Latent or continuous chain-of-thought methods replace explicit textual rationales with a number of internal latent steps, but these intermediate computations are difficult to evaluate beyond correlation-based probes. In this paper, we view latent chain-of-thought as a manipulable causal process in representation space by modeling latent steps as variables in a structural causal model (SCM) and analyzing their effects through step-wise do-interventions. We study two representative paradigms (i.e., Coconut and CODI) on both mathematical and general reasoning tasks to investigate three key questions: (1) which steps are causally necessary for correctness and when answers become decodable early; (2) how influence propagates across steps and how this structure compares to explicit CoT; and (3) whether intermediate trajectories retain competing answer modes and how output-level commitment differs from representational commitment across steps. We find that latent-step budgets behave less like homogeneous extra depth and more like staged functionality with non-local routing, and we identify a persistent gap between early output bias and late representational commitment. These results motivate mode-conditional and stability-aware analyses, together with corresponding training/decoding objectives, as more reliable tools for interpreting and improving latent reasoning systems. Code is available at https://github.com/J1mL1/causal-latent-cot.

Being probabilistic models, during inference large language models (LLMs) display rare events: behaviour that is far from typical but highly significant. By definition all rare events are hard to see, but the enormous scale of LLM usage means that events completely unobserved during development are likely to become prominent in deployment. Here we present an end-to-end framework for the systematic analysis of rare events in LLMs. We provide a practical implementation spanning theory, efficient generation strategies, probability estimation and error analysis, which we illustrate with concrete examples. We outline extensions and applications to other models and contexts, highlighting the generality of the concepts and techniques presented here.

Autoregressive large language models (LLMs) deliver strong performance but require inherently sequential decoding, leading to high inference latency and poor GPU utilization. Speculative decoding mitigates this bottleneck by using a fast draft model whose outputs are verified in parallel by the target LLM; however, existing methods still rely on autoregressive drafting, which remains sequential and limits practical speedups. Diffusion LLMs offer a promising alternative by enabling parallel generation, but current diffusion models typically underperform compared with autoregressive models. In this paper, we introduce DFlash, a speculative decoding framework that employs a lightweight block diffusion model for parallel drafting. By generating draft tokens in a single forward pass and conditioning the draft model on context features extracted from the target model, DFlash enables efficient drafting with high-quality outputs and higher acceptance rates. Experiments show that DFlash achieves over 6x lossless acceleration across a range of models and tasks, delivering up to 2.5x higher speedup than the state-of-the-art speculative decoding method EAGLE-3.

Sampling from a distribution $p(x) \propto e^{-\mathcal{E}(x)}$ known up to a normalising constant is an important and challenging problem in statistics. Recent years have seen the rise of a new family of amortised sampling algorithms, commonly referred to as diffusion samplers, that enable fast and efficient sampling from an unnormalised density. Such algorithms have been widely studied for continuous-space sampling tasks; however, their application to problems in discrete space remains largely unexplored. Although some progress has been made in this area, discrete diffusion samplers do not take full advantage of ideas commonly used for continuous-space sampling. In this paper, we propose to bridge this gap by introducing off-policy training techniques for discrete diffusion samplers. We show that these techniques improve the performance of discrete samplers on both established and new synthetic benchmarks. Next, we generalise discrete diffusion samplers to the task of bridging between two arbitrary distributions, introducing data-to-energy Schrödinger bridge training for the discrete domain for the first time. Lastly, we showcase the application of the proposed diffusion samplers to data-free posterior sampling in the discrete latent spaces of image generative models.

Aerodynamic inverse design can improve vehicle and aircraft efficiency, but practical design rarely seeks performance alone: vehicle refinement must reduce drag while preserving visual features linked to design language, brand recognition and user perception. Traditional CFD-driven optimization is accurate but slow for broad exploration, and current learning-based methods are still largely performance-driven and lack a coherent target linking optimization, generation and visual consistency. Here we formulate visual preservation and aerodynamic improvement as one probability target. Designs consistent with a reference shape or view define a learned visual design distribution, which is reweighted by aerodynamic cost. Optimization then refines an initial geometry toward a low-cost, high-probability design, whereas guided generation samples lower-cost 3D candidates from the same input view. OpenFOAM evaluation shows that visual-feature-preserving optimization reduces vehicle drag by 5.8\% relative to the initial vehicle and reduces the best valid aircraft drag-to-lift objective by 28.8\% relative to the initial aircraft while preserving input visual features. For view-based generation, guidance reduces vehicle drag by 3.0\% and the aircraft drag-to-lift objective by 68.6\% relative to direct generation from the same view, while maintaining visual consistency. Wind-tunnel tests with 3D-printed vehicle prototypes provide an independent wake-level check, and controlled analyses explain the distributional mechanisms behind these results. This work provides a probabilistic foundation and practical route for visual-feature-preserving aerodynamic refinement and early-stage 3D design exploration.

This paper proposes FedNMap, a normal map-based method for composite federated learning, where the objective consists of a smooth loss and a possibly nonsmooth regularizer. FedNMap leverages a normal map-based update scheme to handle the nonsmooth term and incorporates a local correction strategy to mitigate the impact of data heterogeneity across clients. Under standard assumptions, including smooth local losses, weak convexity of the regularizer, and bounded stochastic gradient variance, FedNMap achieves linear speedup with respect to both the number of clients and the number of local updates for nonconvex losses, both with and without the Polyak-Łojasiewicz condition. To the best of our knowledge, this is the first algorithm establishing linear speedup for nonconvex composite federated learning. Numerical experiments corroborate our theoretical findings and demonstrate the linear speedup of FedNMap.

The design of Analog and Mixed-Signal (AMS) integrated circuits remains heavily reliant on expert knowledge, with transistor sizing a major bottleneck due to nonlinear behavior, high-dimensional design spaces, and strict performance constraints. Existing Electronic Design Automation (EDA) methods typically frame sizing as static black-box optimization, resulting in inefficient and less robust solutions. Although Large Language Models (LLMs) exhibit strong reasoning abilities, they are not suited for precise numerical optimization in AMS sizing. To address this gap, we propose AutoSizer, a reflective LLM-driven meta-optimization framework that unifies circuit understanding, adaptive search-space construction, and optimization orchestration in a closed loop. It employs a two-loop optimization framework, with an inner loop for circuit sizing and an outer loop that analyzes optimization dynamics and constraints to iteratively refine the search space from simulation feedback. We further introduce AMS-SizingBench, an open benchmark comprising 24 diverse AMS circuits in SKY130 CMOS technology, designed to evaluate adaptive optimization policies under realistic simulator-based constraints. AutoSizer experimentally achieves higher solution quality, faster convergence, and higher success rate across varying circuit difficulties, outperforming both traditional optimization methods and existing LLM-based agents.

Chain-of-thought (CoT) reasoning has become a central mechanism for eliciting multi-step reasoning in Large Language Models (LLMs). Yet recent evidence presents a tension: hidden states appear to already encode future reasoning before CoT fully unfolds, while explicit steps still remain crucial for tasks requiring compositional computation. To deepen the understanding between LLM's internal states and its verbalized reasoning trajectories, we investigate the latent planning strength of LLMs, through our probing method, Tele-Lens, applying to hidden states across diverse task domains. Our empirical results indicate that LLMs exhibit a myopic horizon, primarily conducting incremental transitions without precise global planning. Leveraging this characteristic, we propose a hypothesis on enhancing uncertainty estimation of CoT, which we validate that a sparse set of pivot positions can effectively represent the uncertainty of the entire path. We further underscore the significance of exploiting CoT dynamics, and demonstrate that automatic recognition of CoT bypass can be achieved without performance degradation. Our code, data and models are released at https://github.com/lxucs/tele-lens.

LLM-driven agents excel at sequential decision-making but often rely on on-the-fly reasoning, re-deriving solutions even in recurring scenarios. This insufficient experience reuse leads to computational redundancy and instability. To bridge this gap, we propose Skill-Pro, a framework enabling agents to autonomously learn reusable procedural skills from interaction experiences without parameter updates. By formalizing a Skill-MDP, Skill-Pro transforms passive episodic narratives into executable Skills defined by activation, execution, and termination conditions to ensure executability. To achieve reliable reusability without capability degradation, we introduce Non-Parametric PPO, which leverages semantic gradients for high-quality candidate generation and a PPO Gate for robust Skill verification. Through score-based maintenance, Skill-Pro sustains compact, high-quality procedural memory. Experimental results across in-domain, cross-task, and cross-agent scenarios demonstrate that Skill-Pro achieves superior reuse rates and significant gains with extreme memory compression. Visualized evolutionary trajectories and Skill distributions further reveal how Skill-Pro transparently accumulates, refines, and reuses procedural knowledge to facilitate long-term autonomy.

Joint-Embedding Predictive Architectures (JEPA) learn view-invariant representations and admit projection-based distribution matching for collapse prevention. Existing approaches regularize representations towards isotropic Gaussian distributions, but inherently favor dense representations and fail to capture the key property of sparsity observed in efficient representations. We introduce Rectified Distribution Matching Regularization (RDMReg), a sliced two-sample distribution-matching loss that aligns representations to a Rectified Generalized Gaussian (RGG) distribution. RGG enables explicit control over expected $\ell_0$ norm through rectification, while its continuous truncated component admits a maximum-entropy characterization under expected $\ell_p$ norm and support constraints. Equipping JEPAs with RDMReg yields Rectified LpJEPA, which strictly generalizes prior Gaussian-based JEPAs. Empirically, Rectified LpJEPA learns sparse, non-negative representations with favorable sparsity--performance trade-offs and competitive downstream performance on image classification benchmarks, showing that RDMReg can enforce sparsity while preserving task-relevant information.

We consider the problem of unsupervised skill segmentation and hierarchical structure discovery in reinforcement learning. While recent approaches have sought to segment trajectories into reusable skills or options, most rely on action labels, rewards, or handcrafted annotations, limiting their applicability. We propose a method that segments unlabelled trajectories into skills and induces a hierarchical structure over them using a grammar-based approach. The resulting hierarchy captures both low-level behaviours and their composition into higher-level skills. We evaluate our approach in high-dimensional, pixel-based environments, including Craftax and the full, unmodified version of Minecraft. Using metrics for skill segmentation, reuse, and hierarchy quality, we find that our method consistently produces more structured and semantically meaningful hierarchies than existing baselines. Furthermore, as a proof of concept, we demonstrate that these discovered hierarchies accelerate and stabilise learning on downstream reinforcement learning tasks.

Real-world federated systems seldom operate on static data: input distributions drift while privacy rules forbid raw-data sharing. We study this setting as Federated Domain-Incremental Learning (FDIL), where (i) clients are heterogeneous, (ii) tasks arrive sequentially with shifting domains, yet (iii) the label space remains fixed. Two theoretical pillars remain missing for FDIL under realistic deployment: a guarantee of backward knowledge transfer (BKT) and a convergence rate that holds across the sequence of all tasks with partial participation. We introduce SPECIAL (Server-Proximal Efficient Continual Aggregation for Learning), a simple, memory-free FDIL algorithm that adds a single server-side ``anchor'' to vanilla FedAvg: in each round, the server nudges the uniformly sampled participated clients update toward the previous global model with a lightweight proximal term. This anchor curbs cumulative drift without replay buffers, synthetic data, or task-specific heads, keeping communication and model size unchanged. Our theory shows that SPECIAL (i) preserves earlier tasks: a BKT bound caps any increase in prior-task loss by a drift-controlled term that shrinks with more rounds, local epochs, and participating clients; and (ii) learns efficiently across all tasks: the first communication-efficient non-convex convergence rate for FDIL with partial participation, O((E/NT)^(1/2)), with E local epochs, T communication rounds, and N participated clients per round, matching single-task FedAvg while explicitly separating optimization variance from inter-task drift. Experimental results further demonstrate the effectiveness of SPECIAL.

Current LLM post-training methods optimize complete reasoning trajectories through Supervised Fine-Tuning (SFT) followed by outcome-based Reinforcement Learning (RL). While effective, a closer examination reveals a fundamental gap: this approach does not align with how humans actually solve problems. Human cognition naturally decomposes problem-solving into two distinct stages: first acquiring abstract strategies (i.e., meta-knowledge) that generalize across problems, then adapting them to specific instances. In contrast, by treating complete trajectories as basic units, current methods are inherently problem-centric, entangling abstract strategies with problem-specific execution. To address this misalignment, we propose a cognitively-inspired framework that explicitly mirrors the two-stage human cognitive process. Specifically, Chain-of-Meta-Thought CoMT focuses supervised learning on abstract reasoning patterns without specific executions, enabling acquisition of generalizable strategies. Confidence-Calibrated Reinforcement Learning (CCRL) then optimizes task adaptation via confidence-aware rewards on intermediate steps, preventing overconfident errors from cascading and improving execution reliability. Experiments across four models and ten benchmarks show 2.10% and 3.86% improvements in-distribution and out-of-distribution respectively over standard methods, while remaining highly robust to variations in teacher model selection, optimization methods, and symbolic perturbations.

We present a unified framework for quantifying the similarity between representations through the lens of \textit{usable} information, offering a rigorous theoretical and empirical synthesis across three key dimensions. First, addressing functional similarity, we establish a formal link between stitching performance and conditional mutual information. We further reveal that stitching is inherently asymmetric, demonstrating that robust functional comparison necessitates a bidirectional analysis rather than a unidirectional mapping. Second, concerning representational similarity, we find that reconstruction-based metrics and standard tools (e.g., CKA, RSA) act as estimators of usable information under specific constraints. Crucially, we show that similarity is relative to the capacity of the predictive family: representations that appear distinct to a rigid observer may be identical to a more expressive one. Third, we demonstrate that representational similarity is sufficient but not necessary for functional similarity. We unify these concepts through a task-granularity hierarchy: similarity on a complex task guarantees similarity on any coarser derivative, establishing representational similarity as the limit of maximum granularity: input reconstruction.

Machine unlearning seeks to remove the influence of specific training data from a model, a need driven by privacy regulations and robustness concerns. Existing approaches typically modify model parameters, but such updates can be unstable, computationally costly, and limited by local approximations. We introduce Representation Unlearning, a framework that performs unlearning directly in the model's representation space. Instead of modifying model parameters, we learn a transformation over representations that imposes an information bottleneck: maximizing mutual information with retained data while suppressing information about data to be forgotten. We derive variational surrogates that make this objective tractable and show how they can be instantiated in two practical regimes: when both retain and forget data are available, and in a zero-shot setting where only forget data can be accessed. Experiments across several benchmarks demonstrate that Representation Unlearning achieves more reliable forgetting, better utility retention, and greater computational efficiency than parameter-centric baselines.

Learning from Noisy Labels (LNL) remains a fundamental challenge in deep learning because real-world datasets often contain corrupted annotations. Most existing methods rely on label correction or sample selection mechanisms. In contrast, we study LNL from an optimization perspective by establishing a theoretical connection between label noise and the flatness-seeking behavior of Sharpness-Aware Minimization (SAM). Based on this analysis, we propose Noise-Compensated Sharpness-Aware Minimization (NCSAM), which uses a noise-compensated perturbation to counteract the optimization bias induced by noisy labels. By correcting distorted SAM perturbations, NCSAM mitigates the memorization of noisy labels during training while preserving the simplicity of optimization-based learning. Experiments on synthetic and real-world noisy-label benchmarks show that NCSAM consistently improves over SAM-based optimization baselines and remains competitive with representative noisy-label learning methods.

Document-level Information Extraction (DocIE) aims to produce an output template with the entities, relations, and events of interest occurring in the given document. Standard practices include prompting decoder-only LLMs using greedy decoding to avoid output variability. Rather than treating this variability as a limitation, we show that sampling can produce substantially better solutions than greedy decoding, especially when using reasoning models. We thus propose ThinkTwice, a sampling and selection framework in which the LLM generates multiple candidate templates for a given document, and a selection module chooses the most suitable one. We introduce both an unsupervised method that exploits agreement across generated outputs, and a supervised selection method using reward models trained on labeled DocIE data. To address the scarcity of golden reasoning trajectories for DocIE, we propose a rejection-sampling-based method to generate silver training data that pairs output templates with reasoning traces. Our experiments show the validity of unsupervised and supervised ThinkTwice, consistently outperforming greedy baselines and the supervised state-of-the-art.

Black-box variational inference (BBVI) with Gaussian mixture families offers a flexible approach for approximating complex posterior distributions without requiring gradients of the target density. However, standard numerical optimization methods often suffer from instability and inefficiency. We develop a stable and efficient framework that combines three key components: (1) affine-invariant preconditioning via natural gradient formulations, (2) an exponential integrator that unconditionally preserves the positive definiteness of covariance matrices, and (3) adaptive time stepping to ensure stability and to accommodate distinct warm-up and convergence phases. The proposed approach has natural connections to manifold optimization and mirror descent. For Gaussian posteriors, we prove exponential convergence in the noise-free setting and almost-sure convergence under Monte Carlo estimation, rigorously justifying the necessity of adaptive time stepping. Numerical experiments on multimodal distributions, Neal's multiscale funnel, and a PDE-based Bayesian inverse problem for Darcy flow demonstrate the effectiveness of the proposed method.

Post-training pretrained autoregressive models (ARMs) into masked diffusion models (MDMs) has emerged as a cost-effective way to overcome the limitations of sequential generation. Yet it remains unclear whether post-trained MDMs acquire genuinely new computational mechanisms or merely re-express autoregressive computation in a non-autoregressive form. Through a comparative circuit analysis of ARMs and their MDM counterparts post-trained from the same backbones, we uncover two complementary axes of reorganization. Structurally, the shift is task-dependent: MDMs preserve autoregressive circuitry on locally causal tasks but abandon inherited pathways and front-load computation into early layers on global tasks. Semantically, the shift is consistent across regimes: sharp, localized specialization in ARMs gives way to distributed integration in MDMs. Together, these findings show that diffusion post-training is not a surface-level change in the generation procedure but a reorganization of internal computation whose depth depends on the task.

Realistic text-to-SQL workflows often require joining multiple tables. As a result, accurately retrieving the relevant set of tables becomes a key bottleneck for end-to-end performance. We study an open-book setting where queries must be answered over large, heterogeneous table collections pooled from many sources, without clean scoping signals such as database identifiers. Here, dense retrieval (DR) achieves high recall but returns many distractors, while join-aware alternatives often rely on extra assumptions and/or incur high inference overhead. We propose CORE-T, a scalable, training-free framework that enriches tables with LLM-generated purpose metadata and pre-computes a lightweight table-compatibility cache. At inference time, DR returns top-K candidates; a single LLM call selects a coherent, joinable subset, and a two-step additive adjustment stage restores strongly compatible tables. Across Bird, Spider, MMQA, and Beaver, CORE-T improves over DR by up to 22.7 points in table-selection F1 while returning up to 40% fewer tables, and by up to 24.4 points in multi-table execution accuracy, and uses 1.64-4.20x fewer total selection tokens than LLM-intensive baselines.

Counting and tracking dense crowds in large-scale scenes is a highly practical yet challenging problem. Existing methods mostly rely on fixed-camera datasets with limited scene coverage, making them inadequate for crowd analysis in large-scale scenes. To bridge this gap, we introduce MovingDroneCrowd++, the largest video-level dataset dedicated to dense crowd counting and tracking with fast-moving drones, captured under diverse flight altitudes, camera angles, and illumination conditions. Existing methods, however, still fail to achieve satisfactory video individual counting or tracking performance under these challenging aerial conditions. To this end, we propose GD3A (Global Density map Decomposition via group-wise Descriptor Association), a video individual counting method that first establishes pixel-level correspondences between pedestrian descriptors across frames via optimal transport with an adaptive dustbin score. Then, group-wise association is adopted to guide the decomposition of the global density map into shared, inflow, and outflow density maps. We further introduce a pedestrian tracking method, DVTrack (Descriptor Voting Track), which converts descriptor-level matching into instance-level association through descriptor voting. Our methods rely on the association results of group-wise multiple descriptors for each pedestrian rather than a single vector. Since intra-group matching errors do not affect the final counting and tracking results, our methods are more robust in dense crowds and challenging aerial conditions. Experiments show that our methods achieve substantial gains in both crowd counting and tracking on moving-drone videos with dense crowds and complex motions, reducing counting error by 47.4% and improving tracking accuracy by 64.6%. Code, dataset, and pretrained models are available at https://github.com/fyw1999/MovingDroneCrowd.

Social media platforms are increasingly dominated by long-form multimodal content, where harmful narratives are constructed through a complex interplay of audio, visual, and textual cues. While automated systems can flag hate speech with high accuracy, they often function as "black boxes" that fail to provide the granular, interpretable evidence, such as precise timestamps and target identities, required for effective human-in-the-loop moderation. In this work, we introduce TANDEM, a unified framework that transforms audio-visual hate detection from a binary classification task into a structured reasoning problem. Our approach employs a novel tandem reinforcement learning strategy where vision-language and audio-language models optimize each other through self-constrained cross-modal context, stabilizing reasoning over extended temporal sequences without requiring dense frame-level supervision. Experiments across three benchmark datasets demonstrate that TANDEM significantly outperforms zero-shot and context-augmented baselines, achieving 0.73 F1 in target identification on HateMM (a 30% improvement over state-of-the-art) while maintaining precise temporal grounding. We further observe that while binary detection is robust, differentiating between offensive and hateful content remains challenging in multi-class settings due to inherent label ambiguity and dataset imbalance. More broadly, our findings suggest that structured, interpretable alignment is achievable even in complex multimodal settings, offering a blueprint for the next generation of transparent and actionable online safety moderation tools.

Autoregressive (AR) models have achieved remarkable success in image synthesis, yet their sequential nature imposes significant latency constraints. Speculative Decoding offers a promising avenue for acceleration, but existing approaches are limited by token-level ambiguity and lack of spatial awareness. In this work, we introduce Multi-Scale Local Speculative Decoding (MuLo-SD), a novel framework that combines multi-resolution drafting with spatially informed verification to accelerate AR image generation. Our method leverages a low-resolution drafter paired with an up-sampling step to propose candidate image tokens, which are then verified in parallel by a high-resolution target model. Crucially, we incorporate a local rejection and resampling mechanism, enabling efficient correction of draft errors by focusing on spatial neighborhoods rather than raster-scan resampling after the first rejection. When integrated with parallel decoding resampling, MuLo-SD achieves substantial speedups -- up to $\mathbf{5\times}$ -- outperforming both speculative decoding and parallel decoding baselines in terms of acceleration, while maintaining comparable semantic alignment and perceptual quality. These results are validated using GenEval, DPG-Bench, and FID/HPSv2 on the MS-COCO 5k validation split. Extensive ablations highlight the impact of up-sampling design, probability pooling, and local rejection and resampling with neighborhood expansion. Our approach sets a new state-of-the-art in speculative decoding for image synthesis, bridging the gap between efficiency and fidelity. Project page is available at https://qualcomm-ai-research.github.io/mulo-sd-webpage/ .

We study how syntactic and semantic information is encoded in inner layer representations of Large Language Models (LLMs), focusing on the very large DeepSeek-V3. We find that, by averaging hidden-representation vectors of sentences sharing syntactic structure or meaning, we obtain vectors that capture a significant proportion of the syntactic and semantic information contained in the representations. In particular, subtracting these syntactic and semantic ``centroids'' from sentence vectors strongly affects their similarity with syntactically and semantically matched sentences, respectively, suggesting that syntax and semantics are, at least partially, linearly encoded. We also find that the cross-layer encoding profiles of syntax and semantics are different, and that the two signals can to some extent be decoupled, suggesting differential encoding of these two types of linguistic information in LLM representations.

Fine-grained recognition of marine organisms is important for ecological research, biodiversity monitoring, habitat conservation, and evidence-based policy-making. However, many existing approaches primarily rely on object- or ROI-centered representations. These limitations can reduce discriminative performance in challenging underwater scenes, where visually similar organisms often appear under diverse environmental conditions. To address these challenges, we propose MATANet (Multi-context Attention and Taxonomy-Aware Network), a framework for fine-grained taxonomic recognition of marine organisms. MATANet is motivated by expert taxonomic identification practices, in which both organism-level morphology and contextual cues are considered during recognition. The framework consists of two main components. First, the Multi-Context Environmental Attention Module (MCEAM) models cross-attention between the primary region of interest (ROI) and multi-scale surrounding environmental regions, thereby combining local morphological cues with habitat-level contextual information. Second, the Hierarchy-Aware Representation Learning Module (HRLM) uses taxonomic hierarchy as auxiliary supervision to regularize representation learning and encourage semantically structured embeddings across taxonomic levels. By jointly modeling organism appearance, environmental context, and taxonomic structure, MATANet learns more discriminative representations for fine-grained taxonomic recognition. Experiments on FathomNet2025 and LifeCLEF2015-Fish demonstrate that MATANet consistently improves recognition performance over existing methods. Additional experiments on FAIR1M further examine the applicability of the proposed framework beyond underwater imagery. Notably, MATANet ranked first in the FathomNet 2025 Challenge at the CVPR 2025 FGVC12 workshop.

Tokenizer transplant in cross-vocabulary model composition reconstructs donor-only embedding rows as weighted combinations over shared lexical anchors and reuses those coefficients on the base. We identify a structural geometric property of this reconstruction: the same coefficient vector reaches different sets in the donor and base anchor spans, an \emph{asymmetric realizability} gap. Across 65 donor-base pairs under OMP, with cross-operator validation on CLP, WECHSEL, and FOCUS, we construct \textit{breaker tokens}: single coefficient vectors that remain statistically inert in the donor anchor span while producing a high-salience reconstruction in the base. The same Gemma-2-2B donor checkpoint admits this construction against 13 different downstream bases drawn from five model families. The planted direction passes weight-merging with a clean reference unchanged. In a deployer case study, standard LoRA fine-tuning suppresses the breaker primarily on prompts whose distribution matches the training corpus and is not a sufficient mitigation against this attack family in our setting. The tested spectral filters miss the asymmetry. We discuss potential misuse in the open-weight composition supply chain.

Solving partial differential equations (PDEs) on shapes underpins many shape analysis and engineering tasks; yet, prevailing PDE solvers operate on polygonal/triangle meshes while modern 3D assets increasingly live as neural representations. This mismatch leaves no suitable method to solve surface PDEs directly within the neural domain, forcing explicit mesh extraction or per-instance residual training, preventing end-to-end workflows. We present a novel, meshfree formulation that learns a local update operator conditioned on neural (local) shape attributes, enabling surface PDEs to be solved directly where the (neural) data lives. The operator integrates naturally with prevalent neural surface representations, is trained once on a single representative shape, and generalizes across shape and topology variations, enabling accurate, fast inference without explicit meshing or per-instance optimization while preserving differentiability. Across analytic benchmarks (heat diffusion and Poisson equations on the sphere) and on diverse shapes and neural surface representations, our method achieves accuracy comparable to classical solvers while enabling a unified, end-to-end pipeline across neural and traditional surface representations. Our source code and project page: https://welschinger.github.io/Learning-to-Solve-PDEs-on-Neural-Shape-Representations/.

The paper establishes generalization bounds for multitask deep neural networks using operator-theoretic techniques. The authors propose a tighter bound than those derived from conventional norm based methods by leveraging small condition numbers in the weight matrices and introducing a tailored Sobolev space as an expanded hypothesis space. This enhanced bound remains valid even in single output settings, outperforming existing Koopman based bounds. The resulting framework maintains key advantages such as flexibility and independence from network width, offering a more precise theoretical understanding of multitask deep learning in the context of kernel methods.

This paper presents novel generalization bounds for vector-valued neural networks and deep kernel methods, focusing on multi-task learning through an operator-theoretic framework. Our key development lies in strategically combining a Koopman based approach with existing techniques, achieving tighter generalization guarantees compared to traditional norm-based bounds. To mitigate computational challenges associated with Koopman-based methods, we introduce sketching techniques applicable to vector valued neural networks. These techniques yield excess risk bounds under generic Lipschitz losses, providing performance guarantees for applications including robust and multiple quantile regression. Furthermore, we propose a novel deep learning framework, deep vector-valued reproducing kernel Hilbert spaces (vvRKHS), leveraging Perron Frobenius (PF) operators to enhance deep kernel methods. We derive a new Rademacher generalization bound for this framework, explicitly addressing underfitting and overfitting through kernel refinement strategies. This work offers novel insights into the generalization properties of multitask learning with deep learning architectures, an area that has been relatively unexplored until recent developments.

Motion planning for autonomous driving (AD) faces a critical trade-off. While traditional rule-based pipelines offer verifiable safety and interpretability, they often fail to generalize in complex scenarios. Conversely, emerging learning-based methods-including imitation learning (IL), reinforcement learning (RL), and generative AI-offer greater adaptability but are often constrained by opacity and safety risks. Existing surveys typically analyze these AI methods in isolation, overlooking the potential of integrating them with rigorous control frameworks. To bridge this gap, this paper presents the first systematic review of the Data-Driven Optimal Control (DDOC) paradigm, explicitly examining how it synergizes the theoretical guarantees of optimal control with the adaptive capabilities of modern machine learning. Building on this framework, we propose the first roadmap for DDOC-based motion planning, structuring its implementation into three critical dimensions: customization, dynamics adaptation, and self-tuning. Finally, to close the remaining reality gap, we identify four future research directions, thereby accelerating the transition to trustworthy and human-like autonomous driving.