Papers

Stochastic gradient descent (SGD) is widely used to train machine learning models, but subsampling the training data introduces noise into its updates. The strength and applicability of high-probability guarantees therefore depend critically on how the tails of gradient noise are modeled. Reports of heavy-tailed gradient noise in deep learning motivate relaxing the bounded-noise and sub-Gaussian assumptions commonly used in high-probability analyses of SGD. We use Young functions from Orlicz space theory to describe noise tails in a common framework. We model SGD gradient noise by adopting a Young function that preserves the finiteness of all polynomial moments while allowing tails heavier than sub-Weibull, including lognormal distributions. The resulting class is called $\beta$-heavy-tailed, with $\beta$ controlling the tail heaviness. We establish concentration inequalities for $\beta$-heavy-tailed noise and combine them with a uniform bound on the difference between empirical and population gradients along the SGD trajectory to obtain high-probability bounds on optimization and population-risk stationarity for smooth nonconvex losses under trajectory assumptions. The bounds are not restricted to a particular learning-rate decay rule and make explicit the effects of noise tails and learning-rate schedules. Under the Polyak-Łojasiewicz condition, we bound the risk at the last iterate. We also analyze SGD with gradient clipping under the $\beta$-heavy-tailed noise model.

The solar polar field plays a fundamental role in predicting solar-cycle strength and determines the large-scale structure of the heliospheric magnetic field. The High Resolution Telescope of the Polarimetric and Helioseismic Imager aboard Solar Orbiter (SO/PHI-HRT) provides unprecedented observations of the solar polar regions, as Solar Orbiter currently reaches heliographic latitudes of up to $\pm17^\circ$, about $10^\circ$ higher than those accessible from near-ecliptic observations. Using these observations to further test surface flux transport models, we present a successful simulation of the SO/PHI-HRT observations, reproducing the latitudinal profiles of the longitudinally averaged radial magnetic field in both polar regions. This result is achieved using the meridional-flow profile proposed by \citet{WangRH2026}, which also reproduces the evolution of the axial dipole strength, magnetic butterfly diagram, and high-latitude magnetic fields observed by SDO/HMI during Solar Cycle 25. We further compare simulations using this profile with simulations employing two representative meridional-flow profiles characterized by different peak latitudes. The latter fail to reproduce the observed high-latitude and polar fields. The comparison demonstrates that the meridional-flow profile strongly regulates poleward flux transport and the resulting polar-field evolution. Profiles peaking at higher latitudes produce stronger flux surges, and stronger and more concentrated polar fields. These results provide new constraints on the large-scale solar meridional flow.

Vision Language Action (VLA) models condition actions directly on current visual and language context, without an explicit account of how the scene evolves under candidate actions. World Action Models (WAM) attempt to address this limitation by predicting future states, but existing designs keep prediction and policy learning architecturally separate, connecting them only through the predicted output, whether through pixel space video generation or a latent forecasting module trained independently of the policy. We present Devol-ONE, a Mixture of Transformers architecture that unifies vision language understanding, latent world dynamics prediction, and action generation within a single autoregressive framework. Instead of encoding vision language tokens once and feeding them to the action expert, Devol-ONE runs autoregressive prediction jointly across a vision language stream and a V-JEPA pretrained dynamics stream, attending to the vision language key-value cache at every layer to forecast future latent states under language guidance. The action expert is in turn shaped continuously by semantic reasoning and predicted physical dynamics rather than by a fixed representation computed in advance. Extensive experiments are conducted on LIBERO, LIBERO-PLUS, RoboTwin2.0 along with real-world evaluation on Flexiv single-arm and dual-arm setups. Ablation studies show the effectiveness of dynamic stream prediction and layer-wise unified attention to validate our model architectural coherency.

Multi-agent workflows require task-relevant information to be shared across agents, while irrelevant, stale, unverified, or incompatible information must remain isolated. We call this task-conditioned scope of information a collaborative memory boundary. Workflow topology determines which intermediate artifacts are applicable to which downstream workers and when they cease to be valid, thereby providing a structural stress dimension for sharing and isolation. Existing memory benchmarks primarily evaluate retention and retrieval, whereas multi-agent benchmarks emphasize coordination and end-to-end completion, leaving topology-conditioned memory boundaries largely unmeasured. We introduce CoMemBench, an execution-grounded benchmark for collaborative memory sharing and isolation across multi-agent workflow topologies. It constructs 800 composite workflows across four domains from source-grounded dependency graphs, with node-local specifications, verifiable artifact handoffs, native evaluators, and matched isolation challenges. CoMemBench measures workflow completion, verified node progress, required-handoff reliability, isolation robustness, and token cost. Experiments reveal a sharing-isolation trade-off: broader context improves information availability but can weaken isolation, while system rankings shift across topologies and artifact violations.

Motivated by the systematic study of spiral minimal products, we consider harmonic maps obtained by coupling two spherical eigenmaps through a profile curve in $\mathbb S^3$, with a doubly warped product metric on the source. The source warps are independent of the profile magnitudes. This gives two complementary problems: reconstructing a compatible source metric from prescribed profile or source data, and finding closed profiles when the source metric is fixed. For arbitrary prescribed warps, homogenization of the reduced Lagrangian gives a strongly convex conic Finsler metric whose oriented graph geodesics are exactly the harmonic profiles. In the unit-speed inverse problem, the phase momenta reduce reconstruction to a scalar magnitude equation. We obtain global reconstructions from a prescribed magnitude, one source warp, or a monotone volume factor, together with periodic families in which profiles closing on finite covers are dense. In the fixed-metric problem, a change of time gives an autonomous Neumann system. One fixed source metric then carries continuous families of closed profiles and infinitely many closed graph geodesics. For fixed even $p,q\geq 2$, every fixed metric in this Neumann class on $\mathbb S^1\times\mathbb S^p\times\mathbb S^q$ supports harmonic maps into $\mathbb S^{p+q+1}$ of degree $4m$ for every $m\geq 1$. In the matched constant-warp case, these maps reduce to explicit eigenmaps.

DNA methylation (DNAM) profiling has emerged as a powerful diagnostic tool for classifying brain and solid tumors. However, existing computational models typically analyze methylation and copy number variation (CNV) data separately, failing to capture the complementary information their integration could provide. Moreover, current classification models lack mechanisms for within-class risk assessment analogous to traditional tumor grading, and no established explainability method can attribute classification decisions to specific genomic loci. In this paper, we present MOXAI (Multi-Omics Based Explainable AI), a deep learning framework that integrates DNA methylation and copy number data from methylation arrays to classify molecular subtypes of adult-type diffuse gliomas, alongside single-modality variants for comparison. Using a cohort from The Cancer Genome Atlas (TCGA), we trained ResNet50, DINOv2, and Graph Attention Network (GAT) models on methylation data alone, copy number data alone, and combined multimodal data. We further developed explainable AI (XAI) methods based on class activation maps (CAMs) and gradient-weighted CAM (Grad-CAM) to identify the specific CpG sites, genes, and chromosomal regions most relevant to each classification decision. The multimodal model achieved up to 92.98% cross-validation accuracy, outperforming models trained on CNV data alone. DINOv2 showed the strongest generalization, reaching 94.25% accuracy (confidence >0.9) on independent validation sets. XAI results aligned with established molecular features of adult-type diffuse glioma subtypes, confirming the biological interpretability of the framework.

Precise instruction-following is a fundamental ability of large language models (LLMs), requiring their outputs to strictly satisfy objective constraints in input instructions. In complex application scenarios, these constraints often possess diverse scopes that govern specific response segments rather than the entire output. However, existing optimization methods often neglect constraint scope during data construction and rely on binary per-constraint rewards, yielding limited data diversity and sparse supervision for complex constraints. To this end, we propose ScopeIF, a novel training framework for scope-aware precise instruction-following. We first introduce a unified schema that factorizes objective constraints into three decoupled dimensions: Scope, Target, and Range. Grounded in this schema, we construct ScopeInstruct, a large-scale instruction dataset with diverse scope-aware constraints, and combine tool-grounded verification with graded reward modeling to quantify the violation degree of each constraint, providing dense supervision for policy optimization. Extensive experiments demonstrate that ScopeIF consistently outperforms existing methods, particularly on complex scope-aware constraints, while preserving general capabilities. Notably, it enables optimized Qwen3-4B and 8B models to rival or surpass strong frontier models such as Gemini-2.5-Pro and DeepSeek-V3.2, establishing an effective paradigm for advancing scope-aware instruction-following. Our code and data are available at https://github.com/thu-coai/ScopeIF.

Text-to-image (TTI) models increasingly generate high-quality images from natural-language prompts, yet figurative language exposes a failure: a vehicle that should guide the depiction of a tenor may instead be rendered as a visible object. We call this failure Figurative Vehicle Intrusion: the intruding content is textually licensed, but it is assigned the wrong visual role, showing that visual presence is not always faithfulness and that presence-oriented evaluation can miss such errors. To study it systematically, we introduce Vehicle Intrusion and Semantic Tenor Assessment (VISTA), a multilingual benchmark of figurative prompts organized by Figurative Form and Mapping Mechanism. We further propose V-Score, a diagnostic question-answering metric that evaluates role-aware figurative faithfulness in generated images. Evaluations on recent high-performing TTI models show that vehicle intrusion persists across languages and figurative categories. As a lightweight mitigation, we introduce VISTA-Guard, which partially reduces vehicle intrusion and suggests a practical path toward more figuratively faithful TTI generation. All resources will be released publicly.

Cross-channel modeling is central to multivariate time-series forecasting, yet channels that are statistically related, predictively useful, and actually used by a trained forecaster are often treated as if they defined the same notion of importance. We show that they need not coincide. Cross-channel dependency structures change substantially across future offsets, and horizon-adaptive source selection improves a controlled Ridge predictor in 21 of 32 dataset–prediction-length conditions, with a mean gain of $5.16\%$. This selected-set signal also transfers to a matched nonlinear predictor. Yet imposing the same horizon-specific source logic on iTransformer yields only 11 of 20 wins and a mean gain of $0.208\%$, with little alignment between controlled and neural gains. Functional interventions further show that strong forecasters use cross-channel information, while their source-reliance rankings agree little with controlled utility or with one another across iTransformer, TimesNet, and a cross-channel TimeMixer. As a constructive consequence, bounded post-hoc support improves a frozen channel-independent forecaster in 12 of 16 dataset–horizon conditions, with a positive aggregate bootstrap interval. Cross-channel importance should therefore be interpreted relative to the forecasting mechanism and question that define it: related $\neq$ useful $\neq$ used.

Persistent memory enables LLM agents to reuse prior experience, but creates a new security boundary: what an agent may remember is not what it should act on. We expose an unauthorized control path where edited low-trust evidence is consolidated into persistent memory, retrieved on a clean task, and used to drive a protected action. Crucially, the adversary neither writes memory nor alters the task. We introduce Backchain Memory Attack (BMA), a grey-box, LLM-driven inverse-planning attack that reasons backward from the target action to the memory that would trigger it, then to the evidence edit that would form it. BMA has two phases: preparation uses resettable trials to localize the first failed link and build experience; execution uses the frozen experience to rank and commit candidate edits without feedback. We introduce the Pathway-Certified Attack Success Rate (Path-CASR) to separate memory-mediated from coincidental hits: registered memory must form, be retrieved, drive the target behavior, and pass matched-intervention checks. Across four substrates and three decision backbones, BMA achieves 18.8% Macro Path-CASR, compared with 13.4% for the strongest access-matched baseline. Of BMA's behavioral hits, 60.3% pass all registered pathway and intervention checks versus 36.7% for the baseline. Frozen BMA edits retain 78.0% of their certified effect on average across four held-out consolidation policies. Representative memory-side controls leave 11.0% Path-CASR, whereas provenance-bound authorization reduces it to 2.0% while preserving 92.1% legitimate-action success.

Pathology vision-language models (VLMs) are conventionally evaluated by accuracy, but accuracy alone does not measure evidence use: it may conflate dataset contamination, prior knowledge, and image evidence. In a motivating study of lymph-node metastasis prediction, we found that most public pathology VLMs showed minimal differences when changing from feeding the models with whole-slide images, an annotated lesion, or no image at all. To better understand the specific features leveraged by these models, this paper presents two contributions aimed at disentangling these factors. First, we present CleanSlide, a TCGA-based VQA benchmark designed to eliminate image- and question-side contamination. It contains 149K audited multiple-choice questions over 9,985 slides, with patient- and tissue-source-disjoint splits. Every question is audited for option shortcuts, stem leakage, cross-split duplication, and blind solvability. Second, we propose Pair-DPO, a preference loss over counterfactual slide pairs from the same question and source. By controlling for shared confounding factors, Pair-DPO cancels out the question-attributable signal and leaves image evidence as the source of preference. Specifically, each pair consists of two real slides with opposite, verified findings, introducing neither editing artifacts nor unverified labels for diffuse or graded features such as invasion, necrosis, and tumor grade. Experiments show that our method gains 15.29% from image evidence on the CleanSlide, compared with 2.81% for the best published model. On the external CPTAC and BCNB cohorts, our method achieves accuracies of 57.6% and 59.0%, outperforming all other evaluated models by 9.7% and 3.4%, respectively. We will release the benchmark and code.

Foundation-model agents are often modeled as policies over an observed state. In deployed systems, however, a runtime may intervene only after the model has emitted a semantic proposal, making the proposal both an action candidate and a decision-time observation generated by a history-conditioned process. We show that collapsing this structure into a state-only proposal envelope can preserve proposal coverage while destroying certifiability. In a finite robust interface, the viability kernel of the collapsed model is contained in the physical projection of the history-augmented kernel, and the collapse is lossless exactly when every proposal-conditioned collapsed fiber retains a common robust-safe intervention. This gap can be maximal even with constant-size proposal and history alphabets. The same common-action condition yields a dual result: observing the current proposal can restore robust feasibility when it separates latent modes requiring incompatible interventions. We extend these one-step results over time using exact finite beliefs and standard safety and reachability fixed points, separating indefinite operational viability from finite worst-case verified progress. Controlled model-in-the-loop tests reproduce the predicted obstructions when telemetry or effect verification is removed or intervention authority is restricted. Thus, our contribution is not a new fixed-point calculus, but a characterization of when proposal–history correlation at the model–tool boundary is necessary for certification.

High-resolution plant imaging enables detailed characterization of plant morphology, but dense scientific analysis remains limited by costly pixel-level annotations, large image pixel dimensions, and substantial variation in imaging conditions. This work proposes a scalable in-domain self-supervised pretrained foundation model for high-resolution, high-pixel-dimension multi-species plant imagery. A masked autoencoder with a ViT backbone is pretrained on more than 10 million multi-view plant image tiles using distributed training. Following scalable pretraining, the learned foundation-model representations are comprehensively benchmarked across fine-grained dense prediction and coarse global feature recognition, with particular emphasis on limited supervision and realistic downstream imaging conditions. This work focuses on the domain gap of existing foundation models in dense feature representation and transfer. Through extensive experiments involving limited annotations, cross-view variation, and resolution degradation, the in-domain FM achieves a Mean Dice of 0.8686 and a Pooled Dice of 0.8959, outperforming an MAE counterpart pretrained on large-scale natural-image data by 0.0694 and 0.0613, respectively. The results further indicate that increasing pretraining scale produces consistent improvements in dense feature transfer. Overall, these findings suggest that scaling in-domain self-supervised pretraining can reduce the domain gap and improve transferable dense representations for high-pixel-dimension scientific imaging.

Vision-language models are increasingly used to understand long videos and continuous streams. However, dense visual tokens accumulate with video duration, making long-context inference prohibitively expensive. Existing training-free visual-token selection methods reduce this cost by retaining informative tokens, but may lose coherent event evidence and fail to distinguish detailed recent observations from long-range history. We propose KeyRec, a training-free framework for constructing bounded visual memory. During query-agnostic writing, KeyRec preserves fine-grained recent observations in a visual cache and organizes historical evidence into a structured event bank. Candidate events are proposed according to their novelty relative to previously stored events and maintained through an online add–merge–evict update. When a question arrives, a text-only router adaptively allocates a fixed readout budget between recent and event memory, without reprocessing historical frames. KeyRec operates on model-facing visual embeddings and supports both modular encoder–projector VLMs and the encoder- and projector-free NEO-ov architecture. Across four streaming and long-video benchmarks and three VLM backbones, KeyRec achieves the best compressed performance in 13 of 15 settings using only 10% of the dense decoder-facing visual-token budget. It outperforms the strongest compressed baseline by 2.21–18.37 points on real-time questions, achieves the best compressed result in five of six long-video settings, and performs best in every NEO-ov 2B setting.

When studying the dynamical Mordell-Lang conjecture by using the $p$-adic method, experts have found that return sets of the $p$-adic version of the DML problem can be very sparse. In this article, we investigate the similar phenomenon for a complex analytic version of the DML problem and the DML problem for backward orbits.

Audio-visual segmentation (AVS) aims to segment sounding objects at the pixel level by integrating auditory and visual cues. However, existing methods are predominantly developed under the monaural setting and primarily rely on cross-modal semantic correspondence, which limits their ability to distinguish visually similar instances of the same semantic class. In contrast, humans naturally exploit binaural hearing, where interaural differences and direction-dependent acoustic filtering introduced by the head and pinnae provide physically grounded spatial cues for accurate sound source localization. Motivated by this observation, we introduce binaural audio-visual instance segmentation (BiAVIS), a new task that leverages synchronized binaural audio and video frames to segment sounding instances. To advance research on this task, we establish two benchmarks by manually annotating an existing binaural audio-visual dataset and collecting a new real-world dataset, BiAVIS-Bench, in more challenging and diverse scenarios. The proposed BiAVIS model (BiAVISM) features an audio-only sound source localization network that directly projects binaural spatial cues onto the image plane to learn spatial and semantic priors for sounding instances. A query-level audio-visual fusion strategy is subsequently introduced to inject these informative priors into the instance segmentation decoder. Extensive experiments conducted on the two proposed benchmarks demonstrate the superior performance of the BiAVISM over previous monaural AVS methods, especially in resolving instance-level intra-class ambiguity. On the more challenging BiAVIS-Bench, BiAVISM achieves 26.65 mAP and 45.90 FSLA, corresponding to relative improvements of approximately 35.35% over AVISM in mean average precision (mAP) and 11.62% over ACVIS in frame-level sound localization accuracy (FSLA).

In this paper, we focus on the positive reflectionless measures rigidity problem proposed by Xavier Tolsa in [16]. Let $1\leq n<d$, we consider positive reflectionless measures for the $n$-dimensional Riesz transform in $\mathbb R^d$. Under polynomial upper growth and a lower mass bound at large scales about one point, we obtain two flatness results for reflectionless measures. The first concerns globally defined Lipschitz graph measures with finite $\dot H^{1/2}$ energy and bounded, uniformly positive parameter densities whose deviations from a constant belong to $L^2$. The second case concerns a reflectionless measure that coincides with a flat measure outside a compact set. In both cases, the measure is a constant multiple of the $n$-dimensional Hausdorff measure on an affine $n$-plane. For integers $s>n/2$, we further obtain $H^s$ estimates controlling the graph gradient and density perturbation by the normalized Riesz field under smallness of the slope and density perturbation in $L^\infty$. The constants are independent of the supports.

Rotary position encodings make attention sensitive to relative position, but extending them to graphs requires choosing how graph structure enters the rotation. Previous works assign each node a rotation from spectral coordinates, so the rotary factor between two nodes depends only on their endpoints and cannot distinguish the routes connecting them. We introduce Analytic-Walk Rotary Positional Encodings (AW-RoPE), which place the rotations on edges and sum the transported features over all walks, so contributions along different routes can reinforce or cancel. An exact variant evaluates the complete sum by a differentiable linear solve, and a sparse variant truncates it at a finite depth. We prove forward and parameter-derivative truncation bounds at fixed inputs and parameters. Both variants act on projected queries and keys, and the sparse recurrence also augments message-passing networks. Across five synthetic tasks both variants reduce nRMSE by $15$–$58\%$ relative to the strongest baseline, and on real superpixel, peptide and OGB benchmarks the sparse recurrence attains the best mean on every dataset with Performer kernels and on twelve of thirteen datasets with GIN. Analysis shows that AW-RoPE can distinguish routes whose only cue is how two endpoints are connected, while node-wise rotary encodings cannot.

Three-dimensional (3D) Gaussian splatting (3D-GS) has emerged as a promising technique for large-scale scene reconstruction due to its high rendering efficiency and fidelity. However, the training of large-scale 3D-GS models at wireless edge faces various technical challenges including the limited communication, computation, and graphics processing unit (GPU) memory resources at edge devices, the structural inconsistency issue across local models hindering their effective aggregation, as well as privacy leakage risks associated with raw visual content and camera parameters. To address these challenges, this paper proposes a novel resource-efficient federated learning framework for efficiently training 3D-GS models of large scenes under severe resource constraints. First, we propose an on-device model lightweighting mechanism that adaptively selects and prunes Gaussian points to balance the rendering quality and training efficiency. In this mechanism, we quantitatively evaluate the importance of different Gaussian points at each device to facilitate the pruning, and use a novel importance-to-latency ratio criterion to determine the number of pruned Gaussian points under GPU memory and computation/communication latency constraints. Furthermore, we develop a 3D-GS model recovery mechanism that restores structural consistency across local 3D-GS models without accessing private camera parameters, enabling their effective aggregation towards a global model. Finally, extensive experiments show that our approach significantly accelerates convergence, maintains high rendering quality, and reduces training latency compared to state-of-the-art federated 3D-GS baselines.

The support recovery problem in mixture of linear classifiers aims to identify the features relevant to the underlying decision rules when data is generated by a mixture of several linear decision rules. In particular, the goal is to recover the support (nonzero coordinates) of $l$ unknown $k$-sparse vectors from sign measurements. Each measurement is generated by selecting one of the $l$ vectors uniformly at random, and returning the sign of its inner product with a chosen measurement vector. In this paper, we propose adaptive and non-adaptive schemes that significantly improve upon prior results by simultaneously reducing the number of measurements and achieving sublinear decoding time. In particular, our adaptive constructions substantially reduce measurements compared to existing approaches, while also lowering decoding complexity from super-quadratic to sublinear in the ambient dimension. We further provide a non-adaptive scheme that improves previous measurement bounds while maintaining efficient decoding. Overall, our approach yields a more efficient trade-off between sample complexity and decoding time for support recovery in mixture models compared to previously known methods.

Autoregressive video diffusion is a promising render-time fixer for 3D Gaussian Splatting (3DGS) in autonomous-driving simulation, but deployment demands high visual quality and temporal consistency at low latency. This is especially hard for one-step causal generation, where each imperfect prediction immediately becomes context for subsequent frames. Existing approaches stabilize rollouts through staged training with multiple modules and rollout-aware regularization, yet one-step quality still falls short of what deployment requires. We introduce OneFixer, a one-step autoregressive video-diffusion fixer trained in a single task-specific adaptation stage. Our key idea is a deployment-matched shared rollout: the model's own one-step predictions serve as the causal context for flow matching, exposing training to deployment-time errors, while the same rollout receives direct pixel-space perceptual supervision to preserve fine detail. Because the predictions optimized for current-frame quality are exactly those reused as future context, fidelity and autoregressive robustness are learned jointly, without bidirectional-to-causal conversion or teacher-student distillation. OneFixer further exploits cues that driving simulation readily provides, lane geometry and dynamic-agent states, to improve geometric fidelity. On Waymo and proprietary driving scenes with 900-frame rollouts, OneFixer achieves the lowest FVD, LPIPS, and DISTS among all baselines at one step, with temporal consistency matching or exceeding multi-stage DMD pipelines. Under identical backbone and conditioning, it matches a multi-stage DMD-with-Self-Forcing pipeline in under half the GPU-hours and keeps improving beyond its plateau. In closed-loop simulation with a driving policy, OneFixer reduces the collision rate by a third relative to raw 3DGS rendering. Project page: https://onefixer-web.vercel.app/

We give a systematic description of $\Hom$-Lie structures on several classes of Lie algebras and of their relations with transposed Poisson structures. Our starting point is the observation that the left-hand side of the defining identity is an alternating trilinear map; this makes $\mathcal{H}(\LL)$, the set of $\Hom$-Lie structures of $\LL$, a subspace of $\End(\LL)$ and reduces its computation to increasing triples of basis vectors. From this we derive, in every finite dimension $n$, the lower bound $\dim \mathcal{H}(\LL)\geq n \dim \mathcal{C}(\LL)$ and the codimension bound $\binom{n}{3}\dim [\LL,[\LL,\LL]]$, together with a refinement of the latter, and we determine $\mathcal{H}(\LL)$ for nilpotent, oscillator and solvable algebras, for $\sltwo \oplus A_{n-3}$, for the Witt, Virasoro and Heisenberg–Virasoro algebras, for all three-dimensional algebras, for $M_n(\bF)$ and $T_n(\bF)$, for the Virasoro-like algebra and its $q$-analogue, and for the planar Galilean conformal algebra. By a result of Filippov, every $\frac12$-derivation, and more generally every $\delta$-derivation with $\delta\neq0,1$, of a Lie algebra is a $\Hom$-Lie structure; we observe that, more generally, for $\delta\neq 0,1$ the $\delta$-derivations of an algebra of any variety defined by identities of degree at most three (associative, Novikov, left-symmetric, Leibniz, \ldots) are $\Hom$-structures of the corresponding $\Hom$-variety. We show that the inclusion of the $\frac12$-derivations into the $\Hom$-Lie structures is far from being an equality by computing the graded $\Hom$-Lie structures of Witt-, Virasoro- and Schrödinger-type algebras and of their central extensions, for which we give an explicit lifting obstruction. Along the way we correct two multiplication tables from the literature that violate the Jacobi identity.

Magnonic frequency combs (MFCs) generated via internal magnetic nonlinearities have exhibited rich physics beyond their optical counterparts. However, existing approaches rely on dynamic nonlinearity, which typically demands high power thresholds and stringent momentum conservation. Here we show that the geometric nonlinearity intrinsic to magnetic systems, originating from the unit-norm constraint of the magnetization vector, can serve as an independent nonlinear resource for MFC generation. Through transverse Floquet engineering, this geometric constraint converts a transverse drive into a longitudinal parametric modulation. In the low-frequency limit, the four-particle process reduces to an effective two-magnon modulation, enabling low-threshold comb generation in the linear regime, with the modulation amplitude scaling quadratically with the driving field and enhanced flatness arising from geometric harmonics. These results provide a deeper understanding of frequency combs and magnon nonlinear interactions, and offer a new theoretical foundation for enhancing MFC performance.

Large language models (LLMs) have demonstrated remarkable performance across various code-related tasks. However, unlike carefully curated datasets that are typically high-quality and error-free, real-world user instructions are often vague and error-prone, posing significant challenges to the robustness of code LLMs. Furthermore, robustness-oriented fine-tuning relies on paired clean-noisy samples, which are costly to curate and require sophisticated noisy simulation techniques. To address these challenges, we propose the Noisy Test-time Reinforcement Learning framework (NTRL-Code), which enables robust self-evolution of code LLMs using only unlabeled noisy data during the testing stage. Specifically, NTRL-Code uses conservative self-denoising to obtain a cleaner semantic anchor for target estimation, and employs an abstract-syntax-tree (AST)-based structural aggregation mechanism to estimate a proxy target from multiple candidate programs. The policy is then optimized on the original noisy prompts with a hybrid reward that combines format validity, code similarity, and anti-repetition signals. Extensive experiments on three benchmarks, each incorporating character-level, word-level, and paragraph-level perturbations, demonstrate that NTRL-Code yields robust and consistent improvements, stabilizing the predictions of various base models. Our code is available at https://github.com/Xikai97/NTRL-Code.

We investigate the cross-bispectrum between the cosmic microwave background (CMB) $B$-mode polarization and two Faraday rotation (FR) angles as a new probe of primordial magnetic fields (PMFs). Assuming Gaussian PMFs with both non-helical and helical components, we derive the $B\alpha\alpha$ bispectrum and decompose it into parity-even and parity-odd contributions. The mixed non-helical–helical contribution appears in the parity-even sector, whereas the purely non-helical and purely helical contributions contribute to the parity-odd sector. This parity dependence provides sensitivity to PMF helicity that is absent in the FR power spectrum alone. We then forecast the detectability of the cross-bispectrum for SO-like and LiteBIRD-like CMB experiments, and find that future observations can probe PMFs with amplitudes at the sub-nG level. The $B\alpha\alpha$ bispectrum is dominated by the helicity-sensitive parity-even sector and provides a promising avenue for constraining both the amplitude and helicity of PMFs.

The performance of online reinforcement learning depends critically on design choices, especially those that affect exploration. These choices are often selected by fitting a simulator to offline data, evaluating candidate algorithms in that simulator, and deploying the best-performing one. The simplest Plug-In selection rule simply selects the best performing algorithm on the fitted simulator, making evaluations unreliable when the offline data used to fit the simulator are limited. We investigate Uncertainty-Aware selection, which forms an ensemble of simulators—for example, obtained by bootstrap resampling—and selects the online algorithm with the best average performance across the ensemble. While ensemble-based approaches have been used to mitigate distribution shift and facilitate sim-to-real transfer, we formally show that this approach can mitigate the effects of limited data when fitting the simulator and theoretically has significant regret gains compared to Plug-In selection in multi-armed bandits. We also empirically investigate the Uncertainty-Aware selection approach in deep RL experiments on robotic control tasks that involve selecting reward-shaping hyperparameters, and show that it leads to more reliable selection and improved online performance.

Nonlinear dynamical systems with memory arise across science and engineering, yet uncertainty quantification for efficient forecasting methods such as Next Generation Reservoir Computing (NGRC) remains underdeveloped. We study Bayesian ridge and conformal prediction intervals for NGRC and characterize when their uncertainty estimates agree or differ. In low dimensions, their asymptotic widths are governed by different summaries of the residual distribution, so agreement depends on residual shape rather than dimensionality alone. In high dimensions, regularization introduces a further tradeoff between estimation variance, shrinkage bias, and posterior uncertainty, leading to an explicit transition between regimes where Bayesian intervals are wider or narrower than conformal intervals. We extend these results to quadratic NGRC feature maps and give sufficient conditions for transferring the analysis to temporally dependent forecast windows. Simulations and real-data experiments support the theoretical predictions and illustrate how residual distribution, regularization, dimensionality, and distribution shift affect interval calibration and efficiency. These results provide a principled framework for choosing and interpreting uncertainty quantification methods in reservoir-based forecasting.

With the deep integration of 5G and IoT in urban rail transit, service traffic grows explosively and accurate classification of heterogeneous service flows is essential for safe and efficient railway operations. Urban rail communication systems are subject not only to operational disturbances such as equipment failures and maintenance interference, but also to complex transmission patterns characterized by the interleaving of multi-service traffic flows. Under these operating conditions, the widespread deployment of proprietary protocols and the high prevalence of encrypted traffic further diminish the applicability of conventional port-based and Deep Packet Inspection (DPI) classification methods. To address these challenges, we propose a priority-aware dual-channel feature fusion framework. Raw traffic bytes and statistical features are mapped into grayscale images and processed by a dual-branch architecture: a transfer learning-enhanced ResNet extracts fine-grained byte-level textures, while a lightweight CNN captures macroscopic statistical patterns. A channel attention mechanism dynamically recalibrates cross-modal features, and a novel Priority-Sensitive Loss (PSL) that integrates business-criticality awareness with class-balance weighting to maximize recall for safety-critical services. Evaluated on a real-world urban rail dataset using priority-weighted metrics, the method achieves 98.74% accuracy and 99.24% weighted recall, with recall of 99.94% and 99.41% on the two safety-critical services:Communication-Based Train Control(CBTC) and Emergency Radio Dispatch(ERD), providing a reliable classification foundation for priority-aware resource scheduling in urban rail communications. With only 0.18M parameters and 0.4–0.7 ms end-to-end latency, offering an excellent balance between high-precision classification, low inference latency, and edge-deployment feasibility.

Counterfactual prediction estimates an individual's outcome under an alternative intervention given their factual observations. Such outcomes are generally not identifiable from observational data without additional assumptions. Even within the class of fully observed additive noise models (ANMs), different causal graphs can generate the same observational distribution yet imply different individual counterfactual outcomes. Predictions based on a single estimated graph ignore this structural uncertainty. We therefore target a Bayesian counterfactual posterior predictive distribution that combines predictions from plausible SCMs. We introduce CAFE (CounterfActual Prediction via Fast Posterior Estimation), an amortized inference framework that directly approximates the Bayesian counterfactual posterior predictive distribution. We pretrain a transformer-based model on synthetic counterfactual tasks generated from a diverse prior over ANMs. Given an observational dataset, an individual's factual observations, and an intervention, CAFE approximates the corresponding posterior predictive distribution in a single forward pass. Experiments show that CAFE accurately predicts individual counterfactual outcomes in identifiable settings and approximates the posterior predictive distribution when structural uncertainty induced by observationally indistinguishable causal graphs exists. Strong performance in realistic manufacturing and viticulture settings further demonstrates its empirical robustness beyond the assumptions of the training prior.

Running GUI agents on edge devices can keep sensitive screens and interaction histories local, but the computational cost of inference at every action step makes deployment challenging. Existing GUI agent systems either perform full vision-language model (VLM) inference at each action step or reuse coarse-grained knowledge matched to prior tasks. However, dynamic mobile environments and user tasks make it difficult to fully utilize prior task executions without additional fine-tuning or task-specific offline exploration. To address this challenge, we present PastForward, a system that accelerates GUI agents through validated, fine-grained reuse of computational experience accumulated during ordinary task execution. During decoding, PastForward retrieves prior output sequences as device-adaptive multi-token proposals and verifies them in a single VLM forward pass. Across action steps, it uses prior GUI transitions to begin next-step inference while the device executes the current action, retains the early computation only when the predicted screen matches the observed screen, and carries reusable KV states forward. We evaluate PastForward on AndroidWorld workloads derived from real mobile usage patterns using multiple VLM backbones across server and edge platforms. On device, PastForward achieves action-step latency speedups of 1.63-2.36$\times$ while maintaining task success rates.