Papers

We construct a finite-dimensional Auslander-regular algebra $R$ with global dimension three, which is right diagonal but not left diagonal; moreover, any simple right $R$-module with grade $i$ has projective dimension $i$, but there is a simple left $R$-module with grade one and projective dimension two. It answers a question raised by Iyama negatively.

Near the ocean surface, tropical cyclone winds change rapidly with height, but direct measurements are limited because aircraft dropsondes provide only sparse and irregular observations. Continuous wind profiles are important for understanding hurricane boundary-layer processes, improving storm-surge prediction, supporting offshore engineering, and assessing coastal hazards. In this study, we developed an artificial intelligence model that combines machine learning with physical principles to reconstruct continuous wind profiles from sparse observations. The model is designed to preserve the observed surface winds while generating realistic changes in wind speed and direction with height. Tests using more than two decades of NOAA hurricane observations show that the method accurately reproduces the vertical structure of tropical cyclone winds over a wide range of storm intensities. The framework can also extend satellite-derived surface wind measurements into three-dimensional near-surface wind fields, providing new opportunities for hurricane research, operational forecasting, and engineering applications.

Determining precise and homogeneous absolute ages of open clusters (OCs) remains a challenge in stellar astrophysics, mainly due to parameter degeneracies in photometric methods and line-of-sight extinctions. We present a novel method for estimating the ages of intermediate-age and old OCs, based on the strong initial-mass dependence of the surface oxygen isotopic ratio, 16O/17O, measured in RGB stars following the first dredge-up. Using updated theoretical stellar models computed with the FuNS code, we demonstrate how post-FDU CNO isotopic abundances reflect initial stellar masses. We analysed high-resolution near-infrared spectra for 11 RGB stars belonging to four Galactic OCs. For the intermediate-age clusters NGC 7789, NGC 7044, and NGC 6819, we derive ages of 1.80, 1.81, and 2.31 Ga, respectively. For the two stars in NGC 6819 the derived initial stellar mass (1.625 Mo) and age are in excellent agreement with independent estimates from asteroseismology and eclipsing binaries. Conversely, ages estimated by means of machine learning algorithms, trained to recognise specific features in the cluster CMDs, are systematically lower. Regarding the old and super-metal-rich cluster NGC 6791, the low signal-to-noise ratio and the possible line blending hinder precise mass and age constraints. With these limitations, we can only fix a lower bound of about 4 Ga for its age. The surface oxygen isotopic ratio in RGB stars provides a powerful, independent stellar clock, making high-resolution near-infrared spectroscopy of oxygen isotopes a key tool for Galactic archaeology.

Reconstructing protein structures from cryo-electron microscopy (cryo-EM) maps is essential for understanding macromolecular assemblies. Although learning-based methods have improved protein reconstruction, information from hetero components remains underused. Our analysis finds both false predictions and reference protein sites near hetero components; filtering nearby candidates can improve or impair chain construction. We introduce CryoCue, a framework that uses hetero information to guide protein reconstruction. An anchor-supervised detector learns hetero representations across five component classes. Multiscale hetero features guide backbone localization, while predicted hetero candidates condition structure refinement through their class, confidence, and frame-relative geometry. Experiments show that CryoCue improves backbone localization near hetero components and achieves more accurate protein structure reconstruction.

GoldenViewVQA requires models to jointly answer driving-scene questions and identify the camera view containing the supporting visual evidence, making precise evidence localization as important as answer correctness. We present CoVeR-VQA, a training-free multi-stage verification and correction framework for grounded multi-view VQA. Starting from GPT-5.6 zero-shot predictions, CoVeR-VQA progressively applies view-specific verification with Gemini-3.6-Flash, prior-guided joint verification with Claude-Opus-5, and cross-split group-level verification that exploits semantically filtered question groups from shared multi-view scenes and validation-derived prior knowledge. On the official GoldenViewVQA test set, the four-stage CoVeR-VQA pipeline achieves 84.75% Joint Accuracy, improving the GPT-5.6 zero-shot baseline by 13.56 percentage points, while reaching 94.92% Answer Accuracy and 86.44% View Accuracy. The final submitted run achieves 88.14% Joint Accuracy after two additional evaluator-informed post-hoc corrections. Our analysis shows that supporting-view localization remains the primary source of residual errors, highlighting the importance of explicit evidence verification for reliable multi-view multimodal reasoning.

World Action Models (WAMs) enable generalist robot manipulation by conditioning an action expert on representations from a pretrained video Diffusion Transformer (DiT). In closed-loop control, the video DiT runs at every chunk to encode the current observation into layerwise key-value (KV) pairs that the action expert queries. This prefill dominates the per-chunk computational cost, yet existing training-free accelerations leave it fully dense. We present WAM-Cache, a training-free framework that retains layerwise key-value representations across chunks and recomputes only a sparse refresh set of tokens. Crucially, we find that the intuitive heuristic of refreshing visually drifted tokens plateaus far below the dense baseline, even with an oracle predicting ground-truth KV drift. Downstream action accuracy is instead governed by where the action expert attends, not by what moved. WAM-Cache therefore selects the refresh set by uniting the action expert's cross-attention with visual latent surprise, complemented by a strict age bound that suppresses compounding error. On Fast-WAM, WAM-Cache cuts video DiT prefill FLOPs by 32-42% across RoboTwin 2.0, LIBERO, and real-world experiments, while staying within 0.7-1.8 percentage points of the dense policy in simulation and 2.5 points on a real robot.

In this paper, we study the global regularity of oblique boundary value problems for n-1 type augmented Hessian equations on a bounded domain, without imposing any convexity condition either on the domain or on the matrix-valued function in the n-1 type augmented Hessian equations. We establish a global existence and uniqueness theory for classical elliptic solutions by deriving global a priori estimates up to second-order derivatives. Besides the known applications for n-1 type Monge-Ampere operators in optimal transportation and geometric optics, the general theory here embraces equations raised by Li-Sheng, Some Dirichlet problems arising from conformal geometry. Pac. J. Math. 251, 2011, 337-359 and Guan-Qiu-Yuan, Fully nonlinear elliptic equations for conformal deformations of Chern-Ricci forms. Adv. Math. 343, 2019, 538-566.

Many applications of language models require estimating the expectation of a test functional under the model. Obtaining precise estimates can be computationally expensive. We show how to improve estimation precision by exploiting next-token conditional probabilities available as a by-product of sampling. Our approach uses potentials: real-valued functions of prefixes that induce an additive decomposition of the test functional. We construct a family of estimators parameterized by these potentials and derive conditions for variance reduction. Across applications including entropy estimation, watermark detection, and rare-event probability estimation, our estimators achieve substantial variance reductions relative to Monte Carlo and importance sampling baselines at comparable computational cost.

Modern DRAM chips are susceptible to read disturbance phenomena such as RowHammer, where repeatedly accessing (hammering) a row of DRAM cells (i.e., a DRAM row) induces bitflips in other physically nearby (victim) DRAM rows. A common practice to avoid such bitflips is to preventively refresh victim rows that might otherwise experience bitflips. Unfortunately, preventive refreshes cause long latencies and need to be performed urgently before the aggressor row is activated again to ensure data integrity. This is done by prioritizing them over demand memory requests, thereby potentially imposing significant delays on those requests and causing performance and energy overheads. Our goal in this work is to alleviate these overheads by scheduling preventive refreshes off the critical path of demand memory requests. We propose MORDOR, a new preventive refresh scheduling policy that significantly reduces system performance degradation and energy consumption caused by preventive refresh operations. MORDOR is integrated into the memory controller and operates alongside memory-controller-based read disturbance mitigation techniques to intelligently delay preventive refresh operations, while maintaining their data integrity guarantees. MORDOR leverages the key observation that a preventive refresh operation targeting an aggressor row can be delayed to serve any other demand memory request, as long as that memory request does not access the aggressor row. By doing so, MORDOR executes latency-critical memory requests before long-latency preventive refresh operations, while mitigating read disturbance bitflips. We evaluate MORDOR by integrating it into six state-of-the-art read disturbance mitigation techniques. Our comprehensive evaluation shows that MORDOR significantly improves system performance and energy efficiency at low area cost.

We study, within a toy model, how a thermal bath of cosmological perturbations can decohere the minisuperspace degrees of freedom of the universe, treating the perturbations as an environment in the framework of open quantum systems. Instead of tracing out the perturbations from a semiclassical ansatz for the total wave function, as in earlier approaches, we incorporate their backreaction on the background through an effective second-order coupling and derive a master equation. The model describes a spatially flat semiclassical universe during slow-roll inflation with a dust clock field, while scalar cosmological perturbations in a phenomenologically assumed thermal state constitute the environment. The master equation is non-Markovian, since the bath correlation functions do not decay in time. Within this framework, we find that, for a representative set of parameter estimates, the characteristic decoherence timescale corresponding to the thermal contribution can be shorter than the Hubble timescale. In addition, we address the question of whether the pointer-state structure induced by the decoherence in such a framework could provide a criterion for the choice of semiclassical states in quantum cosmology.

This letter investigates age-of-information (AoI) minimization in multi-user wireless networks operating in the finite-blocklength (FBL) regime, which is critical for low-latency transmission of short state-update packets. While rate-splitting multiple access (RSMA) provides a powerful and flexible framework for interference management in multi-user FBL systems, the joint optimization of its parameters, such as precoding vectors, power allocation, and rate-splitting ratios, to guarantee information freshness results in analytically intractable complexity. To address this challenge, we propose an actor–critic deep reinforcement learning (DRL) framework to learn dynamic resource-allocation policies in multi-user multiple-input single-output (MU-MISO) broadcast channels. Simulation results show that the proposed RSMA-RL framework achieves consistently lower AoI than the state-of-the-art benchmarks, with substantial gains observed at low signal-to-noise ratio (SNR) and short blocklengths, while matching benchmark performance at high SNR with significantly lower online complexity via a single neural-network forward pass at execution.

For a graph $G$ and a set $B\subseteq V(G)$, the spread $\mathrm{sp}(B)$ of $B$ is the difference between the largest and the smallest degree in $G$ of a vertex of $B$, and for an integer $k\geq 0$ the parameter $\mathrm{sp}(G,k)$ is the largest cardinality of a set $B$ with $\mathrm{sp}(B)\leq k$. Caro, Lauri and Zarb asked for the minimum of $\mathrm{sp}(G,k)$ over the maximal planar graphs of order $n$; we write $\mathrm{MP}(n,\delta ,k)$ for this minimum over the maximal planar graphs of order $n$ and minimum degree $\delta \in \{3,4,5\}$. This manuscript is intended as an exposition of the subject of spread in the degree sequence of a graph $G$, with emphasis on maximal planar graphs. We apply the general lower bound of the companion paper \cite{P1} to this class, together with further ideas, some based on Caro–West and Caro–Lauri–Zarb and some new. In particular we asymptotically determine the values of $\mathrm{MP}(n,\delta ,k)$ for every pair $(\delta ,k)$ with $\delta \in \{3,4,5\}$ and $k\geq 0$. This solution recovers the case $\mathrm{MP}(n,\delta ,0)$, which is the repetition number $\mathrm{rep}(G)$ introduced by Caro and West.

Multimodal Alzheimer's disease (AD) diagnosis benefits from integrating heterogeneous clinical, imaging, genomic, and biomarker evidence, but clinical cohorts frequently suffer from irregular modality missingness. Existing fusion methods often synthesize absent inputs, risking the introduction of artificial surrogates, or pool available signals into uninterpretable latent spaces. We present CoPoE (Disease-Coordinate Product-of-Experts), a disease-coordinate framework that maps multimodal evidence into a structured latent space partitioned into four distinct biological and clinical axes: genetic Risk, molecular Pathology, Neurodegeneration, and clinical Stage (R/P/N/S). Each observed modality parameterizes a diagonal Gaussian expert over the full RPNS vector, and a masked Product-of-Experts architecture fuses only the available modalities. Consequently, absent modalities add no factor to the fusion path, allowing the network to preserve a robust, decomposable posterior for any non-empty modality subset without synthetic imputation in the RPNS path. Through extensive missing-modality experiments on the ADNI dataset, CoPoE achieves the best all-modality performance and the highest mean AUROC across all 15 observed-subset evaluations among standardized missing-modality fusion baselines under a shared non-PET ADNI embedding benchmark, while substantially improving raw-probability ECE, Brier score, and NLL. Furthermore, PET-supervised probing shows evidence enrichment within the pathology (P) block under full modalities, with tau-related signal retained even when direct fluid biospecimen inputs are withheld. Our code is available at https://github.com/labhai/CoPoE.

An exploration is presented of two-dimensional, circular Couette flow of an elasto-viscoplastic fluid described by Saramito's (Bingham) constitutive law. Axisymmetrical base states are constructed. As has been noted previously, such states are not unique, with stresses over any plugs depending on the initial polymer stress, and the shear rate and stress may jump discontinuously across the yield surfaces. We show that base states with continuous stress profiles are linearly unstable at zero Reynolds number when they contain regions with relatively low shear rate. Unstable modes become stronger and localized to the yield surfaces as the azimuthal wavenumber increases. We report numerical simulations exploring the nonlinear dynamics of the instability. The linear unstable modes saturate at finite amplitude to create spatio-temporally complicated states. Polymer stress diffusion is added to ease these numerical simulations, eliminating normal-stress discontinuities and instability at the shortest wavelengths. Instability and transition to complex dynamics occur whenever the base flow contains regions with relatively low shear rate.

System One models output calibrated probabilities over typed answers such as categorical choices, ordinal levels, or binary outcomes, via a non-generative interface. Software can act on these probabilities through thresholds, cost-weighted choices, and escalation rules. Consequently, if these probabilities are miscalibrated or wording-sensitive, the software ma take unintended actions leaving human operators with no textual rationale to inspect. Current evaluations largely report accuracy and calibration on public classification datasets without a clear reference. We present TypedBench, a benchmark for typed decision models like Jev built from seven policy-labelled generators and nine evaluation suites. We report accuracy as median and range across paraphrases, and calibration error relative to the finite-sample noise floor of a matched, perfectly calibrated predictor. We assess probability quality through selective prediction, ordinal proper scoring rules, and realised cost under asymmetric cost matrices. We evaluate a hosted model, an open encoder, and a family of open decoders spanning 0.8B-9B parameters on identical items. The hosted model follows the stated policy but is wording-sensitive and systematically underconfident; under asymmetric costs, using its probabilities can be worse than taking its top answer. Decoders route exactly and are slow as options or questions are added. The decoder is least accurate on policy questions and degrades with more options. Overall, typed decision models must be evaluated jointly on policy adherence, wording robustness, probability quality, and induced decision outcomes.

Higher-order images produced by photons that orbit close to the unstable photon region of a black hole encode information about the spacetime geometry and leave characteristic signatures accessible with long interferometric baselines. We develop an analytical description of these signatures for a compact source in the spacetime of a slowly rotating Kerr black hole. Using the strong deflection limit, we derive the complex visibility function for a source of finite size at linear order in the black-hole spin. For a static equatorial source, we obtain a direct relation between the dimensionless Kerr spin parameter and the angular displacement of successive higher-order images belonging to the same parity sequence. We then extend the construction to a compact source on a circular equatorial orbit by evaluating each image contribution at the corresponding retarded source position. Frame dragging and source motion modify the angular positions of the images and leave distinct imprints on the long-baseline visibility pattern. For the configuration considered here, these effects act in opposite angular directions, so that the resulting structure is determined by their competition. Our results provide an analytical framework for identifying the imprints of black-hole spin and source dynamics in the interferometric signatures of higher-order images.

We introduce weak $A_n$-formality for Galois cochain algebras and, for profinite groups whose mod-$p$ cohomology is concentrated in degrees at most two, characterise weak and genuine $A_n$-formality through finite embedding problems and the projective system they form. We then study $A_n$-formality for number fields. Let $K$ be a number field and let $p$ be an odd prime with $\mu_p\not\subset K$. For $p\geq 5$, and for $p=3$ under a natural local cyclotomic condition, we prove that every associated finite $A_3$-embedding problem is solvable. In contrast, for every odd $p$ with $\mu_p\not\subset K$, we show that no compatible family of finite-stage solutions exists, and hence $C^\bullet(G_K,\mathbb F_p)$ is not genuinely $A_3$-formal. The proof uses Chebotarev density, governing fields, and the Gras-Munnier criterion to obstruct the compatibility of finite-stage solutions, and it builds on previous work of Maire-Mináč-Ramakrishna-Tân. This shows that genuine $A_3$-formality detects a global compatibility obstruction for number fields invisible to every individual finite embedding problem and invisible to obstructions arising from individual strong Massey vanishing problems.

Neural Machine Translation (NMT) models, while capable of producing highly fluent outputs, remain vulnerable to hallucinations, which are translations that are natural yet semantically unrelated to the source. This vulnerability is acute in low-resource settings like Sinhala-to-English, where weak cross-lingual alignment leads to hallucinations. This paper introduces a framework for reference-free hallucination detection in this language pair. We present a 45,000-sample synthetic dataset generated through a probabilistic chain of five linguistically motivated corruption strategies, with a semantic rescue mechanism that uses character-level similarity to distinguish hallucinations from morphological variants. We fine-tune mDeBERTa-v3 for token-level sequence labelling, reaching a token-level F1 of 0.841 +/- 0.001 over three seeds on a source-disjoint test set, and study a three-signal ensemble integrating neural risk scores, sequence log-probabilities, and cross-lingual semantic embeddings (LaBSE). A source-ablation control shows that the detector relies on the Sinhala source rather than on surface artefacts of the corruption process: shuffling or removing the source reduces sentence-level AUROC from 0.970 to chance. We benchmark eight NMT systems spanning five model families and find that detector firings vary by an order of magnitude across architectures.

Conditional independence testing is a ubiquitous problem in scientific discovery. The widely employed model-X assumption shifts the modelling burden from the dependence of the output on the inputs to the dependencies within the inputs. Log-optimal e-variables have been studied in this setting, but it remains unclear how to incorporate machine learning models into their design. Other approaches test exchangeability directly, yielding an e-variable with lower power in theory but, surprisingly, higher power in practice. We explain this phenomenon by decomposing the error into null enlargement, approximation, and estimation error. The decomposition shows that GRO e-variable estimates can be beaten because of their worse approximation and estimation errors, and we explore intermediate null hypotheses between model-X conditional independence and exchangeability to reduce these errors. Moreover, the model-X assumption often only holds up to an estimation error, invalidating exact type-I error guarantees. We provide estimation error bounds that accommodate triple robustness results, achieving fast convergence rates.

Symbolic regression combines structural search with numerical fitting, but aggregate fit scores do not describe how the remaining error varies across inputs. We introduce RISR, a residual-informed method that uses these error patterns to guide formula discovery and learn which corrections are worth fitting. A residual encoder compresses aligned inputs, targets, current predictions, and residuals into continuous tokens that condition a language model to propose formulas. For subsequent refinement, a dual-view relational encoder uses additive and regularized multiplicative residuals to predict the post-fit utility of candidate corrections. We evaluate RISR on scientific tasks from the LLM-SRBench. RISR achieves 63.57% and 38.50% ID accuracy at the 1% and 0.1% pointwise relative-error tolerances, respectively. The corresponding OOD accuracies are 56.07% and 38.24%. RISR outperforms the reported baselines using the same backbone. The results show that our residual-informed approach can improve numerical equation recovery.

This paper addresses the design of flatness-based tracking controllers for backward-flat nonlinear discrete-time systems. First, we show that backward-flat discrete-time systems can be constructively obtained from differentially flat continuous-time systems by applying an implicit Euler discretization to a structurally flat triangular representation. Subsequently, two approaches for the exact linearization of backward-flat systems are considered. Besides a dynamic feedback based on prelongations, we show that a linearizing feedback involving lower-order backward-shifts of the flat output can be employed without explicitly implementing the corresponding dynamic extension. This allows the order of the resulting tracking error dynamics to be reduced while requiring only stored values of past system trajectories. Based on the resulting linear input-output representation, flatness-based tracking control laws are derived. The proposed discretization and controller design are illustrated for a 2D gantry crane.

A link stream is a set of interactions between pairs of vertices, each one lasting during some time interval, and a clique of a link stream is a set of vertices together with a time interval during which all of them interact. A clique is maximal if neither its vertex set nor its interval can be enlarged. All known algorithms listing the maximal cliques of a link stream may spend time exponential in the size of a clique for each clique they output. Here, we approach the question under the light of two parameters of the instantaneous graphs of the stream, their maximum degree $\Delta$ and their degeneracy $k$. We prove that a link stream with $m$ links has $O(m\Delta^2 3^{\Delta/3})$ maximal cliques, and that a link stream with $n$ vertices and $|\mathcal{T}|$ distinct end times has $O(n|\mathcal{T}|k^2 3^{k/3})$ maximal cliques. Both bounds are tight up to a factor polynomial in $\Delta$ and $k$ respectively, and the second one improves the factor $2^k$ of previous bounds to $3^{k/3}$. Then we present two algorithms. The first one has setup time $O(m\log m)$ and polynomial time delay $\mathrm{poly}(\Delta)\log m$. The second one has setup time $O(m\log m+mk^2\log^3 n)$ and polynomial time delay $\mathrm{poly}(k)\log m$. To the best of our knowledge, these are the first algorithms with polynomial time delay for this problem. We also give an online version of the second algorithm, and we show that our results apply to the $\Delta$-cliques and $(\Delta,\gamma)$-cliques of temporal graphs.

Reinforcement learning is commonly used to train language agents in interactive environments, but cannot be directly applied when rewards are unavailable. Recent methods use environmental feedback as privileged context for hindsight self-distillation, but our analysis suggests that simply conditioning the teacher on feedback is insufficient, motivating us to rethink how environmental feedback is used in agentic self-distillation. Given that environmental feedback contains rich supervision for modeling how the environment responds to agent actions, we introduce agentic SElf-distilLation with environmental Feedback modeling (SELF), a framework that jointly optimizes environmental feedback modeling and hindsight self-distillation. SELF learns to predict environmental responses while distilling guidance from a feedback-conditioned self-teacher into the policy. Our analysis reveals a mutually reinforcing mechanism: environmental feedback modeling strengthens hindsight supervision and policy learning, while self-distillation enhances the model's ability to model environmental feedback. With Qwen3-8B, SELF outperforms SDPO and GRPO by 6.4 and 4.1 percentage points in $\tau$-bench success rate, and by 10.71 and 3.57 percentage points in AppWorld task goal completion, respectively. These results show that SELF uses environmental feedback more effectively within agentic self-distillation, improving agent capabilities.

We show that a free-by-cyclic group with infinite order monodromy is finite index rigid, that is, any two isomorphic finite index subgroups have the same index.

World models in end-to-end autonomous driving predict future scene evolution to provide foresight for trajectory planning. Existing methods mainly study how to predict the future and how to use it, but less often ask which future representation is actually most useful for planning. To this end, we propose PlanWAM, a Planning-Shaped World Action Model. The key idea is to let the planning task shape the future-state representation, so that it retains the information most useful for planning. A latent world model then predicts this planning-shaped future latent representation from historical observations and uses it for planning, enabling foresighted planning. Specifically, we first use a Temporal Register Pyramid to compress multi-frame historical information in a recency-aware manner, learning a compact history representation oriented toward future reasoning and planning. We then introduce a privileged future posterior branch that observes ground-truth future frames, and shape its future latent representation with trajectory-planning objectives to obtain a planning-shaped future latent representation. Hindsight-to-Foresight Distillation trains a prior branch that depends only on history to predict this future latent representation. The predicted future latent representation serves as planning context and guides trajectory generation and selection. PlanWAM achieves 93.8 PDMS / 90.9 EPDMS on NAVSIM-v1/v2 navtest and reaches 38.7 HD-Score on closed-loop HUGSIM in a zero-shot setting, demonstrating leading planning performance across both open-loop and closed-loop evaluations. Extensive experiments further demonstrate that planning-shaped future representations provide an effective and deployable form of foresight for world-action models.

AI-generated image detectors are commonly trained on fixed generator domains and become difficult to maintain as new generative models emerge. Continual adaptation is challenging because replaying historical generated images is costly, whereas updating shared parameters with limited current-domain data can overwrite prior forensic knowledge. We propose EvoKnow, a replay-free framework that formulates continual AI-generated image detection as forensic knowledge evolution. EvoKnow preserves a shared forensic basis learned from base domains, incrementally adds isolated residual experts for complementary generator-relevant evidence, and retrieves expertise through an Analytical Incremental Router (AIR) updated in closed form from current-stage generated images and accumulated sufficient statistics. Experiments demonstrate effective cross-generator generalization, few-shot expansion, and long-horizon continual adaptation. With ten generated images per arriving generator, EvoKnow achieves 96.70% average accuracy on non-base GenImage generators and 94.48% accuracy on Chameleon without target-benchmark adaptation. Under a strict replay-free continual learning protocol, EvoKnow achieves state-of-the-art continual learning performance, attaining 96.32% mean stage-wise accuracy and 4.32% average forgetting.

Diffusion models have achieved remarkable success in generative modeling, with their sampling procedures routinely modified to control generation and improve efficiency. These modifications introduce perturbations along the sampling trajectory, raising a central question: how do such perturbations affect generated output? To address this question, we develop a theoretical framework to investigate perturbation propagation, combining dynamical analysis of the sampling process with an information-theoretic characterization of output responses. Within this framework, we quantify perturbation strength using the Kullback–Leibler (KL) divergence between perturbed and reference trajectory distributions, termed as path cost, which is shown to bound, but do not determine, changes in the output distribution. Building on this analysis, we derive a response identity that connects the propagation and accumulation of local perturbations with the information captured by a selected feature mean, explaining why changes in the output distribution can remain undetected by its first-order response. We test our theoretical analysis through controlled interventions at equal path cost in pretrained diffusion models, revealing distinct patterns of output sensitivity across sampling stages and spatial frequencies. To assess whether our framework can diagnose perturbations arising from practical approximations, we apply it to cache-based acceleration and show that our propagation analysis reliably identifies sampling intervals where caching causes larger image errors.

JEV models make multimodal decisions by directly scoring candidates. Although the common context is encoded once, candidate evaluation can still repeat matching token histories, duplicate inference states, and execute the full backbone. In this paper, we study these sources of redundancy and present FastJEV for compact candidate evaluation. We jointly organize history reuse and state storage, since sharing computation requires preserving states for later branches. We first introduce shared context anchoring to reuse recurrent initial states and omit unused final recurrent caches. We extend this reuse through candidate prefix sharing, retaining the intermediate states needed by subsequent branches. To further reduce the depth of these paths, we apply decision guided pruning based on relative score changes measured on a small unlabeled set. Our method retains full context encoding and all candidates without additional training. We evaluate FastJEV across three OmniJev model sizes on five public benchmarks and reconstructed LIBERO-10 offline questions. At the selected pruning budgets, the complete method reduces candidate depth by 43.75% to 45.83%, while retaining 93.66% to 97.52% of the original task scores on average across the six evaluation sets. Through controlled experiments, we show how candidate overlap and branching structure affect the execution cost of history reuse. In our implementation, candidate prefix sharing can reduce repeated computation while increasing latency. These findings motivate designing sharing granularity and execution schedules together for efficient JEV inference.

Hairy black holes (BHs), characterized by nontrivial scalar or matter fields, introduce additional degrees of freedom beyond mass, charge, and spin, providing a framework for testing deviations from the Kerr paradigm. We investigate a class of rotating hairy black holes constructed within the gravitational decoupling framework, whose spacetime satisfies the Einstein field equations with a conserved energy-momentum tensor consistent with the strong energy conditions. In our previous work (Paper I; Dasgupta et al. 2026), we studied their horizon structure and test-particle dynamics and confronted two kinematic high-frequency quasi-periodic oscillation (HFQPO) models with observations of six black hole sources. Building on that analysis, we here test nine resonance models against the same HFQPO data, enabling a systematic comparison of eleven models (two kinematic and nine resonance) within the hairy Kerr framework. A comprehensive analysis based on the two kinematic models (Paper I) and the nine resonance models reveals that the HFQPO data with the current level of precision cannot rule out the hairy Kerr scenario. By implementing the Akaike Information Criterion and by examining the consistency of the inferred spins with previous independent spin estimates, our analysis provides a systematic framework for assessing the relative performance of different HFQPO models for each source. These results highlight the potential of HFQPOs to probe black hole hair and the need for more precise observations and a better understanding of the physical origin of QPOs.

We study a strong form of genuine multipartite nonlocality (GMNL), where an $n$-partite scenario admits a quantum strategy generating outcomes belonging to a restricted set with certainty, whereas every strategy built from nonclassical resources shared among at most $k<n$ parties fails this criterion with positive probability. This generalizes what is referred to as strong contextuality/nonlocality, or pseudotelepathy, beyond ruling out local models. For the simplest five-party Bell scenario of two binary-outcome measurement settings per party, we use the inflation technique to demonstrate that a game with a perfect quantum strategy witnesses a robust separation from models built from bipartite resources under local operations and shared randomness (LOSR), establishing the behavior is LOSR-GMNL. We provide broader context for this result by investigating its simulability with resources shared among three or four parties under different resource models and alternative definitions of GMNL. A central open question is whether $n$-party quantum resources can achieve such a separation from models built from $(n-1)$-party resources, for $n\ge 3$. We make progress here by constructing a family of robustly LOSR-GMNL games with $\epsilon$-optimal quantum strategies experimentally indistinguishable in the limit from true probability-one-winning strategies for any desired level of precision.