Machine Learning (Statistics)
Papers
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All of arXiv
Wednesday 7 October
We develop a bias-aware digital-twin calibration and control framework for multiscale bioprocess models within a biological systems-of-systems (Bio-SoS) paradigm. The digital twin is represented by a stochastic differential equation (SDE) model and calibrated from sparse observations using quasi-likelihood estimation and adjoint sensitivity analysis. SDE generator-based moment expansions characterize truncation-induced parameter bias, while forward-backward adjoints quantify how calibration uncertainty propagates to value functions and policy performance. The resulting parameter-error distribution supports both policy-directed data acquisition and uncertainty-aware policy optimization through a second-order Gaussian-averaged objective. We characterize the asymptotic behavior of the resulting exploration criterion and derive a physical-system performance under the optimized policy. To implement these ideas, we develop an Actor-Simulator algorithm that jointly updates model parameters, selects informative experiments, and optimizes control policies. Numerical studies demonstrate improved calibration accuracy, sample efficiency, and control performance relative to state-of-the-art baselines.
High Energy Physics (Theory)
Emergent $\mathcal N=3$ and Frozen $\mathcal N=2$ SCFTs from $\mathcal N=1$ Gauge Theory
Four-dimensional $\mathcal{N}=3$ superconformal field theories (SCFTs) are an exotic class of quantum field theories that admit no conventional Lagrangian description. In this Letter, we construct an $\mathcal{N}=1$ supersymmetric gauge theory and argue that its infrared fixed point exhibits supersymmetry enhancement to an $\mathcal{N}=3$ SCFT. The ultraviolet theory has gauge group $SU(2)^3$, a set of chiral multiplets, and a suitable superpotential. By performing $a$-maximization, we obtain infrared central charges $a=c=5/4$, matching those of the rank-one $\mathcal{N}=3$ $\mathbb{Z}_3$ S-fold SCFT. The ultraviolet gauge-theory description allows us to compute the full superconformal index with four independent fugacities. We then examine various limits of the full index and further propose a closed-form expression for the Macdonald index, reproducing all known results for the proposed $\mathcal{N}=3$ theory. More remarkably, we argue that further gauging the $\mathcal{N}=3$ theory yields the frozen rank-one $\mathcal{N}=2$ SCFT conjectured from Seiberg–Witten geometry, providing strong evidence for its existence and unlocking its previously inaccessible full superconformal index. Our construction thus opens a systematic route to exploring the refined protected structure of these exotic, intrinsically strongly coupled theories using conventional $\mathcal{N}=1$ Lagrangian techniques.
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General Relativity and Quantum Cosmology
Ringdown analysis of GW250114 with RingCWB
The binary black hole merger GW250114, the loudest gravitational-wave signal detected to date, offers an opportunity to perform a precise test of Einstein's general relativity (GR). Its exceptionally high signal-to-noise ratio enables accurate measurements of the quasi-normal modes (QNMs) and properties of the remnant black hole. In this work, we present a ringdown analysis of GW250114 using the RingCWB algorithm. We measure the dominant $(2,2,0)$ QNM along with its first overtone and constrain the fractional deviations in frequency and damping time from their GR-predicted values, finding $\delta f_{220} = 0.004_{-0.023}^{+0.022}$ and $\delta\tau_{220} = 0.010_{-0.087}^{+0.096}$ , both consistent with zero within the quoted uncertainties. These results represent stringent constraints on deviations from GR. The analysis also places tight constraints on the remnant spin, consistent with a binary black hole formed through stellar evolution.
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Computer Vision
RT-DETR-World: Transferring Rich LLM Semantics to Real-Time Open-Vocabulary Detection
Open-vocabulary detection (OVD) recognizes categories unseen during training through textual category queries, yet achieving strong generalization with real-time efficiency remains challenging. Beyond vocabulary scaling, zero-shot generalization may benefit from reusable visual–semantic cues learned from seen data, including attributes, actions, states, and contextual relations. Existing real-time OVD methods primarily emphasize vocabulary coverage and efficient region/query–text matching; under strict efficiency constraints, compact detectors may struggle to absorb rich instance semantics and scene context. We propose RT-DETR-World, a compact DETR-style detector that transfers the rich semantics conveyed by descriptions during training while retaining lightweight query–text matching at inference. We construct GroundingCapv2 with three levels of supervision: category names for standard OVD, object descriptions conveying instance-level semantics, and image descriptions conveying object relations and scene context. These descriptions serve only as training-time semantic supervision. To help the compact detector absorb these semantics, we propose Dual-Path Description Alignment (DDA), combining a deployment-consistent MiniLM pathway with a training-only LLM teacher. MiniLM provides query–category supervision and object-description alignment, while offline teacher features supervise matched queries and global visual representations at the object and image levels, respectively. All teacher features are precomputed, and the teacher-side modules are removed after training. We further propose Relation-Aware Negative Relaxation (RNR), which uses teacher-derived semantic similarities to relax related negatives while preserving exact positives. Experiments demonstrate competitive zero-shot accuracy and a favorable accuracy–efficiency trade-off. The code will be released.
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Mathematical Physics
Matrix Product State Representatives of Symmetry-Protected Phases
We provide a simple ansatz for finding integer spin $SO(3)\times\Z_2^T\times\Z_2^R$-invariant matrix product states representing a phase for each triple of $\Z_2$ topological indices studied in the literature by Tasaki \cite{tasakiheistop}\cite{tasakitop} and Ogata (corresponding to time-reversal and reflection symmetries) \cite{ogatatime}\cite{ogatareflection}. Every combination of trivial and non-trivial indices has a spin-$1$ $SU(2)$, time-reversal, and site-reflection symmetric MPS representative with injectivity length $l\leq 8$. We provide some exact examples for spin-$1$ and a Fortran program which will find representatives of any triple for any integer spin, as well as some data from random sampling for small spin. The existence of such states agrees with the classification of Chen, Gu, and Wen \cite{chen}, and with the recent results of Tasaki \cite{tasakinew} equating the hidden-order and one of Ogata's indices, wherein the Ogata index is that associated to the dihedral $D_2$ symmetry.
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Astrophysics of Galaxies
Complex Organic Molecules in Protostars with ALMA Spectral Surveys (COMPASS) V. Tracing cavity walls and shocked knots with nonthermally desorbed CH$_3$OH in BHR71-IRS1
Complex organic molecules are detected in both cold molecular clouds and the warm inner regions of protostars. Whether they are eventually inherited by protostars and planets or whether their chemistry is reset by in situ reactions remains unclear. Understanding the desorption mechanisms of these molecules is essential for tracing their chemical evolution. As part of the ALMA Large Program Complex Organic Molecules in Protostars with ALMA Spectral Surveys (COMPASS), we investigate the CH$_3$OH emission that extends beyond the hot corino of BHR71-IRS1. We identified extended CH$_3$OH emission around BHR71-IRS1. We assessed characteristic emission structures by applying a principal component analysis. The physical properties of their line-emitting gas were derived under the local thermodynamic equilibrium (LTE) assumption through both rotational diagram and spectral modeling analyses. In total, 26 extended CH$_3$OH lines have been detected. These emission lines are distributed across (1) X-shaped cavity walls, (2) northern and southern shocked knots, and (3) eastern and southeastern components. The cavity walls exhibit excitation temperatures of $\sim$ 25~K and column densities of $\sim$ 10$^{14}$~cm$^{-2}$, while the knots show relatively higher excitation temperatures (70$-$120~K) and column densities ($10^{14}-10^{16}$~cm$^{-2}$). The physical properties of eastern and southeastern components are not well constrained under LTE conditions. Plausible desorption mechanisms are evaluated by comparing the physical parameters with model predictions. The low excitation temperatures and narrow line widths in the cavity walls favor a reactive desorption scenario driven by far-ultraviolet irradiation from IRS1. In contrast, the knots with higher excitation temperatures and column densities support the dust sputtering scenario induced by C-type shocks.
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Physics Education
Using Learning Analytics to Study Novice Learners' Work on Quantum Circuit Simulator Tasks
Interactive quantum circuit simulators are increasingly used to support introductory quantum computing education for learners from varied disciplinary backgrounds. These environments can also generate detailed response logs of submitted circuits, but such data are rarely transformed into evidence that instructors can use for course redesign and development. We present a learning analytics framework for quantum circuit simulator tasks and report its task-level branch on anonymised logs from an introductory quantum computing course delivered in the TIM learning environment. The task branch characterises exercises through participation, completion, first-attempt accuracy, valid-attempt counts, sessionised active time, and observed answer-space reporting of common correct and incorrect constructions. The dataset covers the 2024-2025 cohort of 492 learners, 47,533 valid submissions, and 21 obligatory quantum circuit exercises. The framework identifies bottleneck tasks, broad solution spaces, and recurring wrong-answer patterns that are not visible from final scores alone. Its most distinctive output is a plain-text representation of the observed answer space, designed to make open-ended circuit submissions directly interpretable to instructors. We show how response logs can reveal actionable task-design issues and support concrete course redesign. A learner-level branch is retained only as an ongoing research extension and is not a central empirical contribution of the present paper.
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Computer Vision
SpatialUQ: Post-Hoc Uncertainty Quantification from Spatial Consistency in Black-Box Vision Models
Clinical vision models are often deployed as frozen black boxes with no access to internals, retraining, or ground truth at inference time. We introduce SpatialUQ, a post-hoc uncertainty method using only output probabilities. It measures the Jensen-Shannon divergence between the global prediction and the mean of five fixed spatial crops in six deterministic forward passes. The premise is simple, trustworthy predictions are spatially consistent. On NIH ChestX-ray14 (DenseNet-121, $N{=}25{,}596$), our Multicrop Uncertainty Score (MUS) reaches $0.784$ failure-detection AUC versus $0.664$ for MC-Dropout ($p{<}10^{-6}$) at one-fifth the compute, with native calibration ($\text{SCE}{=}0.049$ vs.\ $0.127$ for $\ell_1$), the best-calibrated among methods above 0.78 AUC. A supervised fusion of MUS with entropy, confidence, and $\ell_1$ reaches $0.832$, outperforming a five-member ensemble ($0.813$). MUS scales with model quality, reaching $0.899$ with BiomedCLIP ($\rho = 0.846$), while this relationship remains meaningful in-distribution ($\rho = 0.523$) but breaks down under severe distribution shift (VinBigData, $\rho = 0.027$). MUS is well-suited to diffuse findings but is less dependable for small focal lesions such as nodules. Code and experimental materials are publicly available at https://huggingface.co/datasets/kawsher11/SpatialUQ.
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Artificial Intelligence
Ream: Unfolding Mutual Awareness in Human-Agent Workspaces
As AI agents work alongside humans in shared workspaces, a mutual awareness challenge arises: agents act at speeds that outpace human monitoring, and users' evolving interests are not always expressed in chat. This challenge is especially pressing in literature review, where both parties retrieve, read, and synthesize a growing body of papers. We present Ream, a literature review workspace that supports mutual awareness through structured artifacts, bidirectional engagement tracking, and localized visualizations. Users can see each party's activity within these documents, and agents can retrieve the same history to guide their work. In studies with eighteen researchers, participants used these traces to inspect evidence, steer agents, communicate through annotations, and reflect on their research focus. Shared histories also helped agents build on earlier work. These findings inform how engagement traces within shared documents can support transparency, personalized assistance, and coordination in human-agent knowledge work.
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Robotics
Sparse Feature Policy Unlearning Mitigates State Hallucination in Vision-Language-Action Models
Vision-Language-Action (VLA) models have shown strong generalization in robotic manipulation by leveraging rich representations from pretrained vision-language models. However, their deployment in real-world environments remains limited by recurring unreliable behaviors. In this work, we study state hallucination, a recurring failure pattern in which a VLA continues acting as if an unrealized robot-object state had been achieved. Our analyses find that state hallucination coincides with weakened attention to task-relevant visual regions, and a mechanistic interpretation via sparse autoencoders reveals that hallucination-associated sparse features are activated when these failures occur. Based on this analysis, we propose SOUL (Sparse feature pOlicy UnLearning), which selectively unlearns policy knowledge associated with state hallucination behaviors, where sparse features identified from hallucination failures and successful behaviors serve as explicit forgetting and retention targets, respectively. Experiments across VLA architectures in simulated and real-world environments show that our method substantially reduces hallucinated failures and improves task success without substantially compromising the existing manipulation capabilities. These results suggest that interpretable feature analysis provides a practical basis for selectively modifying undesirable knowledge in robot policies.
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Artificial Intelligence
Cognitive Schemas, Laws and Tasks
This paper asks how explicit representations can support reusable cognitive schemas in knowledge-based problem solving. We develop a structural framework in which schemas are organized by the information and relations required for their use, rather than introduced as unrelated primitives. The framework also distinguishes context-dependent relations from more stable structures that can be reused across different representations. Tasks are described through the information available, the unknowns to be determined, and the constraints that admissible solutions must satisfy. This makes it possible to separate limitations of the representation from limitations of the solving procedure. In particular, we distinguish inconsistency, underdetermination, and contextual insufficiency, where the current representation lacks distinctions or relations required by the external task meaning. We also show formally when a reduction of representation preserves the task-relevant solution structure. The resulting task–schema interface offers a structured way to describe representational conditions relevant to problem solving. It supports the reuse and stabilization of derived knowledge while remaining independent of the particular mechanism used to generate candidate solutions. This may provide a useful component for future solver architectures that combine structured knowledge, verification, and learned proposal mechanisms.
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Analysis of PDEs
Logarithmic Hessian estimates for non-uniformly elliptic equations in non-divergence form
We establish uniform logarithmic Hessian estimates for solutions of non-uniformly elliptic equations in non-divergence form. The proof is based on a measure estimate from convex analysis without localization or covering arguments. Moreover, we construct a counterexample that rules out uniform power-type Hessian estimates and shows the sharpness of the logarithmic exponent in the plane. Finally, we extend our estimates to strong solutions and apply them to obtain regularity results for Grushin-type equations.
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Artificial Intelligence
The Attribution Blind Spot: Layerwise Trajectory Diagnostics for Source Reliance in Retrieval-Augmented Language Models
A retrieval-augmented model can match a document without relying on it. Controlled knowledge conflicts make source choice observable and let us ask a second question that prediction alone cannot answer: which internal-state properties define useful intervention directions? We study paired hidden-state changes with Latent Trajectory Shift (LTS), a signed projection onto a training-fitted first principal component (PC1), and keep verified training exposure separate from behavioral source choice. Across the evaluated conflicts, state-change magnitude is often the stronger predictor, whereas signed PC1 is the stronger selective controller: equal-norm interventions change source preference while better preserving non-target behavior, and the frozen direction transfers across the tested datasets and aligned model pairs. A same-system OLMo study further combines positive choice and control results with inconclusive exposure detection at the achieved power. The central result is a separation: representations that diagnose what a model will choose need not be the representations that best control that choice.
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Computer Vision
Gaussian Material Fields for Volumetric Multi-Energy CT Decomposition
Volumetric material decomposition in multi-energy computed tomography requires a representation that organizes multiple three-dimensional material fields in a common spatial domain while retaining differences in composition and local structure. We observe that spatial primitives can be shared across materials without tying their coefficients, but their local capacity must respond to material-specific reconstruction needs. We introduce Gaussian material fields, which represent multiple material distributions with shared anisotropic 3D Gaussian primitives and independent nonnegative material coefficients. The shared geometry defines a continuous spatial basis, while the coefficients determine each primitive's contribution to the individual material fields. To reconstruct this representation from multi-energy projections, a differentiable spectral forward model combines Gaussian material path integrals with a calibrated basis matrix, enabling joint optimization of spatial geometry and material composition. Material-aware adaptive density control retains material-specific refinement evidence before aggregation and adjusts local representation capacity to accommodate both spatially extensive components and sparse details. Experiments use synthesized multi-energy projections generated from pseudo-reference material maps constructed by conventional methods from publicly available CT data. Across 15 cases, our approach improves average PSNR by 4.03 dB and SSIM by 4.96% over the strongest baseline, while reducing NRMSE by 33.45%. Material-wise comparisons and component ablations support improved recovery of localized structures, while runtime and memory measurements show favorable computational scaling. These results establish Gaussian material fields as an explicit, adaptive representation for volumetric multi-material reconstruction.
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Information Theory
Function-Correcting Lee-distance Codes for Symbol-Pair Read Channels
Function-correcting codes (FCCs) protect specified function evaluations of messages against errors while reducing the redundancy required for reliable communication. We study FCCs for symbol-pair read channels, motivated by high-density storage systems that read overlapping symbol pairs. Phase-shift keying (PSK) modulation is well-suited to such systems due to its bandwidth efficiency and noise robustness. While FCCs for symbol-pair read channels have been studied under the Hamming metric, the Lee metric is a more appropriate error model for $q$-ary PSK and, hence for $q$-ary symbol-pair read channels. We generalize the symbol-pair Lee distance, previously defined only over $\mathbb{Z}_4$, to $\mathbb{Z}_q$, $q\ge2$, and introduce function-correcting symbol-pair Lee-distance codes (FCSPLCs) over $\mathbb{Z}_q$, specializing to $q=2^m$, $m\ge1$, for $2^m$-ary PSK constellations. We investigate their redundancy requirements by introducing irregular-pair Lee-distance codes and relating the optimal redundancy of FCSPLCs to the shortest length of such codes. We derive Plotkin-type and Gilbert–Varshamov-type bounds on the optimal redundancy through lower and upper bounds on the shortest length of irregular-pair Lee-distance codes. For bijective functions, we obtain corresponding Plotkin-type and Gilbert–Varshamov-type bounds for classical Lee metric codes for symbol-pair read channels over $\mathbb{Z}_q$, which, to the best of our knowledge, are the first such bounds for the Lee metric symbol-pair setting. We then specialize the FCSPLC framework to pair-locally bounded functions, the Pair-Lee weight function, and the Pair-Lee weight distribution function, giving explicit constructions and corresponding bounds on the optimal redundancy. Finally, for linear functions, we derive a Plotkin-type lower bound on the optimal redundancy.
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Analysis of PDEs
Interior $C^2$ Estimates for 2-Sum Hessian Equations
This paper establishes an interior $C^2$ estimate for solutions of \[ \sigma_2(D^2u)+\alpha(x)\sigma_1(D^2u)=f(x,u,Du)>0, \] on the positive branch $\Delta u>0$, under the assumptions $\alpha\ge0$ and $D^2\alpha=\beta I$. Using one extra variable and a quartic correction, the equation is reduced to a quadratic Hessian equation in one higher dimension. The terms involving $D^2u$ cancel, so the interior estimate of Li–Wu \cite{LW} applies. The gradient-independent case is also treated. Finally, an example shows that an $L^\infty$ bound on $\alpha$ alone is not enough.
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Computation and Language
Goldsmith: Gold-Loss-Guided Definition Optimization with an Agentic Annotation Harness
Many annotation projects begin before experts have a stable guideline or enough labels to train a task-specific model. We present Goldsmith, an agentic pipeline that turns a small gold set—expert-annotated calibration examples representing the intended task boundaries—into a reusable structured annotation definition. Goldsmith treats this definition as a trainable textual object. Candidate definitions are run on the same gold examples and scored with an executable structured loss, while the output schema, formatting, retrieval, repair, judging, and human review remain in an external harness. A large language model (LLM) editor converts the highest-loss failures into textual-gradient revisions, which are accepted only when the measured loss decreases. In prompt-optimization comparisons, Goldsmith improves over direct rewriting, OPRO, APE, and PromptBreeder under matched evaluation protocols. The resulting definition also improves downstream annotation when combined with retrieval, score-based routing, and human review across typed span, pair-level relation, and fixed-trigger event-argument tasks. These results show that scarce expert supervision can support both task-definition learning and scalable annotation.
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Robotics
SiGNgapore - An Interactive Dataset for Sign-based Visual Navigation
Robots navigating open-world, human-centered environments must look beyond prebuilt high-fidelity maps and leverage navigational aids embedded in their surroundings, particularly, signs. To advance sign-guided visual navigation, we introduce SiGNgapore, an interactive, multimodal dataset designed to benchmark sign-guided multi-step navigational decision-making. SiGNgapore covers diverse public spaces in Singapore, including shopping malls, public transportation hubs, and hospitals, featuring multi-floor, multi-building layouts and indoor-outdoor transitions. It consists of 56 long-horizon navigation missions and 456 scenes, each containing a navigational sign and its surrounding environment. We provide synchronized RGB, depth, IMU, and odometry data for each scene. We additionally provide the layout map and the GPS-aligned scene graph for selected mission sites. Beyond navigational decision-making, SiGNgapore supports a variety of spatial-semantic reasoning tasks, including navigational sign parsing and visual sign grounding, with the ultimate aim of driving progress in mapless robot navigation.
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Databases
Correspondences as Decisions: JevNexus for Decision-Centric Schema Matching
Schema matching increasingly uses generative language models to rerank retrieved column candidates, although the underlying task is a bounded correspondence decision. We present JevNexus, which combines typed pairwise decisions with schema/instance evidence and invokes listwise refinement only when the evidence disagrees and the fused margin is small. The evaluation covers 561 cases from six benchmark families. JevNexus obtains dataset-macro MRR and Hits@1 of 0.930 and 0.909, compared with 0.926 and 0.903 for Magneto, while reducing mean latency from 123.452 to 15.929 seconds (7.750). Paired analysis finds no statistically significant difference in either MRR or Hits@1. The gate invokes listwise refinement for only 5.665% of source columns and avoids the degradation caused by unconditional refinement. Code and experimental artifacts are available at https://github.com/RazeenLI/JevNexus.
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Audio and Speech Processing
Mitigating Accent-Language Confusion in Self-Supervised Speech Representations for Language Identification
Spoken language identification (LID) aims to recognize the target language regardless of accent. In practice, however, LID models fine-tuned from self-supervised speech representations frequently confuse accents with languages, misclassifying non-native (L2) speech as the speaker's first language (L1). We show that non-native speech representations lie between native target-language and native L1 poles, causing systematic misclassification. To address this, we introduce a geometric projection that estimates an L1-bias direction solely from native speech and removes it before the frozen LID head. Across five MMS-LID models and non-native corpora, this projection substantially improves target language identification for L2-accented speech while preserving predictions for native speech. These results show that accent-induced L1 bias can be corrected directly within the representation space without L2 training data or model adaptation.
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Quantum Physics
The Geometry of Lee-Yang Tensors
We provide a geometric description of Lee-Yang tensors, building upon several recent results of Bravyi, Gosset, Liu, and Wong. By applying tools from complex Perron-Frobenius theory, we generalize one of their key lemmas to bound the spectral ratio of non-normal operators with Lee-Yang radius greater than one. As a direct consequence, we provide a local-to-global principle for bounding spectral gaps of Suzuki-Fisher Hamiltonians, a family of $2$-local Hamiltonians, using only the Lee-Yang radius of each local operator to bound the gap from below. On the other hand, we develop a simple perturbative technique to show that the Gibbs states of $k$-local Hamiltonians, $k \geq 3$, cannot have Lee-Yang radius at least one for all inverse temperatures $\beta \geq 0$. We apply this same method to conclude that Suzuki-Fisher Hamiltonians are precisely those Hamiltonians whose Gibbs states are Lee-Yang at all inverse temperatures $\beta \geq 0$.
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Artificial Intelligence
MIMESIS: Learning User Simulators as Training Environments for Interactive Agents
Training and evaluating interactive language agents typically requires rich user interactions, yet collecting human feedback is expensive and difficult to scale. Simulated users offer a scalable alternative, but they must both resemble real user behavior and provide useful learning experiences for agents. In contrast, most agent-training frameworks rely on off-the-shelf assistant LLMs, whose helpfulness can make them overly cooperative, explicit, and behaviorally homogeneous compared with real users. We introduce MIMESIS, a purpose-built user simulator trained on human conversations with explicit reasoning supervision and 13 realistic behavioral patterns derived from real user interactions. Empirically, our 9B model achieves a SOUL-Index of 65.7, surpassing the strongest frontier model. Compared with Claude-Opus-5, the strongest baseline on RealUserSim and SimulatorArena, MIMESIS improves behavioral fidelity by 13.4 points and reduces Turing distance by 3.6 points, respectively. We then freeze the simulator and train an agent by interacting with the frozen simulator using multi-turn reinforcement learning. Across eight environments, training with MIMESIS yields better agent performance than training with GPT-5.5 under all nine unseen user simulators, demonstrating stronger generalization to new user simulators. Moreover, we propose Coached On-Policy Self-Distillation (CSD), which leverages simulator-generated private reasoning traces and subsequent utterances as feedback on how well the agent addresses user needs. A coach converts this information into concise coaching notes that describe how the agent can better anticipate user needs and adapt its behavior over the course of an interaction. CSD turns this feedback into dense, token-level supervision beyond sparse task rewards, yielding further gains across all nine evaluation user models.
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Combinatorics
Graph Sensitivity of Cartesian Products with Matched Bridges
For a graph $G$, let $f_t(G)$ denote the minimum of the maximum degree of an induced subgraph with $\alpha(G)+t$ vertices, where $\alpha(G)$ is the independence number, and write $f(G)=f_1(G)$. Huang's theorem gives $f(Q_k)\ge\lceil\sqrt{k}\rceil$ for the $k$-dimensional hypercube $Q_k$. We extend this lower bound to Cartesian products of $k$ bipartite graphs with perfect matchings and prove that equality holds when the factors are connected and each has a matched bridge. In particular, we prove that $f(T_1\Box\cdots\Box T_k)=\lceil\sqrt{k}\rceil$ whenever each $T_i$ is a tree with a perfect matching. We determine the sensitivity of every Cartesian product of paths, settling the even-path case left open by Zeng and Hou [J. Graph Theory 107 (2024), 169–180]. For these tree products, with $D=\lceil\sqrt{k}\rceil$, we also prove that $f_t(T_1\Box\cdots\Box T_k)=D$ whenever $1\le t\le 2^{D-\lceil\log_2D\rceil-1}$. When $t=2$, this equality holds for all $k\ge 2$, provided that at least one factor is not $K_2$. Matching cuts give an additional exact range for products of even-order paths. Finally, we prove that $f_2(Q_k)=\lceil\sqrt{k}\rceil$ for every $k\ge 2$ with $k\not\in \{4,9\}$, whereas $f_2(Q_4)=3$ and $3\le f_2(Q_9)\le 4$.
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Dynamical Systems
Typical expansive measures for infinite-dimensional maps
A classical theorem by Mañé states that compact metric spaces admitting expansive homeomorphisms must be finite-dimensional. It is a natural question, raised by Morales and Sirvent, whether this dimensional constraint extends to the measure-theoretic notion of expansiveness. In this paper, we answer this question in the negative. We prove that the shift map on the Hilbert cube is expansive with respect to the product Lebesgue measure. Furthermore, we establish a general sufficient condition: any homeomorphism admitting a full-support expansive measure is densely measure-expansive. As a consequence, we show that the set of expansive and topologically stable measures for the shift map contains a dense $G_\delta$ subset, revealing a rich measure-theoretic structure despite the infinite dimensionality of the phase space.
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Optics
Vector beams for real-time monitoring of crystalline symmetry on {\mu}m length scale
Symmetry constrains and determines the physical properties of crystalline solids. Determining crystalline symmetry often requires large-scale diffraction facility and advanced analysis software and therefore cannot be realized with real-time feedback. Alternatively, optical anisotropy has also been exploited for elucidating the rotation, mirror and inversion symmetries of solids on smaller tabletop setups. Second harmonic generation, in particular, has demonstrated a remarkable sensitivity to subtle changes in these symmetries during phase transitions. To access the full nonlinear susceptibility of a crystal in a cryogenic or vacuum environment, angle-by-angle rotation of the scattering plane of an obliquely incident and outgoing beam in co-ordination with their polarization states is required. This typically results in a bulky and wobbly setup, significant feedback latency, and a focal spot size > 20 {\mu}m unsuitable for microscopic samples such as few-layer 2D materials. In this work, we make use of vector beams to realize a non-rotating oblique-incidence setup, demonstrating a real-time (> 10 fps) visualization of crystalline symmetry on a sample area of ~ 2 {\mu}m in diameter. Both the feedback latency and focal spot size represent more than an order of magnitude improvement over previous designs based on a Gaussian beam and mechanically-rotating stages. Here, the use of a vector beam greatly simplifies and reduces the cost of nonlinear optical anisotropy measurements, heralding widespread applications of this approach in both research and industrial settings, for example, for strain monitoring and crystal alignment. Our work may also promote broader integration of structured optical field into solid state and condensed matter research in the future.
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High Energy Astrophysical Phenomena
Axion effects on hybrid stars: earlier hadron-quark phase transition and larger quark-matter cores
We investigate the effects of axions on the properties of hybrid stars and the possible hadron-quark phase transition in their cores within the Maxwell construction. The hadronic phase is described by the improved isospin- and momentum-dependent interaction (ImMDI) model, while the quark phase is modeled by a three-flavor Nambu–Jona-Lasinio (NJL) model with an axion-modified Kobayashi-Maskawa-'t Hooft (KMT) interaction. Based on the obtained equation of state, we analyze the properties of hybrid-star matter, including the speed of sound and the polytropic index, as well as the structural characteristics of hybrid stars, including the mass-radius relation and the properties of the quark core. Our study shows that the axion field $a/f_a$ slightly stiffens the equation of state of quark matter but significantly shifts the hadron-quark phase transition to lower baryon densities. These two effects compete in influencing the equation of state of hybrid-star matter, and may even soften it, which is different from the effect of the vector coupling interaction. Consequently, the axion field has only a weak influence on the maximum mass of hybrid stars, but significantly increases the mass and radius of the quark core, especially for weak vector coupling. These results indicate that, within the present Maxwell construction, the primary role of the axion is to promote an earlier hadron-quark transition at low densities and to enlarge the quark core.
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Robotics
Precise SE(3) End-Effector Tracking in Whole-Body Humanoid Control
Precise end-effector tracking during humanoid whole-body motion is challenging due to floating-base oscillations, gravity, dynamic coupling, and locomotion-induced disturbances. We propose ResGAC, a whole-body humanoid controller for precise end-effector pose tracking that combines geometric admittance control (GAC) with residual reinforcement learning. GAC provides structured $\SE$ task-space feedback and generates nominal arm joint-position targets, while residual RL compensates for unmodeled dynamics and coordinates locomotion and balance in the shared joint-position action space. The left-invariant geometric formulation allows the same GAC law to be used across manipulation reference frames. This enables the use of a ground-attached heading frame that preserves planar locomotion while removing pelvis roll, pitch, and heave from the manipulation reference, thereby reducing reference-induced end-effector motion during locomotion. ResGAC is validated on a real Unitree G1 humanoid. Across four standing end-effector tracking benchmarks, ResGAC consistently outperforms representative baselines, including SONIC, achieving lower translational and rotational errors. Real-world experiments further demonstrate reduced propagation of pelvis motion to the desired end-effector pose using the proposed ground-attached heading frame. ResGAC achieves $90\%$ success in a standing peg-in-hole task compared with $50\%$ for SONIC, and accurate world-frame $\SE$ end-effector pose tracking during lower-body motion. Experimental videos are included in the supplementary material and are also available on the project website: https://resgac.github.io/ResGAC-website/.
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Computer Vision
InstanceBench: Diagnosing Referential Reasoning and Target Identity in Referring Expression Segmentation
Referring Expression Segmentation (RES) links natural-language descriptions to pixel-level object masks. Yet standard evaluation provides limited insight into instance-level referential reasoning: it does not systematically distinguish referential logics, test target preservation across valid grounding paths, or separate target-selection from mask-generation errors. We introduce InstanceBench, an instance-centered diagnostic benchmark comprising 6,194 images, 9,264 target instances, and 25,077 human-verified expressions. Each target-centric expression set (TCES) fixes the image and target mask while pairing a minimal expression with a same-target variant that uses another valid cue or grounding path. A compact referential-logic taxonomy spans direct target evidence, same-class selection, relational and compositional grounding, and exclusion, while logic-critical construction suppresses simpler shortcuts. Identity-aware metrics measure target retention and set-level success while separating selection from mask-generation errors. Across 22 native-mask RES checkpoints from 18 model families, the strongest checkpoint reaches 67.1% mIoU but only 59.6% All@0.7. Controlled interventions confirm language sensitivity, while failure decomposition identifies target selection rather than mask decoding as the main bottleneck. On a controlled training subset, matched supervision improves identity-aware performance, showing that the diagnosed capability responds to targeted supervision. Collectively, InstanceBench supports a measure-diagnose-improve cycle: measuring target consistency across grounding paths, localizing failure sources, and evaluating targeted interventions.
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High Energy Astrophysical Phenomena
Polarised X-ray emission from the accreting millisecond pulsar SAX J1808.4-3658 during an X-ray outburst and a type-I X-ray burst
Modelling the X-ray pulse profiles of accreting millisecond pulsars (AMSPs) is a key technique to constrain the masses and radii of neutron stars. To this end, measuring the properties of polarised X-rays provides crucial information on the system geometry. We present the significant detection by IXPE of linearly polarised 2-8 keV X-rays during the decay of the 2025 outburst of the 2.5 ms AMSP SAX J1808.4-3658, with an average polarisation degree of $2.9\%\pm0.5\%$ and a polarisation angle of $46{\deg}\pm5{\deg}$, broadly consistent with the direction observed in the optical band. This level of polarisation is similar to that found in the only other source of this class that has been targeted so far. By using a pulse-phase timing solution obtained with IXPE and NuSTAR, which confirms the long-term evolution of the pulsar spin and orbit, we did not find any significant pulse phase-resolved variability in the Stokes parameters. Interpreting the polarised X-rays as originating from hot spots on the NS surface indicates they are almost aligned with the spin axis. We also report an indication for linearly polarised emission with a degree of $16\%\pm6\%$ (2-6 keV) during the peak of a type-I thermonuclear X-ray burst, with an angle almost orthogonal to that of the persistent emission. If confirmed, this level would exceed expectations for X-rays reflected by a thin accretion disc.
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Machine Learning
CHASE: Channel-Aligned Structure Exploitation for Geometry-Aware Model Engineering
Geometric and Spectral Alignment (GSA) characterizes trained networks through spectral concentration, physical-channel alignment, support structure, and changes in singular bases. In this paper, we propose CHASE (Channel-Aligned Structure Exploitation) to use these structures in practical model design. CHASE covers six applications across model modification, reconfiguration, and compression. CORA, COEC, and CORAM apply GSA to parameter-efficient finetuning, structured-pruning compensation, and model merging. We further develop three new methods. CAGA uses GSA to identify multi-head attention heads that can share a KV representation and constructs the shared key and value heads through geometric alignment and low-rank subspace extraction. SAKV uses GSA to determine which adjacent layers can share a low-rank KV-cache representation and the retained rank for each layer group. CAPS uses GSA spectral structure to group output neurons and selects retained input channels separately for each group. Results from CORA, COEC, and CORAM establish the effectiveness of GSA for adaptation, pruning compensation, and model merging. Experiments on CAGA show that geometric shared-head construction substantially improves MHA-to-GQA conversion, and SAKV and CAPS improve over representative baselines for KV-cache compression and structured pruning. These results show that the structures identified by GSA can be used directly to design methods for a range of model operations.