Bing Cheng

Bing Cheng, Howell Tong

Being infinite dimensional, non-parametric information geometry has long faced an "intractability barrier" due to the fact that the Fisher-Rao metric is now a functional incurring difficulties in defining its inverse. This paper introduces a novel framework to resolve the intractability with an Orthogonal Decomposition of the Tangent Space ($T_fM = S \oplus S^{\perp}$), where $S$ represents an observable covariate subspace. Through the decomposition, we derive the Covariate Fisher Information Matrix (cFIM), denoted as ${\bf G}_f$, which is a finite-dimensional and computable representative of information extractable from the manifold's geometry. Significantly, by proving the Trace Theorem: $H_G(f) = \text{Tr}({\bf G}_f)$, we establish a rigorous foundation for the G-entropy previously introduced by us, thereby identifying it as a fundamental geometric invariant representing the total explainable statistical information captured by the probability distribution associated with a model. Furthermore, we establish a link between ${\bf G}_f$ and the second derivative (i.e. the curvature) of the KL-divergence, leading to the notion of Covariate Cramér-Rao Lower Bound(CRLB). We demonstrate that ${\bf G}_f$ is congruent to the Efficient Fisher Information Matrix, thereby providing fundamental limits of variance for semi-parametric estimators. Finally, we apply our geometric framework to the Manifold Hypothesis, lifting the latter from a heuristic assumption into a testable condition of rank-deficiency within the cFIM. By defining the Information Capture Ratio, we provide a rigorous method for estimating intrinsic dimensionality in high-dimensional data. In short, our work bridges the gap between abstract information geometry and the demand of explainable AI, by providing a tractable path for assessing the statistical coverage and the efficiency of non-parametric models.

Hao Zhou, Rongxiao Huang, Shaoming Li et al.

Marketing optimization plays an important role to enhance user engagement in online Internet platforms. Existing studies usually formulate this problem as a budget allocation problem and solve it by utilizing two fully decoupled stages, i.e., machine learning (ML) and operation research (OR). However, the learning objective in ML does not take account of the downstream optimization task in OR, which causes that the prediction accuracy in ML may be not positively related to the decision quality. Decision Focused Learning (DFL) integrates ML and OR into an end-to-end framework, which takes the objective of the downstream task as the decision loss function and guarantees the consistency of the optimization direction between ML and OR. However, deploying DFL in marketing is non-trivial due to multiple technological challenges. Firstly, the budget allocation problem in marketing is a 0-1 integer stochastic programming problem and the budget is uncertain and fluctuates a lot in real-world settings, which is beyond the general problem background in DFL. Secondly, the counterfactual in marketing causes that the decision loss cannot be directly computed and the optimal solution can never be obtained, both of which disable the common gradient-estimation approaches in DFL. Thirdly, the OR solver is called frequently to compute the decision loss during model training in DFL, which produces huge computational cost and cannot support large-scale training data. In this paper, we propose a decision focused causal learning framework (DFCL) for direct counterfactual marketing optimization, which overcomes the above technological challenges. Both offline experiments and online A/B testing demonstrate the effectiveness of DFCL over the state-of-the-art methods. Currently, DFCL has been deployed in several marketing scenarios in Meituan, one of the largest online food delivery platform in the world.

Tao Lin, Yuxin Du, Jiting Liu et al.

Vision-Language-Action models have emerged as a promising paradigm for robotic manipulation by unifying perception, language grounding, and action generation. However, they often struggle in scenarios requiring precise spatial understanding, as current VLA models primarily rely on 2D visual representations that lack depth information and detailed spatial relationships. While recent approaches incorporate explicit 3D inputs such as depth maps or point clouds to address this issue, they often increase system complexity, require additional sensors, and remain vulnerable to sensing noise and reconstruction errors. Another line of work explores implicit 3D-aware spatial modeling directly from RGB observations without extra sensors, but it often relies on large geometry foundation models, resulting in higher training and deployment costs. To address these challenges, we propose Evo-Depth, a lightweight depth-enhanced VLA framework that enhances spatially grounded manipulation without relying on additional sensing hardware or compromising deployment efficiency. Evo-Depth employs a lightweight Implicit Depth Encoding Module to extract compact depth features from multi-view RGB images. These features are incorporated into vision-language representations through a Spatial Enhancement Module via depth-aware modulation, enabling efficient spatial-semantic enhancement. A Progressive Alignment Training strategy is further introduced to align the resulting depth-enhanced representations with downstream action learning. With only 0.9B parameters, Evo-Depth achieves superior performance across four simulation benchmarks. In real-world experiments, Evo-Depth attains the highest average success rate while also exhibiting the smallest model size, lowest GPU memory usage, and highest inference frequency among compared methods.

Chuyue Wang, Jie Feng, Yuxi Wu et al.

Accurate and reliable search on online healthcare platforms is critical for user safety and service efficacy. Traditional methods, however, often fail to comprehend complex and nuanced user queries, limiting their effectiveness. Large language models (LLMs) present a promising solution, offering powerful semantic understanding to bridge this gap. Despite their potential, deploying LLMs in this high-stakes domain is fraught with challenges, including factual hallucinations, specialized knowledge gaps, and high operational costs. To overcome these barriers, we introduce \textbf{AR-Med}, a novel framework for \textbf{A}utomated \textbf{R}elevance assessment for \textbf{Med}ical search that has been successfully deployed at scale on the Online Medical Delivery Platforms. AR-Med grounds LLM reasoning in verified medical knowledge through a retrieval-augmented approach, ensuring high accuracy and reliability. To enable efficient online service, we design a practical knowledge distillation scheme that compresses large teacher models into compact yet powerful student models. We also introduce LocalQSMed, a multi-expert annotated benchmark developed to guide model iteration and ensure strong alignment between offline and online performance. Extensive experiments show AR-Med achieves an offline accuracy of over 93\%, a 24\% absolute improvement over the original online system, and delivers significant gains in online relevance and user satisfaction. Our work presents a practical and scalable blueprint for developing trustworthy, LLM-powered systems in real-world healthcare applications.

Rong Bian, Yu Geng, Zijian Yang et al.

A mathematical knowledge graph (KG) presents knowledge within the field of mathematics in a structured manner. Constructing a math KG using natural language is an essential but challenging task. There are two major limitations of existing works: first, they are constrained by corpus completeness, often discarding or manually supplementing incomplete knowledge; second, they typically fail to fully automate the integration of diverse knowledge sources. This paper proposes AutoMathKG, a high-quality, wide-coverage, and multi-dimensional math KG capable of automatic updates. AutoMathKG regards mathematics as a vast directed graph composed of Definition, Theorem, and Problem entities, with their reference relationships as edges. It integrates knowledge from ProofWiki, textbooks, arXiv papers, and TheoremQA, enhancing entities and relationships with large language models (LLMs) via in-context learning for data augmentation. To search for similar entities, MathVD, a vector database, is built through two designed embedding strategies using SBERT. To automatically update, two mechanisms are proposed. For knowledge completion mechanism, Math LLM is developed to interact with AutoMathKG, providing missing proofs or solutions. For knowledge fusion mechanism, MathVD is used to retrieve similar entities, and LLM is used to determine whether to merge with a candidate or add as a new entity. A wide range of experiments demonstrate the advanced performance and broad applicability of the AutoMathKG system, including superior reachability query results in MathVD compared to five baselines and robust mathematical reasoning capability in Math LLM.

Xiaohan Wang, Yu Zhang, Guibin Jiang et al.

Marketing optimization, commonly formulated as an online budget allocation problem, has emerged as a pivotal factor in driving user growth. Most existing research addresses this problem by following the principle of 'first predict then optimize' for each individual, which presents challenges related to large-scale counterfactual prediction and solving complexity trade-offs. Note that the practical data quality is uncontrollable, and the solving scale tends to be tens of millions. Therefore, the existing approaches make the robust budget allocation non-trivial, especially in industrial scenarios with considerable data noise. To this end, this paper proposes a novel approach that solves the problem from the cluster perspective. Specifically, we propose a multi-task representation network to learn the inherent attributes of individuals and project the original features into high-dimension hidden representations through the first two layers of the trained network. Then, we divide these hidden representations into $K$ groups through partitioning-based clustering, thus reformulating the problem as an integer stochastic programming problem under different total budgets. Finally, we distill the representation module and clustering model into a multi-category model to facilitate online deployment. Offline experiments validate the effectiveness and superiority of our approach compared to six state-of-the-art marketing optimization algorithms. Online A/B tests on the Meituan platform indicate that the approach outperforms the online algorithm by 0.53% and 0.65%, considering order volume (OV) and gross merchandise volume (GMV), respectively.

Chuhan Qiao, Jianghua Huang, Daxing Zhao et al.

Current evaluations of medical consultation agents often prioritize outcome-oriented tasks, frequently overlooking the end-to-end process integrity and clinical safety essential for real-world practice. While recent interactive benchmarks have introduced dynamic scenarios, they often remain fragmented and coarse-grained, failing to capture the structured inquiry logic and diagnostic rigor required in professional consultations. To bridge this gap, we propose MedConsultBench, a comprehensive framework designed to evaluate the complete online consultation cycle by covering the entire clinical workflow from history taking and diagnosis to treatment planning and follow-up Q\&A. Our methodology introduces Atomic Information Units (AIUs) to track clinical information acquisition at a sub-turn level, enabling precise monitoring of how key facts are elicited through 22 fine-grained metrics. By addressing the underspecification and ambiguity inherent in online consultations, the benchmark evaluates uncertainty-aware yet concise inquiry while emphasizing medication regimen compatibility and the ability to handle realistic post-prescription follow-up Q\&A via constraint-respecting plan revisions. Systematic evaluation of 19 large language models reveals that high diagnostic accuracy often masks significant deficiencies in information-gathering efficiency and medication safety. These results underscore a critical gap between theoretical medical knowledge and clinical practice ability, establishing MedConsultBench as a rigorous foundation for aligning medical AI with the nuanced requirements of real-world clinical care.

Shuli Zhang, Hao Zhou, Jiaqi Zheng et al.

Online Internet platforms require sophisticated marketing strategies to optimize user retention and platform revenue -- a classical resource allocation problem. Traditional solutions adopt a two-stage pipeline: machine learning (ML) for predicting individual treatment effects to marketing actions, followed by operations research (OR) optimization for decision-making. This paradigm presents two fundamental technical challenges. First, the prediction-decision misalignment: Conventional ML methods focus solely on prediction accuracy without considering downstream optimization objectives, leading to improved predictive metrics that fail to translate to better decisions. Second, the bias-variance dilemma: Observational data suffers from multiple biases (e.g., selection bias, position bias), while experimental data (e.g., randomized controlled trials), though unbiased, is typically scarce and costly -- resulting in high-variance estimates. We propose Bi-level Decision-Focused Causal Learning (Bi-DFCL) that systematically addresses these challenges. First, we develop an unbiased estimator of OR decision quality using experimental data, which guides ML model training through surrogate loss functions that bridge discrete optimization gradients. Second, we establish a bi-level optimization framework that jointly leverages observational and experimental data, solved via implicit differentiation. This novel formulation enables our unbiased OR estimator to correct learning directions from biased observational data, achieving optimal bias-variance tradeoff. Extensive evaluations on public benchmarks, industrial marketing datasets, and large-scale online A/B tests demonstrate the effectiveness of Bi-DFCL, showing statistically significant improvements over state-of-the-art. Currently, Bi-DFCL has been deployed at Meituan, one of the largest online food delivery platforms in the world.