Papers

An answer judge instructed to grade the final commitment should reject an explicitly wrong final value even when an earlier value matches the reference. We show that adding one colon to a candidate can violate this requirement depending on the presentation of the structured judging request. Numeric references certify the error, and paired interventions distinguish the candidate edit from the integration's presentation choices. On 200 previously unused DROP and GSM8K source clusters, the edit increased Jev's false acceptance from 1.0% to 26.0% with three output labels and from 3.0% to 26.5% with the published four-label grading instruction under sorted JSON keys. Both candidate variants were rejected under insertion presentation. These interactions passed the prespecified statistical correction even though Jev met the control thresholds under both grading configurations and presentations. Most excess acceptances occurred among candidates assigned larger numerical errors. GPT-6 Sol produced no observed cue-condition false acceptances, with missing responses unresolved. The result shows that basic judging competence can coexist with sharply different vulnerability to a fixed candidate edit across logically equivalent request presentations. The reference-aware grammar and compound ordering change limit the finding's operational scope and leave its internal cause unmeasured.

The cooling of neutron stars (NSs) provides insight into their composition and equation of state. However, a complete understanding of this phenomenon is still an open question. The early stage of NS cooling is dominated by neutrino emission from the core, which rapidly cools the star. Urca processes are one such mechanism where neutrinos escape from the core, carrying away most of the heat. Nucleonic and hyperonic direct Urca processes are known rapid cooling mechanisms. The possible appearance of $\Delta$ baryons in dense matter introduces additional weak-interaction channels, including $\Delta$ direct Urca processes. Although such processes have been discussed in the context of $\Delta$-admixed NS matter, their neutrino emissivities and impact on NS cooling have not been systematically investigated. In this work, for the first time we incorporate the neutrino emissivities of the relevant $\Delta$ direct Urca processes into NS cooling simulations. We investigate the thermal evolution of $\Delta$-admixed NSs and assess the impact of these additional neutrino emission channels on their cooling behavior. We find that $\Delta$ direct Urca processes can provide an efficient neutrino-cooling mechanism and significantly accelerate the thermal evolution of NSs. Our results demonstrate that $\Delta$ baryons and their associated weak-interaction processes can play an important role in explaining NSs with unusually low surface temperatures and provide a new connection between the composition of dense matter and NS cooling observations.

The emerging low-altitude economy demands unmanned aerial vehicle (UAV)-enabled integrated sensing and communication (ISAC) for reliable connectivity and environmental awareness. In particular, embodied UAV agents offer a promising means of supporting autonomous operations through a closed loop linking perception, decision-making, and physical actions. However, each UAV has access only to local observations, and effective cooperation requires exchanging local states and intentions. Directly sharing such information can incur substantial signaling overhead and hinder timely coordination in dynamic environments. To deal with this problem, this paper investigates a cooperative ISAC network of embodied UAV agents and formulates a joint token communications (TokCom) and physical control problem to minimize total propulsion energy subject to communication and sensing rate requirements. Then, we propose a state–intent TokCom (SI-TokCom) framework driven by multi-agent embodied policy learning. Specifically, separate pretrained codebooks enable compact exchanges of local states and intentions, while UAV agents jointly learn to select and compose tokens and determine physical actions based on local observations and received tokens. Simulation results show that SI-TokCom achieves 98.9% and 99.1% of the centralized baseline's communication and sensing rates, respectively. Compared with the local baseline, it improves the corresponding rates by 5.0% and 43.6%, respectively, with essentially unchanged propulsion energy. These results highlight the potential of TokCom for communication-efficient cooperation among embodied UAV agents in ISAC systems.

In this paper, we introduce a metric-guided dynamic loss controller (DLC) for multi-objective image restoration. Conventional image restoration pipelines usually train with a fixed weighted combination of multiple losses, without changing the relative importance of fidelity, perceptual similarity, and no-reference quality during optimization. DLC is an architecture- and loss-term-agnostic training-time controller: it does not modify the restoration architecture or introduce new differentiable loss terms, but dynamically reweights the existing training losses. During training, DLC periodically evaluates the current model on a small fixed feedback subset and uses the resulting quality metrics to update the loss-weight vector through an LLM-based controller. Because DLC operates on existing loss terms rather than task-specific architectures, the same controller formulation can be instantiated across diverse image restoration training pipelines. We evaluate DLC on three restoration domains: low-light image enhancement, deraining, and real-world super-resolution, using both reference-based and no-reference quality metrics. Across these settings, DLC considers metric-dependent trade-offs during optimization and guides training toward balanced operating points across fidelity and perceptual quality. The results show that DLC can move models toward more favorable operating points across different restoration domains, supporting its role as a practical plug-in controller for multi-objective image restoration.

We study randomized nonuniform polynomial-size transformations that output explicit binary affine filters for circuit inputs whose nonempty satisfying sets are affine. The filter may depend on the entire input description; no affine basis is supplied. For every fixed $\delta<1$, a worst-case singleton success guarantee $\Omega(n^{-\delta})$, where $n$ is the witness arity, implies $NP\subseteq P/poly$. More generally, any success guarantee $\omega(\log n/n)$ yields satisfiability circuits of size $(s+2)^{O(1)}2^{o(v)}$ for length-$s$ descriptions with at most $v$ witness variables, hence subexponential in $v$ when $s=v^{O(1)}$. Conversely, SAT search-to-decision gives deterministic perfect isolation, making polynomial-resource fixed-exponent strong affine isolation equivalent to $NP\subseteq P/poly$. For explicit unions of at most $n^\beta$ affine components, success $\Omega(n^{-\delta})$ implies the same collapse whenever $\beta,\delta\ge0$ and $\beta+\delta<1$. The inverse-linear endpoint is not claimed.

Motion estimation in echocardiography is essential for quantitative assessment of cardiac function and myocardial mechanics, but remains challenging due to image artifacts, limited image information, speckle decorrelation, and the scarcity of ground-truth displacement fields. Anatomy-guided approaches can provide structural information, yet often rely on expert-labeled myocardial segmentations. We propose EchoDiST, a framework for unsupervised echocardiographic myocardial motion estimation that integrates self-distillation-based joint learning with a diffusion-conditioned motion estimation network. Here, unsupervised motion estimation refers to learning without ground-truth displacement fields. The self-distillation strategy jointly optimizes anatomical segmentation and myocardial motion estimation under limited anatomical annotations. Diffusion-based conditioning is used during training with stochastic perturbations, while inference requires only a single deterministic forward pass without iterative reverse-diffusion sampling. EchoDiST was evaluated on three echocardiographic datasets, including two external test datasets under cross-view and cross-dataset settings. Compared with seven representative learning-based methods, EchoDiST consistently improved anatomical alignment, myocardial strain assessment, and motion-derived functional and cardiac-phase assessment. These gains were statistically significant across the evaluated tasks and datasets. Overall, EchoDiST provides an effective approach for reliable myocardial motion estimation under limited anatomical supervision and supports downstream quantitative assessment of cardiac function.

While domain-specific Large Language Models (LLMs) have encoded vast biomedical knowledge, their limited context windows often hinder a deep understanding of nuanced relationships within and across texts. To address this limitation, we introduce BioBigBird, a bidirectional language model pre-trained on extensive biomedical literature and clinical data, specifically designed to handle long-range dependencies. BioBigBird leverages a sparse attention mechanism to process sequences up to 4096 tokens, and its training incorporates a multi-stage process to mitigate noise from the large-scale pre-training corpus. We further enhance its performance by employing a multi-task learning (MTL) framework that jointly optimizes for Named Entity Recognition and Relation Extraction. Comprehensive evaluations on the BLURB benchmark reveal that our MTL-enhanced BioBigBird achieves highly competitive results against state-of-the-art models. Our work contributes an effective methodology for developing powerful, long-context language models for specialized domains, demonstrating the value of extended sequence processing for complex text analysis. Our models are publicly available at https://huggingface.co/collections/bisectgroup/biobigbird.

We present the radio-astro-tools code suite, which consists of several Python packages that enable analysis of radio data, especially interferometric spectral cubes, in the context of the Astropy software ecosystem. While these tools were designed with radio data in mind, they are built to be general and have applications on data sets at other wavelengths. The core package, spectral-cube, handles reading, writing and analysis of cube data, and it enables straightforward parallelization via dask and joblib backends. Support packages include casa-formats-io and radio-beam, which handle reading of CASA tables & images and reading and manipulation of point spread functions, respectively. The pvextractor package facilitates creation of position-velocity diagrams. The uvcombine package implements the "feather" algorithm for combining single-dish and interferometric data. The development of radio-astro-tools included several contributions to other repositories, including matplotlib, astropy, and regions to support interaction between CASA and other parts of the astronomy software ecosystem. We also present a detailed set of tutorials written in Jupyter notebooks that can be run interactively in a browser, providing more accessible access to data analysis for radio spectral-line data cubes.

Quantum key distribution (QKD) promises theoretically secure communication. However, it encounters challenges in implementation security and performance due to inevitable device imperfections. Since the proposal of measurement-device-independent (MDI) QKD, the critical step toward practical security is to secure QKD with imperfect sources. The source imperfections manifest as state-preparation uncertainty (SPU) in various aspects, e.g., encoding uncertainty, intensity fluctuation, and imperfect vacuum states. Here, we perform an MDI-QKD experiment and achieve both high practical security and superior performance. We address the general form of SPU and guarantee a tight estimation of the secret key rate based on the operator dominance method. We achieve secure key distribution over 303.37 km, which not only represents the farthest distance in experiments involving SPU but also considers the most SPU scenarios. Our experimental results represent a significant step toward promoting practical and secure quantum communication.

We study the quantized $K$-theoretic Coulomb branches of framed star-shaped quivers with central gauge dimension $n\geq2$, $r-1$ one-dimensional outer gauge vertices, and a one-dimensional framing at the central vertex. For $n=2$ and arbitrary $r\geq1$, and for every $n\geq2$ with $1\leq r\leq5$, we prove that the loop-graded Koszul-perverse heart is a monoidal categorification of the associated quantum cluster algebra over $\mathbb{Z}[v^{\pm1}]$. This quantum cluster algebra coincides with its upper quantum cluster algebra. For all $n\geq2$ and $r\geq1$, we construct an explicit initial seed and identify the associated upper quantum cluster algebra with the Grothendieck ring of this heart. Every mutation is realized by a short exact sequence, and every quantum cluster monomial is represented by a simple object.

Addario-Berry, Reed, Scott, and Wood (JoCG 2026) proved that the $n$-dimensional associahedron has chromatic number at most $22500\cdot\log_3 n+O(1)$. We present a much simpler proof that the chromatic number of the $n-1$-dimensional associahedron is at most $6 \log_2 n + 18$. Since this paper's appearance as a preliminary abstract in the Japan Conference on Discrete and Computational Geometry, Graphs, and Games held from September 7-10, 2026, the bound has been improved to $O(\log \log n)$ by Oum and Wood (arXiv September 30, 2026). It is hoped that the simple method here could give insights to further improvements.

This paper studies time-varying composite optimization problems with convex but not necessarily strongly convex objective functions, on compact domains and with bounded temporal variability. As a baseline, we first analyze the time-varying proximal gradient (TV-PG) method. We show that its asymptotic function value gap is bounded by $O(\delta^{1/2})$ as $\delta\to0$, where $\delta$ measures the temporal variability of the objective function. This dependence on $\delta$ is tight in the worst case for TV-PG. Our main contribution is a time-varying accelerated proximal gradient method that improves the asymptotic upper bound on the function value gap to $O(\delta^{2/3})$. The method builds on a novel acceleration scheme whose momentum parameter is determined by the current iterates, with no explicit dependence on the iteration index. We establish the bounds for both the baseline and accelerated methods through a unified analysis based on potential functions. Numerical experiments on a synthetic problem and autoregression problems with real-world datasets demonstrate the tracking performance of the proposed algorithm.

In our book Why machines will never rule the world [13, 14] we argue that arti- ficial general intelligence is mathematically impossible. This is because the human beings and the processes which exhibit intelligence are complex systems whose be- haviour cannot be captured by the kinds of models that we can generate with or without computers. Proponents of contemporary machine intelligence respond with two lines of argument: a theoretical one, grounded in the universal approximation theorems for neural networks and the Church-Turing-Deutsch principle; and an em- pirical one, grounded in rapidly rising scores on standardized benchmarks. In this communication we examine and reject both responses. First, we show serious issues in the physicalist counter-argument based on the Church-Turing-Deutsch principle. Second, we review recent evidence to the effect that prominent benchmarks are compromised by training-data contamination, flawed test construction, and strate- gic optimization. Our central argument remains: That models required to perform cognitive behaviour in open-ended, thermodynamically complex and non-ergodic environments are not and will not become achievable.

On-policy distillation (OPD) trains a student model by aligning its policy with a teacher model on trajectories generated by the student model itself. Through this process, the student policy moves toward the teacher on the prompts used for distillation. However, these prompts are often private and costly, creating a need for prompt-level membership auditing. Existing methods mainly rely on likelihood-based confidence signals or student policy drift between checkpoints, but they do not capture the teacher-induced direction of the student update. In this paper, we propose Policy Alignment Membership Auditing (PAMA), a new auditing framework tailored for OPD. Our key observation is that a member prompt directly contributes to the teacher-guided policy update, while a non-member prompt only experiences indirect effects through cross-prompt generalization. Based on this directional trace, PAMA measures whether the student update moves toward reducing the teacher loss on a candidate prompt. Specifically, we introduce Teacher Alignment Gain (TAG) to estimate the teacher-aligned update direction from model outputs, and further combine it with student drift and uncertainty alignment signals for reliable membership auditing. We evaluate PAMA on six datasets and three teacher-student model families. On MATH, the primary evaluation benchmark, PAMA achieves AUC values of 0.791–0.941, improving AUC by 14.6–20.6% over state-of-the-art baselines.

Many dynamical systems generate influences whose consequences are not fully exhausted in the realized trajectory at the moment they arise. Such consequences are often treated as absent, delayed or statically stored, leaving unclear how unrealized influence retains future relevance as the system evolves. Here we formulate causal-fate dynamics, in which generated influence may be realized, remain latent, or be transformed by subsequent dynamics, and give an exact finite-transport representation when the relevant maps are specified. A connectome-constrained Caenorhabditis elegans model first motivates the biological hypothesis that unresolved inter-neuronal influence may persist and contribute to later propagation; it does not establish such a mechanism in living animals. We next examine operational Internet routing, where a dynamically updated cross-observer history retains predictive information beyond the current local route state. We then use the representation to construct a Transformer architecture that explicitly transports and selectively realizes latent contextual influence while retaining language-modeling function. The three studies distinguish a model-motivated scientific hypothesis, an observational phenomenon compatible with future-relevant history and an executable construction for carrying unrealized influence through subsequent computation.

The transient response of surface acoustic wave sensors is important for understanding their dynamic behavior, propagation delay, and response to time-varying signals. In this work, the time-domain propagation characteristics of a magnetoelectric SAW sensor based on a multilayer Love-wave delay line are investigated using complementary numerical and experimental approaches. Time-domain analysis is employed to determine the delay time and to extract the phase and group velocities, while frequency-domain analysis provides an independent characterization of the wave dispersion. Both numerically and experimentally, the phase and group velocities are found to differ, reflecting the dispersion of the Love wave in the multilayer structure. At the operating frequency of 146 MHz, the simulated group velocity obtained from wave-field tracking agrees within 0.4% with the value determined from the frequency-domain dispersion relation. The simulated delay time and group velocity also show good agreement with experiment, with deviations of 2.7% in delay time and 0.9% in group velocity. These results demonstrate the consistency of the time- and frequency-domain analyses and provide a quantitative characterization of the transient propagation behavior of SAW sensors.

Optical sub-diffraction imaging has become an essential tool in modern research. Recently, a new imaging strategy has been demonstrated that exploits the strongly nonlinear excitation-emission response of rare-earth-doped nanocrystals operating in the photon avalanche (PA) regime. This approach benefits from simple optical instrumentation, near-infrared excitation and emission, low cytotoxicity, and high photostability. However, its practical implementation is hindered by relatively high (10-100s of kW/cm2) excitation power densities required to initiate the PA process. We aim to mitigate this limitation through electromagnetic field enhancement provided by metallic nanostructures. The results of microscopic studies of individual photon-avalanching nanocrystals coupled to a silver island film demonstrate a greater than tenfold reduction in the excitation power density required to trigger the avalanche emission. These experimental results, corroborated by numerical modelling, which elucidates the role of plasmon-mediated electromagnetic field enhancement in modifying the photon avalanche dynamics, paves the way towards new generation of low excitation power probes for sub-diffraction imaging and sensing.

Multimodal brain tumor segmentation typically leverages multiple MRI modalities, yet incomplete modality acquisition is common in clinical practice due to protocol heterogeneity and scan failures. Although recent methods maintain segmentation accuracy under missing modality conditions, they frequently overlook prediction reliability, leading to miscalibrated confidence estimates that hinder clinical adoption. Existing calibration techniques are largely modality-agnostic or assume that prediction difficulty decreases monotonically as additional modalities become available. However, in brain tumor segmentation, prediction difficulty depends primarily on which modalities are absent rather than how many, leading to combination-specific and spatially heterogeneous calibration errors. To address this, we propose Missing Modality-Aware Local Temperature Scaling (MMA-LTS), a post-hoc voxel-wise confidence calibration method. It estimates a spatially adaptive temperature field conditioned on a modality-availability learnable token and a voxel-wise difficulty score. Experiments on BraTS 2020 and FeTS 2024 show that MMA-LTS improves calibration while preserving the segmentation accuracy of state-of-the-art models across diverse missing-modality scenarios, thereby enhancing trustworthiness toward clinical deployment.

Deploying frozen learned skills, such as Vision-Language-Action (VLA) policies, in new environments requires identifying initiation configurations that support reliable execution. In skill composition, an initiation configuration affects not only the current skill but also the physical state passed to subsequent skills, so successful execution of an individual skill does not necessarily imply successful completion of the composed task. Estimating target-specific capability through extensive rollouts is costly in real-world deployment, while directly reusing historical experience can be unreliable under environment changes. We propose EVIS, an Experience-Guided and Behavior-Validated Initiation Search framework for discovering reliable initiation configurations under limited target interaction. EVIS uses historical execution experience to prioritize promising candidates and target-environment behavior to validate whether they remain effective. We evaluate EVIS on single-skill and two-stage manipulation tasks with frozen VLA policies. EVIS reduces mean target-environment queries and improves reliable candidate discovery under small interaction budgets. These results show that combining historical guidance with target-side behavioral validation can reduce the interaction cost of deploying frozen learned skills in new environments.

In this paper, we first construct a universal quasi-Polish space Y with the property that every quasi-Polish space is homeomorphic to a closed subspace of Y. This gives a hyperspace F(Y) of all quasi-Polish spaces which is itself a quasi-Polish space. We then prove that the collection of all Polish closed subspaces of Y forms a coanalytic, non-Borel subset of F(Y). In particular, this collection is {\Pi}11-complete.

Vision-Language-Action (VLA) models have emerged as a prominent framework for complex robotic manipulation, building on the strong semantic understanding of pretrained Vision-Language Models (VLMs). However, such VLM backbones offer insufficient physical dynamics priors, which limits the generalization capabilities of robot policies. Recent efforts therefore integrate video-generation World Models (WMs) into robot policies through various strategies, using predictive dynamics to facilitate action generation. Despite these advances, harnessing semantic understanding and dynamics prediction as complementary guidance for action generation remains challenging. In this paper, we introduce $\mathrm{ACT}^3$, a simple yet effective Action-Centric Tri-Stream Transformer that fuses semantic and dynamics information into control actions while preserving the distinct roles of context streams. Specifically, $\mathrm{ACT}^3$ enables the dedicated action expert to access VLM and WM representations through layerwise attention, with each backbone attending only within its own stream. This straightforward interaction design maintains independent forward propagation in the context streams while allowing both backbones to be updated through control supervision. Experiments on both simulated and real-world robotic manipulation benchmarks show that the proposed $\mathrm{ACT}^3$ yields results superior to its counterparts.

Prediction aggregation aims to combine information from multiple predictors into a more informative one. We study this question in the setting of calibrated predictors, where each prediction must equal the conditional expectation of the quantity being predicted given the predictor's signal. Given several calibrated input predictors and the feature distribution, but not the underlying Bayes probabilities, we ask when one can construct refined calibrated predictors that preserve the information in the original predictors and cannot be further refined using the available information. We formulate calibrated predictors as signaling schemes and define refinement through feature-independent garblings: a predictor refines another if its signal can simulate the other's signal. Constructibility is characterized through observable linear information: each signal corresponds to a vector over the feature space, and a new signal is constructible exactly when its vector lies in the linear span of the input signal vectors. Under this formulation, we establish a sharp algorithmic picture. For deterministic output predictors, bilateral refinement admits a polynomial-time algorithm based on a bipartite graph between the two input signal partitions, while refinement with an arbitrary number of input predictors is $\mathsf{NP}$-hard. In contrast, when randomized output predictors are allowed, we give a polynomial-time algorithm for any number of input predictors by decomposing constructible signal vectors into extreme rays of the associated polyhedral cone.

Many automatically focusing algorithms for scanning electron microscopes exist. Typically, these optimize a single derived metric (such as image sharpness) without considering the intrinsic beam shape. We describe an algorithm to automatically focus and stigmate scanning electron microscopes based on the autocorrelation of captured images. In the first part of this work, we develop the theoretical basis of using the autocorrelation to approximate the current beam shape. In the second part, we use this to condition the beam shape on various surfaces, using Bayesian optimization to tune both working distance and, in particular, stigmation. Through a comparison of the full width at half maximum of the autocorrelation arrays before and after optimization and a visual comparison of images taken of the sample surface before and after optimization, we show that the algorithm is able to successfully optimize the scanning parameters. Overall, our algorithm can effectively focus on a variety of topographies at different magnifications.

We report the experimental and numerical demonstration of stimulated Brillouin scattering-induced stabilization of Kerr-driven modulation instability in fiber Fabry–Perot resonators. We show that Brillouin scattering shapes the modulation instability spectrum into a stable multi–free-spectral-range cascade that is otherwise unstable in the absence of Brillouin effects. We further identify that this stabilization originates from the real part of the Brillouin response, leading to an asymmetric Kerr-Brillouin interaction governed by the relative position of the Brillouin frequency shift with respect to the cavity resonances. These results establish stimulated Brillouin scattering as an additional degree of freedom for controlling nonlinear dynamics in Kerr resonators.

We propose Fresco++, a unified optimization framework for fine-grained and view-consistent head avatar reconstruction. Head avatar optimization is typically driven by per-view image supervision, which can lead to premature fitting of unstable high-frequency details and inconsistent local appearance across viewpoints. Fresco++ addresses these challenges by regulating both the progression of visual detail and the formation of cross-view supervision during optimization. For frequency-aware optimization, a progressive curriculum first stabilizes low-frequency structures and then introduces high-frequency constraints to recover fine facial and hair details without amplifying spurious responses at early stages. For cross-view optimization, we introduce Canonical Group Consensus, which associates local observations through shared canonical surface regions and establishes correspondence across different viewpoints. Geometric and visibility-aware screening removes unreliable observations, while the remaining multi-view evidence is aggregated in feature space to form a consensus target for supervising the current rendering. This design enforces local consistency without relying on a specific image-space parameterization and avoids additional rendering of the auxiliary view. Together, the frequency curriculum and canonical consensus provide stable optimization from coarse structures to fine details while maintaining coherent appearance across viewpoints. Extensive experiments on NeRSemble demonstrate improved reconstruction quality and cross-view consistency, while evaluations across diverse avatar representations further confirm the generality and transferability of Fresco++.

Quantum annealing must be sufficiently slow to prevent defect formation. We study this problem in the random transverse-field Ising model via the adiabatic theorem to obtain the limiting rate at which defect formation can be avoided. Our approach based on the strong-disorder renormalization group (SDRG) technique views the annealing process as a gradual aggregation of strongly coupled clusters, giving access to the elementary events of error formation. We present a scaling theory of the statistics of these events in general dimensions and confront it to an extensive numerical analysis carried out in one, two, and three dimensions by an efficient implementation of the SDRG method. This approach is also validated by exact diagonalization in one dimension by means of the free-fermion technique. Our results consistently show a logarithmically slow decrease of the error density with the annealing time, characterized by the dimension-dependent critical exponents of the corresponding infinite-disorder fixed point of the model. Furthermore, we provide a map of individual events of potential defect formation in the excitation energy - control parameter plane, which may help in the design of optimal annealing paths.

Affective computing has progressed from categorical emotion recognition to open-ended affective analysis with large multimodal models. Yet affective science describes emotion as an unfolding process shaped by appraisal, regulation, and social interpretation, which remains underexplored computationally. We propose TRACE, a cognition-oriented framework that formalizes an affective episode through three interrelated stages: Condition, Affect, and Effect, integrating observable cues with cognitive factors such as internal stance and regulation of emotional display. Based on this formulation, TRACE-Bench evaluates multimodal models in real-world social scenes through five tasks spanning grounded affect recognition, regulation decoding, cause reasoning, effect reasoning, and full-chain reconstruction, with 3,746 structured question-answer pairs over 646 videos. A matched human-model comparison reveals a substantial performance gap, while affect-specialized models also generally lag behind general-purpose MLLMs. Model outputs show recurring failures, including treating displayed behavior as genuine feeling and fabricating unsupported events during long-chain generation. We further propose TRACER, a cognition-grounded structured reasoning method that couples each inference with explicit premises from factual observations, cognitive appraisals, and established upstream conclusions, forming a traceable graph of intermediate and target conclusions. TRACER outperforms all evaluated model baselines on each of the five tasks. Project page: https://cogaffc.github.io/TRACE

For a graph $F$ with at least one edge, a $k$-uniform hypergraph is Berge-$F$-saturated if it contains no Berge-$F$, but adding any missing hyperedge creates a Berge-$F$. The saturation number $\text{sat}_k(n,\text{Berge-}F)$ is the minimum number of edges in such a hypergraph on $n$ vertices. English, Gordon, Graber, Methuku and Sullivan conjectured a linear upper bound for every fixed finite family of forbidden graphs. We prove the single-graph case: $\text{sat}_k(n,\text{Berge-}F)=O_{F,k}(n)$ for every fixed integer $k\ge2$ and every fixed finite simple graph $F$ with at least one edge. The proof combines a sparse construction with degree and matching arguments.

Public mobile and wearable mental-health datasets often provide summarized feature tables rather than synchronized raw sensor streams. In these releases, each anchor corresponds to a survey or label time and may combine phone or wearable summaries, prior symptom scores, demographics, clinical variables, and source-availability indicators. We propose the Modality-Conditioned Temporal Recursive Context Model (MC-TRCM), which preserves each feature source as a separate token and incorporates missingness as part of the input context. Observed sources are encoded with values and missingness summaries, absent sources use learned absence tokens, dataset and task embeddings condition fusion, and a recursive prediction head refines each output over validation-selected steps. We evaluated MC-TRCM on six predefined endpoints from DepreST-CAT and Prediction of Severity Change-Depression (PSYCHE-D) using participant-level splits and validation-only model selection. MC-TRCM achieved the lowest mean absolute error on DepreST-CAT Patient Health Questionnaire-9 (PHQ-9) and Generalized Anxiety Disorder-7 (GAD-7) severity, improving over the best tabular reference by 0.181 and 0.217 scale points. Classification endpoints showed task-dependent behavior: MC-TRCM matched the best rounded GAD-7 category balanced accuracy, was numerically highest by 0.002 balanced-accuracy points on PSYCHE-D multiclass prediction, and remained close to the strongest references on PHQ-9 category and PSYCHE-D binary prediction. Ablations support Feature-wise Linear Modulation, absence tokens, missingness projections, and recursive refinement, while calibration and feature-source controls characterize endpoint behavior. Our code is available at https://github.com/Botwwt/MC-TRCM.

Synthetic tabular generators are commonly optimized for distributional fidelity, but statistical similarity alone does not guarantee preservation of causal effects. In this paper, we study whether causal fidelity can be improved directly within a fully generative tabular model. Causal Fidelity is defined with respect to a target estimand as the discrepancy between inferential distributions obtained from real and synthetic data, and theoretical results show that high statistical fidelity does not generally imply high causal fidelity. We then propose a causal-fidelity-aware training framework which adds a causal discrepancy penalty to the generative objective. The framework is instantiated with a causal-penalized TabDDPM and optimized using an on-policy score-function estimator. We further establish conditions under which causal regularization improves expected causal fidelity. Experiments across diverse treatment-effect simulations and two benchmark datasets evaluate the ability of our method to improve causal fidelity while preserving competitive statistical fidelity.