Papers

Let \(R\) be any unital ring equipped with a Sylvester matrix rank function, and let \(Q\) be the rank completion of the matrix system defined by block-diagonal embeddings along a factor sequence. We prove that both \(\GL(Q)\) and \((Q,+)\) are exotic: every strongly continuous unitary representation is trivial. We also prove that \(\GL(Q)\) is Bourbaki bounded and admits no nonzero escape function. For every \(\varepsilon>0\), let \(B_\varepsilon\) be the open ball centered at the identity. The least positive integer \(N\) such that \(\GL(Q)=B_\varepsilon^N\) is \(\lfloor\varepsilon^{-1}\rfloor+1\). Neither regularity nor irreducibility is required. Our proof of exoticness uses a uniform Kazhdan estimate for additive integer matrix groups together with rank-one matrix perturbations, rather than the character-theoretic and continuous ring methods used previously. The geometric conclusions follow from factorizations using diagonal corner subgroups.

Universal power-law decay of spin-mixing oscillations has been observed in a harmonically trapped spin-$3/2$ Fermi gas, whose exactly equally spaced spectrum represents a highly special case. To gain insight into the origin of this behavior, we investigate the dynamics in traps with increasing and decreasing level spacings, represented by the infinite square well and the Pöschl–Teller potential, respectively. Despite pronounced differences in their single-particle spectra, all systems exhibit power-law decay of coherent oscillations, described by $A(t) = A_{0} - \gamma t^{\alpha}$. The exponent $\alpha$ remains insensitive to particle number, interaction strength, and the overall energy scale, but exhibits systematic differences among traps with distinct spectral structures. In contrast, the decay parameter $\gamma$ is strongly influenced by both the spectral structure and the overall energy scale. These findings demonstrate that power-law decay is not restricted to the harmonic trap but persists across qualitatively distinct spectral structures. The observed variation of $\alpha$ among different traps further suggests that the underlying single-particle spectrum plays an important role in shaping the decay dynamics.

Building strong chart-to-code systems increasingly relies on reinforcement learning, whose effectiveness depends critically on the quality of the reward signal. Large Multimodal Models (LMMs) play a natural critical role in jointly assessing chart visual appearance and task requirements. They are therefore increasingly used as visual critics and reward models, yet their reliability as judges remains largely unexplored. To this end, we introduce ChartJudgeBench, a diagnostic vision-language benchmark for assessing LMM judges in chart-to-code workflows. It includes 1,003 Chart Perception Alignment (CPA) instances for pairwise chart comparison and 650 Chart Reasoning Judgment (CRJ) instances for binary Accept/Reject verification in Chart Reproduction and Chart Editing. Together, these tasks emulate the core judging decisions required in agentic refinement and RL-based chart optimization. Our evaluation of strong LMMs reveals four systematic limitations: (i) positional bias in pairwise comparison, (ii) a strong tendency to overpredict Accept, (iii) difficulty in matching visual styles and aesthetics, and (iv) an unexpected leniency bias in RL-trained models. These findings show that current LMM judges require explicit reliability validation before being used as critics or reward models in chart-to-code optimization. The code and data are available on ChartJudgeBench.

The Platonic Representation Hypothesis (PRH) claims that independently trained models converge on a shared statistical model of reality, yet recent work finds that the evidence weakens under some conditions. In this paper, we measure what models share through the directions (displacement vectors) between samples. Under a single orthogonal alignment limited to just rotation and reflection, these displacement vectors are substantially preserved across 44 independently trained vision and language encoders spanning modalities and asymmetric capability pairs, consistent with the PRH. Pointwise similarity, however, is lower. Representations split into a shared semantic component that is linearly aligned across models, and a private component that is not, which we interpret as having model-specific capabilities. We trace this geometry to concept-level structure: within a model, parent concepts are orthogonal to their child variation vectors; across models, concept displacements are parallel. We predict (and experiments confirm) that fine-tuning preserves Pointwise similarity but reduces displacement similarity, and relational distillation does the opposite. Because semantics align linearly but capabilities do not, we propose importing capabilities from one model to another using a single cached forward pass through the source. We call this Shadow Casting. As a proof of concept, our ShadowCLIP instantiation outperforms strong fine-tuned baselines at far less compute. A cache can be released alongside open model weights, letting one model's capabilities be downloaded and imported into other models with frozen backbones.

We ask how little geometry a person has to draw to control both where people stand and where the camera moves in a generated video. Our answer is a ground plane and one cylinder per person. A user draws a grid on the ground, places one cylinder where each person should stand, moves the cylinders and the camera over 81 frames, and the model renders a photoreal video in which the people occupy the cylinders' positions, move as the cylinders move, and are seen from the drawn camera. Appearance comes from a text prompt and a background reference image; layout and motion come from the geometry. Because no dataset pairs such a signal with video, we build the pairs ourselves: an automatic engine writes 2000 captions from a combinatorial seed, generates a clip for each with a text-to-video model, and lifts every clip back to its geometry with person tracking, background inpainting, an agentic ground-mask loop, feed-forward multi-view reconstruction and a plane fit, with no real footage and no manual labels. A LoRA on Wan2.2-Fun-Control trained on 1935 such tuples follows drawn layouts and camera paths on hold-out clips: the generated people match the cylinders' count, order, position and height, the text changes who they are, the reference image changes where they are, and dolly-in, orbit, pan and crane paths are followed, dolly-out only weakly.

We study different notions of convergence of metric measure spaces by means of isometric embeddings into the Urysohn universal metric space $\mathbb U$. Due to the universality of $\mathbb U$, the collection $\mathbb X_1$ of isomorphism classes of normalised metric measure spaces can be canonically identified with the quotient (set) $\mathscr P_\sim(\mathbb U)=\mathscr P(\mathbb U)/\sim$ of the space $\mathscr P(\mathbb U)$ of Borel probability measures on $\mathbb U$, where $\mu\sim\nu$ if $\nu$ is the pushforward of $\mu$ under an isometry between their respective supports. By making crucial use of the ultrahomogeneity of $\mathbb U$, we show that, under the above identification, Gromov's box topology on $\mathbb X_1$ coincides with the quotient topology induced by the weak topology of $\mathscr P(\mathbb U)$. More quantitatively, the truncated $1$-Wasserstein distance on $\mathscr P(\mathbb U)$ induces a complete and separable distance ${\sf d}_{\rm mG}$ on $\mathbb X_1\cong\mathscr P_\sim(\mathbb U)$, which metrises the quotient topology of $\mathscr P_\sim(\mathbb U)$ and is Hölder equivalent to the box distance $\square$.

Recently, the existence of regular solutions $(u,p)$ to the stationary incompressible Navier–Stokes equations on $\mathbb R^n$ with bounded compactly supported forces $f$ for $5\le n\le15$ was established by Li–Yang (Comm. Math. Phys., 2022). However, it is still unknown whether there exists a regular solution for dimensions $n>15$. Here we answer this question and obtain the existence of regular solutions to the stationary Navier–Stokes equations in arbitrarily high dimensions. The key innovation is to combine an averaged signed pressure-potential identity with $L^2$-BMO estimates for the Bernoulli source flux, yielding a Bernoulli supremum bound independent of the size of the skew coefficient representing the drift. Together with the energy estimate for the comparison solution, this yields a sublinear bound for the Newtonian potential of the positive Bernoulli function, removing the upper dimension restriction in the earlier existence argument. We also construct periodic solutions and whole-space solutions for forces in $L^\infty\cap L^{2n/(n+2)}$. For compactly supported forces, we record two far-field profiles, their velocity, gradient and pressure remainders, and the corresponding cancellation criteria.

Modern AI model training imposes unprecedented computational demands, making it a key contributor to datacenter energy consumption. Yet a significant fraction of the energy consumed during training does not translate to useful computation due to bottlenecks throughout the training pipeline. We present PAFT, a phase-aware, dynamically adaptable GPU frequency tuning system that reduces energy consumption of training workloads with minimal performance overhead. The key insight behind PAFT is that bottlenecks represent an energy optimization opportunity, rather than purely a performance problem: when GPUs are bound to stall, PAFT opportunistically reduces their clock frequencies to match the pace of bottlenecked devices, saving energy without impacting execution time. PAFT achieves this by continuously monitoring pipeline behavior and applying fine-grained frequency adjustments, adapting to workload and system changes. Experiments conducted on twelve widely used models show that PAFT consistently outperforms all baselines, achieving energy savings of up to 46% with an average overhead of 4%.

Visual segmentation systems encounter objects outside their training distribution during real-world deployment, hindering reliable autonomous systems that depend on scene parsing in the perception stage. Many recent methods address this by using self-supervised foundation models to train density estimators that yield low likelihood in anomalous image regions. Although promising, these methods suffer from poor feature semantics or they lack spatial consistency, both of which undermine critical downstream decisions. We address this problem with~\method, a generative method based on class-conditional density estimation over self-supervised representations. SAFe trains lightweight normalizing flows that produce class-conditional normalized likelihood estimates over frozen DINOv3 features. We combine density estimates from transformer features with density scores over multi-scale convolutional features to capture both global semantics and local detail. We introduce a method-agnostic post-processing step based on SAM3 that connects per-location likelihoods into spatially coherent segments while suppressing false positives, and enables instance-level anomaly detection without retraining. The post processing further distinguishes novel categories among anomalous objects by a similarity-based agglomerative clustering scheme. SAFe sets a new state of the art on the PANIC, OoDIS, SMIYC ObstacleTrack with strong performance on the ISSU benchmark.

The cosmic distance duality relation (CDDR), $D_L(z)(1+z)^{-2}/D_A(z) \equiv 1$, is a fundamental relation in modern cosmology linking luminosity distance $D_L$ and angular diameter distance $D_A$. We define $\eta(z) \equiv D_L(z)(1+z)^{-2}/D_A(z)$ and reconstruct the relevant quantities over $0 < z < 2.5$ using two independent non-parametric methods: Gaussian processes (GP) and artificial neural networks (ANN). Specifically, we reconstruct $D_L$ from three different Type Ia supernovae (SNe$~$Ia) compilations (PantheonPlus, Union3, and DES-Dovekie), the baryon acoustic oscillation distance ratio $D_M/D_H$ from SDSS and DESI, and the Hubble function $H(z)$ from cosmic chronometer (CC) data. Our CDDR test is independent of both the cosmological model and the sound horizon $r_d$ calibration, as $D_M/D_H$ naturally eliminates $r_d$. We render our GP reconstructions insensitive to mean-function and kernel choices via full Bayesian marginalization over hyperparameters, with ANN as a cross-check$-$revealing the impact of data sparsity on the latter. Our results show no significant deviation from the CDDR exceeding $2\sigma$, and for the CC+BAO+DES-Dovekie combination it remains within $1\sigma$ over most of the redshift range. With $r_d$ eliminated, varying the only remaining external parameter $M_B$ systematically shifts $\eta(z)$ through the $M_B$-$H_0$ degeneracy, indicating that the observed $\eta\neq1$ signal is closely tied to $H_0$ tension among datasets and is likely driven by $M_B$ systematics rather than a true CDDR violation. Future high-quality CC, BAO, and SNe$~$Ia data$-$with either improved $M_B$ calibration or $M_B$-free distance measurements$-$will be essential for extending this calibration-free approach.

Sparse attention reduces the quadratic cost of global self-attention while retaining strong empirical performance, but how its restricted interactions shape the evolution of token representations remains theoretically underexplored. Modeling tokens as particles on the unit sphere, we introduce opinion leader dynamics, a framework that identifies two mechanisms through which token groups converge internally while maintaining distinct limiting directions. In the explicit model, fixed representatives induce a potential that attracts tokens toward distinct local maxima. In the implicit model, disconnected interaction groups evolve toward separate consensus directions. We formulate both models as reverse Wasserstein gradient flows and establish exponential convergence under suitable conditions. We further connect these theoretical predictions to token evolution in frontier sparse-attention LLMs that motivate our framework. Across four benchmarks, Kimi-K3, MiniMax-M3, and DeepSeek-V4-Flash consistently exhibit clearer cluster separation and higher clustering scores than the dense-attention model GLM-4.7-Flash in projected token representations. These observations support the relevance of the predicted multiple-group structure to trained frontier LLMs, while finite-particle simulations illustrate the theoretical convergence behavior. Together, our results connect restricted token interactions to distinct group-level attractors, providing a dynamical account of how sparse attention can support alignment within groups while preserving separation between them.

In this work, we propose a novel design of high-rate Calderbank–Shor–Steane (CSS) quantum low-density parity-check (QLDPC) codes based on quasi-dyadic matrices. The Tanner graphs associated with the two component classical codes used to construct the proposed CSS codes are characterized by a girth of at least $6$. We also derive an exact count of length-$4$ cycles in the quaternary representation of the parity-check matrix. Monte Carlo simulations under code-capacity and phenomenological noise models show that the proposed codes have competitive finite-length logical error rate performance compared with state-of-the-art codes in both these settings.

AI is increasingly used to automate computer security testing, and the tools must decide for themselves whether an attack succeeded. A finding that a deterministic rule confirms by observation is reported as fact, whereas one that an LLM judges exploitable is treated as an opinion. We ask whether the system under test can forge that confirmation. In offline security testing of a four-stage AI-assisted pipeline, nine of its fifteen confirmation mechanisms are forgeable, and forgeability is predicted entirely by whether the decision reads attacker-controlled data. We formalise this as an auditable attack surface and test it prospectively: on sixteen held-out mechanisms, predictions fixed before any attack separated forgeable from unforgeable mechanisms exactly, and across 12,203 mechanisms in public scanner templates the prediction was 99.9% accurate. Deterministic rules proved cheaper to forge than eight open-weight LLM judges, failing at 2% of attacker-controlled response content against a median of 50%. No implementation of one check was both robust and precise, and routing between a rule and an AI judge raised forgery to 99%. Moving the decisive evidence to a channel the attacker cannot write cuts attack success from 97% to 0%, and an escalate verdict recovers the sensitivity this costs. The protection fails when the scanned host is itself the adversary. The results bear on AI security agents and on benchmarks that score success by string matching.

Evaluation benchmarks for Indian language automatic speech recognition (ASR) suffer from two systematic biases: optimistic scores from clean, controlled audio conditions, and pessimistic scores from overly rigid transcription standards that penalize valid linguistic variations. We introduce Vimarsha, a 100-hour benchmark spanning all 22 scheduled Indian languages, designed to address both distortions. Vimarsha combines demographically diverse on-field recordings with carefully mined in-the-wild audio selected for acoustic difficulty, alongside a lattice of variations framework that encodes multiple valid transcriptions per utterance. Evaluations of 10 state-of-the-art ASR models reveal substantial shifts in model rankings under realistic conditions, geographic and demographic performance disparities, and systematic failure modes across speaking rates and acoustic environments.

This paper describes the SKstars submission to SHROOM-Visions 2026, a shared task on fine-grained hallucination detection in large vision-language model outputs. The task requires systems to identify hallucinated character spans, assign hallucination categories, and provide confidence estimates for their predictions. Our approach combines zero-shot predictions from Qwen2.5-VL-72B-Instruct with those of a LoRA-adapted Qwen2.5-VL-7B-Instruct model. The outputs of the two models are integrated through a lightweight ensemble procedure, followed by span refinement and confidence adjustment. We evaluate the main system components on a small internal development subset and report the performance of the submitted system on the official English test set. SKstars achieved a Cor+Lbl score of 0.2902, ranking 15th among 29 teams, and obtained Cor and IoU scores of 0.3642 and 0.3151, respectively, ranking 18th on both metrics. The results show that combining a large zero-shot model with a smaller adapted model provides a practical framework for multilingual and fine-grained hallucination localization, while also highlighting the difficulty of transferring development-set improvements to hidden test data. Code and predictions: https://github.com/aliathar1401/SK-Stars-shroom-visions-2026

Speculative decoding losslessly accelerates large language model inference by having a lightweight draft model predict future tokens for verification by the target model. Recent block diffusion drafters further reduce drafting latency by predicting multiple tokens in parallel. However, existing block drafters project target hidden states at every input position into a separate drafter-side KV cache, incurring per-request memory and KV-write overhead that grow with concurrency; directly reusing target KVs in place removes this cache but fails to sustain draft quality throughout the block. We propose a hybrid target-context injection method that complements direct target KV reuse with target hidden states only at the last input position, requiring no separate drafter-side KV cache. Building on this design, we propose H-Spec, a hybrid Mamba-attention parallel drafter that consumes the two target-context sources through complementary modules. Mamba modules are initialized with projected last-token target hidden states, while attention modules reuse target KVs in place. Despite its recurrent formulation, Mamba's parallel scan allows H-Spec to preserve block-parallel drafting. Across three target models and diverse tasks, H-Spec improves over the best baseline by 5.0–13.3% in mean accepted length and 5.3–12.6% in batch-size-1 inter-token latency speedup. Under concurrent serving, H-Spec consistently achieves higher throughput while maintaining lower KV cache utilization than baselines across evaluated concurrency levels.

Looped Language Models (LoopLMs) perform "latent reasoning" by recursively refining internal latent representations with shared weights, offering a more effective alternative to explicit verbal reasoning. Despite their effectiveness, we find that LoopLMs remain prone to loop instability: unstable refinement across iterations can produce localized uncertain "hard" tokens associated with reasoning errors. To address this, we propose LoopCD, loop-wise contrastive decoding that enhances the reasoning performance of LoopLMs by intervening on these tokens at inference time. Specifically, we exploit the internal dynamics of LoopLMs and contrast the logits from earlier iterations with logits from the last refined iteration to form the final sampling distribution. We find that this strategy is highly efficient, introducing only negligible inference overhead and requiring no additional training, while effectively improving reasoning performance by naturally refining reasoning-critical hard tokens. Extensive experiments show that our method improves the performance of recent representative LoopLMs across various reasoning tasks.

Reliable perception is essential for underwater vehicles operating in complex environments, where light attenuation and scattering often degrade visibility and compromise optical sensing. Forward-looking sonar (FLS) offers an alternative by providing high-frame-rate acoustic imaging under poor optical conditions. However, real-time FLS mapping remains challenging due to unresolved target elevation, spatially non-uniform noise, and fragmented target boundaries, which hinder feature extraction and introduce geometric ambiguity during projection. To address these challenges, we propose a cascaded feature reconstruction pipeline combining fast Fourier transform (FFT)-based denoising, fast multiscale constant false alarm rate (MCFAR) detection, and gradient-adaptive boundary connection to extract geometric features from degraded sonar images with low latency. We integrate attitude-aware geometric projection with incremental occupancy accumulation to construct a depth-referenced 2.5D map for local mapping in confined underwater environments. The sonar's vertical position is referenced to an external sensor, while target elevation is assigned under an explicit geometric assumption rather than measured directly by FLS. Experiments in a 3 m X 5 m pool demonstrate centimeter-scale planar mapping accuracy, with a root-mean-square error (RMSE) below 3 cm across three sequences and an average processing time of 42.4 ms per frame.

Evaluation scores used around LLM systems – including reward models, rerankers, and LLM judges – can track surface form instead of the quality they claim to measure. When presented with a terse correct solution and a commented buggy solution for the same MBPP problem, a public preference reward model selects the correct one no better than a coin flip (0.507). Subtracting the predictable surface component from such scores is increasingly common, but removal alone does not yield a more valid measurement: the removed component may carry construct-relevant signal, and residualization cannot tell which is which. Under designed interventions – unit-test labels with comment-only edits – residualization attenuates the reward model's format effects by about 0.12 on both correct and buggy code, while the correct-versus-buggy margins move by less than 0.01. In observational NLI and QA settings, we freeze a held-out replication before scoring and re-evaluate it using labels from disjoint annotators; this supports only a narrower conclusion: better agreement with the construct labels on a pre-declared slice where a surface-only predictor errs, not a repaired score. Full-population agreement falls in every observational setting with a reported positive slice gain, and within-question ranking falls in every such QA setting. When construct and surface features are entangled, residualization can decorrelate a score while degrading construct alignment, and, in a controlled model, configurations just as damaging to construct alignment pass every pre-adjustment check, so no committed gate is a guarantee. We assemble these distinctions into a reporting protocol whose outcomes, refusal included, state what an adjusted score may be claimed to show: an audit-time diagnostic reported beside the construct-alignment cost it incurs, never a replacement for the raw score.

Pedestrian head orientation recognition plays an important role in autonomous driving by providing valuable cues for understanding pedestrian attention and anticipating potential crossing behavior. However, reliable recognition in real-world traffic scenes remains challenging because pedestrian head regions are often captured at low resolution. To address this challenge, we propose a lightweight Low-Resolution Head Orientation Convolutional Neural Network (LRHO-CNN) for pedestrian head orientation recognition. We construct a new dataset by extracting pedestrian head images from multiple public datasets and manually annotating them into eight orientation categories. The collected images are systematically preprocessed and augmented to increase data diversity and better represent variations in illumination and image quality. The experimental analysis compares LRHO-CNN with three fine-tuned baseline models, namely ResNet-18, ResNet-34, and VGG-16. The results demonstrate that LRHO-CNN achieves the highest classification accuracy among the evaluated models. LRHO-CNN is further evaluated on the JAAD and PIE datasets, demonstrating its effectiveness in recognizing pedestrian head orientation in real-world traffic scenes and providing informative head-orientation cues that can support downstream pedestrian behavior and intention prediction.

Many spatial (3D) vehicles, including AUVs and fixed-wing aircraft, are effectively nonholonomic and subject to limited actuation, such that continuous time-invariant stabilization is fundamentally obstructed by Brockett's necessary condition. To overcome this obstruction, we exploit the geometric singularity of spherical coordinates to design a backstepping continuous, time-invariant feedback law that exponentially stabilizes a 3D nonholonomic vehicle actuated solely by forward surge velocity, pitch rate, and yaw rate. The resulting closed-loop region of attraction excludes only the coordinate singularity, codimension-two, measure-zero set of initial conditions in which the vehicle lies on the line through the target orthogonal to the target plane, thereby covering the largest possible domain. We further construct a strict control Lyapunov function to prove global exponential stability of the origin on this domain with a user-specified decay rate, while simultaneously preventing the system from approaching the singular set. Finally, we show that the closed-loop system is exponentially attractive to the origin in Cartesian coordinates. Numerical simulation examples in both spherical and Cartesian coordinates illustrate the effectiveness of the control law.

Diamond has the highest thermal conductivity among natural materials. Reducing isotope scattering can further push the limit of thermal conductivity of diamond. Here, we report the room-temperature thermal conductivity of a diamond single crystal with an exceptionally low ppm-level 13C content. Secondary ion mass spectrometry (SIMS) reveals a 13C concentration of only ~0.00024% and negligible other impurities, placing this sample as the most isotopically purified diamond samples reported to date. Time-domain thermoreflectance measurements show a room-temperature thermal conductivity of ~3100 W m-1 K-1. Although this value is markedly higher than that of natural diamond, it remains comparable to the best reported values for less isotopically 12C pure diamond. This result suggests that additional phonon-scattering mechanisms beyond isotope scattering may exist at this extreme isotopic purification level. Vacancy defects may contribute to the remaining suppression of thermal conductivity.

Artificial intelligence (AI) has advanced at a rapid pace in recent years. Initially, breakthroughs in large language models caught widespread attention. However, recent generations of frontier AI models have adopted multimodal capabilities as a first class citizen, with vision capabilities being central to that. In this paper, we evaluate three recently released models on the task of diagnosing dermatological conditions from patient-submitted images. The models chosen are at the low to mid tier in terms of pricing and thus represent a floor on current AI capabilities, not a ceiling. We evaluate AI performance relative to a panel of three certified dermatologists, who grade each image, and we present four interesting findings. Firstly, depending on the metric, the tested AI models are either on par or slightly trail humans in terms of inter-clinician agreement. Secondly, we find that asking AI models for a confidence rating produces poorly calibrated answers, meaning use of confidence thresholds should not be relied upon in a clinical setting. Thirdly, the effect of providing additional patient metadata is strongly model-specific, with one of the three models degrading on every metric considered. Finally, model cost is not predictive of performance. The best-performing model we tested costs on average $0.0045 per case.

Vision-language navigation requires embodied agents to navigate environments using natural language instructions and visual observations. Existing approaches typically decompose navigation into sequential language-guided decisions or rely on online exploration without prior environmental knowledge. Scene graph representations offer compact semantic memory but remain decoupled from downstream navigation, which still depends on dense metric maps. To close this gap, we propose an object–path graph that unifies open-vocabulary semantic reasoning with topological navigation. The proposed representation jointly supports semantic grounding, graph-based localization, and navigation within a single lightweight topological framework. Building on this graph, we introduce a navigation strategy that combines global path planning with local inter-node execution through lightweight node localization and semantic visual servoing, enabling navigation directly over the graph without dense metric reconstruction. Experiments on HM3D and Replica demonstrate competitive performance in open-vocabulary object grounding through the proposed hierarchical graph structure, while achieving effective navigation performance. Real-world robot experiments further validate the practicality of the proposed framework.

We formalize Hastad's PARITY lower bound in Lean using the switching lemma. For every fixed d >= 2, formulas and DAG circuits of computation depth at most d computing PARITY on n inputs require size exp(Omega_d(n^(1/(d-1)))) for all sufficiently large n. This matches the classical upper bound up to constants in the exponent and implies that PARITY is not in nonuniform AC0. We also construct a polynomial-size, logarithmic-depth bounded-fan-in formula family for PARITY, providing a witness to NC1 is not a subset of AC0 for the formalized models. The Lean source code is available at https://github.com/formalcs/circuit-complexity and is checked with Lean 4.33.1 and mathlib 4.33.1.

Autonomous endoscopic navigation requires the policy model to predict actions from texture-poor monocular observations, make safe control decisions, and retain evidence of lesions after they leave the field of view. Existing vision-language-action (VLA) models primarily rely on visual appearance and short-term context, limiting geometric grounding and episode-level reporting. We introduce StenoVLA-3D, a 3D-aware VLA framework for navigating through stenotic regions. We integrate point-maps into the Cosmos-Reason 2 backbone through learned geometry-gated fusion, and also propose a temporal state branch to model traversal progress. Our reasoning-and-action backbone predicts grounded reasoning with actions, while dedicated heads estimate stenosis shape and generate the final lesion report. We further introduce EndoCausal, an episode-level dataset with lesion annotations, actions, and temporally grounded reasoning. On 40 held-out recorded test episodes, StenoVLA-3D reaches 95.2% semantic accuracy and 83.4% action accuracy. On the physical 3-DoF endoscope, it attains 88.9% and 77.8% task success in esophageal and colonic phantoms (36 trials each), substantially outperforming the evaluated baselines.

Large language models have achieved remarkable progress on Text-to-SQL through reasoning-enhanced fine-tuning, yet existing approaches predominantly rely on massive instruction corpora under the assumption that scale drives performance. We challenge this paradigm by investigating a fundamental question: what is the minimal data requirement for effective Text-to-SQL instruction tuning? We propose LIMIT(Less Is More for Instruction Tuning in Text-to-SQL), a data-centric framework that demonstrates strong database reasoning can emerge from an extremely compact training set when examples are strategically selected. LIMIT operates through four stages: difficulty-aware filtering that identifies samples within the model's learning frontier, chain-of-thought synthesis with consistency-based selection, multi-dimensional quality scoring via LLM-as-judge, and genetic algorithm optimization that jointly maximizes schema coverage and sample quality. On the BIRD and Spider benchmark, LIMIT selects only 796 and 863 samples while achieving 100% table coverage, enabling Qwen3-8B to reach 69.1% and 88.9% execution accuracy.This result surpasses methods trained on 20 times more data and establishes a new state-of-the-art among open-source approaches. Our findings suggest that careful data curation, rather than scale, is the key to efficient Text-to-SQL learning.

This paper studies general leader-follower linear-quadratic stochastic graphon games with indefinite control weights. The model consists of one leader and a continuum of followers, where the followers interact through graphon aggregate terms and are coupled with the leader through their dynamics and cost functionals. Compared with existing related models, the state equations considered here allow more general diffusion terms, including diffusion coefficients depending on the states, controls, leader variables, and graphon aggregate terms. Using the stochastic maximum principle, we characterize the followers' Nash response and the leader's optimal control through coupled forward-backward stochastic systems with graphon aggregate terms. Under suitable Riccati solvability and convexity conditions, we construct a Stackelberg-Nash equilibrium for the limiting graphon game. We further design decentralized strategies for the associated finite-player network game and prove that they form an approximate Stackelberg-Nash equilibrium, which yields a propagation of chaos result. The framework covers, as special cases, indefinite linear-quadratic stochastic graphon games, Stackelberg mean field games, and stochastic graphon games with random effects.

We prove the Courtade-Kumar conjecture: among all Boolean functions $f\colon \{-1,1\}^n\to\{-1,1\}$, a dictator retains the most information about a uniformly random input observed through independent binary noise.

Nonequilibrium flow and transport problems are inherently multiscale. Kinetic theory provides a fundamental physical basis for describing such phenomena, since it connects microscopic transport and interaction processes with emergent macroscopic behavior across regimes. In many situations, however, continuum descriptions lose validity in parts of the domain, whereas fully resolved kinetic descriptions become prohibitively expensive when numerical resolution remains tied to the smallest collision scales. Over the past two decades, a broad class of multiscale kinetic methods has therefore been developed to bridge rarefied, transitional, and continuum regimes in gas dynamics and other carrier-based transport systems. Existing reviews have clarified important parts of this field, including general numerical methods for kinetic equations, asymptotic-preserving methodology, and specific method families. This review adopts a different perspective by examining the subject through four interacting layers: numerical methods, computational strategies, asymptotic properties, and framework-level formulations. It surveys the main developments along these lines and emphasizes the common principles that connect them, including transport-interaction coupling, asymptotic consistency, scale-adaptive representation, and scale-dependent physical description. From this perspective, multiscale kinetic computation has evolved into a broader transport methodology for nonequilibrium systems across scales.