High-Dimensional Statistics: Reflections on Progress and Open Problems

Over the past two decades, the field of high-dimensional statistics has experienced substantial progress, driven largely by technological advances that have dramatically reduced the cost and effort for data collection and storage across a broad range of domains, including biology, medicine, astronomy, and the social and environmental sciences. Modern datasets are increasingly complex, often exhibiting rich dependency, heterogeneity, and other features that challenge traditional statistical methods. In response, high-dimensional statistics has evolved to address more sophisticated estimation and inference problems. This evolution has, in turn, fostered deep connections with and contributions to a wide range of research areas, including optimization, concentration of measure, random matrix theory, information theory, and theoretical computer science. Given the rapid pace of recent developments in high-dimensional statistics, our goal is to synthesize representative advances, highlight common themes and open problems, and point to important works that offer entry points into the field.

STRIDE-ED: A Strategy-Grounded Stepwise Reasoning Framework for Empathetic Dialogue Systems

Empathetic dialogue requires not only recognizing a user's emotional state but also making strategy-aware, context-sensitive decisions throughout response generation. However, the lack of a comprehensive empathy strategy framework, explicit task-aligned multi-stage reasoning, and high-quality strategy-aware data fundamentally limits existing approaches, preventing them from effectively modeling empathetic dialogue as a complex, multi-stage cognitive and decision-making process. To address these challenges, we propose STRIDE-ED, a STRategy-grounded, Interpretable, and DEep reasoning framework that models Empathetic Dialogue through structured, strategy-conditioned reasoning. To support effective learning, we develop a strategy-aware data refinement pipeline integrating LLM-based annotation, multi-model consistency-weighted evaluation, and dynamic sampling to construct high-quality training data aligned with empathetic strategies. Furthermore, we adopt a two-stage training paradigm that combines supervised fine-tuning with multi-objective reinforcement learning to better align model behaviors with target emotions, empathetic strategies, and response formats. Extensive experiments demonstrate that STRIDE-ED generalizes across diverse open-source LLMs and consistently outperforms existing methods on both automatic metrics and human evaluations.

Robust Regression with Adaptive Contamination in Response: Optimal Rates and Computational Barriers

We study robust regression under a contamination model in which covariates are clean while the responses may be corrupted in an adaptive manner. Unlike the classical Huber's contamination model, where both covariates and responses may be contaminated and consistent estimation is impossible when the contamination proportion is a non-vanishing constant, it turns out that the clean-covariate setting admits strictly improved statistical guarantees. Specifically, we show that the additional information in the clean covariates can be carefully exploited to construct an estimator that achieves a better estimation rate than that attainable under Huber contamination. In contrast to the Huber model, this improved rate implies consistency even when the contamination is a constant. A matching minimax lower bound is established using Fano's inequality together with the construction of contamination processes that match $m> 2$ distributions simultaneously, extending the previous two-point lower bound argument in Huber's setting. Despite the improvement over the Huber model from an information-theoretic perspective, we provide formal evidence -- in the form of Statistical Query and Low-Degree Polynomial lower bounds -- that the problem exhibits strong information-computation gaps. Our results strongly suggest that the information-theoretic improvements cannot be achieved by polynomial-time algorithms, revealing a fundamental gap between information-theoretic and computational limits in robust regression with clean covariates.

Principled Fast and Meta Knowledge Learners for Continual Reinforcement Learning

Inspired by the human learning and memory system, particularly the interplay between the hippocampus and cerebral cortex, this study proposes a dual-learner framework comprising a fast learner and a meta learner to address continual Reinforcement Learning~(RL) problems. These two learners are coupled to perform distinct yet complementary roles: the fast learner focuses on knowledge transfer, while the meta learner ensures knowledge integration. In contrast to traditional multi-task RL approaches that share knowledge through average return maximization, our meta learner incrementally integrates new experiences by explicitly minimizing catastrophic forgetting, thereby supporting efficient cumulative knowledge transfer for the fast learner. To facilitate rapid adaptation in new environments, we introduce an adaptive meta warm-up mechanism that selectively harnesses past knowledge. We conduct experiments in various pixel-based and continuous control benchmarks, revealing the superior performance of continual learning for our proposed dual-learner approach relative to baseline methods. The code is released in https://github.com/datake/FAME.

RAISE: Requirement-Adaptive Evolutionary Refinement for Training-Free Text-to-Image Alignment

Recent text-to-image (T2I) diffusion models achieve remarkable realism, yet faithful prompt-image alignment remains challenging, particularly for complex prompts with multiple objects, relations, and fine-grained attributes. Existing training-free inference-time scaling methods rely on fixed iteration budgets that cannot adapt to prompt difficulty, while reflection-tuned models require carefully curated reflection datasets and extensive joint fine-tuning of diffusion and vision-language models, often overfitting to reflection paths data and lacking transferability across models. We introduce RAISE (Requirement-Adaptive Self-Improving Evolution), a training-free, requirement-driven evolutionary framework for adaptive T2I generation. RAISE formulates image generation as a requirement-driven adaptive scaling process, evolving a population of candidates at inference time through a diverse set of refinement actions-including prompt rewriting, noise resampling, and instructional editing. Each generation is verified against a structured checklist of requirements, enabling the system to dynamically identify unsatisfied items and allocate further computation only where needed. This achieves adaptive test-time scaling that aligns computational effort with semantic query complexity. On GenEval and DrawBench, RAISE attains state-of-the-art alignment (0.94 overall GenEval) while incurring fewer generated samples (reduced by 30-40%) and VLM calls (reduced by 80%) than prior scaling and reflection-tuned baselines, demonstrating efficient, generalizable, and model-agnostic multi-round self-improvement. Code is available at https://github.com/LiyaoJiang1998/RAISE.

A 26-Gram Butterfly-Inspired Robot Achieving Autonomous Tailless Flight

Flapping-wing micro air vehicles (FWMAVs) have demonstrated remarkable bio-inspired agility, yet tailless two-winged configurations remain largely unexplored due to their complex fluid-structure and wing-body coupling. Here we present \textit{AirPulse}, a 26-gram butterfly-inspired FWMAV that achieves fully onboard, closed-loop, untethered flight without auxiliary control surfaces. The AirPulse robot replicates key biomechanical traits of butterfly flight, including low wing aspect ratio, compliant carbon-fiber-reinforced wings, and low-frequency, high-amplitude flapping that induces cyclic variations in the center of gravity and moment of inertia, producing characteristic body undulation. We establish a quantitative mapping between flapping modulation parameters and force-torque generation, and introduce the Stroke Timing Asymmetry Rhythm (STAR) generator, enabling smooth, stable, and linearly parameterized wingstroke asymmetry for flapping control. Integrating these with an attitude controller, the AirPulse robot maintains pitch and yaw stability despite strong oscillatory dynamics. Free-flight experiments demonstrate stable climbing and turning maneuvers via either angle offset or stroke timing modulation, marking the first onboard controlled flight of the lightest two-winged, tailless butterfly-inspired FWMAV reported in peer-reviewed literature. This work corroborates a foundational platform for lightweight, collision-proof FWMAVs, bridging biological inspiration with practical aerial robotics. Their non-invasive maneuverability is ideally suited for real-world applications, such as confined-space inspection and ecological monitoring, inaccessible to traditional drones, while their biomechanical fidelity provides a physical model to decode the principles underlying the erratic yet efficient flight of real butterflies.

Sharp Inequalities between Total Variation and Hellinger Distances for Gaussian Mixtures

We study the relation between the total variation (TV) and Hellinger distances between two Gaussian location mixtures. Our first result establishes a general upper bound: for any two mixing distributions supported on a compact set, the Hellinger distance between the two mixtures is controlled by the TV distance raised to a power $1-o(1)$, where the $o(1)$ term is of order $1/\log\log(1/\mathrm{TV})$. We also construct two sequences of mixing distributions that demonstrate the sharpness of this bound. Taken together, our results resolve an open problem raised in Jia et al. (2023) and thus lead to an entropic characterization of learning Gaussian mixtures in total variation. Our inequality also yields optimal robust estimation of Gaussian mixtures in Hellinger distance, which has a direct implication for bounding the minimax regret of empirical Bayes under Huber contamination.

LookBench: A Live and Holistic Open Benchmark for Fashion Image Retrieval

In this paper, we present LookBench (We use the term "look" to reflect retrieval that mirrors how people shop -- finding the exact item, a close substitute, or a visually consistent alternative.), a live, holistic and challenging benchmark for fashion image retrieval in real e-commerce settings. LookBench includes both recent product images sourced from live websites and AI-generated fashion images, reflecting contemporary trends and use cases. Each test sample is time-stamped and we intend to update the benchmark periodically, enabling contamination-aware evaluation aligned with declared training cutoffs. Grounded in our fine-grained attribute taxonomy, LookBench covers single-item and outfit-level retrieval across. Our experiments reveal that LookBench poses a significant challenge on strong baselines, with many models achieving below $60\%$ Recall@1. Our proprietary model achieves the best performance on LookBench, and we release an open-source counterpart that ranks second, with both models attaining state-of-the-art results on legacy Fashion200K evaluations. LookBench is designed to be updated semi-annually with new test samples and progressively harder task variants, providing a durable measure of progress. We publicly release our leaderboard, dataset, evaluation code, and trained models.

Mind the Generative Details: Direct Localized Detail Preference Optimization for Video Diffusion Models

Aligning text-to-video diffusion models with human preferences is crucial for generating high-quality videos. Existing Direct Preference Otimization (DPO) methods rely on multi-sample ranking and task-specific critic models, which is inefficient and often yields ambiguous global supervision. To address these limitations, we propose LocalDPO, a novel post-training framework that constructs localized preference pairs from real videos and optimizes alignment at the spatio-temporal region level. We design an automated pipeline to efficiently collect preference pair data that generates preference pairs with a single inference per prompt, eliminating the need for external critic models or manual annotation. Specifically, we treat high-quality real videos as positive samples and generate corresponding negatives by locally corrupting them with random spatio-temporal masks and restoring only the masked regions using the frozen base model. During training, we introduce a region-aware DPO loss that restricts preference learning to corrupted areas for rapid convergence. Experiments on Wan2.1 and CogVideoX demonstrate that LocalDPO consistently improves video fidelity, temporal coherence and human preference scores over other post-training approaches, establishing a more efficient and fine-grained paradigm for video generator alignment.

Learning Confidence Ellipsoids and Applications to Robust Subspace Recovery

We study the problem of finding confidence ellipsoids for an arbitrary distribution in high dimensions. Given samples from a distribution $D$ and a confidence parameter $α$, the goal is to find the smallest volume ellipsoid $E$ which has probability mass $\Pr_{D}[E] \ge 1-α$. Ellipsoids are a highly expressive class of confidence sets as they can capture correlations in the distribution, and can approximate any convex set. This problem has been studied in many different communities. In statistics, this is the classic minimum volume estimator introduced by Rousseeuw as a robust non-parametric estimator of location and scatter. However in high dimensions, it becomes NP-hard to obtain any non-trivial approximation factor in volume when the condition number $β$ of the ellipsoid (ratio of the largest to the smallest axis length) goes to $\infty$. This motivates the focus of our paper: can we efficiently find confidence ellipsoids with volume approximation guarantees when compared to ellipsoids of bounded condition number $β$? Our main result is a polynomial time algorithm that finds an ellipsoid $E$ whose volume is within a $O(β)^{γd}$ multiplicative factor of the volume of best $β$-conditioned ellipsoid while covering at least $1-O(α/γ)$ probability mass for any $γ< α$. We complement this with a computational hardness result that shows that such a dependence seems necessary up to constants in the exponent. The algorithm and analysis uses the rich primal-dual structure of the minimum volume enclosing ellipsoid and the geometric Brascamp-Lieb inequality. As a consequence, we obtain the first polynomial time algorithm with approximation guarantees on worst-case instances of the robust subspace recovery problem.