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arXiv2026

An integer determinant approach to the length of Type II codes and the weights of shadows

It is well known that the length $n$ of a binary Type II code is divisible by $8$. The classical proof relies on Gleason's theorem on weight enumerators. Motivated by a question of Vera Pless, we give elementary proofs of this fact that avoid invariant theory. Our main tool is a congruence modulo $8$ for the determinant of the integer Gram matrix $AA^{\mathsf T}$ of a binary orthogonal matrix $A$, obtained directly from the Leibniz expansion. It gives a short proof of a theorem of Janusz: the number of rows of weight congruent to $3 \pmod 4$ in a binary orthogonal matrix is divisible by $4$. From this single statement we derive both the length restriction for Type II codes and the theorem of Conway and Sloane that every vector in the shadow of a binary self-dual code of length $n$ has weight congruent to $n/2 \pmod 4$. We also give two short character-theoretic proofs of the length restriction and explain how all of these arguments detect the Arf invariant of a quadratic form.

cs.IT↗
arXiv2026

Adaptive Aerial Loco-Manipulation Policy Learning via LLM-Assisted Proactive Task Generation

Loco-manipulation extends the workspace of conventional manipulation by combining mobility with physical interaction, while aerial loco-manipulation further expands this capability into three-dimensional space, enabling robots to reach environments inaccessible to ground-based systems. Moving to an aerial platform, however, gives rise to a demanding control problem, since the vehicle must track trajectories accurately in three dimensions while the motion of the arm and its interaction with the environment continuously shift the center of mass, alter the inertia, and impose force and moment disturbances on the body. Conventional controllers address these effects through explicit models and estimation, whereas learning-based controllers infer dynamics from experience, yet control rewards provide no direct target for the response information retained from history, and fixed task sampling can leave persistent tracking difficulties insufficiently explored. We present ALMA, an aerial loco-manipulation framework for adaptive flight control under external arm commands. ALMA employs a contextual flight policy that adapts from recent measurements and actions, using action-conditioned prediction of future measurement representations to train its context to retain response information relevant to flight control. To expand the experience available for this adaptation, an evolutionary process uses a large language model (LLM) to analyze observed control difficulties and propose new structures of arm motion for subsequent training. In simulation, ALMA reduces position root-mean-square error (RMSE) by up to 24.7% relative to the strongest baseline, while the same policy transfers zero-shot to the aerial manipulator and reduces hover position RMSE by 79.6% during periodic arm motion relative to the real-world baseline.

cs.RO↗
arXiv2026

The ALMA-QUARKS survey: A Keplerian Circumbinary Disk Candidate in the High-mass Star-forming Region IRAS 08303-4303

We present the ALMA Band 6 continuum and molecular line observations of IRAS 08303-4303, a high-mass star-forming region, with an angular resolution of $\sim 0.3''$ ($\sim 700$ au at the distance of 2.35 kpc). Six dense condensations are identified in the 1.3 mm continuum, and at least four of them are associated with molecular outflows. The estimated outflow parameters, particularly mass outflow rates $\geq 10^{-4}$ $M_{\odot}$ yr$^{-1}$, suggest that the driving sources are high-mass young stellar objects. Two of the condensations are forming a wide protobinary system with a separation of $\sim 900$ au. They reside within a single rotating structure, identified as a circumbinary disk which has a mass of about 2 $M_{\odot}$. This structure is traced by multiple molecular lines and exhibits a Keplerian rotation pattern. Based on the Keplerian rotation assumption, the enclosed mass is derived to be between 32 and 61 $M_{\odot}$: 22-43 $M_{\odot}$ for the primary and 10-18 $M_{\odot}$ for the secondary. The circumbinary disk is on the whole gravitationally stable, yet some parts with Toomre $Q < 2$ indicate potential fragmentation. Various molecular lines reveal a streamer-like structure connecting to the circumbinary disk, suggesting transfer of material from the envelope to the protobinary system through it. Despite the observational rarity of such circumbinary disks around high-mass YSOs, the high binary fraction among massive stars underscores their significance. This source, therefore, serves as a key laboratory for understanding the formation of high-mass binary systems.

astro-ph.SR↗
arXiv2026

Constrain the number of inner horizons from gravitational Noether charges

A central question in the study of black hole interiors is how matter and geometry constrain the number of horizons. In Einstein gravity, one known method is to use the ADM decomposition of the field equations to derive a differential inequality for the lapse, which then constrains the possible multiple inner horizons. We show that the same obstruction can instead be formulated through the Komar integral as a bulk-boundary balance of gravitational Noether charge. In higher-curvature gravity, a direct ADM analysis becomes more complicated, whereas the gravitational Noether charge naturally retains this bulk-boundary structure. We naturally apply the gravitational Noether charge analysis to Lovelock gravity. We introduce a TCC-like curvature condition and prove that, together with the thermodynamically motivated assumption of positive Wald entropy, it allows at most one nondegenerate inner Killing horizon inside a nondegenerate event horizon. This suggests that the obstruction reflects a compatibility between bulk gravitational response and horizon thermodynamics.

gr-qc↗
arXiv2026

Breaking the Coupling: Efficient Concurrency Fuzzing for Linux Kernel Data Race Detection

Detecting data races in the Linux kernel requires exploring both the input space and the thread-interleaving space. Existing kernel concurrency fuzzers couple these two searches by exploring interleavings during fuzzing, often spending substantial scheduling effort on inputs with little potential to trigger real races. In this paper, we present a new concurrency fuzzing paradigm that decouples concurrent-input generation from thread-interleaving exploration, enabling expensive scheduling to focus on promising inputs. To identify inputs that warrant targeted scheduling, we introduce May Race Pairs (MRPs), which represent conflicting memory-access pairs observed within a dynamically determined time threshold. Our framework first generates and executes concurrent syscall groups without controlled scheduling, collecting MRPs to guide further input mutation and identify schedule-worthy inputs. It then uses a separate scheduling instance to explore targeted interleavings and confirm real data races. To improve the effectiveness of both stages, we incorporate LLM-assisted semantic mutation for generating diverse syscall groups, backpressure-guided dynamic threshold control for balancing candidate production and scheduling consumption, and history-aware context recovery, context-aware interleaving scheduling, and candidate MRP prioritization for efficient race confirmation. We implement our framework for the Linux kernel and evaluate it on eight common kernel modules in Linux 6.17. It discovers 187 unique real-world data races, including 59 harmful races. Under the same testing budget, our approach detects substantially more data races than existing kernel concurrency fuzzers, including SegFuzz and CONZZER. These results demonstrate the effectiveness of decoupling concurrent-input generation from interleaving exploration and concentrating scheduling effort on promising candidates.

cs.OS↗
arXiv2026

DRILL: Training World Models to Improve Policies, Not Predict Pixels

World models are increasingly used to reduce environment interaction when post-training vision-language-action (VLA) policies with reinforcement learning. Yet they are typically trained to predict pixels one step ahead, even though their role here is not merely to render visually faithful videos but to produce learning signals from imagined rollouts that improve the policy. We show that this mismatch is substantial: lower pixel MSE can produce worse policy gradients, and a world model trained for policy utility can yield better downstream policies despite 17% higher pixel MSE on the next frame. We propose the Downstream-Return Imagination Learning Loop (DRILL), a bilevel framework that updates the world model to maximize the policy's return after an inner GRPO update on imagined rollouts. DRILL has two instantiations. DRILL-VWI is a closed-form surrogate, requiring no additional simulator rollouts, that reweights prediction errors by policy visitation, the group-relative GRPO advantage, and model confidence. DRILL-IMG is a full meta-gradient method that differentiates through the inner update using truncated Hessian-vector products. We show that DRILL-VWI recovers the local one-step component of the DRILL-IMG meta-gradient under score-compatibility and small-residual assumptions. Across five manipulation simulators and two VLA backbones, DRILL-IMG raises mean success rate by 13.1 points over WMPO and 7.9 points over RLVR-World, and complements RLVR pretraining rather than competing with it. More broadly, we believe video world models for VLA reinforcement learning can be productively trained by the policy gradients they produce, not only by pixel-level prediction.

cs.CV↗
arXiv2026

xVGAE: A Hierarchical Variational Graph Autoencoder for Exchangeable Graphs

Graphs play a crucial role in many applications, ranging from drug discovery to social network modeling and astronomy. Generative models for graphs have substantially advanced in recent years, but we identify relatively simple scenarios where state-of-the-art models struggle to converge within a standard compute budget, or exhibit prohibitively slow generation times. We propose a generative architecture that achieves quality competitive with state-of-the-art models and is orders of magnitude faster at generation. Our approach is inspired by the Aldous-Hoover theorem, a classic representation theorem that characterizes any probability distribution of graphs that is invariant to permutations of node indices or exchangeable. This theorem establishes that three ingredients suffice: a graph-level latent variable, a set of exchangeable node-specific latent variables, and a so-called graphon function that maps graph- and node-level variables to the probability of an edge between any node pair. Given a training set of graphs, our exchangeable Variational Graph AutoEncoder (xVGAE) learns an approximation to their underlying graphons, as well as graph- and node-level latent variables. We show that our xVGAE encodes latent representations that correlate with graph- and node-level properties, and can (quickly, in one shot) generate new graphs that closely match key training set statistics.

stat.ML↗
arXiv2026

A recurring changing state AGN discovered in the SAMI Galaxy Survey and SDSS

We present a detailed analysis of the AGN in galaxy J085337.26+014303.6 at z=0.0582. A combination of SDSS and SAMI Galaxy Survey data shows that this object has gone through at least one full changing-look AGN cycle, from type 1.9 in 2001 to type 1 in 2015 and 2021, and then type 1.9 again in 2022. While the broad lines in this object show evidence of dust obscuration, detailed spectral analysis plus WISE photometry demonstrate that the changes in this object are related to a physical state change, not changing obscuration. In fact, the WISE light curve suggests that this object may have briefly returned to a type 1.9 state in 2020. In the optical, the host galaxy dominates the light (e.g. only ~10 per cent contribution from the AGN at 4000 Angstoms within a central aperture), even in the high state. In contrast, the brightest WISE W2-band measurements place the AGN at a similar luminosity to the entire host galaxy. The broad Balmer lines show evidence of multiple components, with a weak very-broad component (FWHM=5000-6000 km/s) visible in the low type 1.9 state, and a stronger broad component of FWHM~2000 km/s dominating in the high type 1 state. We propose that this is caused by two spatially distinct regions within the broad line region.

astro-ph.GA↗
arXiv2026

Robot Motion Transition with Human Motion Prior

Humanoid motion-tracking policies can reproduce diverse behaviors, yet connecting independently acquired motions into a continuous sequence remains challenging. Interpolation connects boundary poses without considering whether their relative position, heading, and timing provide suitable conditions for a transition. A generative motion prior can produce richer motion, but poorly arranged boundaries may cause it to generate excessive locomotion, turning, or another unintended action. We present Spatio-Temporal Alignment with a Motion Prior (STAMP), a framework for connecting independently acquired humanoid motions through a Robot-to-Human-to-Robot process. STAMP uses human motion space to draw on rich motion priors and reuse transition knowledge across robot embodiments. Its key component is a learned alignment model that determines the boundary conditions for motion inbetweening. Given the two motions retargeted to a human rig, the alignment model ranks candidate positions, headings, and transition durations for the following motion. A human motion prior generates the transition under the selected alignment. The completed sequence is retargeted to the robot and used as a reference to train a motion-tracking policy. We evaluate the tracking success of the generated transitions on Unitree~G1 and~ROBOTIS K1. Physical robot demonstrations further show that STAMP connects independently acquired motions into long-horizon sequences. Project page: https://childtoy.github.io/STAMP-project

cs.RO↗
arXiv2026

HC-AINet: An Auditory-Inspired Network with Harmonic Compensation for Low-Complexity Speech Enhancement

Speech enhancement on resource-constrained devices requires noise suppression with limited computation and minimal loss of spectral detail. Auditory-inspired subband processing reduces computation, but its smooth gains have limited ability to distinguish harmonic peaks from neighboring noise. We propose a harmonic-compensated auditory-inspired network (HC-AINet) for low-complexity speech enhancement. A triangular equivalent rectangular bandwidth (ERB) filterbank supplies compact features to a lightweight network comprising inverted-residual units, temporal Conformer layers, and parallel frequency-gated convolutions. The network predicts global and harmonic gains together with fusion weights. A harmonic-location map derived from the noisy spectrum confines the harmonic contribution to selected bins on the original frequency grid, while the global branch controls the broader spectral envelope. The compensated magnitude, noisy phase, and a magnitude-derived minimum-phase cue jointly condition a compact phase estimator for waveform reconstruction. On VoiceBank-DEMAND, the 64-band model achieves a PESQ of 3.20 and a STOI of 0.95 with approximately 0.27 million parameters.

eess.AS↗
arXiv2026

TEAR: Task-Evidence Authority Routing for Robotic Manipulation

Reliable robotic manipulation in field-deployed settings requires more than executing a capable controller. As the execution conditions change, the system must decide, online and on the robot side, which control source should hold authority. Human teleoperation adapts readily to contact-rich and semantically ambiguous situations but depends on a stable communication link. Local autonomy is executed without continuous human intervention, but may fail under semantic ambiguity, long-horizon drift, and unforeseen contingencies. These two control sources exhibit complementary reliability profiles. We formulate this complementarity as a control authority routing problem and present Task-Evidence Authority Routing for Robotic Manipulation (TEAR), an edge-deployable framework that allocates authority between human teleoperation and local autonomy. TEAR arbitrates on the robot side using network-state evidence, which governs the usability of teleoperation, and task-semantic evidence, which reflects whether autonomous execution remains consistent with the current task. A lightweight temporal arbitrator observes both forms of evidence together with robot state and current authority to time authority transfers. Across simulated and real-world trials under dynamic network conditions, TEAR achieves task success rates close to pure teleoperation while limiting teleoperation to 19.8-27.4% of control steps and improves success by 30-40% over autonomy-only execution in our settings. These results demonstrate the potential of complementary authority routing to sustain successful manipulation with substantially reduced dependence on continuous human control.

cs.RO↗
arXiv2026

Spatial Decay and Asymptotic Stability of Forced Waves at the Critical Speed for the Fisher-KPP Equation in a Shifting Environment

In this paper, we investigate the spatial decay and asymptotic stability of forced waves for the Fisher-KPP equation in a shifting heterogeneous environment, focusing on the critical speed $c_*=2\sqrt{r_+}$. Within the framework of regular variation, we establish a complete classification of critical wave tails in terms of the asymptotic behavior of the environmental deviation $r_+-r(z)$ as $z\to+\infty$. In each case, we derive precise spatial decay that characterize how the environmental tail modifies the leading-order decay of the wave at criticality. We further establish asymptotic stability estimates of forced waves. For initial data satisfying an exponentially weighted boundedness condition, we prove an $O(t^{-1/2})$ convergence rate in the uniform norm. Under stronger spatial decay assumptions on the weighted initial data, this rate improves to $O(t^{-1-σ/2})$, for $σ\in[0,1]$, in both the uniform norm and a weighted norm. Moreover, no smallness assumption on the initial perturbations is needed for our results.

math.AP↗
arXiv2026

An Approximate-Diagonal Characterization of Amenable Actions on C*Algebras

We introduce relative $h$-diagonals for crossed products $A\rtimes_αΓ$ by discrete groups, which are positive-form approximate diagonals in the Haagerup tensor product taken relative to $A$. We show that $α$ is amenable if and only if $A\rtimes_αΓ$ admits a relative $h$-diagonal, an analogue of Johnson's theorem for $L^{1}(G)$.

math.OA↗
arXiv2026

TESSA: A Governance-Oriented Custom GPT for SME Guidance under the EU AI Act: Design, Implementation, and Evaluation

The increasing adoption of generative AI presents new opportunities while raising AI governance and regulatory challenges, particularly for small and medium-sized enterprises (SMEs) navigating the European Union Artificial Intelligence Act (EU AI Act). To support AI governance education, this study developed TESSA, a governance-oriented educational artifact within the OpenAI Custom GPT environment. Following a design science research approach, TESSA was evaluated against baseline ChatGPT using 100 benchmark scenarios through governance alignment assessment, human expert review, and consistency testing. Preliminary LLM-assisted assessment showed governance alignment rates of 90% for TESSA and 83% for baseline ChatGPT, while independent validation by an AI regulation law practitioner yielded 71% and 70%, respectively. Human expert review indicated that both systems provided generally strong governance guidance, while TESSA maintained high consistency across repeated executions. The findings suggest that governance-oriented grounding can support structured, practical, and stable AI-assisted compliance guidance for SMEs. The study contributes (i) a governance-oriented Custom GPT artifact for AI governance education, (ii) a human-validated regulatory update mechanism, and (iii) a multidimensional evaluation framework for governance-oriented AI artifact.

cs.AI↗
arXiv2026

Neural Spectral Capacity with Residual Context for Heterogeneous Resource Allocation within Transformers

Predicting relative trained performance from architectural specifications can guide design when training costs limit experimentation. Neural Spectral Capacity (NSC) provides such a heuristic, but scores projections independently and assigns identical scores to compatible reorderings of the same layer configurations. We introduce Residual-Aware Neural Spectral Capacity (ResNSC) for Transformers, using a specification-derived statistical reference for accumulated residual updates to determine the input and residual-state statistics in each projection's capacity calculation, while retaining additive evaluation without data or instantiated weights. When residual widths vary, earlier choices affect later scores, so we augment NSC's allocator (NSC-DP) with residual history beyond its layer-and-budget state. ResNSC-DP jointly allocates residual and feed-forward widths under a resource budget, with certified bounds on the best numerically evaluated ResNSC score within a specified finite candidate set. At the 121M and 374M pretraining scales, selected architectures achieve lower mean perplexity than uniform, variable-width, and tapered allocations on FineWeb-Edu, WikiText-2, and LAMBADA at comparable parameter budgets. In inherited-weight LLaMA-7B pruning using the LoNAS supernet, ResNSC-DP improves eight-task average accuracy over NSC by 3.28--5.46 percentage points across eight matched parameter budgets. Paired reversals preserve the projection shapes and NSC scores yet worsen performance in both settings, exposing performance differences hidden by position-independent scoring. The code for this work is available at https://github.com/Optima-CityU/neural-spectral-capacity.

cs.LG↗
arXiv2026

Loop to Look Better: Learning Adaptive Depth for Question-Guided Perception in Vision-Language Models

Visual perception should be iterative and task-directed, with representations refined in response to the question and the need for further processing. While Vision-Language Models (VLMs) increasingly support extended reasoning, their visual tokens are still typically acquired in a single, task-agnostic encoder pass. This creates an evidence-acquisition bottleneck: models may reason longer without refining the visual evidence needed to answer the question. We propose LoopLook, a lightweight encoder-side recurrent perception framework that equips pretrained VLMs with adaptive visual depth. LoopLook recurrently revisits a middle-to-late window of the vision encoder, injecting question representations at each loop to guide visual refinement. A learned stopping mechanism adaptively determines the recurrent depth, while a token-wise Mixture-of-Looks (MoL) combines representations from different loops, allowing each visual token to selectively integrate information acquired across recurrent steps. Across four backbones and eight benchmarks, LoopLook consistently improves performance over the baseline, yielding gains of up to 8.6% on MMStar and 8.1% on HallusionBench. Our analysis shows that LoopLook progressively refines visual attention and adaptively allocates depth according to task difficulty. It also better preserves task-relevant visual information under reduced input resolution, while increasing time to first token (TTFT) by only 5.1-6.5%. By bringing recurrence from reasoning back into perception, LoopLook transforms visual perception from a one-shot glimpse into an adaptive process of recurrent refinement.

cs.CV↗
arXiv2026

Bezier-Guided Adaptive Flow for Cross-domain Sequential Recommendation

Cross-domain sequential recommendation aims to alleviate data sparsity and cold-start problems by transferring useful preference knowledge across domains. However, users exhibit varying degrees of preference consistency across domains, while existing methods often rely on global alignment objectives or coarse-grained transfer strategies. Such approaches may introduce irrelevant information and provide limited flexibility in adapting semantic representations to individual user preferences. To address these challenges, we propose BGAFlow, a personalized framework that combines state-adaptive semantic evolution with user-specific transfer control. BGAFlow first establishes a shared semantic space through unified dual-domain pretraining with user profiles inferred by a large language model (LLM). Based on latent interest overlap, it then estimates a personalized horizon to determine the appropriate transfer extent for each user. To enable semantic adaptation, BGAFlow constructs a conditional Bezier curve as a geometric reference and learns a residual flow that progressively refines the trajectory based on intermediate preference states. The learned flow incorporates dynamic preference feedback to adjust transfer directions, while recommendation supervision and trajectory regularization encourage effective and smooth adaptation. Extensive experiments on real-world datasets demonstrate that BGAFlow consistently outperforms state-of-the-art baselines, validating the benefits of personalized transfer control and state-adaptive semantic evolution.

cs.IR↗
arXiv2026

Nonlinear Drift Waves and Electrostatic Density Cavities in Upper Ionosphere

Nonlinear drift waves are investigated to explain the mechanism for the creation of one dimensional (1D) and two dimensional (2D) electrostatic density cavities in the presence of density gradient in direction perpendicular to the geomagnetic field. Ion motion along field lines has to be neglected for the formation of density depletion because nonlinear contribution of their parallel motion overcomes the effect of drift waves which create negative nonlinear potential. It is pointed out that a straightforward but appropriate model for drift waves can explain the generation of density cavities having widths in xy-plane if the external magnetic field is assumed to be along z-axis i.e. ${\bf B}_0 = B_0 \hat{z}$. The general nonlinear equation for drift waves takes the form of Zakharov-Kuznetson (ZK) equation when ion nonlinear vorticity term is ignored and it admits the solution in the form of 2D solitary wave. In 1D case, the ZK equation reduces to Korteweg de Vries (KdV) equation which admits solution in the form of 1D soliton. In both cases, the nonlinear potential becomes negative. The order of magnitude of the amplitude and width of density cavities is found to be in agreement with the satellite observations in upper ionosphere.

physics.plasm-ph↗