Papers

The complex polynomial Bohnenblust–Hille inequality states that, for a $d$-homogeneous polynomial $P:\mathbb C^N\to\mathbb C$, $P(z)=\sum_{|\alpha|=d}c_\alpha z^\alpha$, the coefficient norm $(\sum_{|\alpha|=d}|c_\alpha|^{p_d})^{1/p_d}$ is bounded by $B_d^{\mathrm{pol}}\|P\|_\infty$, where $p_d=2d/(d+1)$ and $B_d^{\mathrm{pol}}$ is independent of $N$. Here $\|P\|_\infty$ is the supremum norm on the unit polydisc. This inequality has a Boolean analogue for the Fourier–Walsh coefficients of functions of degree at most $d$, with the supremum taken over $\{-1,1\}^N$. In this setting, Defant, Mastyło and Pérez obtained subexponential bounds, and Ivanisvili established polynomial growth. Further polynomial estimates were obtained by Slote, Tseng and Volberg in the Boolean setting and by Slote and Volberg for cyclic groups. We study these coefficient inequalities in a broader framework of finite systems of functions that encompasses and extends the Boolean and cyclic settings. This framework also admits a natural $\ell_p$ formulation, leading to Hardy–Littlewood-type inequalities. For orthonormal systems, we obtain polynomial bounds for the Bohnenblust–Hille constants and, for sufficiently large $p$, for the constants in these Hardy–Littlewood-type inequalities. In the Boolean case, the polynomial power is $5/2$, with a cubic logarithmic factor.

Object Navigation in unseen environments remains a fundamental challenge in embodied AI, as it requires agents to generalize visual and spatial reasoning to novel layouts. While recent advances in large language model (LLM) and vision-language model (VLM) have enhanced semantic mapping, spatial memory, and waypoint selecting for navigation, successful navigation requires more than selecting the next promising waypoint. A robot must also recognize stalled progress, escape unproductive behaviors, and revisit overlooked target cues. Addressing these challenges requires both specialized navigation strategies and a high-level policy that coordinates their execution. Motivated by the analysis of failed navigation episodes, we propose LERR-Nav, an object navigation framework that coordinates exploration, recovery, and reminiscing through a learned high-level policy. The framework comprises four complementary navigation strategies: value-function-guided exploration, LLM-guided exploration, recovery from stalled or repetitive behavior, and memory-guided reminiscing. To support history-aware coordination, we maintain the execution memory that preserves textual summaries of all strategy executions alongside a sliding window of map sequences. To learn the coordination policy, we initialize a high-level vision-language agent from Qwen2.5-VL-7B-Instruct and train it through a two-stage curriculum. The first stage uses map-centric supervised fine-tuning (SFT) to establish spatial grounding. The second stage performs SFT on variable-length navigation segments to learn which navigation strategy to invoke next based on current maps and the hybrid execution memory. Experiments on HM3D and MP3D demonstrate state-of-the-art navigation performance, while ablation studies validate the contributions of individual components.

We study how a higher-rank classical collective order parameter can select one dominant projective eigenline and, in a $p=2$ realization, support a dynamically autonomous low-energy director sector. In a fully connected projective-rotor model, the collective second moment is a positive semidefinite tensor $T$ of fixed trace. Conventional projective ordering drives its effective rank toward one, selecting a single dominant eigenline. Rank polarization alone, however, does not determine dynamical autonomy: extrinsic-curvature criteria depend on the chosen state-space metric, and the equilibrium tensor does not determine the transverse free-energy Hessian. A two-harmonic model makes this logical independence explicit by producing families with identical $T$ and $r_{\rm eff}$ but different transverse quadratic forms. We then construct rotationally invariant locking interactions that leave a prescribed ordered tensor exactly fixed while increasing every non-Goldstone restoring coefficient as $\Theta(\lambda)$ within a globally controlled stable regime. For a phenomenological inertial realization with a finite positive kinetic matrix, the lowest transverse normal-mode frequency grows as $\Theta(\lambda^{1/2})$; more generally, the low-frequency transverse susceptibility is suppressed as $O(\lambda^{-1})$, including in overdamped dynamics. The construction therefore proves that spectral selection and infrared transverse suppression are independent data. For $p>2$ the selected eigenline has a $(p-1)$-dimensional director manifold; the one-dimensional Goldstone sector used in the dynamical construction is specific to $p=2$. Promoting the selected internal eigenline to a physical clock requires additional soldering and integrability structure.

For a fixed prime $p$, a group is called a $p'$-group if the orders of all its elements are coprime to $p$. It is well known that in a finite $p'$-group an automorphism of order $p$ is regular if and only if it is a splitting automorphism of period $p$. In the Kourovka Notebook, V.\,D.~Mazurov asked whether these two notions coincide for periodic $p'$-groups. We answer this question in the negative by constructing a periodic group of prime period $q$ that admits a regular automorphism of order $p \neq q$ which is not splitting.

Deep classifiers deployed in safety-critical services like autonomous-driving perception remain vulnerable to small adversarial perturbations. Certified $\ell_2$ defenses today face a costly trade-off: randomized smoothing (RS) requires hundreds of noisy queries per input, while Lipschitz networks (LN) constrain the architecture and sacrifice clean accuracy. We take a detection-oriented approach instead: rather than certifying that predictions are invariant inside an $\ell_2$ ball, we certify that adversarial inputs within an $\ell_2$ ball are detected — a guarantee aligned with security-critical deployments where missing an attack is costlier than flagging a clean input. To realize this, we prove a Lipschitz-margin reduction from certified $\ell_2$ robustness to certified detection, which reduces the problem to handling a single Lipschitz constant $L$. We introduce two detector families: $\mathbb{D}_{Adv}$, which estimates $L$ from a single defender-side perturbed pair, and $\mathbb{D}_{lc}$, which augments that pair with a local margin centroid to keep the estimate above what the certificate requires. Both deploy on any pretrained classifier without retraining. With a valid global bound, the detector is fully certified at that radius; with a local estimate $L'$, certification is sample-wise and applies only when our certified condition holds. Across MNIST, CIFAR-10, and ImageNet-1k on four backbones (LeNet-5, VGG16, ResNet-50, ViT-B/16), our detectors match or outperform five baselines (CTT, SortNet, CRM, ContraNet, A$^2$D). For CIFAR-10 with 1-Lipschitz SortNet, our reduction delivers $100\%$ certified detection at the lowest FPR among compared certified detectors; on the standard CIFAR-10 VGG16, our detectors reject all evaluated in-budget adversarial examples, with 62-82% both rejected and formally certified.

We review a many-body formulation of gravitational anomalies as obstructions to realizing the complete low-energy data by a local bosonic lattice quantum system of the same dimension. In this formulation, an anomalous theory can be realized at the boundary of a gapped bosonic lattice bulk, whose topological order gives a one-to-one classification of the anomaly. An invertible bulk reproduces conventional anomaly inflow; a bulk with non-trivial topological excitations yields a non-invertible generalization. To describe the holographic theory of anomalies, we explain the distinction between uniquely defined topological order and many versions of topological quantum field theory and discuss the boundary-to-bulk map. As an application of the holographic theory of anomalies, we describe morphisms between local quantum theories (such as quantum field theories). These morphisms are built from a bulk domain wall and an invertible boundary junction, which give rise to a sandwich picture. Chiral boson/fermion theory, Laughlin edges, and boundaries of $\mathbb{Z}_2$ higher gauge theory with bosonic or fermionic point-like excitations illustrate the different kinds of information about non-invertible anomalies contained in transport coefficients, superselection sectors, and condensation data. In particular, a fermionic theory can be viewed as a theory with a particular non-invertible gravitational anomaly. Those examples also reveal that {\it symmetry $\sim$ gravitational anomaly $\sim$ topological order in one higher dimension}.

Generating complete 3D assets from sparse, unposed images requires preserving observed geometry while completing unseen regions. Joint reconstruction and generation offers a way to address both goals: reconstruction recovers the geometry observed in the input images, while generation contributes learned shape priors. However, combining camera-relative reconstruction with canonical-space generation introduces a coordinate mismatch that makes direct geometric interaction more difficult. Moreover, conditioning each 3D location on all views without accounting for their relevance may mix useful geometric evidence with unrelated image content, hindering local detail recovery. We present UniForge3D, which jointly models reconstruction and generation in a shared anchor-guided space, resolving their coordinate mismatch. This space follows the anchor view's azimuth while keeping the object upright. The two branches exchange features bidirectionally to predict per-view point maps and a complete sparse voxel structure. We further condition point-map prediction on the generated structure to establish pixel-to-voxel correspondences and select the most informative input view for each voxel. Features from the selected views then guide detailed shape generation, helping preserve observed geometric details. Our method achieves state-of-the-art appearance and geometry results on Toys4K and GSO, generating complete 3D assets with improved fidelity. Project webpage: https://xishuxishu.github.io/uniforge3d-project/

Beat tracking, chord estimation, and structure analysis are staple tasks of music information retrieval. Their datasets are drawn largely from Western popular music, and jazz remains a repertoire on which state-of-the-art systems underperform. We present JSIR, the Jazz Standards dataset for Information Retrieval. Its 267 recordings of 44 jazz standards span 25.6 hours, 3.7 times the audio of JAAH, the closest existing resource. For each recording, we provide annotations for beat and downbeat positions, chords, and sections, all produced by a jazz musician and revised in several passes. In baseline experiments, models trained with JSIR also improve on other jazz datasets: the downbeat F-measure of a state-of-the-art beat tracker rises from 87.7% to 89.2%, and the seventh-chord accuracy of a pop-trained chord estimator on JAAH from 34% to 41%. We publicly release the annotations, the annotation tool used to create them, and a web application that displays them in sync with the audio.

Multi-frequency electrical impedance tomography (EIT) often requires specialized hardware. This challenge is especially pronounced in biomedical applications. We developed a 16-electrode EIT system using an Arduino GIGA R1 WiFi for generation and acquisition, with a discrete current source, three analog multiplexers, and basic signal conditioning. Dual cores separate waveform timing from switching and acquisition. A 3D-printed tank with silver-wire electrodes was tested at 11 frequencies (1-180 kHz). Across the 10-180 kHz analysis band, median repeat-frame signal-to-noise ratio was 48 dB, acquisition rate was ~0.18 frames/s per frequency (~60 s per sweep), and cross-session baseline drift was ~6%. KCl phantoms contained an insulating ABS cylinder or KCl-filled dialysis bags (0.001-1.0 M) spanning positive and negative conductivity contrasts. Boundary voltages were analyzed without reconstruction to estimate inclusion position, contrast polarity, and relative magnitude. Leave-one-session-out matching located ABS inclusions in 29/30 runs at 160 kHz (87-97% across the band; chance 33%). For dialysis bags, polarity was correctly identified in all 36 nonzero-contrast runs. Signed voltage projections correlated with the cylindrical contrast factor (R^2=0.68 across runs; R^2=0.89 for the aggregate fit). Concentration was ordered (Spearman rho=0.85), despite saturation above ~10-fold contrast. Bag position accuracy ranged from 6/6 at the highest contrasts to 2/6 at matched conductivity. The matched-conductivity bag produced a ~1.7% RMS perturbation against 0.4-0.6% repeat-frame variability. These results demonstrate that microcontroller-based multi-frequency EIT can support selected detection and identification tasks through direct boundary-voltage analysis, supporting future studies of muscle electrochemistry.

Sexual harassment represents a pervasive societal challenge, with a substantial proportion of incidents remaining unreported due to insufficient evidence and delayed intervention mechanisms. Smart surveillance systems capable of detecting such incidents in real-time could assist law enforcement and serve as a deterrent. However, video-based harassment detection poses significant challenges, including variations in clothing, illumina- tion, partial occlusions, low resolution, and diverse camera view- points. Despite its social importance, this problem has received limited research attention, primarily due to the scarcity of large- scale annotated video datasets. To address this gap, we extend the Sexual Harassment Video (SHV) dataset to 600 short video clips sourced from YouTube and annotated into harassment and non-harassment categories using consistent labeling guidelines. We fine-tune three state-of-the-art video transformer models, VideoMAE, ViViT, and TimeSformer, pretrained on Kinetics- 400, for binary harassment classification. Experimental results show that all three models achieve competitive classification performance, with TimeSformer attaining the highest test accu- racy of 92.27%, outperforming VideoMAE 91.71% and ViViT 91.16% on the extended SHV test set. Our analysis reveals that performance is notably influenced by dataset size, video quality, frame sampling strategy, and model architecture. This work presents a comprehensive evaluation of modern video transformers for this sensitive real-world task.

As speech generation and real-time spoken dialogue systems advance, neural mean opinion score (MOS) predictors are increasingly used to evaluate speech quality. However, many existing predictors are trained primarily on English read speech and generalize inconsistently across languages and speaking styles. In particular, their reliability on Korean speech has not been adequately validated. We propose KOMOS, a Korean MOS predictor for evaluating the overall quality of both read and spontaneous speech. To train and evaluate KOMOS, we collect 5,000 ratings from 29 native Korean listeners for 1,000 utterances spanning real recordings, synthesized speech, and degraded speech. KOMOS achieves an utterance-level Spearman rank correlation (SRCC) of 0.900, compared with 0.703 for UTMOS v1 and 0.767 for UTMOS v2. The inference code is publicly available at https://github.com/upskyy/komos and the trained model at https://huggingface.co/upskyy/komos.

We study invariant probabilities for nonlinear two-population branching systems with competition, cooperation, or predator–prey interaction, driven by Brownian noise and spectrally positive stable jumps. Without immigration, every invariant probability of a conservative competitive or predator–prey system is concentrated on the boundary under either boundary convention. With nontrivial axis dynamics, coordinatewise continuation admits only the point mass at the origin. For cooperative systems, we give criteria for boundary concentration and interior stationarity, including a sharp criterion for bilinear cooperation with a common relative noise exponent. With immigration, explicit parameter conditions yield existence and stationary moment bounds. For square-root diffusions with positive immigration, these conditions ensure interior concentration and full support on the closed quadrant. Further lower bounds on immigration rates give uniqueness and convergence of time-averaged transition laws.

Amyotrophic lateral sclerosis (ALS) diagnosis remains challenging due to heterogeneous symptoms and reliance on clinical assessment, underscoring the need for objective, data-driven approaches that leverage patient-generated physiological signals. We propose Siam-ALS, an explainable Siamese deep learning framework that jointly models synchronized electroencephalography (EEG) and eye-tracking (ET) signals. EEG captures ALS-related changes in brain activity, while ET provides information about oculomotor control, allowing the model to learn complementary patterns associated with ALS. The framework employs two modality-specific encoders: a convolutional EEG encoder that captures spatiotemporal neural patterns and an MLP-based ET encoder that models oculomotor dynamics. These modality-specific features are processed through weight-sharing Siamese branches and fused into a compact 64-dimensional joint embedding. A lightweight classifier is used to predict ALS, while pairwise metric learning helps the model learn more effective patterns from the small, diverse ALS datasets. Performance was evaluated on the public EEGET-ALS dataset using strict subject-level cross-validation, where Siam-ALS achieved an accuracy of 0.988 and an AUROC of 0.998, demonstrating strong performance compared with classical machine learning, DL, and non-Siamese fusion approaches. Cross-dataset evaluation on the independent BigP3BCI dataset achieved an AUROC of approximately 0.98, supporting the generalization capability of Siam-ALS across different BCI paradigms. To enhance interpretability, six XAI methods were evaluated in the learned embedding space, with SHAP achieving the highest, though statistically comparable, fidelity in identifying important EEG and ET patterns that contribute to ALS predictions. Overall, Siam-ALS provides an accurate, generalizable, and explainable framework for multimodal ALS detection.

We present Gugak-VocalSet, the first publicly available audio dataset for Korean traditional singing with dense annotations of sigimsae, a structured pitch contour system of vocal expressions. Gugak-VocalSet contains 24.5 hours of unaccompanied solo vocal recordings across 305 tracks of representative repertoire curated by the National Gugak Center, performed by 20 professional singers in a controlled studio environment with fixed key and tempo. In addition to genre, lyrics, and mood/timbre tags, the dataset provides a unified sigimsae ontology and approximately 68,000 segments (71,700 instances including multi-label) of audio-grounded sigimsae annotations; the ontology adopts a functional-position-based hierarchy designed for consistent application across genres, and 14 expert annotators specializing in Korean traditional music performed segment-level labeling accordingly. Baseline experiments on sigimsae classification and event detection show that domain-informed F0 representations remain competitive with, and on classification surpass, frozen probing of a general-purpose music foundation model, while pitch and spectral cues play complementary roles in event-level detection. Companion page: https://www.danbinaerin.com/Gugak-VocalSet/

We investigate the metallicity dependence of the tilt of the velocity ellipsoid using more than 572,000 stars selected from GALAH and Gaia. We find that the tilt angles of disk stars can be well described by the relation $\alpha = \alpha_{0}\,\mathrm{arctan}(Z/R)$, and the $\alpha_{0}$ differ significantly among different disk populations, with $\alpha_{0}$ are 0.78 $\pm$ 0.05, 0.86 $\pm$ 0.07, and 0.77 $\pm$ 0.07 for the whole sample, the Low-[$\alpha$/Fe] and the High-[$\alpha$/Fe] populations, respectively. These results indicate that Galactic disk populations are globally tilted toward cylindrical alignment, implying that the gravitational potential of the Galactic baryonic disk plays a dominant role in shaping the kinematics of dynamically relaxed stars. Our detailed analysis further reveals a metallicity dependence of $\alpha_{0}$ for various populations, with the Low-[$\alpha$/Fe] and the High-[$\alpha$/Fe] populations are respectively $\alpha_{0}$ = 0.12 $\mathrm{sin}$(3.72 [Fe/H] + 1.09) + 0.75 and $\alpha_{0}$ = 0.20 $\mathrm{sin}$(2.99 [Fe/H] + 1.90) + 0.71. These results indicate that the metallicity dependence observed in the Low-[$\alpha$/Fe] population may be primarily associated with resonances induced by the Galactic bar, while the behavior of the High-[$\alpha$/Fe] population may also have been affected by additional dynamical and evolutionary processes, such as violent heating associated with mergers, accretion, and/or the formation of these stars in an environment shaped by mergers of gas-rich systems and/or a turbulent ISM.

For a $k$-uniform hypergraph $L$, let $h_L(n,q)$ be the minimum number of copies of $L$ in an $n$-vertex $k$-graph with $\mathrm{ex}(n,L)+q$ edges. Let $t_L(n,q)$ be the minimum number of copies obtained by adding $q$ edges to an extremal $L$-free $k$-graph. A graph is color-critical if deleting a suitable edge decreases its chromatic number. Let $\mathcal K_k(F)$ be the expanded graph obtained by adding $k-2$ new vertices to each edge of $F$, with disjoint sets of new vertices for distinct edges. Mubayi proved that, for every clique $K_r$ with $r\ge4$ and fixed $ q>0$, $ h_{\mathcal K_3(K_r)}(n,q)\ge qt_{\mathcal K_3(K_r)}(n,1)$ for every sufficiently large $n$. Pikhurko and Yilma later proved that, for every color-critical graph $F$, there is a constant $\epsilon_F>0$ such that $h_{F}(n,q)=t_{F}(n,q)$ for every sufficiently large $n$ and $1\le q\le\epsilon_F n$. We extend this equality to expanded color-critical graphs. Let $d>k\ge3$. For every color-critical graph $F$ with $\chi(F)=d+1$, there is a constant $\epsilon>0$ such that $ h_{\mathcal K_k(F)}(n,q)=t_{\mathcal K_k(F)}(n,q)$ for every sufficiently large $n$ and $1\le q\le\epsilon n^{k-1}$. Let $q_L(n)$ be the largest integer $q$ such that $h_L(n,s)=t_L(n,s)$ for every integer $1\le s\le q$. We give a sufficient condition for $q_L(n)=\Theta_L(n^{k-1})$ and an explicit family satisfying it. We also give a different sufficient condition under which $q_L(n)=\Omega_L(n^{k-1/2})$ and an explicit family satisfying it. \noindent Keywords. Supersaturation; extremal graph; color-critical graph; chromatic number; expanded graph; hypergraph.

We investigate set-theoretic solutions of the Yang–Baxter equation from a categorical perspective. The paper has two main objectives. On the one hand, several existing constructions and classification results in the literature are recast in categorical terms, thereby showing that certain hypotheses previously imposed on such solutions are in fact superfluous. On the other hand, the categorical approach leads naturally to new classes of Yang-Baxter solutions. Our approach consists in identifying suitable subcategories of the category $\mathcal{YB}$ of Yang-Baxter solutions and providing categorical characterisations of the solutions they encode. As an application, we prove that the category of Płonka bi-magmas is isomorphic to the subcategory of $\mathcal{YB}$ consisting of solutions of the Baaj-Long-Skandalis equation. Along the way, we introduce and study a new class of Lyubashenko type solutions and examine the extent to which non-degenerate bijective solutions of the braid equation arise from skew left braces.

Programmable hardware typically uses fixed architectures, whereas complex physical systems obtain diverse behavior by connecting reusable local elements through different interaction rules. Memristive devices combine writable states with nonlinear dynamics, but translating these local properties into reconfigurable collective order and symmetry-governed transport remains challenging. Here we develop modular circuits configured through programmable connections between identical memristive units. Experiments establish binary conductance states as Ising-type pseudospins and show that signed feedback between units selects uniform or staggered pseudospin order. Circuit-model simulations then examine controllable domain-wall motion and pattern recovery. A symmetry encoder combines measured conductance patterns with sublattice labels and a selected symmetry rule to configure a fixed transport layer, implementing circuit analogs of ferromagnetic, antiferromagnetic, and altermagnetic transport symmetries. Although the antiferromagnetic and altermagnetic encodings share a compensated pattern, their distinct voltage spreading illustrates how programmed circuit symmetry affects transport. Device-calibrated simulations show that memristive dynamics generates history-dependent features for reservoir computing. By separating local memory from programmable interactions, symmetry encoding and task-specific readout, this architecture provides a modular route from device dynamics to collective order, symmetry-dependent transport, and learning.

High-quality coding problems are expensive to collect. Benchmarks such as SWE-bench rely on substantial human curation, while synthetic alternatives typically rely on costly model generation and validation. In this work, we show that new coding problems can be created at almost no cost by composing existing ones. We formulate problem generation as code composition: verified atomic problems are combined into level-$N$ tasks, and a task is kept only if every atomic problem remains unsolved and a joint reference solution passes the same check used at evaluation time. The entire task-construction process is programmatic and requires no language-model generation or validation. We instantiate this approach in four coding settings: multi-bug repair, proof completion, complexity analysis, and clone equivalence. The generated tasks are challenging for frontier models, which all degrade as compositional depth increases. The generated tasks are also useful as training data: rejection-sampling fine-tuning on them improves Qwen3.5-9B at every composition level.

We introduce and study trigonometric weight functions of type $B$ and type $C$ arising from integrable lattice models. These functions give $q$-deformations of the factorial $K$-theoretic Schur $P$- and $Q$-functions of Ikeda and Naruse, with the $P$-functions specialized to the type $B$ case. We realize them as specializations of partition functions of a six-vertex model with triangular boundary conditions and derive their algebraic properties using the Yang-Baxter equation and properties of the $R$- and $K$-matrices. We introduce normalized weight functions and establish diagonal evaluation formulas, divisibility properties, and bounds on Newton polytopes analogous to those in type $A$, together with recursive relations and stability. We further derive branching formulas relating these functions to type $A$ weight functions, and prove equal-cardinality orthogonality and all-cardinality biorthogonality relations.

World models and video understanding models are increasingly deployed in dynamic visual environments, yet their robustness to physical adversarial threats remains largely underexplored. We study whether a single physical adversarial texture can mislead the victim model across different real-world scenarios where observing viewpoints vary along uncontrolled object–camera trajectories. We identify that heterogeneous video semantics and trajectories induce poorly aligned gradients for optimizing the adversarial texture. To address that, we propose the Trajectory-aware adversarial Alignment and Refinement Attack (TARA), which incorporates trajectory-aware optimization to capture the evolving geometric variations of a printed texture under real-world scenarios. To improve cross-instance optimization compatibility, TARA incorporates trajectory-aware contrastive alignment to encourage attacked representations from diverse video–trajectory instances to approach a shared adversarial region and then performs trajectory-aware task refinement to translate the aligned representation into task-level prediction errors. For reproducible evaluation, we develop a geometry-grounded tracking pipeline that provides physically plausible adversarial regions with temporally consistent trajectories on EPIC-KITCHENS-100 and Something-Something V2. We further collect real-world print-and-recapture videos to validate attack effectiveness under physical deployment conditions. Together, the annotated benchmarks and real-world captured data form a reproducible testbed for future evaluation. Notably, our results reveal that a single printable adversarial texture can persistently disrupt world models and video understanding models under physical conditions, highlighting the fundamental security challenge.

Open-vocabulary audio-visual event localization aims to infer explicit segment-level categories for both seen and unseen audio-visual events. Existing solutions rely heavily on hand-crafted prompt templates, whose predictions are highly sensitive to subtle wording variations. Learnable prompts remove this manual tuning burden, but when trained solely on seen events, they tend to overfit to seen categories and distort the inter-event semantic topology required for generalization to unseen categories, a failure we term semantic topology drift. In this paper, we propose SIMPLE, a semantic structure-aligned prompt learning framework that aligns cross-category semantic topology between learnable and hand-crafted prompts across asynchronous audio and visual streams. Specifically, our SIMPLE combines Learnable Continuous Prompt Tuning (LCPT) with Semantic Topology Consistency Regularization (STCR). The LCPT automates prompt engineering through data-driven optimization, while the STCR module aligns the category-wise similarity distributions of learnable and hand-crafted prompts under random category subset sampling to alleviate semantic topology drift. Comprehensive experiments and analyses on the OV-AVEBench demonstrate that our SIMPLE framework achieves state-of-the-art performance on the seen and unseen splits, while using roughly half the trainable parameters and roughly one-third the training time.

The inherent variability of fMRI responses across trials encourages a generative view of the stimulus-to-response mapping. Prior generative encoders often operate in compressed latent spaces and condition predominantly on semantic features, which provide limited low-level cues for early visual cortex. We propose StimFlow, which synthesizes fMRI directly in native voxel space using conditional flow matching with a linear path. This design aligns training and inference distributions, enabling competitive performance with a single sample and reducing reliance on averaging. To match the visual hierarchy, StimFlow combines structural DINOv2 features with semantic CLIP features, which prove complementary along the cortical processing stream. With a single sample, StimFlow achieves a per-voxel Pearson correlation of 0.371, matching baselines that average five draws. Generation in voxel space allows direct ROI analysis and concept localization without a decoder. Furthermore, it recovers over half of full-data performance from just one hour of scans, supporting efficient cross-subject adaptation.

Let $G$ be a finite $2$-transitive permutation group. We determine the orbits of $G$ on the unordered triples of its point set, together with the three-point stabilizer and its image inside $S_3$, for every affine and almost simple family in the finite $2$-transitive classification. These data classify the $G$-invariant triple systems and the simple $2$-\mbox{$(v,3,\lambda)$} designs admitting $G$, and yield in a uniform way the standard objects attached to them: the incidence and block graphs (with arc-transitivity and strong regularity in the Steiner case), the constant-weight and design codes, and the Schurian coherent configurations on triples.

Current fMRI encoding models frame prediction as deterministic regression, yet identical stimuli evoke a distribution of neural responses (arising from physiological noise, hemodynamic variability, and cognitive fluctuations) that a single point estimate cannot capture. This work introduces MultiFlow, a generative fMRI encoding framework based on Conditional Flow Matching (CFM) and a formulation termed Stimulus-Informed Source Flow Matching (SISFM). SISFM generalises CFM by conditioning the source distribution on the stimulus: a learnable temporal convolution shapes the source mean with an HRF-length receptive field, while a variance head shrinks its scale, shortening the expected transport path. SISFM is instantiated with a Diffusion Transformer (DiT-X) decoder parameterising the velocity field, with sub-layer Attention Residuals, heterogeneous fusion of ten frozen vision, audio, language, and audiovisual backbones, and per-subject Yeo-network heads. On the Algonauts 2025 dataset, a single MultiFlow checkpoint recovers most of the benefit of large deterministic ensembles: it trails the 1000-model TRIBE ensemble in-distribution by 0.003 PCC (0.3163 vs. 0.3195), and the strongest in- and out-of-distribution ensembles (VIBE-20, MedARC-50) by 0.010 and 0.009 PCC, using a single trained model rather than an ensemble of 20-1000. The same checkpoint also provides stimulus-conditioned uncertainty estimates and sample-based diversity.

Semantic sensing extends integrated sensing and communication (ISAC) beyond physical parameter estimation by exploiting task-oriented representations from radio echoes. Nevertheless, existing multimodal sensing remains largely limited to vision-assisted radio physical parameter estimation or typically processes the visual and radio modalities separately, leaving radio representations underutilized for visual task enhancement. Feature-level fusion enables closer cross-modal interaction, while echo interference complicates the learning of user-specific radio representations and its semantic consistency with the visual entities. To address these challenges, this paper proposes a multimodal semantic sensing framework for orthogonal frequency-division multiplexing (OFDM)-ISAC systems. We propose a radio encoder to learn radio representations oriented toward visual localization from superimposed pilot echoes, together with Variational Radio-Visual Grounding (VRVG) to promote semantic consistency between the learned radio representations and visual spatial features. The radio representations are then formulated as semantic probes to highlight the corresponding entities in the visual scene through cross-modal fusion. Experiments using real-world RCooper dataset show that the resulting synergistic radio-visual embeddings enable accurate radio-visual user matching and significantly improve both user-specific visual localization and physical parameter estimation performance. The results substantiate the benefits of radio representation learning and semantically consistent fusion for multimodal semantic sensing.

Vision-Language-Action (VLA) models are typically deployed as isolated single-agent policies. When several such agents share a workspace, they can coordinate implicitly, by observing one another, or explicitly, by exchanging messages, but it remains unclear when explicit communication becomes necessary. We introduce CoLA (Coordination via Learned Adapters), which keeps each agent's VLA backbone frozen and trains a lightweight message channel and a per-arm diffusion action head on top, with fully decentralised execution. Across three tasks that differ in how much each agent can observe, the channel matters only when information is private. On an occluded tray handover, where the box's colour marker is visible to one agent only, CoLA reaches 76.0% success versus 1.3% with messages zeroed throughout training. On two-arm and three-arm handover tasks, removing messages has no measurable effect with a shared overhead camera (90.6% vs. 88.3% at two arms; 63.5% vs. 60.0% at three), but lowers success on the two-arm task's wrist-only variant (74.8% vs. 64.3%). This architecture generalises across different VLA backbones as well. With a frozen $\pi_{0.5}$ backbone on the same occluded tray task, CoLA matches the overall success rate of a LoRA-fine-tuned baseline (37.3% vs. 34.7%) using a fraction of the trainable parameters. When CoLA places the box, it selects the correct tray 71.8% of the time, whereas the independently fine-tuned baseline, whose placing arm never sees the marker, selects it at chance level (34.7% against 33.3%).

Influence functions enable principled data selection for large language models (e.g., identifying influential training samples for model editing, debugging, or efficient fine-tuning). However, scaling IFs to LLMs is hindered by the intractability of billion-scale Hessian matrices and the prohibitive memory overhead of backpropagation (BP). While many classical IF approximations reduce Hessian complexity, they still rely on BP for gradient computation, requiring massive storage for intermediate activations that impedes practical data selection at scale. To address this, we propose ZOIF, a zeroth-order framework for influence estimation that operates entirely via forward passes, enabling memory-efficient data selection under resource constraints. ZOIF decomposes influence estimation into three BP-free stages: (1) approximating the average proxy gradient via zeroth-order estimation; (2) reformulating and solving the inverse Hessian-vector product as an auxiliary zeroth-order optimization to bypass explicit inversion; and (3) deriving per-sample influence scores via a forward finite difference along the previously computed parameter update direction. Experiments show that ZOIF selects data subsets with downstream utility competitive with, and in some cases exceeding, the evaluated baselines, yet at substantially lower peak memory cost and with comparable overall computation time.

The cyclic steepest descent method computes the exact steepest descent stepsize at the start of each cycle and reuses it for a fixed number $m\ge2$ of iterations. We study this method for strictly convex quadratics whose Hessian has exactly two distinct eigenvalues, of arbitrary multiplicities, and determine its behavior from every initial point. At the minimizer no update is needed. For nonoptimal initializations, a gradient in one eigenspace gives one-step termination. If both eigenspace components are nonzero and have equal norm, the stepsize never changes and the error contracts by the same constant factor at every iteration. In the remaining case, both components are nonzero and unequal in norm, and the method converges doubly exponentially and hence $R$-superlinearly. Thus $R$-superlinear convergence fails exactly on an explicit cone of initial points of measure zero. The proof reduces the method to an exact scalar recurrence for the ratio of the two eigenspace components at the start of each cycle. We also determine the leading term of the logarithm of the error at every iteration within a cycle, which identifies the exact exponent of the doubly exponential decay and shows that this convergence is not $Q$-superlinear.

In nature, animals interact with complex terrains and often generate forces, deformations, and vibrations across the body and environment. Such interaction-induced mechanical information may guide behavior, yet its generation and use are difficult to resolve because movement rapidly and continually reconfigures the interactions that produce it. Sensory neurophysiology and biomechanics have revealed how mechanical information is transformed within sensory, neural, and musculoskeletal subsystems, whereas studies in complex terrains reveal rich whole-body interactions and behavioral outcomes. Connecting these levels remains a challenge. Here, I present a focused perspective on how biologically guided robotic physical models can help identify candidate mechanical information generated through whole-body interactions, test its physical mechanisms and behavioral benefits, and generate biological hypotheses. Three case studies illustrate this approach, multi-legged locomotor transitions to traverse dense clutter, limbless vertical body bending to propel through uneven terrain, and rapid spider leg crouching to help vibration sensing of prey on a web. Across these systems, correspondence between robots and animals supports the biological plausibility of these candidate physical mechanisms and motivates better measurements and models to determine how the relevant mechanical information is sensed and used to modulate behavior.