Manipulating Deformable Linear Objects (DLOs) is challenging in robotics due to their infinite-dimensional configuration space and complex nonlinear dynamics. In teleoperation, depth uncertainty hinders state perception and reaction. AssistDLO addresses this challenge as an assistive teleoperation framework for DLO manipulation that combines real-time multi-view state estimation, visual assistance (VA), and a geometry-aware shared-autonomy controller based on Control Barrier Functions (SA-CBF). While traditional shared autonomy methods often rely on simple geometric attractors and may fail to preserve DLO geometry, SA-CBF acts as a geometry-aware funnel, facilitating precise grasping while preserving the operator's high-level authority. The framework is evaluated in a bimanual knot-untangling user study (N = 22) using ropes with varying length and rigidity. Results show that the effectiveness of the assistance depends strongly on operator expertise and DLO properties. SA-CBF provides the strongest gains for naive users, acting as a skill equalizer that increases task success from 71% to 88%, and is effective for stiffer ropes. Conversely, expert users prefer VA, and highly compliant, long ropes benefit more from visual support than localized action assistance. Ultimately, these findings demonstrate that effective DLO teleoperation cannot rely on a fixed strategy, highlighting the critical need for adaptive, user-aware, and material-aware shared autonomy.

Human label variation has been established as a central phenomenon in NLP: the perspectives different annotators have on the same item need to be embraced. Data collection practices thus shifted towards increasing the annotator numbers and releasing disaggregated datasets, harmful language being most resourced due to its high subjectivity. While this resulted in rich information about \textit{who} annotated (sociodemographics, attitudes, etc.), the \textit{what} (e.g., linguistic properties of items), and their interplay has received little attention. We present the first large-scale analysis of four reference datasets for harmful language detection, bringing together annotator characteristics, linguistic properties of the items, and their interactions in a statistically informed picture. We find that interactions are crucial, revealing intersectional effects ignored in previous work, and that a strong role is played by lexical cues and annotator attitudes. Effect patterns, however, vary considerably across datasets. This urges caution about generalization and transferability.

Optimizers that exploit the matrix structure of gradients are central to modern LLM pre-training, with two distinct frontiers: explicit Kronecker-factored preconditioning -- most recently KL-Shampoo, which estimates the preconditioner via KL divergence minimization -- and orthogonalization of the gradient momentum, exemplified by Muon and analyzed as steepest descent under the spectral norm. The two routes are typically developed in isolation. We make a structural observation about KL-Shampoo's Kronecker preconditioners: their eigenvalue spectra exhibit a \emph{spike-and-flat} shape -- a few dominant eigenvalues followed by an approximately uniform tail -- across layers and training stages, holding exactly under a rank-$ρ$ signal-plus-noise gradient model. We exploit this structure by restricting one of KL-Shampoo's Kronecker factors to a parametric family aligned with the spike-and-flat shape: full spectral structure on a tracked $r$-dimensional subspace, single shared eigenvalue across the remaining $n-r$ directions. On these directions, we apply orthogonalization. An identity shows that this orthogonalization recovers the algebraic form of full KL-Shampoo's preconditioner. On four pre-training scales (GPT-2 124M / 350M, LLaMA 134M / 450M), Pro-KLShampoo consistently outperforms KL-Shampoo at every subspace rank we test in validation loss, peak per-GPU memory, and wallclock time to reach each loss level.

Reliable simulation evaluation of robot manipulation policies serves as a high-fidelity proxy for real-world performance. Although existing benchmarks cover a wide range of task categories, they lack visual realism, creating a large domain gap between simulation and reality. This undermines the reliability of simulation-based evaluation in predicting real-world performance. To mitigate the sim-to-real visual gap, we conduct a systematic analysis to isolate the effects of lighting and material. Our results show that these factors play a critical role in geometric reasoning and spatial grounding, yet are largely overlooked in existing benchmarks. Motivated by the analysis, we propose VISER, a visually realistic benchmark for evaluating robot manipulation in simulation. VISER features a high-fidelity dataset of over 1,000 3D assets with physically-based rendering (PBR) materials, along with 3D scenes created from these assets through curated layouts or generation. To this end, we propose an automated pipeline leveraging Multi-modal Large Language Models (MLLMs) for material-aware part segmentation and material retrieval, enabling scalable generation of physically plausible assets. Building on the high-fidelity 3D asset dataset, we construct diverse evaluation tasks, such as grasping, placing, and long-horizon tasks, enabling scalable and reproducible assessment of Vision-Language-Action (VLA) models. Our benchmark shows a strong correlation between simulation and real-world performance, achieving an average Pearson correlation coefficient of 0.92 across different policies.

Local temporal patterns in real-world time series continuously shift, rendering globally shared transformations suboptimal. Current deep forecasting models, despite their scale and complexity, rely on fixed weight matrices applied uniformly to all temporal tokens. This creates a static pattern response: models settle into a compromised average, unable to adapt to changing local dynamics. We introduce Dynamic Pattern Recalibration (DPR), a backbone-agnostic mechanism that resolves this via token-level recalibration. Through a lightweight "Perceive-Route-Modulate" pipeline, DPR computes a soft-routing distribution over a learned basis of adaptive response patterns, generating a time-aware modulation vector that recalibrates hidden states via a residual Hadamard product. As a backbone-agnostic adapter, DPR enhances forecasting across diverse architectures with minimal overhead, confirming it addresses a general bottleneck. As a minimalist standalone model, DPRNet achieves competitive performance across 12 benchmarks, validating dynamic recalibration against macroscopic parameter scaling.

Reliable confidence estimation enables safe deployment of chain-of-thought (CoT) reasoning through text-only APIs. Yet the dominant black-box baseline, self-consistency over K samples, is linearly expensive and ignores the geometry of the trace. We propose a black-box trajectory-confidence score: we embed a CoT as a sliding-window trajectory and measure its convergence to external answer anchors with a one-parameter softmax. The method needs no logits, hidden states, or supervised calibrators. Across six (benchmark, reasoner) settings on MedQA-USMLE, GPQA Diamond, and MMLU-Pro with Gemini 3.1 Pro and Claude Sonnet 4.6, fusing this score with coverage and verbalized-confidence channels at K=4 yields Pareto improvements over self-consistency at K=8 in 6/6 settings (median AUC 0.78 vs 0.71, deltaAUC=+0.075). A fixed-pick control (+0.060) and E5 cross-embedder replication rule out answer switching and single-vendor artifacts. Geometry peaks in the penultimate window across benchmarks and reasoners, and inverts at the terminal window on GPQA Diamond. Three unscaffolded regimes separate black-box confidence into a judge-mediated Coverage prior (C), within-trace Geometry (G), and a conditional Verbalization channel (V). Across 18 benchmark x reasoner x proposer settings, C and G provide independent signal in 18/18 and 16/18, while V contributes residual signal in 6/18. Swapping the judge from GPT-5-mini to Claude Sonnet 4.6 leaves G-only AUC unchanged (|delta|<=0.013) and shifts C-only AUC by at most +/-0.02 (kappa=0.82). Fusion beats the best single channel in 17/18 settings (median AUC 0.78, max 0.92).

Automated privacy audits of web and mobile applications often analyse outbound HTTP traffic to detect Personally Identifiable Information (PII) leakage. However, existing learning-based detectors typically depend on scarce, manually labelled traffic and are tightly coupled to fixed label taxonomies, limiting transferability across domains and evolving definitions of PII. This paper investigates whether Large Language Models (LLMs) can support taxonomy-agnostic annotation of explicitly transmitted PII values in HTTP message bodies when the taxonomy is provided at runtime. We introduce a multi-stage LLM-based pipeline that combines deterministic pre-processing with label-level classification, targeted instance-level value annotation, and output validation. To enable controlled evaluation and exemplar-based prompting without relying on sensitive real-user captures, we further propose an LLM-based generator for synthetic HTTP traffic with manually validated, taxonomy-derived PII annotations. We evaluate the approach across three taxonomies spanning different PII domains and granularity levels. Results show that the pipeline accurately detects PII types and extracts corresponding values for concrete PII taxonomies. Overall, our findings position LLMs as a promising foundation for flexible, taxonomy-agnostic traffic annotation and for creating labelled data under evolving privacy taxonomies.

Molecular generative models often assume meaningful latent geometry, but apparent property predictability can reflect sequence-level shortcuts rather than chemical organization. We study this issue in an unsupervised autoregressive Transformer-VAE trained on SELFIES. After training, we freeze the model, fit linear probes to RDKit descriptors, and use the probe weights as candidate global steering directions. To separate chemical signal from SELFIES artifacts, we introduce a confound-aware evaluation based on residualization, confound-direction alignment analysis, and decoded-molecule traversal. This is necessary because SELFIES length, branch tokens, ring tokens, and token entropy are strongly encoded in the latent space. Under this confound-aware evaluation, we find robust monotonic steering for cLogP, FractionCSP3, HeavyAtomCount, TPSA, BertzCT, and HBA. Nonlinear probes further show that some properties admit stable global directions, while others are better described by local latent gradients. Overall, our results show that chemically meaningful steering can emerge in entangled molecular latent spaces, but only when validated through decoded molecules and controlled for representation-level confounds.

We introduce the metagame, a conceptual framework for quantifying second-order interaction effects of model explanations. For any first-order attribution $ϕ(f)$ explaining a model $f$, we measure the directional influence of feature $j$ on the attribution of feature $i$, denoted as meta-attribution $φ_{j \to i}(f)$, by treating the attribution method itself as a cooperative game and computing its Shapley value. Theoretically, we prove that attributions hierarchically decompose into meta-attributions, and establish these as directional extensions of existing interaction indices. Empirically, we demonstrate that the metagame delivers insights across diverse interpretability applications: (i) quantifying token interactions in instruction-tuned language models, (ii) explaining cross-modal similarity in vision-language encoders, and (iii) interpreting text-to-image concepts in multimodal diffusion transformers.

The ability to reliably distinguish human-written text from that generated by large language models is of profound societal importance. The dominant approach to this problem exploits the likelihood hypothesis: that machine-generated text should appear more probable to a detector language model than human-written text. However, we demonstrate that the token-level signal distinguishing human and machine text is non-uniform across the hidden space of the detector model, and naively averaging likelihood-based token scores across regions with fundamentally different statistical structure, as most detectors do, causes a form of Simpson's paradox: a strong local signal is destroyed by inappropriate aggregation. To correct for this, we introduce a learned local calibration step grounded in Bayesian decision theory. Rather than aggregating raw token scores, we first learn lightweight predictors of the score distributions conditioned on position in hidden space, and aggregate calibrated log-likelihood ratios instead. This single intervention dramatically and consistently improves detection performance across all baseline detectors and all datasets we consider. For example, our calibrated variant of Fast-DetectGPT improves AUROC from $0.63$ to $0.85$ on GPT-5.4 text, and a locally-calibrated DMAP detector we introduce achieves state-of-the-art performance across the board. That said, our central contribution is not a new detector, but a precise diagnosis of a significant cause of under-performance of existing detectors and a principled, modular remedy compatible with any token-averaging pipeline. This will serve as a foundation for the community to build upon, with natural avenues including richer distributional models, improved calibration strategies, and principled ensembling with hidden-space geometry signals via the full Bayes-optimal decision rule.

Every major data modality now has a foundation model that understands it natively: text has language models, images have vision models, audio has audio models. Tabular data, the modality on which many consequential real-world AI decisions are made, does not. Every approach to tabular AI today, from gradient-boosted trees to the latest tabular foundation models, requires a preprocessing pipeline before any model can consume the data. None of them understand tabular data as a modality. We introduce the Data Language Model (DLM), the missing foundation model for tabular data. A DLM understands tables the way a language model understands sentences: natively, without serialization or preprocessing, directly from raw cell values. It is the tabular data layer on which AI models, agents, and vertical AI applications can be built, eliminating the preprocessing pipelines that currently stand between raw data and every AI system that consumes it. We present Schema-1, the first DLM: a 140M parameter model trained on more than 2.3M synthetic and real-world tabular datasets. Schema-1 outperforms gradient-boosted ensembles, AutoML stacks, and the tabular foundation models we evaluate on established row-level prediction benchmarks. On missing value reconstruction it achieves lower reconstruction error than all classical statistical methods and frontier large language models on mean performance across conditions, establishing that structural understanding of a dataset's own distributional geometry is more useful for imputation than world knowledge encoded in language. It identifies the industry sector of any unseen dataset from raw cell values alone, reliably across any domain, a task no prior tabular model can perform. It is the native tabular understanding layer that has been missing from the AI stack.

Single-step retrieval-augmented generation (RAG) provides an efficient way to incorporate external information for simple question answering tasks but struggles with complex questions. Agentic RAG extends this paradigm by replacing single-step retrieval with a multi-step process, in which the large language model (LLM) acts as a search agent that generates intermediate thoughts and subqueries to iteratively interact with the retrieval system. This iterative process incurs substantial latency due to the autoregressive generation of lengthy thoughts and subqueries. To address this limitation, we propose LatentRAG, a novel framework that shifts both reasoning and retrieval from discrete language space to continuous latent space. Unlike existing explicit methods that generate natural language thoughts or subqueries token-by-token, LatentRAG produces latent tokens for thoughts and subqueries directly from the hidden states in a single forward pass. We align LLMs with dense retrieval models in the latent space, enabling retrieval over latent subquery tokens and supporting end-to-end joint optimization. To improve transparency and encourage semantically meaningful latent representations, we incorporate a parallel latent decoding mechanism that translates latent tokens back into natural language. Extensive experiments on seven benchmark datasets show that LatentRAG achieves performance comparable to explicit agentic RAG methods while reducing inference latency by approximately 90%, substantially narrowing the latency gap with traditional single-step RAG.

Autoraters, also referred to as LLM-as-judges, are increasingly used for evaluation and automated content moderation. However, there is limited statistical analysis of how modifications in a rubric presented to both humans and autoraters affect their score agreement. Rubrics that ask for an overall or \emph{holistic} judgment - for example, rating the ``quality'' of an essay - may be inconsistently interpreted due to the complexity or subjectivity of the criteria. Conversely, rubrics can ask for \emph{analytic} judgments, which decompose assessment criteria - for example, ``quality'' into ``fluency'' and ``organization''. While these rubrics can be edited to improve the individual accuracy of both human and automated scoring, this approach may result in disagreement between the two scores, or with the associated holistic judgment. Designing and deploying reliable autoraters requires understanding not just the relationship between human and autorater annotations but how that relationship changes as holistic or analytic judgments are elicited. The results indicate that rubric edits providing representative examples and additional context, and reducing positional bias in the rubric increased human-autorater agreement, while higher rubric complexity and conservative aggregation methods tended to decrease it. The findings from the automatic essay scoring and instruction-following evaluation domains suggest that practitioners should carefully analyze domain- and rubric-specific performance to move towards higher human-autorater agreement.

In this paper, we introduce INEUS, a meshfree iterative neural solver for partial integro-differential equations (PIDEs). The method replaces the explicit evaluation of nonlocal jump integrals with single-jump sampling and reformulates PIDE solving as a sequence of recursive regression problems. Like Physics-Informed Neural Networks (PINNs), INEUS learns global solutions over the entire space-time domain, yet it offers a more efficient treatment of nonlocal terms and avoids the computationally expensive differentiation of full PIDE residuals. These features make INEUS particularly well suited for high-dimensional PDEs and PIDEs. Supported by a contraction-based convergence proof for linear PIDEs, our numerical experiments show that INEUS delivers accurate and scalable solutions for various high-dimensional linear and nonlinear examples.

Ensemble models achieve state-of-the-art performance on prediction tasks, but usually require aggregating a large number of weak learners. This can hinder deployment, interpretability, and downstream tasks such as robustness verification. Remedies to this issue fall into two main camps: pruning, which discards redundant learners, and compression, which generates new ones from scratch. We introduce PACE, a framework that interleaves these paradigms in a two-phase strategy. First, new learners are actively generated via a theoretically grounded procedure to enhance the diversity of the initial ensemble. When no more relevant learners can be found, a second phase of pruning is performed on this enriched ensemble. During both operations, PACE allows fine control on the faithfulness to the original ensemble. Experiments show that our method outperforms prior pruning and compression methods while offering principled control of faithfulness guarantees.

Semantic segmentation is a core component of discourse analysis, yet existing models are primarily developed and evaluated on high-resource written text, limiting their effectiveness on low-resource spoken varieties. In particular, dialectal Arabic exhibits informal syntax, code-switching, and weakly marked discourse structure that challenge standard segmentation approaches. In this paper, we introduce a new multi-genre benchmark (more than 1000 samples) for semantic segmentation in conversational Arabic, focusing on dialectal discourse. The benchmark covers transcribed casual telephone conversations, code-switched podcasts, broadcast news, and expressive dialogue from novels, and was annotated and validated by native Arabic annotators. Using this benchmark, we show that segmentation models performing well on MSA news genres degrade on dialectal transcribed speech. We further propose a segmentation model that targets local semantic coherence and robustness to discourse discontinuities, consistently outperforming strong baselines on dialectal non-news genres. The benchmark and approach generalize to other low-resource spoken languages.

Standard cross-entropy is the default classification loss across virtually all of machine learning, yet it treats all misclassifications equally, ignoring the semantic distances that a class hierarchy encodes. We propose Hierarchy-Aware Cross-Entropy (HACE), a drop-in replacement for standard cross-entropy that incorporates a known class hierarchy directly into the loss. HACE combines two components: prediction aggregation, which propagates the model's probability mass upward through the class hierarchy to ensure that parent nodes accumulate the confidence of their children; and ancestral label smoothing, which distributes the ground-truth signal along the path from the true class to the root. We evaluate HACE on CIFAR-100, FGVC Aircraft, and NABirds in two regimes: end-to-end training across six architectures spanning convolutional and attention-based designs, and linear probing on frozen DINOv2-Large features. In end-to-end training, HACE improves accuracy over standard cross-entropy in 15 out of 18 architecture--dataset pairs, with a mean gain of 4.66\%. In linear probing on frozen DINOv2-Large features, HACE outperforms all competing methods on all three datasets, with a mean improvement of 2.18\% over the next best baseline.

We present a deployed system for on-orbit wildfire detection aboard a nine-satellite commercial thermal infrared constellation, operating under demanding joint constraints: sub-megabyte model footprint, sub-150 ms per-batch TensorRT FP16 inference on an NVIDIA Jetson Xavier NX, and an end-to-end alert pipeline targeting under 10 minutes from satellite overpass to fire event communication. The system operates on uncalibrated mid-wave infrared (MWIR) single-band imagery at 200 m ground sampling distance, where fires frequently appear as sub-pixel or single-pixel thermal anomalies under extreme class imbalance -- challenges not addressed by the contextual thermal-thresholding pipelines (MODIS, VIIRS) that currently dominate operational fire monitoring. We present an empirical study of lightweight dense representation learning for this regime using a proprietary nine-satellite MWIR dataset. We compare dense masked autoencoding (DenseMAE) and a hybrid DenseMAE+EMA (exponential moving average) distillation variant, and evaluate representations via linear probing and full-distribution pixel-level average precision (AP) under extreme class imbalance. DenseMAE pretraining enables compact downstream models on the latency-accuracy Pareto frontier: our fastest SSL-pretrained model achieves 0.640 test AP and 0.69 event-level Fire-F1 with 65.34 ms latency per batch and a 0.52 MB engine, without pruning or compression. The best configuration reaches 0.699 AP and 0.744 Fire-F1 below 1 MB, outperforming a supervised baseline (0.650 AP) under comparable constraints.

While generative modeling has achieved remarkable success on tasks like natural language-conditioned image generation, enabling model adaptation from example data points remains a relatively underexplored and challenging problem. To this end, we propose Function Projection for Flow Matching (FP-FM), an algorithm that directly conditions generation on samples from the target distribution. FP-FM learns basis functions to span the velocity fields corresponding to a set of training distributions, and adapts to new distributions by computing a simple least-squares projection onto this basis. This enables efficient generation of samples from diverse target distributions without additional training at inference time. We further introduce multiple variants of FP-FM that provide a trade-off in expressivity and compute by enriching the coefficient calculation, e.g., by making the coefficients dependent on time. FP-FM achieves greatly improved precision and recall relative to baselines across synthetic and image-based datasets, with especially strong gains on unseen distributions.

Curating fully annotated datasets for medical image segmentation is labour-intensive and expertise-demanding. To alleviate this problem, prior studies have explored scribble annotations for weakly supervised segmentation. Existing solutions mainly compute losses on annotated areas and generate pseudo labels by propagating annotations to adjacent regions. However, these methods often suffer from inaccurate and unrealistic segmentations due to insufficient supervision and incomplete shape information. In contrast, we first investigate the principle of good scribble annotations, which leads to efficient scribble forms via supervision maximization and randomness simulation. We further introduce regularization terms to encode the spatial relationship and the shape constraints, where the EM algorithm is utilized to estimate the mixture ratios of label classes. These ratios are critical in identifying the unlabeled pixels for each class and correcting erroneous predictions, thus the accurate estimation lays the foundation for the incorporation of spatial prior. Finally, we integrate the efficient scribble supervision with the prior into a framework, referred to as ZScribbleSeg, and apply it to multiple scenarios. Leveraging only scribble annotations, ZScribbleSeg achieves competitive performance on six segmentation tasks including ACDC, MSCMRseg, BTCV, MyoPS, Decathlon-BrainTumor and Decathlon-Prostate. Our code will be released via https://github.com/DLwbm123/ZScribbleSeg.

End-to-end autonomous driving models generate future trajectories from multi-view inputs, improving system integration but introducing opaque decisions and hard-to-localize risks. Existing methods either rely on auxiliary monitoring models or generate textual explanations, but are decoupled from the planning process and fail to reveal the visual evidence underlying trajectory generation. While attribution offers a direct alternative, planning differs from image classification by taking six-view camera images as input and predicting continuous multi-step trajectories, requiring attribution to capture both critical views and regions and their influence on outputs. Moreover, whether attribution maps can support risk identification remains underexplored. To address this, we propose a hierarchical attribution framework for end-to-end planning. Specifically, using L2 consistency with the original trajectory as the objective, we design a coarse-to-fine region attribution strategy that searches candidate regions across the full six-view input and refines attribution within them. We further extract three attribution statistics as predictive signals for planning risk, including attribution entropy to measure how concentrated the planner's reliance is over the joint visual space, within-camera spatial variance to characterize how spread out the attribution is within each view, and cross-camera Gini coefficient to quantify how unevenly attribution is distributed across the six cameras. Experiments on BridgeAD, UniAD, and GenAD show that these statistics correlate with planning risk, achieving Spearman correlations of $0.30 \pm 0.07$ with trajectory error and AUROC of $0.77 \pm 0.04$ for collision detection. The signal generalizes to held-out scenes with negligible degradation and remains stable under an alternative attribution baseline.

Diffusion-based generators set the current state of the art for synthetic tabular data. These methods approach but rarely exceed real-data utility, and closing this synthetic-real gap has so far been pursued exclusively at training time, via architectural advances, scaling, and retraining of monolithic generators. The inference-time alternative, i.e., refining the outputs of a pre-trained backbone with parameters left untouched, has remained largely unexplored for tabular synthesis. We introduce TARDIS (Tabular generation through Refinement, Distillation, and Inference-time Sampling), an inference-time refinement framework that operates on a frozen pre-trained backbone, configured per dataset by a Tree-structured Parzen Estimator search over score-level guidance during reverse diffusion, with each trial's objective set by an inner grid search over post-hoc sample selectors and an optional soft-label distillation step. The search space encodes a single mathematical pattern we name Bidirectional Chamfer Refinement (BCR): the symmetric Chamfer functional between synthetic and real samples is minimized both continuously, via a score-level gradient, and discretely, via batch-ranking post-generation. The per-dataset search recovers BCR-aligned configurations on most datasets, evidence for BCR as the dominant refinement pattern. Across 15 binary, multiclass, and regression benchmarks TARDIS achieves a median +8.6% downstream-task improvement over models trained on real data (95% CI [+3.3, +16.4], Wilcoxon p=0.016, 11/15 strict wins) and improves over the TabDiff backbone on all 15 datasets (mean +12.9%, p<10^-4), matching the backbone on manifold fidelity, diversity, and sample-level privacy. Inference-time refinement of a pre-trained tabular diffusion backbone reaches and exceeds real-data utility in 1 to 80 minutes on a single consumer-grade GPU.

Graph Federated Learning (GFL) enables collaborative representation learning across distributed subgraphs while preserving privacy. However, heterogeneity remains a critical challenge, as subgraphs across clients typically differ significantly in both semantics and structures. Existing methods address heterogeneity by enforcing the rigid alignment of model parameters or prototypes between clients and the server. However, these alignments implicitly rely on a restrictive global linearity assumption that summarizes local data distributions using a single and globally consistent representation space. This severely compresses the personalized representation space of clients and fails to preserve diverse local graph distributions. To overcome these limitations, we propose Federated Graph Manifold Calibration (FedGMC), a novel paradigm that tackles semantic heterogeneity and structural heterogeneity from a unified manifold perspective. Instead of enforcing rigid alignment, FedGMC introduces a dual manifold calibration mechanism that preserves global commonalities while maximizing the personalized representation space of local clients. Specifically, for semantic heterogeneity, the server constructs a geometrically optimal semantic manifold via equidistant semantic anchors, so as to guide the calibration of local semantic manifolds. For structural heterogeneity, the server constructs a global structural manifold by building global structural templates, so as to guide the calibration of local structural manifolds. Finally, the server dynamically refines both global semantic manifolds and structural manifolds by aggregating local manifolds. Extensive experiments on eleven homophilic and heterophilic graphs demonstrate that FedGMC effectively balances global commonality and local personalization, thereby significantly outperforming state-of-the-art baseline methods.

Understanding how deep neural networks learn representations remains a central challenge in machine learning theory. In this work, we propose a feature-centric framework for analyzing neural network training by relating weight updates to feature evolution. We introduce a simple identity, the Feature Learning Equation, which identifies the weight Gram matrix as the key object capturing feature dynamics. This enables us to interpret gradient descent as implicitly inducing a hypothetical evolution of features, whose covariance structure - termed the Virtual Covariance - characterizes how representations evolve during training. Building on this perspective, we introduce Target Linearity, a measure quantifying the linear alignment between features and targets. By analyzing the training and layer-wise dynamics, we show that deep networks learn to sequentially transform representations toward target-linear structure. This linearization perspective provides a unified interpretation of several empirical phenomena, including Neural Collapse and linear interpolation in generative models.

Graph pooling is commonly applied in graph classification, yet its empirical gains over standard WL-1 expressive GNNs are often marginal or inconsistent. We study this gap by analysing the interaction between node features and graph topology and their effect on pooling objectives. Our analysis reveals that pooling operators require node features that are well-aligned with the graph's topology -- a condition often overlooked and not guaranteed in empirical networks. We formalise fundamental requirements for node features to enable effective pooling, and introduce a quantitative measure of feature quality. Our empirical evaluation shows that, when these requirements are satisfied, pooling can be beneficial and improve performance on appropriate datasets.

World action models (WAMs) provide a powerful generative framework for embodied control, yet transferring knowledge across heterogeneous WAMs remains challenging due to mismatched latent interfaces, high adaptation cost, and the rigidity of conventional distillation objectives. We propose \textbf{CKT-WAM}, a parameter-efficient \textbf{C}ontext \textbf{K}nowledge \textbf{T}ransfer framework that transfers teacher WAM's knowledge into a student WAM through a compact context in the text embedding space, rather than output imitation or dense hidden-state matching. Specifically, CKT-WAM extracts intermediate teacher hidden states, reduces the number of tokens via compressors' learnable-query cross attention (LQCA), and transforms them through an always-on generalized adapter, a lightweight router, and sparsely activated specialized adapters. The resulting context is then appended to the student's conditioning textual embeddings, thereby injecting the transferred knowledge into the student with minimal architectural modification. Experiments show that CKT-WAM consistently improves zero-shot generalization and achieves the best overall performance on LIBERO-Plus, reaching 86.1\% total success rate with only 1.17\% trainable parameters, while approaching full fine-tuning performance. Beyond simulation, CKT-WAM also demonstrates strong real-world long-horizon manipulation ability, achieving the best average success rate of 83.3\% across four multi-step and long-horizon tasks. Code is available at https://github.com/YuhuaJiang2002/CKT-WAM.

In this paper, we propose Lagrangian Gaussian Processes (LGPs) for probabilistic and data-efficient learning of dynamics via discrete forced Euler-Lagrange equations. Importantly, the geometric structure of the Lagrange-d'Alembert principle, which governs the motion of dynamical systems, is preserved by construction in the absence of external forces. This allows learning physically consistent models that overcome erroneous drift in the system's energy, thereby providing stable long-term predictions. At the core of our approach lie linear operators for Gaussian process conditioning, constructed from discrete forced Euler-Lagrange equations and variational discretization schemes. Thereby and unlike prior work, the method enables learning dynamics from discrete position snapshots, i.e., without access to a system's velocities or momenta. This is particularly relevant for a large class of practical scenarios where only position measurements are available, for instance, in motion capture or visual servoing applications. We demonstrate the data-efficiency and generalization capabilities of the LGPs in various synthetic and real-world case studies, including a real-world soft robot with hysteresis. The experimental results underscore that the LGPs learn physically consistent dynamics with uncertainty quantification solely from sparse positional data and enable stable long-term predictions.

Forward-Forward (FF) training allows each layer to learn from a local goodness criterion. In cumulative-goodness variants, however, later layers can inherit a task that earlier layers have already partially separated. We formalize this phenomenon as layer free-riding: under the softplus FF criterion, the class-discrimination gradient reaching block $d$ decays exponentially with the positive margin accumulated by preceding blocks. We then study three local remedies -- per-block, hardness-gated, and depth-scaled -- that recover current-layer separation measures without relying on backpropagated gradients. On CIFAR-10 and CIFAR-100, these remedies dramatically improve layer-separation statistics, with $4\times$--$45\times$ gains in deeper layers, while changing accuracy by less than one percentage point for non-degenerate training procedures. Tiny ImageNet provides a tougher cross-dataset check for our selected block-wise configuration and reveals the same qualitative gap between layer-health diagnostics and final accuracy. Calibration experiments further show that architecture and augmentation choices have a larger effect on final accuracy than the training-rule modifications studied here. Cumulative free-riding is therefore a real and repairable optimization pathology. Nonetheless, for the FF training rules, architectures, and datasets we study, it is not the dominant factor limiting achievable accuracy.

It remains unclear whether graph language models learn structural regularities or merely memorize training graphs; this cannot be resolved by current aggregate fidelity metrics alone. We develop a calibrated diagnostic protocol that combines frequent subgraph mining, a graph-level bootstrap baseline, and three-level frequency stratification to disentangle memorization from structural alignment. Using this framework, we show that graph language models can acquire structural regularities beyond memorization at scale, primarily in the high-frequency regime. This is supported by the following empirical evidence: On five TU benchmarks, LLaMA-style graph language models reach high subgraph-rank correlation, yet their alignment is matched or exceeded by the memorization bootstrap in most cases. At small scale, under our bootstrap diagnostic, fidelity is largely indistinguishable from verbatim recall. In contrast, at large scale with 3.75M graphs, verbatim memorization drops sharply while rank correlation remains near ceiling. Crucially, in a separate fixed-subsample analysis, frequent subgraph mining restricted to the novel-only subset closely tracks the corresponding all-generation Spearman correlation, providing evidence that the alignment is not driven solely by verbatim recall. Across all scales, high-frequency patterns are well reproduced, while rare patterns remain poorly covered, and this deficit narrows only marginally as capacity increases. We observe the same scale-dependent crossover under two distinct graph serializations (canonical DFS code and action sequences), providing evidence of robustness in our analysis.

Multimodal recommender systems exploit visual and textual signals to alleviate data sparsity, but this also makes them more vulnerable to evasion-based promotion attacks. Existing defenses are largely limited to single-modal settings and mainly focus on poisoning-based threats, leaving evasion-based threats underexplored. In this work, we first identify a cross-modal gradient mismatch under the multi-user promotion setting, where visual and textual perturbations are optimized in inconsistent directions due to the dominance of distinct user groups. This phenomenon dilutes the attack effectiveness and leads robust training to underestimate worst-case risks. To address this issue, we propose Untargeted Adversarial Training with Multimodal Coordination (UAT-MC). UAT-MC tackles the challenge of unknown targeted items in evasion-based attacks (as opposed to poisoning-based attacks) by treating all items as potential targets, and introduces a gradient alignment mechanism to explicitly correct this mismatch. This design ensures synchronized perturbations across modalities, thereby maximizing adversarial strength for robust training. Extensive experiments demonstrate that UAT-MC significantly improves robustness against promotion attacks while maintaining acceptable recommendation performance under the defense-accuracy trade-off. Code is available at https://github.com/gmXian/UAT-MC.