2$Tok, a Multi-head Multi-codebook Action Tokenizer designed to minimize reconstruction error and enhance policy performance. Our approach introduces two key structural innovations: (1) we decompose the latent action features into multiple heads, enabling the model to implicitly align specific heads with distinct action dimensions; (2) we assign independent codebooks to each head for quantization. By leveraging the combinatorial nature of multiple codebooks, we significantly expand the representational expressivity of the tokenizer, leading to substantially lower reconstruction loss compared to previous methods. We evaluate the ${M}^2$Tok-based VLA on the RoboTwin, Simpler-Env, and 3 zero-shot real-world tasks. Experimental results demonstrate our method not only achieves superior reconstruction fidelity but also significantly boosts the success rate of VLA models. Comprehensive ablation studies further confirm the effectiveness of the multi-head and multi-codebook mechanisms. Code is available at https://github.com/cpaaax/M2Tok.

We investigate the large-time behavior of small perturbations of stable constant steady states for an attraction-repulsion chemotaxis system in $n$-dimensional Euclidean space. We consider integrable perturbations in one space dimension and, in higher dimensions, perturbations belonging to Lebesgue spaces with suitable exponents. We first establish decay estimates throughout the full admissible range of Lebesgue exponents and show that the nonlinear perturbation is asymptotically approximated by the corresponding linearized evolution. We then identify the leading term of the linearized evolution as an effective heat flow whose diffusion coefficient is explicitly determined by the parameters of the system. Consequently, when the integrability exponent is strictly smaller than the space dimension, the leading asymptotic profile is governed by the heat equation. At the critical endpoint, the difference between the nonlinear perturbation and the effective heat flow vanishes under the natural parabolic scaling. In the one-dimensional integrable case, this yields a Gaussian profile determined by the total mass of the initial perturbation.

We develop a method for measuring the incremental effect of advertising when randomized exper- iments are unavailable. Firms generate abrupt interventions in their own marketing as a byproduct of operations: budgets are cut, channels launch, programs pause. We propose a two-stage proce- dure that treats these events as quasi-experiments. The first stage discovers and dates interventions by exact Bayesian run-length inference on marketing activity series. The second stage runs a causal impact analysis against a variance-constrained structural time series counterfactual, with simulation-based inference, five qualification conditions, and a closed-form power bound. We validate the procedure on the two experimental benchmarks that Meta released with its GeoLift framework. The method identifies the day of intervention exactly in both cases. On the experiment where advertising was removed, it recovers the effect within 6.2 percent of the experimental esti- mate (implied return of 1.50 versus 1.60). On the experiment where advertising was added, its 90 percent interval covers the experimental estimate and excludes zero. Of six estimators evaluated on the same released data, ours is the only one that requires no geographic panel and produces intervals that are both correct on both experiments and narrow enough to act on.

Reliability under sparse and heterogeneous failures remains a fundamental challenge for medical image segmentation. High average accuracy can conceal a small set of structurally distinct and clinically consequential errors. Existing post-hoc correction methods alleviate this problem, but typically estimate false-positive and false-negative corrections from the same fixed prediction. This ignores the dynamic evolution of error states and limits the correction of complex cases. Inspired by iterative error feedback in structured prediction, we propose Failure-Aware Progressive Repair (FAPR). FAPR represents the current segmentation mask as a dynamic failure state and models each repair operation as a state-transition operator. Each accepted correction forms a new prediction state for subsequent error diagnosis and repair, enabling later operations to adapt to preceding changes. Conditional routing selectively activates necessary state transitions, while failure replay exposes the model to rare error states. By keeping the base segmentor frozen, FAPR preserves its established segmentation capability while improving difficult cases. Across three public ultrasound lesion segmentation benchmarks, FAPR improves mean DSC by 1.52%. On the very-hard subsets of BUSI and TN3K, the average gain reaches 13.77%.

The Ramanujan$-$$q$-Airy connection formula relates the convergent series at the origin to the behaviour at infinity of the Ramanujan entire function. We extend this connection to a one-parameter deformation, which embeds the Ramanujan (second-order) $q$-difference operator in a family of third-order equations. By contour integral as $q$-Borel inversion, we give behaviour at infinity in terms of divergent local expansions with connection coefficients uniquely determined. Discrete $q$-Borel$-$Laplace summation yields a convergent, bilateral power series representation, whose dependence on summation path reflects the $q$-Stokes phenomenon. We prove remainder estimates establishing the formal, generally divergent, expansion at infinity as an asymptotic description of the entire function.