Formal theorem provers based on large language models (LLMs) are highly sensitive to superficial variations in problem representation: semantically equivalent statements can exhibit drastically different proof success rates, revealing a failure to respect structural symmetries inherent in formal mathematics. This raises a central question: what are the right symmetries for formal theorem proving? We introduce rewriting categories, a category-theoretic framework capturing the compositional, generally non-invertible transformations induced by proof tactics, and use it to formalize two symmetry notions: proof equivariance, governing how proof distributions transform under rewrites, and success invariance (i.e., invariance of success probability), requiring equivalent statements to be solved with the same probability. We observe that state-based next-tactic provers naturally satisfy proof equivariance by operating on proof states. In contrast, state-of-the-art LLM-based provers satisfy neither property, exhibiting large performance variation across equivalent formulations. To mitigate this, we propose test-time methods that aggregate over equivalent rewritings of the input, showing theoretically that they recover success invariance in the sampling limit, and empirically, that they improve robustness and performance under fixed inference budgets. Our results highlight symmetry as a key missing inductive bias in LLM-based theorem proving and suggest test-time computation as a practical route to approximate it.

Accurate brain tumor segmentation using multiparametric MRI is critical for effective treatment planning. However, in clinical settings, complete acquisition of all MRI sequences is not always possible. The absence of certain MRI modalities results in substantial performance degradation in existing segmentation methods, which typically rely on naive feature concatenation or direct fusion strategies. To address this limitation, we propose a novel segmentation model D3Seg which is designed to maintain stable performance under missing-modality settings. D3Seg introduces Multi-hop Modality Graph Fusion (MMGF) to model higher order inter-modality dependencies, a lightweight diffusion-based imputation mechanism to compensate for missing T1ce representations in latent space, and probability-space decision refinement to mitigate dominant class overconfidence and improve delineation of underrepresented tumor subregions. Extensive evaluation on BraTS 2023 dataset demonstrates that our D3Seg model consistently improves segmentation performance under missing modality configurations. The proposed model achieves approximately 1.5-2.0% Dice improvement on enhancing tumor (ET) and around 1.0% on tumor core (TC) across multiple missing modality configurations compared to the current state-of-the-art model, while maintaining computational efficiency.

Climate emulation is an out-of-distribution (OOD) projection task. This is precisely the challenge where modern Machine Learning (ML) methods are most prone to failure. Consequently, while current ML emulators trained on present climate achieve high in-distribution performance, their future reliability under the inevitable distribution shifts of a changing climate remains a critical, poorly understood blind spot. Addressing this challenge requires a fundamental shift in how we understand, evaluate, and design climate emulators. In this work, we first confirm that climate change drives a statistically significant and progressively growing shift in atmospheric state distributions, rendering standard evaluation protocols insufficient. We empirically establish that seasonal variation serves as an effective proxy for these long-term climate shifts, providing access to $\textit{real-world}$ distribution shifts without recourse to heuristics like synthetic perturbations. Motivated by this link, we introduce a novel evaluation framework that leverages seasonal shifts as a rigorous, zero-overhead testbed for emulator robustness. Our systematic characterisation confirms that current state-of-the-art hybrid-ML emulators degrade significantly under these realistic shifts. Finally, we chart a path forward by identifying compositional generalisation, the ability to form novel combinations from observed elementary components, as a principled route towards robust climate emulation. We demonstrate that physically motivated decompositions substantially improve OOD performance with only modest trade-offs against in-distribution performance, providing an avenue towards ML-driven climate emulators robust to an unknown future.

Idioms pose a fundamental challenge for language models, as their meaning cannot be inferred from surface form alone. Understanding such expressions, therefore, requires semantic abstraction beyond lexical overlap. We introduce IdioLink, a retrieval benchmark designed to test whether models can link idiomatic expressions to conceptually equivalent meanings expressed in literal or paraphrased forms. IdioLink comprises 10,700 documents and 2,140 queries, spanning 107 idioms with both literal and figurative uses. Each document and query is annotated with spans that convey the core meaning. Evaluating strong embedding baselines (e.g., BGE, E5, Contriever, and Qwen), we show that current models struggle to retrieve equivalent meanings across divergent surface realizations, relying instead on topical and shallow semantic cues. IdioLink exposes key gaps in idiom-aware semantic retrieval and provides a challenging testbed for future models.

Predictive modelling is important for health data analysis and data-driven clinical decision-making. However, predictive studies are challenging to design optimally by hand when tens or even hundreds of features require selection, transformation, or interaction modelling. While complex machine learning models offer high performance, their "black-box" nature limits the clinical trust, transparency, and interpretability required for decision-making. We developed and evaluated an Exploratory AI Recommender that provides data-driven recommendations to improve predictive performance of existing interpretable statistical models. The developed framework uses flexible AI modelling to capture complex data patterns and explainable AI techniques to translate the patterns into three recommendation types: feature exclusion, non-linear terms, and feature interactions. We evaluated the framework by comparing predictive performance of a baseline (i.e., no interactions or non-linear terms) Cox Proportional Hazards (CPH) model against an augmented CPH incorporating recommendations suggested by our method. The primary analysis predicts the time to the first occurrence of a fall or related injury in 245,614 patients. Our method recommended excluding 23 features, including non-linear terms for two features, and including 221 suggested feature interactions. The C-index improved from 0.805 (95% CI 0.798-0.812) to 0.815 (95% CI 0.809-0.822), and so did calibration (intercept: -0.006 to 0.003; slope: 1.063 to 0.950). All recommendations were supported by existing literature. The method also proved effective on two additional public datasets, demonstrating wider applicability. The proposed Exploratory AI Recommender demonstrates the potential of explainable AI and data-driven study design to improve the process of developing, and the performance of high-dimensional transparent predictive models.

Static benchmarks capture only part of how large language models behave in practice. Real systems place models inside repeated loops with time limits, formatting constraints, and failure modes. We study this setting in a timed multi-phase Risk environment with explicit victory targets and repeated planning and execution cycles. In a replicated 32-game cross-provider championship under frozen rules, gemini-3.1-pro-preview won 20 of 32 games against gpt-5.1, claude-opus-4-7, and kimi-k2.6, and the pooled winner distribution differs strongly from an equal-strength null (p approx 1.5 x 10^-5). We then separate planning from execution by standardizing execution on a cheaper Gemini Flash scaffold. Under this design, a pooled 32-game planner bakeoff is consistent with near-equality (p approx 0.821), which indicates that much of the earlier provider spread came from end-to-end system behavior rather than planning alone. To study mechanism, we analyze saved planning and execution traces from the provider championship. Gemini refers to the terminal objective far more often than the other models and increases that focus as victory approaches. Gemini also converts more turns into deep conquest chains, even though it is not the cleanest runtime. These results show that live-agent performance depends on objective tracking, execution conversion, cost, and runtime reliability, and they support evaluating LLMs as components in bounded workflows rather than as isolated benchmark respondents.

We introduce a novel 3D hand pose estimator that can accurately recover the shape and pose of people's hands in a room from afar, typically from fixed cameras at room corners, in extremely low-resolution and frequently occluded views. Our key idea is to fully leverage hand-body coordination, its temporal progression, and multiview observations. We achieve this with a novel Transformer-based model, in which hand and body configurations are modeled through correlations between their visual features expressed as per-view tokens, and their temporal coordination is exploited in an autoregressive manner. We introduce a novel dataset, which we refer to as REACH, Room-Environment dataset Annotated with Chest cameras for Hand pose estimation, to train and test our method. REACH is a first-of-its-kind large-scale hand pose dataset that captures accurate hand movements of 50 participants across a wide variety of daily activities. In order to avoid interfering with natural movements while annotating the hands with accurate shape and pose, we leverage concealed chest cameras. Through extensive experiments, including comparative studies with existing methods, we show that our model, REACH-Net, achieves highly accurate 3D hand pose estimation from afar. These results broaden the horizon of 3D hand pose estimation, especially towards "in-the-wild" continuous human behavior analysis.

Aspect-based sentiment analysis (ABSA) requires models to bind sentiment evidence to the correct aspect, making it a natural testbed for fine-grained structural reasoning. We introduce GHI, a Graphormer-over-Conditioned-Hypergraph-Incidence framework that is designed as an incidence-based structural reasoning layer built on a bipartite topology. GHI represents diverse linguistic and semantic evidence as token--hyperedge incidence relations, allowing different structural signals to be incorporated through a unified interface. Extensive experiments on six standard ABSA benchmarks show that GHI outperforms all baselines on the SemEval domains, and multi-seed evaluations show stable improvements over strong DeBERTa. Further experiments show that with only 247M parameters, GHI approaches the performance of 11B Flan-T5 based methods on the ISE benchmark. Moreover, it demonstrates strong robustness on the challenging ARTS datasets, maintaining highly competitive performance where traditional models degrade. These results demonstrate that compact structural reasoning remains a valuable alternative to scale-driven approaches for fine-grained tasks.

We study how we can leverage only a handful of characteristics of a transformer's architecture to closely predict the number of different sequences it can output, both qualitatively and quantitatively. We provide an upper bound depending on the length of the prompt, which we show empirically to be tight up to a factor less than 10, across architectures and model sizes. Our analysis also provides a theoretical explanation for previously observed empirical failures of transformers on simple sequence tasks, such as copying and cramming. Formally, we prove that (i) the maximal length of accessible sequences (those that the transformer can output for some prompt) grows linearly with the prompt length, (ii) beyond a critical threshold, the proportion of accessible sequences decays exponentially with sequence length, and (iii) the linear coefficient relating prompt length to accessible sequence length admits a theoretical upper bound. Notably, these results hold even with unbounded context and computation time.

Backtracking search underlies classical constraint solvers, planners, and theorem provers. Recent transformer-based reasoning systems explore search trees over their own intermediate steps. A common training recipe fits an autoregressive next-token loss on offline solver traces. The model's input at each step is a cumulative trace of all prior decisions. The optimal continue-or-backtrack predictor depends only on the current search state, since two trajectories reaching the same state admit the same viable continuations. We show that decoder-only transformers trained on cumulative traces fail this requirement in two ways: the trace can scatter state features across many positions (scattered retrieval), and the predictor can condition on the trajectory rather than the state (history entanglement). We address scattered retrieval with localization, a trace-level fix that rewrites each decision block to expose state features locally. We address history entanglement with Selective State Attention (SSA), a fixed attention mask that enforces state-based decisions structurally without modifying training data, objective, or parameters. We focus on reactive verification, after propagation has exposed a contradiction. We test SSA on 3-SAT, graph coloring, Blocks World, and backtracking parsing. On same-state pairs that differ only in prior history, SSA emits identical decisions while a cumulative-trained causal baseline does not. Our contribution is a diagnostic of transformer behavior on serialized trajectory data, paired with a structural fix. Pretrained language models that search over their own reasoning steps may face the same failure. Our analysis opens up inference-time context clearing as a candidate way to apply the same isolation without retraining.

Recent advances in large language models and tool-using agents have expanded the range of benchmarked web tasks. Yet an important class of specialized retrieval tasks remains undercharacterized. On many specialized data-retrieval websites, answer-bearing evidence becomes accessible only after establishing the correct site-specific retrieval state through filters, views, hierarchies, or scopes. We term this capability state-gated retrieval (SGR). We introduce SGR-Bench, a benchmark for this setting containing 100 expert-curated tasks spanning six source families and 12 public data ecosystems. Each task requires discovering the appropriate website and configuring its site-specific retrieval state to produce a structured answer. SGR-Bench pairs constraint-guided and goal-oriented formulations of the same underlying problems, enabling controlled comparisons between explicit and implicit guidance for state-gated retrieval. We evaluate eight CLI-based agentic LLM systems and three commercial search-agent products. On SGR-Bench, the strongest system reaches only 66.18% item-level F1, while row-level F1 remains much lower. A manual audit of 156 analyzable failed CLI trajectories shows why: agents often reach a relevant web source, but establish the wrong site-specific retrieval state. Retrieval-scope drift (37.2%) and criterion mismatch (27.6%) dominate, whereas final answer composition accounts for only 10.3%. The dataset and single-case evaluation instructions are available at https://huggingface.co/datasets/PKUAIWeb/SGR-BENCH.

Self-play reinforcement learning trains language models on their own generated tasks, co-evolving a proposer and solver without human labels. Recent systems report strong reasoning gains, but collapse and instability are widely observed and poorly understood. The dominant response treats this as a reward-design problem. We argue instead that self-play stability is governed by two distinct levers: a data-level gate that decides which proposer-generated tasks enter the training pool, and the reward signal that updates the policy on tasks already admitted. Through controlled experiments on a Python output-prediction task and a deterministic-DSL twin task that strips pretraining priors, output ambiguity, and executor noise, we find the two levers are asymmetric. A strict gate is sufficient for stability under every reward variant we test, including a self-consistency reward with no access to ground truth; while no reward variant is sufficient once the gate is removed. This asymmetry exposes a counter-intuitive coupling we call the Grounded Proposer Paradox: a proposer with ground-truth access accelerates collapse faster than an ungrounded one when paired with a self-consistency solver, by concentrating training on clean tasks that form the fastest path to a spurious self-consistent attractor. Replacing the binary gate with a continuous strictness parameter $\varepsilon$ further reveals a two-stage phase transition: training-side metrics decouple at low $\varepsilon$, while validation accuracy holds until $\varepsilon$ is much higher. Data-level gating, not reward calibration, is the binding constraint on self-play stability.

Assurance arguments provide a clear and structured way to explain why stakeholders should trust that a system satisfies certain properties, yet widely used notations, e.g.Goal Structuring Notation (GSN), typically lack an operational semantics for deriving assurance confidence. Existing approaches address structure and soundness but largely reason over truth values, not over confidence in the justification of claims. Subjective Logic (SL) offers a calculus of belief, disbelief, and uncertainty with operators for combining opinions, enabling confidence propagation under incomplete, conflicting, or subjective evidence. However, existing SL-based approaches do not provide a uniform, compositional semantics that covers all argument elements and relations to enable overall confidence assessment. We propose a confidence semantics that represents argument elements as SL opinions and maps relations between elements to SL operators modelling how confidence flows, effectively turning the argument into an analyzable confidence network. The approach provides explicit warrants, principled handling of context, preserved provenance, and compatibility with GSN, along with practical guidance using an exemplary assurance confidence assessment.

Reinforcement learning post-training has improved the reasoning ability of large language models, but often produces unnecessarily long, repetitive, or semantically opaque reasoning traces. Existing efficient reasoning methods mainly regulate response length through explicit budgets or length-aware rewards, leaving intermediate reasoning content weakly supervised. We propose CLORE, a content-level optimization framework that improves reasoning efficiency by editing correct on-policy rollouts. CLORE uses an external augmentation model to delete repetitive segments, illegible or task-irrelevant content, and superfluous reasoning after the solution is established, while preserving the final answer. The resulting augmented--original pairs are optimized with an auxiliary reference-free DPO objective alongside standard policy-gradient training. By restricting augmentation to correct trajectories and performing local deletion, CLORE keeps edited rollouts close to the policy distribution and mitigates off-policy mismatch. Experiments on DeepSeek-R1-Distill-Qwen-7B and Qwen2.5-Math-7B across five mathematical reasoning benchmarks show that CLORE improves the accuracy--efficiency trade-off and remains compatible with GRPO, DAPO, Training Efficient, and ThinkPrune. Content-level analyses further show that CLORE reduces repetitive reasoning, illegible content, and post-answer exploration, supporting content-level supervision as a complementary direction to length-level control.

Video Capsule Endoscopy (VCE) poses a challenging multi-label temporal classification problem, requiring simultaneous localization of 8 anatomical regions and detection of 9 pathological findings across tens of thousands of frames. We present GALAR-TemporalNet v2, a hierarchical temporal model that addresses three core challenges: extreme class imbalance, long-range temporal dependencies, and pathology--anatomy entanglement. Our architecture combines windowed self-attention for local modeling, a Dual-Graph GCN for global frame relationships, and Bidirectional Mamba for selective boundary context encoding. A novel anatomy prototype residual pathway decouples pathological deviation signals from normal organ appearance, and a frame-level GCN skip connection stabilizes training of visually confusable rare classes. The competition version, GALAR-TemporalNet, achieved an overall mAP@0.5 of 0.2644 and mAP@0.95 of 0.2353 on the RARE-VISION test set. Following the competition, the redesigned GALAR-TemporalNet v2 -- incorporating a restructured pathology branch, refined loss functions, and extended post-processing -- improved these results to mAP@0.5 of 0.3409 and mAP@0.95 of 0.3333.

Large language models increasingly require specialization across diverse domains, yet existing approaches struggle to balance multi-domain capacities with strict memory and inference constraints. In this work, we introduce SkillWeave, a modular improvement framework that enables LLMs to specialize under fixed memory budgets. SkillWeave partitions full capabilities of a general-purpose model into skillpacks -- lightweight, domain-specific delta modules -- that reorganize and refine the model's internal knowledge. For efficient deployment, SkillWeave integrates SkillZip to compress skillpacks into compact and inference-ready format, enabling strong multi-domain performance with low-latency execution. On multi-task and agentic benchmarks, a 9B SkillWeave model outperforms several baselines and even surpasses a 32B monolithic LLM, while achieving up to 4x speedup.

This paper presents the Arabic Women and Society Corpus, a ten year collection of 252,487 public Arabic Facebook posts related to women's empowerment and social wellbeing. The corpus was collected from 51,660 pages across 77 countries between 2013 and 2024, resulting in more than 267 million user interactions. Each post includes engagement metrics such as shares, comments, and emotional reactions, providing a unique view of audience sentiment and social attention. The data were processed using an automated pipeline with language identification, normalization, and metadata cleaning to ensure reliability and reproducibility. The corpus enables large scale analysis of gender discourse, social reform, and emotional engagement across Arabic dialects. It supports research in Arabic natural language processing, computational social science, and digital communication studies. The dataset and accompanying documentation will be released under request for research use.

In this study, we compare the performance of four text chunking approaches: Recursive, Khmer-Aware, Sentence-Based, and LLM-Based within a Retrieval-Augmented Generation (RAG) framework applied to Khmer agricultural documents. The document chunks are encoded using the BGE-M3 multilingual embedding model and retrieved using the FAISS library. Performance is evaluated using four metrics: Average Retrieval Score (L2 distance), Answer Relevance, Khmer Coverage, and Khmer Intersection over Union, all measured against ground-truth question-answer pairs. For evaluation, we perform 5-fold cross-validation over 18 question-answer pairs. We observe the best performance for the character-based Recursive chunking method with a chunk size of 300 characters, achieving the lowest L2 distance (0.4295 +- 0.0461), highest Answer Relevance (0.8663 +- 0.0199), and highest Khmer IoU (0.6441 +- 0.0347). A paired t-test shows a statistically significant improvement over the Sentence-Based chunking method in L2 distance (p = 0.0121). These results highlight the importance of segmentation granularity and structural preservation for optimizing dense retrieval in morphologically complex, low-resource languages such as Khmer.

In this paper, we show that high-performing embedding models organize their embedding spaces in a consistent way. We evaluate 25 contemporary embedding models on five MTEB tasks spanning four diverse task categories (retrieval, bitext mining, pair classification, and summarization) in both English and multilingual settings, and reveal that nearest-neighbor overlap and magnitude differences in independent component analysis (ICA) between paired text instances strongly correlate (even up to 0.97) with performance on the given task. Ultimately, we show that embedding tasks display varying degrees of linearity and reliance on retention of local information. Our results further the understanding of embeddings, their relation to model performance, and shed light on possible future training objectives and optimizing conditional embeddings.

Zero-shot temporal action localization (ZS-TAL) consists of classifying and localizing actions in untrimmed videos, where action classes are unseen at training time. Existing work uses Vision and Language Models (VLMs), taking advantage of their strong zero-shot transfer capabilities. Yet, these models face evident challenges with fine-grained action classification, making it difficult to directly use them to distinguish between the presence and absence of an action. Most current methods for ZS-TAL address these challenges by training models on large-scale video datasets, which require annotated data and often result in limited generalization performance. Recently, approaches discarding the use of labeled data have emerged as an alternative. Following this direction, we propose a novel approach, ``Textual Guidance for finer localization of actions in videos'' (TEGU), that compensates for the lack of supervision from training data by exploiting rich textual information derived from large language models and structured text extracted from captions. This additional linguistic context can improve fine-grained discrimination by providing richer cues about fine-grained action differences within videos. We validate the effectiveness of the proposed method by conducting experiments on the THUMOS14 and the ActivityNet-v1.3 datasets. Our results show that, by exploiting rich textual information for improved action localization, TEGU outperforms state-of-the-art ZS-TAL approaches that do not involve training

Achieving high levels of surgical skill through effective training is essential for optimal patient outcomes. Automated, data-driven skill assessment holds significant potential to improve surgical training. While machine learning-based methods are increasingly popular for assessing skills in minimally invasive surgery, their application to open surgery remains limited. We present the results of a dedicated MICCAI challenge designed to benchmark and advance vision-based skill assessment in open surgery. The challenge dataset comprises videos of an open suturing training task recorded with a static GoPro camera in a dry-lab setting, with instrument trajectories available in addition to the primary video modality. The OSS Challenge was hosted over two consecutive years, comprising two and three independent tasks, respectively: (1) classifying skill level into four classes, (2) predicting the full Objective Structured Assessment of Technical Skills across eight categories, and (3) tracking hands and surgical tools. Participants submitted diverse solutions including deep learning-based video models, tracking-driven methods, and hybrid approaches. General-purpose spatiotemporal video models consistently achieved the strongest performance, though conceptually diverse approaches reached competitive levels when well-executed. Predicting fine-grained OSATS scores remains challenging but benefits substantially from increased training data. Keypoint tracking proves difficult given frequent occlusions and out-of-frame instances, limiting current applicability for motion-based skill analysis. This work benchmarks innovative and diverse solutions for surgical skill assessment, highlighting both the promise and current limitations of video-based evaluation in open surgery and identifying critical directions for advancing automated skill assessment toward clinical impact.

Graph of Thoughts (GoT), a generalized form of recent prompting paradigms for large language models (LLMs), has been shown to be useful for elaborate problem solving. By executing a graph of operations, thoughts of the LLM are structured as an arbitrary graph, forming the actual graph of thoughts. Originally, the graph of operations is defined manually, which requires in-depth knowledge about the solution of the problem to solve. Such a static graph of operations is rigid and therefore lacks adaptability. We propose Reinforced Graph of Thoughts (RGoT), an automated approach to the GoT prompting paradigm that leverages reinforcement learning (RL) to adaptively generate a graph of operations from a human-defined set. Results indicate that, under certain constraints, it is possible to construct graphs of operations adaptively to the task's complexity in an automated way.

Blind image quality assessment (BIQA) for ultrahighdefinition (UHD) images remains challenging because native-resolution inference is computationally expensive, whereas aggressive resizing or isolated cropping may suppress scale-sensitive distortions and weaken the relationship between local artifacts and global scene context. This paper aims to improve UHD-BIQA by explicitly modeling the structural dependencies among sampled image regions rather than treating them as independent views, and a graph representation learning framework UHD-GCN-BIQA is proposed. The framework samples aspect-ratio-aligned patches from each UHD image, encodes them as graph nodes, and constructs a hybrid k-nearest-neighbor graph using spatial proximity and feature similarity. Residual graph convolution is used to propagate contextual information across regions, and gated attention pooling aggregates patchlevel evidence into an imagelevel quality prediction. An exponential moving average normalized multiobjective loss function is adopted to stabilize the joint optimization of regression, correlation, and ranking objectives. Experiments on the UHD-IQA benchmark show that UHD-GCN-BIQA achieves PLCC = 0.7784, SRCC = 0.8019, and RMSE = 0.0519, obtaining competitive correlation performance and the lowest RMSE among the compared methods. These results indicate that graph-based region relation modeling is effective for UHD image quality assessment, particularly for improving absolute quality score estimation under high-resolution visual content.

Bandit convex optimization (BCO) is a fundamental online learning framework with partial feedback, where the learner observes only the loss incurred at the chosen decision point in each round. In this work, we investigate whether optimistic gradient predictions can improve worst-case regret guarantees in a prediction-adaptive manner. Specifically, given gradient predictions $m_t$, we seek regret bounds that scale with the cumulative prediction error $S_T=\sum_{t=1}^T \|\nabla f_t(x_t)-m_t\|^2.$ We first establish a negative result: under the single-point feedback protocol, an unavoidable $Ω(\sqrt{T})$ regret lower bound persists even when $S_T=o(T)$, showing that the variance of gradient estimation fundamentally obscures the benefit of accurate predictions. To overcome this barrier, we propose \emph{Two-Point Variance-Reduced Optimistic Gradient Descent} (TP-VR-OPT) for the two-point feedback setting. The key idea is a novel variance-reduced gradient estimator whose variance scales with the prediction error rather than the gradient norm. This yields a regret bound of $O\big(\sqrt{d\,\mathbb{E}[S_T]}\big),$ where $d$ is the decision dimension. Complementing this result, we establish an information-theoretic lower bound that scales as $Ω(\sqrt{\mathbb{E}[S_T]})$, providing a fundamental characterization of the best achievable prediction-adaptive regret and showing that TP-VR-OPT is optimal up to a factor of $\sqrt d$. We further develop adaptive variants that eliminate the need for prior knowledge of $\mathbb{E}[S_T]$ or the horizon $T$, and extend our framework to non-stationary environments, establishing dynamic regret guarantees that adapt simultaneously to the cumulative prediction error and the comparator path length.

Recent feed-forward 3D gaussian splatting methods have made dramatic progress on individual aspects of 3D scene reconstruction, but no existing method jointly addresses dynamic content, multi-view input, and unknown camera poses in a single feed-forward pass. Methods that handle dynamics either require accurate camera poses or accept only monocular input; pose-free multi-view methods address only static scenes; and per-scene optimization methods bridge some of these gaps but at minutes-to-hours cost per scene. We introduce NoPo4D, the first feed-forward system that addresses this empty quadrant. Building on a pretrained geometry backbone and recent 4D Gaussian frameworks, NoPo4D introduces a velocity decomposition that splits Gaussian motion into per-pixel image-plane shifts and depth changes, allowing direct supervision from pseudo ground-truth optical flow on the 2D component. This sidesteps both the differentiable rendering that couples prior posed methods to pose accuracy and the 3D motion ground truth that prior pose-free methods require. The system is rounded out by a bidirectional motion encoder for cross-view and cross-frame feature aggregation, and view-dependent opacity that mitigates cross-view and cross-timestep Gaussian misalignments. On four multi-view dynamic benchmarks, NoPo4D consistently outperforms prior feed-forward baselines, and with an optional post-optimization stage surpasses per-scene optimization methods, while running orders of magnitude faster.

Occlusion-aware prediction remains a critical challenge in autonomous driving due to the inherent uncertainty of unobserved regions. Existing approaches either overestimate risk based on reachable states or struggle to predict accurate trajectories under high occlusion uncertainty. To address these limitations, we propose a unified risk map modeling and learning framework for partially observable environments. Our method integrates traffic flow risk and collision risk through spatiotemporal modeling, enabling fine-grained assessment of occlusion-induced hazards. To address the scarcity of scenarios involving occluded interactions, we introduce a diffusion-based scenario generation framework that produces realistic yet adversarial scenarios. We integrate the modeling and learning of a unified risk map into a framework that supports risk-aware planning under partial observability. Experiments on the Waymo Open Motion Dataset show that our method significantly outperforms the state-of-the-art occlusion-aware baseline, improving minimum time-to-collision by 0.78 times and average time-to-collision by 1.67 times. The proposed framework offers a comprehensive and practical solution for risk-aware planning in partially observable environments.

GPUs have significantly accelerated first-order methods for large-scale optimization, especially in continuous optimization. However, this success has not transferred cleanly to problems with discrete variables, combinatorial structure, and nonlinear objectives, such as certifying optimal solutions for cardinality-constrained generalized linear models. Major challenges include the sequential processing of heterogeneous nodes in branch and bound (BnB) and frequent data movement between the CPU and GPU. We propose a simple, generic, and modular CPU--GPU framework that processes multiple BnB nodes in batches on GPUs. The framework is built around a small set of GPU-efficient routines and uses padding together with lightweight custom kernels to handle irregular node data structures. Experiments show one to two orders of magnitude speedups and zero optimality gap on challenging instances. The framework can also be extended to collect the entire Rashomon set, enabling downstream statistical analysis such as variable-importance analysis and model selection under secondary user-specific measures (e.g., AUC in classification).

Event-based low-light image enhancement (LIE) methods mainly focus on incorporating high dynamic range (HDR) information from events while overlooking the essential global illumination in images and the inherent noise sensitivity of event signals in real-world scenarios. To address these issues, we propose EIC-LIE, an event-illumination collaborative LIE framework. Concretely, we first design an Event-Illumination Collaborative Interaction (EICI) module, which contains two key processes: forward gathering, which gathers HDR features across varying lighting conditions, and backward injection, which provides complementary content for illumination and event representations. Next, we introduce an Illumination-aware Event Filter (IAEF) that dynamically reduces event noise based on brightness statistics derived from images. Additionally, we build a beam-splitter-based hybrid imaging system to collect high-quality event-image pairs with temporal synchronization from dynamic scenes, providing the first high-resolution, real-world event-based LIE dataset. Extensive experiments show that our EIC-LIE outperforms state-of-the-art methods on five real-world and synthetic datasets, significantly surpassing previous methods with improvements of up to 1.24dB in PSNR and 0.069 in SSIM. The code and dataset are released at https://github.com/QUEAHREN/EIC-LIE.

Recent advancements in Multimodal Large Language Models (MLLMs) have demonstrated impressive capabilities in general visual understanding. However, their application to safety-critical driving scenarios remains limited by an inability to accurately perceive and reason about rare high-stakes dynamic events, such as collisions or near-collisions. To address this, we introduce a pipeline that enhances MLLM perception by fusing downsampled video frames with synchronized high-frequency telematics data (IMU and GPS) and semantic insights from specialized computer vision models. Our pipeline generates high-quality pseudo-labels, including descriptive captions and question-answer pairs, specifically designed to train MLLMs to identify and describe Safety-Critical Events (SCEs) in real-world driving footage. We show the effectiveness of our approach fine-tuning the open-source QwenVL-2.5 model via DoRA adapters: our experiments demonstrate significant improvements in identifying and explaining safety-critical events, with fewer than 50M trainable parameters and limited computational budget.

Neural operators have achieved significant success in modern scientific computing due to their flexibility and strong generalization capabilities. Existing models, however, primarily rely on first-order kernel integral approximations, which severely limit their expressivity. To address this, we propose the Infinite-order Kernel Neural Operator (IKNO), which constructs neural operators via infinite-order kernel integrals and admits an elegant closed-form finite approximation. We develop two complementary infinite-order neural operator constructions: IKNO-Vanilla, which applies the full-kernel resolvent on the product grid via Kronecker eigendecomposition, and IKNO-TP, an alternative tensor-product operator that composes per-axis resolvents. Furthermore, we develop fast computation schemes for both variants of IKNO, which achieve outstanding global information aggregation while maintaining high computational efficiency. Empirically, we evaluate our IKNO on both time-dependent and time-independent benchmarks with arbitrary input shapes, including large-scale industrial datasets. Extensive experiments demonstrate that the IKNO method consistently achieves the SOTA accuracy with significant improvements on nearly all benchmark datasets while maintaining scalability to very large point clouds.