arXiv subjects

Bing Cheng

Publications and source records attributed to Bing Cheng.

At least 19 recordsLinked to original sources

arXiv2026

Information Geometry (IG) Lives at Edge or Boundary of SMG (statistically meaningful geometry): - the First Edge Theorem and Applications

Statistically Meaningful Geometry (SMG) is a differential-geometric and information-theoretic framework that lifts over-parameterized models into infinite-dimensional non-parametric Orlicz statistical fiber bundles with an Ehresmann connection, decoupling unobservable vertical gauge noise from horizontal statistically verifiable directions. We prove the First Edge Theorem: Amari's information geometry (IG) and conventional statistics (CS) are not autonomous statistical universes but degenerate boundary layers of the larger gauge-active SMG space. Taking the structural identifiability radius $R\to\infty$ breaks gauge symmetry, collapses vertical fibers, and forces the total space onto the IG manifold; subsequent local asymptotic normality as $N\to\infty$ flattens the remaining curvature, yielding \[ \mathrm{SMG}\xrightarrow{\;R\to\infty\;}\mathrm{IG}\xrightarrow{\;N\to\infty\;}\mathrm{CS}. \] The same fiber-bundle machinery transforms model non-identifiability from a singular collapse into a structured gauge space. Applications include resolving the deep-learning generalization paradox, constructing gauge-invariant gradient descent and holonomy-matched preference alignment for generative AI, and solving weak identification in structural econometrics via intrinsic horizontal geodesic search.

math.GM↗

arXiv2026

The Second Edge Theorem: The Asymptotic Collapse of Sample-Dependent Information Geometry to the Canonical Flat Canvas of Conventional Statistics in Large Sample Limits

This paper establishes the global proof of the Second Edge Theorem: as sample size tends to infinity, sample-dependent information-geometric manifolds---formed by the parameter space, sample-scaled Fisher metric, and dual alpha-connections---undergo metric-topological collapse onto the flat tangent space of Conventional Statistics at the true parameter. We first prove a universal tensor valence scaling law, under which tensor fields of valence one through four degenerate at rates determined by sample size. Score fluctuations stabilize, the Fisher metric freezes to its true-parameter value, affine connections dissolve, and Riemann curvature is annihilated. We then bridge geometric collapse with statistical decision theory, showing that Cheeger--Gromov flattening and Le Cam risk condensation are dual projections of the same asymptotic phase transition. A Fisher-compatible Ehresmann connection extends these results to over-parameterized and singular models, yielding horizontal leaf-space collapse and uniform local asymptotic normality. Unifying the First and Second Edge Theorems yields a nested dual-edge hierarchy: Conventional Statistics is the boundary of Information Geometry, which is itself the boundary of Statistical Mechanics and Geometry. Thus, Conventional Statistics is not a heuristic approximation but the unique zero-curvature thermodynamic attractor of regular parametric information manifolds. This redefines modern statistics as a dynamic non-equilibrium field theory of finite-sample fluctuations, phase transitions, and gauge-invariant interactions.

math.GM↗

arXiv2026

Statistically Meaningful Geometry (SMG) Beyond the Euclidean Paradigm, with Application to Generative AI

Conventional uniform convergence bounds and empirical risk minimization break down in massive over-parameterized models, such as large language transformers and biological sequence networks. With near-infinite unconstrained internal degrees of freedom, their optimization landscapes develop flat vertical gauge valleys, rendering classical generalization metrics vacuous and inducing severe pathologies, specifically generative hallucination and catastrophic forgetting. We introduce the Statistically Meaningful Geometry (SMG) framework, an information-geometric paradigm lifting deterministic parametric models into infinite-dimensional non-parametric Orlicz statistical manifolds. Modeling the total state space as a differential fiber bundle ($\mathcal{M}, \mathcal{B}, \pi, \mathcal{V}, \mathcal{H}, \omega$), we establish a Two-Fold Inference Paradigm. We formalize an Ehresmann connection 1-form $\omega$ as a dynamic geometric filter that strips away vertical gauge noise (Structural Internal Directions, or SID) and isolates learning trajectories along the strictly non-degenerate horizontal distribution (Statistical Variational Directions, or SVD$\chi$). We prove that under connection-filtered pre-training, out-of-distribution predictive variance is strictly upper-bounded by the finite diameter of the identifiable quotient base manifold $\mathcal{B}$, establishing a hard geometric containment of generative hallucinations. By projecting downstream updates onto the orthogonal complement of the historical horizontal carriage, we formalize the SMG Sequential Adaptation Flow, proving the total non-asymptotic elimination of catastrophic forgetting. SMG replaces empirical fine-tuning heuristics with coordinate-free topological constraints, bridging advanced differential geometry with structural reliability in AI.

cs.LG↗

arXiv2026

Statistically Meaningful Geometry and Gauge Symmetry Breaking: A Geometric Foundation for Scientific Discovery and Intelligence Emergence

The rapid scaling of over-parameterized machine learning architectures, particularly LLMs, raises a profound crisis: do these systems exhibit genuine intelligence, or are they merely sophisticated statistical pattern matchers? Classical flat Euclidean statistics cannot differentiate continuous interpolation from the autonomous discovery of novel causal laws. To resolve this, we introduce Statistically Meaningful Geometry (SMG), a framework modeling over-parameterized learning systems as infinite-dimensional non-parametric Orlicz fiber bundles. We prove that under persistent out-of-distribution (OOD) stimuli governed by unmodeled causal mechanisms, continuous optimization fails. Unmodeled variance is rejected by the visible horizontal base manifold, leaking into the unobservable vertical fiber space and generating an accumulation of Active Acausal Tension. Driven by the statistical manifold's non-linear curvature, this tension inevitably strikes a conjugate focal boundary ($T_{\text{crit}} = \pi^2 / K_{\text{max}}$), triggering localized volumetric collapse and a catastrophic matrix singularity ($[G_f]^{-1} \to \infty$). We demonstrate this geometric breakdown acts as the strict non-equilibrium trigger for a Gauge Symmetry Break (GSB). The system purges hidden tension from unobservable gauge redundancies, spontaneously crystallizing a new, mathematically independent horizontal coordinate axis. This non-parametric phase transition registers as a discrete $+1.0$ integer step-jump in observable Structural G-Entropy. By decoupling parameter charts and subjecting emergent axes to a Minimal Energy Path Criterion and a Causal Invariance Filter, we distinguish genuine discovery from malignant hallucinations. Ultimately, SMG provides a parameter-free, falsifiable dashboard to mathematically certify true intelligence, transforming AI for Science into an engine of autonomous paradigm shifts.

cs.LG↗

arXiv2026

LA4VLA: Learning to Act without Seeing via Language-Action Pretraining

Vision-Language-Action (VLA) models are commonly pretrained on robot demonstrations by jointly mapping visual observations and language instructions to actions. However, dense visual-action supervision can dominate the comparatively sparse language-action signal. As a result, policies may rely on visual shortcuts rather than learn how language conditions action execution, making them sensitive to visual variations. To address this limitation, we propose LA4VLA, a language-action pretraining framework that enables policies to acquire language-conditioned action priors without visual observations. These priors capture reusable manipulation skills shared across tasks and scenes, reducing reliance on scene-specific visual cues. Specifically, LA4VLA decomposes expert demonstration trajectories into atomic action segments and pairs each segment with a corresponding low-level action description. This yields LA-33K, a dataset of 33K Language-Action (LA) episodes derived entirely from existing demonstrations without additional robot data collection. We further develop LA4VLA-1B, a lightweight 1B-parameter VLA model, and investigate three paradigms for incorporating language-action supervision into VLA learning: LA-only pretraining, sequential LA-to-VLA pretraining, and mixed LA-VLA pretraining. Across simulation and real-world tasks, LA-pretrained policies consistently outperform matched VLA-pretrained counterparts, while combining LA and VLA supervision leads to further gains. In particular, mixed LA-VLA pretraining improves the average success rate of LA4VLA-1B over the no-pretraining baseline by up to 17.8 and 45.0 percentage points in simulation and real-world tasks, respectively. These results establish LA4VLA as an effective and complementary pretraining strategy for building stronger and more robust VLA policies.

cs.RO↗

arXiv2026

Evo-Depth: A Lightweight Depth-Enhanced Vision-Language-Action Model

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.

cs.CV↗

arXiv2026

Magnetic-field-tunable cyclotron hyperbolic polaritons

Hyperbolic polaritons are conventionally associated with structural anisotropy or phononic Reststrahlen bands. Here, we predict a new class of hyperbolic polaritons arising from magnetic-field-induced cyclotron motion of charge carriers. When a perpendicular magnetic field is applied to high-mobility semimetals, the cyclotron response drives the in-plane dielectric function from metallic- to insulating-like below the cyclotron resonance frequency, while the out-of-plane response remains metallic. This anisotropy creates a hyperbolic dielectric environment that supports field-tunable hyperbolic polaritons. We develop a comprehensive theoretical framework incorporating coupling to other collective excitations and show that these modes can be directly visualized in real space via terahertz near-field nanoscopy. Our work identifies cyclotron motion as a new route to hyperbolic polaritons and establishes a versatile platform for magnetically programmable nanophotonics.

cond-mat.mes-hall↗

arXiv2026

MedConsultBench: A Full-Cycle, Fine-Grained, Process-Aware Benchmark for Medical Consultation Agents

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.

cs.AI↗

arXiv2025

An approach to Fisher-Rao metric for infinite dimensional non-parametric information geometry

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 Cram\'er-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.

stat.ML↗

arXiv2025

AR-Med: Automated Relevance Enhancement in Medical Search via LLM-Driven Information Augmentation

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.

cs.CL↗

arXiv2025

Bi-Level Decision-Focused Causal Learning for Large-Scale Marketing Optimization: Bridging Observational and Experimental Data

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.

cs.LG↗

arXiv2025

Hidden Representation Clustering with Multi-Task Representation Learning towards Robust Online Budget Allocation

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.

cs.LG↗

arXiv2025

AutoMathKG: The automated mathematical knowledge graph based on LLM and vector database

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.

cs.AI↗

arXiv2025

Bolometric Superconducting Optical Nanoscopy (BOSON)

Superconducting transition-edge sensors are renowned for their extraordinary photon sensitivity and energy resolution, finding applications spanning quantum information, astronomy, and nanophotonics. Here, we report the development of BOlometric Superconducting Optical Nanoscopy (BOSON), a novel platform that integrates bolometric detection at the superconducting transition edges with near-field optical techniques. BOSON enables the mapping of photoinduced changes in superconductivity with unprecedented spatial resolution and photon sensitivity. By incorporating BOSON with low-dimensional materials, we achieved polariton imaging at nanowatt excitation levels--at least four orders of magnitude lower than the power typically required in prior near-field nanoscopy experiments. Our findings highlight the potential for BOSON to advance scanning probe based optical platforms to enable the detection of photons, polaritons, and Cooper pair dynamics at the nanoscale. This paves the way for quantum sensing applications using single-polariton detection and can offer deeper insights into quasiparticle dynamics.

quant-ph↗

arXiv2025

Photocurrent Nanoscopy of Quantum Hall Bulk

Understanding nanoscale electronic and thermal transport of two-dimensional (2D) electron systems in the quantum Hall regime, particularly in the bulk insulating state, poses considerable challenges. One of the primary difficulties arises from the presence of chiral edge channels, whose transport behavior obscures the investigation of the insulating bulk. Using near-field (NF) optical and photocurrent (PC) nanoscopy, we probe real-space variations of the optical and thermal dynamics of graphene in the quantum Hall regime without relying on complex sample or electrode geometries. Near the charge neutrality point (CNP), we detect strong optical and photothermal signals from resonant inter-Landau level (LL) magnetoexciton excitations between the 0th and +-1st LLs, which gradually weaken with increasing doping due to Pauli blocking. Interestingly, at higher doping levels and full integer LL fillings, photothermal signals reappear across the entire sample over a ~10-micrometer scale, indicating unexpectedly long cooling lengths and nonlocal photothermal heating through the insulating bulk. This observation suggests thermal conductivity persists for the localized states even as electronic transport is suppressed - a clear violation of the Wiedemann-Franz (WF) law. Our experiments provide novel insights into nanoscale thermal and electronic transport in incompressible 2D gases, highlighting the roles of magnetoexcitons and chiral edge states in the thermo-optoelectric dynamics of Dirac quantum Hall state.

cond-mat.mes-hall↗

arXiv2025

On a fast consistent selection of nested models with possibly unnormalized probability densities

Models with unnormalized probability density functions are ubiquitous in statistics, artificial intelligence and many other fields. However, they face significant challenges in model selection if the normalizing constants are intractable. Existing methods to address this issue often incur high computational costs, either due to numerical approximations of normalizing constants or evaluation of bias corrections in information criteria. In this paper, we propose a novel and fast selection criterion, MIC, for nested models of possibly dependent data, allowing direct data sampling from a possibly unnormalized probability density function. With a suitable multiplying factor depending only on the sample size and the model complexity, MIC gives a consistent selection under mild regularity conditions and is computationally efficient. Extensive simulation studies and real-data applications demonstrate the efficacy of MIC in the selection of nested models with unnormalized probability densities.

stat.ME↗

arXiv2024

Terahertz-induced tunnel ionization drives coherent Raman-active phonon in Bismuth

Driving coherent lattice motion with THz pulses has emerged as a novel pathway for achieving dynamic stabilization of exotic phases that are inaccessible in equilibrium quantum materials. In this work, we present a previously unexplored mechanism for THz excitation of Raman-active phonons. We show that intense THz pulses centered at 1 THz can excite the Raman-active $A_{1g}$ phonon mode at 2.9 THz in a bismuth film. We rule out the possibilities of the phonon being excited through conventional anharmonic coupling to other modes or via a THz sum frequency process. Instead, we demonstrate that the THz-driven tunnel ionization provides a plausible means of creating a displacive driving force to initiate the phonon oscillations. Our work highlights a new mechanism for exciting coherent phonons, offering potential for dynamic control over the electronic and structural properties of semimetals and narrow-band semiconductors on ultrafast timescales.

cond-mat.mes-hall↗

arXiv2024

Decision Focused Causal Learning for Direct Counterfactual Marketing Optimization

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.

cs.LG↗