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Probabilistic Methods · Spectral Methods

Genki Osada

While diffusion models enable new approaches for estimating Local Intrinsic Dimension (LID), existing methods fail in high-dimensional spaces where noise from vast normal directions overwhelms the tangent signal. We propose Local Hessian Spectral Dimension (LHSD), which resolves this by applying spectral filtering to the log-density Hessian, explicitly cutting off large eigenvalues associated with normal directions to count zero-curvature tangent directions. Implemented using Stochastic Lanczos Quadrature (SLQ), LHSD avoids full Hessian construction, achieving linear scalability with dimension $D$. Experiments on synthetic and real data confirm LHSD’s superior robustness and its utility in detecting memorization in large-scale diffusion models.

Applications · Robotics

Rufeng Chen, Yue Chang, Xiaqiang Tang, Hechang Chen, Sihong Xie

Open-vocabulary navigation requires embodied agents to manage significant perception uncertainty stemming from semantic ambiguity and model errors. However, most existing works settle for local optimal deterministic approaches, depriving complex navigation decision-making over multiple composite possibilities that are critical for globally better solutions. In this paper, we propose Probabilistic Scene Graph Navigation (PSG-Nav), which constructs a 3D Probabilistic Scene Graph that uses full semantic categorical distributions to account for perception uncertainty. To efficiently use the local distributions to compose and reason about the optimal navigation landmarks, we propose Multiverse Decision to sample multiple most likely world settings from the joint distribution, and evaluate navigation landmarks based on the compatibility between landmarks and multiverses. To mitigate false positives due to epistemic uncertainty in open-vocabulary navigation, we introduce the Evidential Experience Calibrator, which enables online lifelong adaptation by cross-validating detections against memories of past successes and failures. Extensive experiments on widely-used benchmarks MP3D, HD3D, and HSSD demonstrate that PSG-Nav establishes new state-of-the-art results, achieving a Success Rate of 66.1%, 44.8%, and 67.9%, respectively.

Theory · Online Learning and Bandits

Yu Chen, Yuhao Liu, Jiatai Huang, Yihan Du, Longbo Huang

We investigate episodic Markov Decision Processes with heavy-tailed feedback (HTMDPs). Existing approaches for HTMDPs are conservative in stochastic environments and lack adaptivity in adversarial regimes. In this work, we propose algorithms ```HT-FTRL-OM``` and ```HT-FTRL-UOB``` for HTMDPs that achieve Best-of-Both-Worlds (BoBW) guarantees: instance-independent regret in adversarial environments and logarithmic instance-dependent regret in self-bounding (including the stochastic case) environments. For the known transition setting, ```HT-FTRL-OM``` applies the Follow-The-Regularized-Leader (FTRL) framework over occupancy measures with novel skipping loss estimators, achieving a $\widetilde{\mathcal{O}}(T^{1/\alpha})$ regret bound in adversarial regimes and a $\mathcal{O}(\log T)$ regret in stochastic regimes. Building upon this framework, we develop a novel algorithm ```HT-FTRL-UOB``` to tackle the more challenging unknown-transition setting. This algorithm employs a pessimistic skipping loss estimator and achieves a $\widetilde{\mathcal{O}}(T^{1/\alpha} + \sqrt{T})$ regret in adversarial regimes and a $\mathcal{O}(\log^2(T))$ regret in stochastic regimes. Our analysis overcomes key barriers through several technical insights, including a local control mechanism for heavy-tailed shifted losses, a new suboptimal-mass propagation principle, and a novel regret decomposition that isolates transition uncertainty from heavy-tailed estimation errors and skipping bias.

Applications · Computer Vision

Hsin-Ying Lee, Hanwen Jiang, Yiqun Mei, Jing Shi, Ming-Hsuan Yang, Zhixin Shu

Current motion-controlled image-to-video generation models rigidly follow user-provided trajectories that are often sparse, imprecise, and causally incomplete. Such reliance often yields unnatural or implausible outcomes, especially by missing secondary causal consequences. To address this, we introduce MotiMotion, a novel framework that reformulates motion control as a reasoning-then-generation problem. To encourage causally grounded and commonsense-consistent interactions, we leverage a training-free vision-language reasoner to refine image-space coordinates of primary trajectories and to hallucinate plausible secondary motions. To further improve motion naturalness, we propose a confidence-aware control scheme that modulates guidance strength, enabling the model to closely follow high-confidence plans while correcting artifacts under low-confidence inputs with its internal generative priors. To support systematic evaluation, we curate a new image-to-video benchmark, MotiBench, consisting of interaction-centric scenes where new events are triggered by motion. Both VLM-based evaluation and a human study on MotiBench demonstrate that MotiMotion produces videos with more plausible object behaviors and interaction, and is preferred over existing approaches.

Deep Learning · Large Language Models

Zhenting Qi, Susanna Maria Baby, Stefanie Baby, Kan Yuan, Da-Cheng Juan, Tu Vu, Andrew Tomkins, Cyrus Rashtchian

Recent work suggests that LLMs can improve their abilities through \textit{self-evolution}, using only internally generated supervision. A central open question, however, is not whether self-evolution can help, but: \textit{how far is it from oracle-supervised training under minimal assumptions?} To address this question, we present a controlled empirical analysis of LLM self-evolution under a strict formulation: self-evolution is allowed access only to (i) an unlabeled prompt set and (ii) a base language model, with all supervision signals generated from this model. Under this formulation, we can evaluate many self-evolution approaches in a unified preference optimization framework. Specifically, we analyze four representative self-evolution methods, ranging from single-round verification to multi-turn feedback, iterative training, and curriculum learning. For our primary analysis, we use a clean setting based on the Knights and Knaves logical reasoning dataset, which provides deterministic solutions, systematic verification, and a hierarchy of difficulty levels that enables an evaluation of easy-to-hard generalization. Across this controlled setting, we find that increasingly complex self-evolution strategies yield consistent but limited gains. In general, a substantial performance gap persists relative to oracle supervision. One strategy stands out as effective: we nearly match the oracle performance by using a larger model (Gemma 12B) with iterative revision based on natural language feedback. We also study self-evolution on the OpenThoughts reasoning corpus and evaluate on standard problem-solving benchmarks. In this regime, self-evolution only leads to modest improvements, including when using more resource-intensive strategies or online RL. Overall, our results shed new light on the empirical limits of various types of self-evolution.

General Machine Learning · Causality

Min Xu, Xinyi Yin, Caihua Chen, Yuxuan Han, Houcai Shen, Yunfan Zhang

Offline contextual pricing often relies on logged observational data, but faces challenges from distributional shifts between training and deployment environments. Distributionally robust optimization (DRO) provides a principled approach to off-policy evaluation and learning (OPE/L). However, existing methods are mostly limited to discrete actions. Recent work has explored DRO for continuous treatments using inverse propensity weighting (IPW), while such IPW-based estimators can be sensitive to the convergence rate of propensity score estimates, particularly when estimated nonparametrically, which may lead to larger estimation errors and regret. In this work, we develop a doubly robust (DR) framework for distributionally robust OPE/L in continuous pricing settings. For evaluation, we propose a localized DR estimator that addresses the computational challenges of worst-case expectations by fitting only a small number of regressions, comparable to standard non-robust DR, while achieving semiparametric efficiency under mild product rate conditions. For learning, we leverage the inherent smoothness of demand noise to handle pricing-specific discontinuities in revenue outcomes (e.g., threshold-based purchase decisions), establishing a finite-sample regret bound of $\tilde{\mathcal{O}}_p(T^{-s/(2s+1)})$ for smoothness orders $s=1,2$. This bound improves upon existing regret rates in existing DRO-based off-policy learning (OPL) for continuous treatments. Extensive experiments under various levels of distribution shift validate our proposed framework.

Deep Learning · Generative Models and Autoencoders

Elio Moreau, Florentin Coeurdoux, Grégoire Ferré, Eric Vanden-Eijnden

Understanding the geometry of learned distributions is fundamental to improving and interpreting diffusion models, yet systematic tools for exploring their landscape remain limited. Standard latent-space interpolations fail to respect the structure of the learned distribution, often traversing low-density regions. We introduce a framework based on the string method that computes continuous paths between samples by evolving curves under the learned score function. Operating on pretrained models without retraining, our approach interpolates between three regimes: pure generative transport, which yields continuous sample paths; gradient-dominated dynamics, which recover minimum energy paths (MEPs); and finite-temperature string dynamics, which compute principal curves---self-consistent paths that balance energy and entropy. We demonstrate that the choice of regime matters in practice. For image diffusion models, MEPs contain high-likelihood but unrealistic ``cartoon'' images, confirming prior observations that likelihood maxima appear unrealistic; principal curves instead yield realistic morphing sequences despite lower likelihood. For protein structure prediction, our method computes transition pathways between metastable conformers directly from models trained on static structures, yielding paths with physically plausible intermediates. Together, these results establish the string method as a principled tool for probing the modal structure of diffusion models---identifying modes, characterizing barriers, and mapping connectivity in complex learned distributions.

Hayden Helm, Ben Johnson, Carey Priebe

Evaluating a new model on an existing benchmark is often necessary to understand its behavior before deployment. For modern evaluation frameworks, generating and evaluating a response for all queries can be prohibitively expensive. In practice, responses from previously-evaluated models are often cached -- creating a potential opportunity to use this additional information to decrease the number of queries required to accurately evaluate a new model. In this paper, we introduce an approach for predicting benchmark performance that leverages cached model responses based on the Data Kernel Perspective Space (DKPS), a method for quantifying the relationship between models in the black-box setting. Theoretically, we show that DKPS-based methods are query-efficient under certain conditions. Empirically, we demonstrate that DKPS-based methods achieve the same mean absolute error as baselines with a substantially decreased query budget. We conclude by proposing an offline method for selecting a set of queries that maximizes the goodness-of-fit on reference models, improving prediction accuracy over random query selection.

Optimization · Discrete and Combinatorial Optimization

Peng Chen, Hailiang Zhao, Xueyan Tang, Yixuan Wang, Shuiguang Deng

Learning-augmented paging has been extensively studied in recent years. A key advantage over naive ML-based approaches is \emph{bounded robustness}, which guarantees worst-case performance even when predictions are inaccurate, making these algorithms valuable for real-world systems. Prior work achieves robustness bounds of $2H_k + O(1)$ in the randomized setting, leaving a gap to the optimal competitive ratio $H_k$. We are the first to study how to close this gap. In this paper, we begin by analyzing online optimality and provide a new proof of the latest $H_k$-competitive algorithm, which facilitates analysis in the learning-augmented setting. Then, we review existing learning-augmented paging algorithms and introduce a unifying primitive, the \emph{relative prediction budget}, which captures the essence of how to establish robustness and reveals that prior algorithms either overuse or underutilize predictions. Guided by the above analysis, we develop a new framework that achieves the best-possible robustness for learning-augmented paging: $H_k + O(1)$. Experiments further demonstrate strong practical performance.

Bilgehan Sel, Xuanli He, Alwin Peng, Ming Jin, Jerry Wei

Fine-tuning APIs offered by major AI providers create new attack surfaces where adversaries can bypass safety measures through targeted fine-tuning. We introduce **Trojan-Speak**, an adversarial fine-tuning method that bypasses Anthropic's Constitutional Classifiers. Our approach uses curriculum learning combined with GRPO-based hybrid reinforcement learning to teach models a communication protocol that evades LLM-based content classification. Crucially, while prior adversarial fine-tuning approaches report more than 25\% capability degradation on reasoning benchmarks, Trojan-Speak incurs less than 5\% degradation while achieving 99+\% classifier evasion for models with 14B+ parameters. We demonstrate that fine-tuned models can provide detailed responses to expert-level CBRN (Chemical, Biological, Radiological, and Nuclear) queries from Anthropic's Constitutional Classifiers bug-bounty program. Our findings reveal that LLM-based content classifiers alone are insufficient for preventing dangerous information disclosure when adversaries have fine-tuning access, and we show that activation-level probes can substantially improve robustness to such attacks.

Deep Learning · Other Representation Learning

Chunyu Xie, Bin Wang, Fanjing Kong, Jincheng Li, Dawei Liang, Ji Ao, Dawei Leng, Yuhui Yin

Fine-grained vision-language understanding requires precise alignment between visual content and linguistic descriptions, a capability that remains limited in current models, particularly in non-English settings. While models like CLIP perform well on global alignment, they often struggle to capture fine-grained details in object attributes, spatial relations, and linguistic expressions, with limited support for bilingual comprehension. To address these challenges, we introduce FG-CLIP 2, a bilingual vision-language model designed to advance fine-grained alignment for both English and Chinese. Our approach leverages rich fine-grained supervision, including region-text matching and long-caption modeling, alongside multiple discriminative objectives. We further introduce the Textual Intra-modal Contrastive (TIC) loss to better distinguish semantically similar captions. Trained on a carefully curated mixture of large-scale English and Chinese data, FG-CLIP 2 achieves powerful bilingual performance. To enable rigorous evaluation, we present a new benchmark for Chinese multimodal understanding, featuring long-caption retrieval and bounding box classification. Extensive experiments on 29 datasets across 8 tasks show that FG-CLIP 2 outperforms existing methods, achieving state-of-the-art results in both languages. We will release the model, code, and benchmark to facilitate future research on bilingual fine-grained alignment.

Applications · Computer Vision

Yuanyuan Gao, Hao Li, Yifei Liu, Xinhao Ji, Yuning Gong, Yuanjun Liao, Fangfu Liu, Manyuan Zhang, Yuchen Yang, Dan Xu 等

The pursuit of spatial intelligence fundamentally relies on access to large-scale, fine-grained 3D data. However, existing approaches predominantly construct spatial understanding benchmarks by generating question–answer (QA) pairs from a limited number of manually annotated datasets, rather than systematically annotating new large-scale 3D scenes from raw web data. As a result, their scalability is severely constrained, and model performance is further hindered by domain gaps inherent in these narrowly curated datasets. In this work, we propose \textbf{Holi-Spatial}, the first fully automated, large-scale, spatially-aware multimodal dataset, constructed from raw video inputs without human intervention, using the proposed data curation pipeline. Holi-Spatial supports multi-level spatial supervision, ranging from geometrically accurate 3D Gaussian Splatting (3DGS) reconstructions with rendered depth maps to object-level and relational semantic annotations, together with corresponding spatial Question–Answer (QA) pairs. Following a principled and systematic pipeline, we further construct \textbf{Holi-Spatial-4M}, the first large-scale, high-quality 3D semantic dataset, containing 12K optimized 3DGS scenes, 1.3M 2D masks, 320K 3D bounding boxes, 320K instance captions, 1.2M 3D grounding instances, and 1.2M spatial QA pairs spanning diverse geometric, relational, and semantic reasoning tasks. Holi-Spatial demonstrates exceptional performance in data curation quality, significantly outperforming existing feed-forward and per-scene optimized methods on datasets such as ScanNet, ScanNet++, and DL3DV. Furthermore, fine-tuning Vision-Language Models (VLMs) on spatial reasoning tasks using this dataset has also led to substantial improvements in model performance.

Yuanyuan Gao, Hao Li, Yifei Liu, Xinhao Ji, Yuning Gong, Yuanjun Liao, Fangfu Liu, Manyuan Zhang, Yuchen Yang, Dan Xu 等

The pursuit of spatial intelligence fundamentally relies on access to large-scale, fine-grained 3D data. However, existing approaches predominantly construct spatial understanding benchmarks by generating question–answer (QA) pairs from a limited number of manually annotated datasets, rather than systematically annotating new large-scale 3D scenes from raw web data. As a result, their scalability is severely constrained, and model performance is further hindered by domain gaps inherent in these narrowly curated datasets. In this work, we propose \textbf{Holi-Spatial}, the first fully automated, large-scale, spatially-aware multimodal dataset, constructed from raw video inputs without human intervention, using the proposed data curation pipeline. Holi-Spatial supports multi-level spatial supervision, ranging from geometrically accurate 3D Gaussian Splatting (3DGS) reconstructions with rendered depth maps to object-level and relational semantic annotations, together with corresponding spatial Question–Answer (QA) pairs. Following a principled and systematic pipeline, we further construct \textbf{Holi-Spatial-4M}, the first large-scale, high-quality 3D semantic dataset, containing 12K optimized 3DGS scenes, 1.3M 2D masks, 320K 3D bounding boxes, 320K instance captions, 1.2M 3D grounding instances, and 1.2M spatial QA pairs spanning diverse geometric, relational, and semantic reasoning tasks. Holi-Spatial demonstrates exceptional performance in data curation quality, significantly outperforming existing feed-forward and per-scene optimized methods on datasets such as ScanNet, ScanNet++, and DL3DV. Furthermore, fine-tuning Vision-Language Models (VLMs) on spatial reasoning tasks using this dataset has also led to substantial improvements in model performance.

Applications · Computer Vision

Wei Deng, Xianlin Zhang, Mengshi Qi

Enabling Vision-Language Models (VLMs) to perform spatial reasoning remains challenging. Existing approaches treat VLMs as passive observers, which is difficult for real-world applications. Moreover, reinforcement learning methods rely on sparse rewards, limiting their effectiveness for complex reasoning tasks. Inspired by pigeons’ building and exploiting cognitive maps for navigation, we propose a novel agentic pipeline for spatial reasoning. First, we introduce a new dynamic cognitive map parameterizing scene layout as object positions and orientations, serving as persistent memory for new observations. Second, we propose a novel Spatial Assertion Codes (SAC), Python expressions programmatically describing spatial relationships. By collaborating with the dynamic cognitive map, SAC enables verification of intermediate reasoning steps, providing dense reward signals. We optimize the model via supervised and reinforcement finetuning. Experiments on MindCube benchmark demonstrate state-of-the-art performance with 80.5% overall accuracy, surpassing the best method by 53.2% on the challenging ROTATION subset. We will release the code and data soon.

Deep Learning · Foundation Models

Alesia Ivanova, Sumeet Motwani, Jack Cai, Phil Torr, Riashat Islam, Shital Shah, Christian Schroeder de Witt, Charles London

Large language models excel at short-horizon reasoning tasks, but performance drops as reasoning horizon lengths increase. Existing approaches to combat this rely on inference-time scaffolding or step-level supervision, neither of which scales easily. In this work, we introduce a scalable method to bootstrap long-horizon reasoning capabilities using only existing, abundant short-horizon data. Our approach synthetically composes simple problems into complex, multi-step dependency chains of arbitrary length. We train models on this data using outcome-only rewards under a curriculum that automatically increases in complexity, allowing RL training to be scaled much further without saturating. Empirically, our method generalizes remarkably well: curriculum training on composed 6th-grade level math problems (GSM8K) improves accuracy on longer, competition-level benchmarks (GSM-Symbolic, MATH-500, AIME). It also transfers significantly to diverse out-of-distribution ReasoningGym domains and long-context benchmarks, indicating broader generalization. Importantly, our long-horizon improvements are significantly higher than baselines even at high pass@k, showing that models can learn new reasoning paths under RL. Theoretically, we show that curriculum RL with outcome rewards could achieve an exponential improvement in sample complexity over full-horizon training, providing training signal comparable to dense supervision. h1 therefore introduces an efficient path towards scaling RL for long-horizon problems using only existing data.

Probabilistic Methods · Everything Else

Taeseong Yoon, Heeyoung Kim

Single-pass uncertainty quantification (UQ) methods for classification represent uncertainty by predicting a tractable distribution over the class probability vector. While existing approaches primarily focus on enhancing the expressiveness of this distribution, they often provide limited insight into how predictive uncertainty is structured and aggregated, resulting in weak interpretability. We introduce the *courtroom analogy*, which conceptualizes uncertainty-aware classification as a structured debate among class-specific advocates. Each advocate forms a probabilistic opinion, and a final verdict is reached by aggregating these opinions using input-dependent plausibility weights. In this framework, each advocate's opinion is modeled as a Dirichlet distribution whose concentration parameter is decomposed into shared evidence and class-specific advocacy. This yields a structured mixture of Dirichlet distributions with semantically interpretable parameters. To instantiate this formulation, we propose *Mixture of Dirichlet EXperts* (MoDEX), a single-pass neural architecture that predicts the courtroom parameters, enabling efficient and expressive UQ while explicitly modeling uncertainty aggregation. We demonstrate that MoDEX enjoys strong theoretical properties and achieves state-of-the-art UQ performance across diverse benchmarks, yielding interpretable uncertainty estimates with meaningful semantics.

Reinforcement Learning · Deep RL

Han Fang, Paul Weng, Yutong Ban

Deep Reinforcement Learning (DRL) has emerged as a promising approach for solving Combinatorial Optimization (CO) problems, such as the 3D Bin Packing Problem (3D-BPP), Traveling Salesman Problem (TSP), or Vehicle Routing Problem (VRP), but these neural solvers often exhibit brittleness when facing distribution shifts. To address this issue, we uncover the Satisficing Generalization Edge, which we validate both theoretically and experimentally: identifying a set of promising actions is inherently more generalizable than selecting the single optimal action. To exploit this property, we propose Adaptive Selection After Proposal (ASAP), a generic framework that decomposes the decision-making process into two distinct phases: a proposal policy that acts as a robust filter, and a selection policy as an adaptable decision maker. This architecture enables a highly effective online adaptation strategy where the selection policy can be rapidly fine-tuned on a new distribution. Concretely, we introduce a two-phase training framework enhanced by Model-Agnostic Meta-Learning (MAML) to prime the model for fast adaptation. Extensive experiments on 3D-BPP, TSP, and CVRP demonstrate that ASAP improves the generalization capability of state-of-the-art baselines and achieves superior online adaptation on out-of-distribution instances.

Deep Learning · Large Language Models

Antonin Berthon, Nicolás Astorga, Mihaela van der Schaar

Modern LLMs show mastery over an ever-growing range of skills, as well as the ability to compose them flexibly. However, extending model capabilities to new skills in a scalable manner is an open-problem: fine-tuning and parameter-efficient variants risk catastrophic forgetting, while context-based approaches have limited expressiveness and are constrained by the model's effective context. We explore \textit{skill neologisms}--i.e., soft tokens integrated in the model's vocabulary and optimized to improve capabilities over a specific skill--as a way to selectively extend model capabilities to new skills without weight updates. We first observe that off-the-shelf pre-trained LLMs already demonstrate tokens associated with procedural knowledge. We then show that skill neologisms can be learned to improve model capabilities on specific skills while being composable with out-of-distribution skills, and that independently trained skill neologisms can be composed zero-shot. These results suggest that skill neologisms may provide a scalable path towards skill-based continual learning.

Applications · Health / Medicine

heng rao, Jason Zhang, Yu Gu, Zhenghao Liu, Ge Yu, Jeffrey Su, Yang Cao, Fan Yang, Minghan Chen

Predicting long-horizon trajectories of biological dynamical systems remains challenging due to substantial system heterogeneity. Most existing machine learning approaches are system-specific, requiring retraining for each new system and exhibiting limited generalization across distinct biological regimes. To address this limitation, we create a large-scale benchmark of over 1,000 ODE-based systems biology models spanning diverse organisms, biological processes, and dynamical behaviors. Building on this benchmark, we propose a regime-aware trajectory prediction framework that enables cross-system generalization and uncertainty quantification for unseen systems. Our approach introduces structured initial states derived from biological regime priors, such as growth trends and oscillatory rhythms, into conditional flow matching, replacing the standard Gaussian source distribution. We provide theoretical justification for this initialization and empirically demonstrate state-of-the-art accuracy (31\% MAE reduction), well-calibrated uncertainty (17\% CRPS improvement), and efficient long-horizon inference across the benchmark.

Applications · Everything Else

Ishaan Singh Chandok, Core Francisco Park

Scientific data annotation, such as tracking animals in video or proofreading neural reconstructions, remains bottlenecked by the “last mile” problem: even with strong automation, verification and correction consume substantial human effort. Standard approaches train models to directly predict annotations, discarding the rich supervision in how experts navigate, click, verify, and correct. We introduce a framework for studying behavioral cloning on scientific annotation: 9 synthetic tasks paired with synthetic annotations that simulate realistic human strategies including exploration, mistake correction, and strategic decision-making. Our experiments reveal several findings. First, skills emerge hierarchically: models learn GUI mechanics before task-critical decisions, and commit fewer mistakes than the training data while retaining the ability to correct errors when they occur. Second, scaling models on multi-task behavioral cloning shows that larger models are more data efficient, but exhibit worse decision-making despite similar placement accuracy. Third, multi-task pretraining enables efficient fine-tuning to new tasks, while training from scratch fails entirely. Fourth, linear probes reveal that models internally represent latent variables of the annotation process such as task phase and data position; interestingly, we find a shared mistake representation that generalizes across different annotation tasks. Overall, our framework establishes systematic benchmarks and identifies key bottlenecks, providing a foundation for scaling behavioral cloning to real-world scientific data annotation.