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Chao Gao

Publications and source records attributed to Chao Gao.

At least 37 records · Page 2Linked to original sources
arXiv2026

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.

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arXiv2026

PL-LIT: A LiDAR-Inertial-Thermal SLAM Using Point-Line Features and Thermographic Mapping

Thermal imaging is resilient to adverse conditions, such as intense illumination, low-light operation, and fog, and can therefore mitigate odometry degradation when visible-spectrum imagery becomes unreliable. Nevertheless, most thermal cameras employ automatic gain control (AGC), and thermal images often present low global contrast despite containing informative edge structures. These characteristics undermine brightness constancy and cause conventional optical flow tracking-based odometry pipelines that fundamentally rely on the brightness constancy assumption across consecutive frames. To address these issues, we propose a general LiDAR-Inertial-Thermal SLAM system that accommodates both visible-light and thermal cameras. PL-LIT combines an online photometric calibration module with a deep neural network for point-line feature extraction, enabling more stable and repeatable thermal tracking. For state estimation, we design a tightly coupled LiDAR-Inertial-Thermal formulation within an Error-State Iterated Kalman Filter (ESIKF). We further introduce a line-feature constraint scheme ensuring the reliability of geometric constraints across varying thermal appearances. In addition, PL-LIT builds a probabilistic thermal-intensity voxel map, which supports real-time thermal anomaly detection. Extensive experiments demonstrate that PL-LIT exhibits generality and robustness in visible-light environments, achieves state-of-the-art performance on long-range thermal infrared datasets, and provides practical safety inspection functionality based on thermographic mapping.

cs.RO↗
arXiv2026

Hybrid Sequence Modeling and Reinforced Verification for Controllable Target-Conditioned Decision Making

Target-conditioned sequence models provide a simple interface for controllable offline decision making, but the requested target return can be an unreliable control signal, especially when the target return lies in underrepresented regions of the dataset. This paper proposes Doctor, a hybrid sequence modeling and reinforced verification framework for controllable target-conditioned offline decision making. Doctor trains a shared masked trajectory Transformer with two complementary objectives: masked trajectory reconstruction for candidate generation and in-sample value learning for action-value verification. At inference time, the model samples multiple nearby target returns, generates candidate actions in parallel, and selects the action whose verified value is closest to the requested target return. We analyze this verifier-guided selection rule and show that its value-level alignment error is bounded by candidate-value coverage around the target return and verifier accuracy. Experiments on D4RL and EpiCare show that Doctor improves target-return alignment under reduced high-return coverage, remains competitive on standard offline return-maximization benchmarks, and enables a single policy to modulate between conservative and aggressive operating points in a simulated clinical decision-making task. These results suggest that reinforced verification can improve the controllability of target-conditioned policies.

cs.LG↗
arXiv2026

Modularized Reinforcement Learning on LLMs: From MDP Creation to Exploration and Learning

Reinforcement learning (RL) has become central to LLM post-training, yet the methods that dominate current pipelines, PPO and GRPO, represent only a narrow slice of what RL offers. Understanding why these methods prevail, and what alternatives exist, requires a principled examination of the design decisions that underlie any RL algorithm. This survey organizes that examination around three stages of algorithm construction. We begin with MDP creation: how the reward function, state space, action space, termination condition, and discount factor are, or could be, defined for LLM training. We then turn to exploration, covering temperature sampling, entropy regularization, intrinsic motivation, tree search, and curriculum learning. Finally, we address learning along four classical RL dimensions: model-free versus model-based, value-based versus policy-based versus actor-critic, on-policy versus off-policy, and credit assignment, including both Monte Carlo methods, which rely on full return estimates, and bootstrapping methods, which update estimates using other learned predictions. Mapping the LLM literature onto this taxonomy reveals a strikingly non-uniform distribution of research effort. Critic-free policy gradients and Monte Carlo credit assignment are densely populated, while value-based methods, off-policy actor-critic training, and bootstrapping-based credit assignment remain largely unexplored despite well-established counterparts in classical RL. These gaps represent concrete opportunities for transferring proven RL techniques to LLM training. By making these gaps explicit alongside the methods that have proven effective, this survey offers researchers in both RL and LLMs a shared framework for understanding current practice and identifying promising directions for future work.

cs.LG↗
arXiv2026

Proxy Reconstruction Pre-training for Ramp Flow Prediction at Highway Interchanges

Interchanges are crucial nodes for vehicle transfers between highways, yet the lack of real-time ramp detectors creates blind spots in traffic prediction. To address this, we propose a Spatio-Temporal Decoupled Autoencoder (STDAE), a two-stage framework that leverages cross-modal reconstruction pretraining. In the first stage, STDAE reconstructs historical ramp flows from mainline data, forcing the model to capture intrinsic spatio-temporal relations. Its decoupled architecture with parallel spatial and temporal autoencoders efficiently extracts heterogeneous features. In the prediction stage, the learned representations are integrated with models such as GWNet to enhance accuracy. Experiments on three real-world interchange datasets show that STDAE-GWNET consistently outperforms thirteen state-of-the-art baselines and achieves performance comparable to models using historical ramp data. This demonstrates its effectiveness in overcoming detector scarcity and its plug-and-play potential for diverse forecasting pipelines.

cs.LG↗
arXiv2026

On the Impossibility of Specification Testing of Interference Models Based on Exposure Mappings

Researchers use interference models based on exposure mappings to facilitate estimation of causal effects in randomized experiments with interference. To test the veracity of such models, researchers can use specification tests that aim to detect departures from the stipulated model. However, existing tests suffer from poor power and are often unable to detect important model violations. The main result in this paper is to show that the specification testing problem for exposure mapping models is inherently difficult, and the poor power of existing tests is inescapable. In particular, the worst-case Type I and Type II error rates must sum to one for any specification test of such models, ruling out the existence of a uniformly consistent test. This is the worst-case overall error rate achieved by a naive test that discards all data and arbitrarily rejects the null at random; the testing problem is in this sense impossible. This negative result holds true for all exposure mappings, all sample sizes, for uniformly bounded outcomes, and for alternatives that are maximally separated from the null. While some tests can detect some type of departures from the null model, there will always be relevant departures from the null that are undetectable. Informative specification tests must therefore restrict the alternative model against which they seek to attain power for, beyond the restrictions imposed by the exposure mappings alone. We illustrate this by providing a uniformly consistent test for differentiating no-interference from a network-linear-in-means model.

math.ST↗
arXiv2026

AirDreamer: Generalist Drone Navigation with World Models

Navigating a drone in unseen and cluttered environments requires reliable generalization to unseen scene layouts and understanding of environmental structure relative to the robot's capabilities. Previous methods, which assume the same environment configuration, often rely heavily on human-designed perception pipelines and predefined rules to guide the robot toward the target. This process is environment-dependent and generalizes poorly across environments. Inspired by animal navigation behavior, we design a navigation framework that navigates with a reinforcement-learning-based policy on top of a world-model-based environment understanding to overcome these issues. In addition, a sparse reward function without hand-crafted shaping terms is designed to avoid local minima traps and encourage yaw control behaviors. In simulation and on real drones, our method exhibits emergent capabilities for navigating complex, unseen environments and escaping local optima where other methods fail. In challenging maps, it achieves a 5.3% higher navigation success rate than best baseline. Furthermore, the proposed framework achieves effective sim-to-real transfer without any tuning during deployment. The code will be publicly available.

cs.RO↗
arXiv2026

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.

math.ST↗
arXiv2026

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.The code is available at https://github.com/1170300714/Local-DPO.

cs.CV↗
arXiv2026

NORM-Nav: Zero-Shot Mobile Robot Navigation with Natural Language Behavioral Constraints

Mobile robots operating in human-centered environments must generate not only collision-free paths but also trajectories that follow local behavioral conventions. Conventional costmap-based navigation emphasizes geometric feasibility and often overlooks such requirements, which can result in socially inappropriate behaviors. This paper presents NORM-Nav, a zero-shot framework that integrates natural language behavioral constraints into costmap-based planning. An LLM parses each instruction into structured constraints and grounds them using real-time vision--LiDAR perception. These constraints are encoded as multi-layer costmaps that represent geometric, semantic, directional, and velocity cues and are directly compatible with standard grid-based planners. Simulation and real-world experiments indicate that NORM-Nav improves task success rates and produces trajectories closer to human references than representative baselines. The project website is available at https://ei-nav.github.io/NORM-Nav.

cs.RO↗
arXiv2026

RePack then Refine: Efficient Diffusion Transformer with Vision Foundation Model

Semantic-rich features from Vision Foundation Models (VFMs) have been leveraged to enhance Latent Diffusion Models (LDMs). However, raw VFM features are typically high-dimensional and redundant, increasing the difficulty of learning and reducing training efficiency for Diffusion Transformers (DiTs). In this paper, we propose Repack then Refine, a three-stage framework that brings the semantic-rich VFM features to DiT while further accelerating learning efficiency. Specifically, the RePack module projects the high-dimensional features onto a compact, low-dimensional manifold. This filters out the redundancy while preserving essential structural information. A standard DiT is then trained for generative modeling on this highly compressed latent space. Finally, to restore the high-frequency details lost due to the compression in RePack, we propose a Latent-Guided Refiner, which is trained lastly for enhancing the image details. On ImageNet-1K, RePack-DiT-XL/1 achieves an FID of 1.82 in only 64 training epochs. With the Refiner module, performance further improves to an FID of 1.65, significantly surpassing latest LDMs in terms of convergence efficiency. Our results demonstrate that packing VFM features, followed by targeted refinement, is a highly effective strategy for balancing generative fidelity with training efficiency. Source code is publicly available at https://github.com/guanfangdong/RePack-then-Refine.

cs.CV↗
arXiv2026

GLASS: Global-Local Aggregation for Inference-time Sparsification of LLMs

Inference-time sparsification is a promising path to deploy large language models (LLMs) on resource-constrained devices, yet existing training-free methods typically estimate feedforward network (FFN) neuron importance from the input prompt alone. We show this prompt-only signal is often unreliable, especially for short prompts and long-form decoding, leading to inaccurate masks and degraded generation fidelity. We propose GLASS, a plug-and-play, training-free framework that stabilizes dynamic FFN pruning by aggregating two complementary views of neuron criticality: local prompt-specific activations and a global model-intrinsic prior. GLASS fuses global and local signals via rank aggregation, yielding robust critical-neuron selection even when the prompt is short. We interpret GLASS as the maximum-a-posteriori consensus ranking under a permutation-based probabilistic model, providing a principled foundation for its weighted rank-aggregation rule. We apply GLASS to a diverse set of open-source LLMs, and show that it yields substantial improvements over prior training-free baselines in the challenging short-prompt, long-generation scenarios, achieving up to 45.10% lower perplexity and 25.73% lower KL divergence, while delivering significant on-device decoding speedup.

cs.LG↗
arXiv2026

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 $\mathbb{P}_{D}[E] \ge 1-α$. Ellipsoids are a highly expressive class of confidence sets as they can capture correlations in the distribution, and can approximate any convex set. 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 $γ\in (0,1)$. In particular, setting $γ= o(1)$, this gives a $O(β)^{o(d)}$ volume approximation, with a multiplicative loss in miscoverage. We complement this with a computational hardness result that shows that such a dependence on $β$ seems necessary, even with some slack in coverage. 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.

cs.DS↗
arXiv2026

Adaptive Confidence Intervals in Efron's Gaussian Two-Groups Model

Robust uncertainty quantification is increasingly important in modern data analysis and is often formalized under Huber's model, which allows an $\varepsilon$-fraction of arbitrary corruptions. In many experimental sciences, however, the measurement protocol is well controlled, and contamination is more plausibly introduced upstream. Motivated by this noise-oblivious nature of adversaries, we study confidence intervals for the null location parameter $θ$ in Efron's Gaussian two-groups model, where an unknown fraction $\varepsilon$ of observations have arbitrarily shifted means, but all samples share the same law of additive Gaussian measurement noise with variance $σ^2$. We characterize the minimax-optimal length among confidence intervals with a prescribed coverage level uniformly over the unknown contamination proportion and all noise-oblivious adversaries. Although prior work has shown that the minimax point estimation rate of theta does not deteriorate when $\varepsilon$ becomes unknown, our results reveal that, with a given $σ^2$, the minimax-optimal length of confidence intervals that are adaptive to unknown $\varepsilon$ is of order $σ(n^{-1/4}+\varepsilon^{1/2}/\max\{1, \log(en \varepsilon^2)\}^{1/2})$, which is polynomially worse than the optimal length when $\varepsilon$ is known. When the variance $σ^2$ is also unknown, we show a further degradation: no adaptive confidence interval can be shorter than $Ω(σn^{-1/8})$. Algorithmically, we introduce a Fourier-based certification procedure built on Carathéodory's positive-semidefiniteness constraints. By scanning candidate points and accepting those whose residual characteristic function is certifiably consistent with a Gaussian location mixture, our algorithm attains the minimax lower bound in the known-variance setting and is computable in polynomial time.

math.ST↗
arXiv2026

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. Our data and code are publicly available at https://github.com/jicoder-nwpu/STRIDE-ED.

cs.CL↗
arXiv2026

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.

cs.CV↗
arXiv2026

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.

math.ST↗
arXiv2026

Confidence Intervals for Linear Models with Arbitrary Noise Contamination

We study confidence interval construction for linear regression under Huber's contamination model, where an unknown fraction of noise variables is arbitrarily corrupted. While robust point estimation in this setting is well understood, statistical inference remains challenging, especially because the contamination proportion is not identifiable from the data. We develop a new algorithm that constructs confidence intervals for individual regression coefficients without any prior knowledge of the contamination level. Our method is based on a Z-estimation framework using a smooth estimating function. The method directly quantifies the uncertainty of the estimating equation after a preprocessing step that decorrelates covariates associated with the nuisance parameters. We show that the resulting confidence interval has valid coverage uniformly over all contamination distributions and attains an optimal length of order $O(1/\sqrt{n(1-ε)^2})$, matching the rate achievable when the contamination proportion $ε$ is known. This result stands in sharp contrast to the adaptation cost of robust interval estimation observed in the simpler Gaussian location model.

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