arXiv subjects

Bohan Hu

Publications and source records attributed to Bohan Hu.

6 recordsLinked to original sources

arXiv2026

Nonconvex Carnot Limit Shapes for Branching Random Walks on the Heisenberg Group

We study a supercritical branching random walk on the discrete Heisenberg group driven by the four standard horizontal generators. Horizontal position has scale $n$, whereas the central coordinate records discrete area and has scale $n^2$. On the Galton-Watson survival event, we prove almost sure Hausdorff convergence, under Carnot scaling, of both the rescaled particle positions and the collections of enhanced ancestral paths. The path limit consists of area lifts of horizontal paths $ω$ satisfying $J_t(ω)\le t\logρ$ for every $t\in[0,1]$, where $ρ$ is the offspring mean. In contrast to the classical Euclidean case, the deterministic limit shape is nonconvex for every $ρ>1$. We identify its horizontal projection and interval vertical fibers, determine the saturated shape for $ρ\ge4$, and characterize the origin fiber below saturation by Wulff duality. A hyperbolic representation gives an elliptic integral formula for the Wulff area. The maximal central coordinate $Γ_ρ$ is nondecreasing and concave in $ρ$, equals $1/4$ for $ρ\ge4$, and satisfies $Γ_ρ=(\logρ)/π-(\logρ)^2/(4π) +O((\logρ)^3)$ as $ρ\downarrow1$. For fixed $1<ρ<4$, we obtain $M_n^Z=Γ_ρn^2+O(n^{3/2}\sqrt{\log n})$ almost surely. Above saturation the first correction is a random linear term; at $ρ=4$, under a finite second moment assumption, the deficit $Γ_4n^2-M_n^Z$ has order $n\log\log n$ in probability.

math.PR↗

arXiv2026

Dynamical Equations for Poisson Galton--Watson Trees and Component Densities of Sparse Inhomogeneous Random Graphs

We study Poisson Galton--Watson trees on a standard Borel type space when the offspring kernel is multiplied by a scalar parameter. On finite trees, we identify the Radon--Nikodym derivative between two parameter values and show that it remains measurable after projection to the total progeny measure. Under a uniform bound on the offspring intensities, differentiation yields exact differential and integral equations for the projected laws without irreducibility, reversibility, or a positive eigenfunction. With an additional positive eigenfunction bounded above and away from zero, we relate these equations to an infinite spinal tree, uniform pruning, the Doob transform, and the Aldous--Pitman ascension process. For a uniformly bounded offspring kernel, we also prove uniform exponential integrability of the total progeny throughout the spectrally subcritical regime. As an application, under the graphical-kernel assumptions of Bollobas, Janson and Riordan, the number $K_n$ of connected components satisfies $K_n/n \to {\mathbb E}_π[1/T_u]$ in probability and in $L^1$, where $T_u$ is the total progeny of the associated branching process and $1/\infty=0$. If $q_u(x)$ is its extinction probability from type $x$, re-rooting and extinction duality give the explicit limit $$ \int_S q_u(x)\,π(dx) - {u\over 2}\int_{S\times S}κ(x,y)q_u(x)q_u(y)\,π(dx)π(dy). $$ This extends the finite-type and compact-continuous formulas to the full BJR graphical-kernel setting, allowing separable noncompact type spaces and kernels that may be unbounded or reducible.

math.PR↗

arXiv2026

Towards Event-Robust Acoustic Scene Classification

This paper introduces the Event-Shifted Acoustic Scene (ESAS) dataset, a novel benchmark for evaluating the robustness of Acoustic Scene Classification (ASC) systems against unknown sound events. Existing ASC datasets typically contain recordings of clean and consistent audio, while real-world environments often include diverse and unexpected sound events. To bridge this gap, ESAS simulates real-world acoustic variability by injecting foreground sound events into background scenes with the assistance of large language models. In this work, we present the construction methodology, dataset statistics, and evaluation protocols. Furthermore, a comprehensive evaluation of state-of-the-art ASC systems is conducted using the ESAS benchmark. Experimental results reveal that existing ASC models suffer significant performance degradation when facing the event-shift challenge. The introduction of the ESAS dataset aims to drive future research toward event-robust ASC.

cs.SD↗

arXiv2026

Diff-SQL: SQL Efficiency Optimization via Patch Generation and Constraint Alignment

SQL efficiency optimization aims to transform slow queries into semantically equivalent but faster alternatives. However, directly optimizing SQL with large language models in an end-to-end fashion often induces Objective Misalignment which creates a fundamental tension between optimization and correctness, making direct full SQL rewriting unreliable for execution-facing database applications. To address this problem, we propose Diff-SQL, a two-stage framework that decouples efficiency-oriented optimization from constraint-aware alignment. The first stage identifies optimization opportunities and proposes targeted edits in the form of a unified diff patch, while the second stage is trained with on-policy reinforcement learning to revise outputs under executability and semantic-equivalence constraints. To train and evaluate Diff-SQL, we construct an automated pipeline that mines optimization knowledge from StackOverflow and builds Slow-Fast SQL pairs through cascaded filtering. We further introduce Effi-SQL, a benchmark containing 1,100 human-verified Slow-Fast pairs across five SQL dialects. Experiments show that Objective Misalignment is widespread across existing LLM-based SQL optimization methods, where direct full SQL optimization causes an average 22.7% execution accuracy degradation across frontier models such as Claude-Opus-4.6, with the worst model dropping by 43.0%. Diff-SQL alleviates this trade-off. As an inference-only strategy, it improves R-VES by 10.0% on average while reducing execution accuracy degradation by 6.11% on average across three strong base models. With execution-grounded training, Diff-SQL further enables a 7B model to improve R-VES from 33.42% to 46.83%, demonstrating that the proposed two-stage optimization-and-alignment paradigm can deliver both stronger efficiency and better correctness in local, small model deployment settings.

cs.DB↗

arXiv2026

DeCo-DETR: Decoupled Cognition DETR for efficient Open-Vocabulary Object Detection

Open-vocabulary object detection (OVOD) enables models to recognize objects beyond predefined categories, but existing approaches remain limited in practical deployment. On the one hand, multimodal designs often incur substantial computational overhead due to their reliance on text encoders at inference time. On the other hand, tightly coupled training objectives introduce a trade-off between closed-set detection accuracy and open-world generalization. Thus, we propose Decoupled Cognition DETR (DeCo-DETR), a vision-centric framework that addresses these challenges through a unified decoupling paradigm. Instead of depending on online text encoding, DeCo-DETR constructs a hierarchical semantic prototype space from region-level descriptions generated by pre-trained LVLMs and aligned via CLIP, enabling efficient and reusable semantic representation. Building upon this representation, the framework further disentangles semantic reasoning from localization through a decoupled training strategy, which separates alignment and detection into parallel optimization streams. Extensive experiments on standard OVOD benchmarks demonstrate that DeCo-DETR achieves competitive zero-shot detection performance while significantly improving inference efficiency. These results highlight the effectiveness of decoupling semantic cognition from detection, offering a practical direction for scalable OVOD systems.

cs.CV↗

arXiv2025

GAME: Learning Multimodal Interactions via Graph Structures for Personality Trait Estimation

Apparent personality analysis from short videos poses significant chal-lenges due to the complex interplay of visual, auditory, and textual cues. In this paper, we propose GAME, a Graph-Augmented Multimodal Encoder designed to robustly model and fuse multi-source features for automatic personality prediction. For the visual stream, we construct a facial graph and introduce a dual-branch Geo Two-Stream Network, which combines Graph Convolutional Networks (GCNs) and Convolutional Neural Net-works (CNNs) with attention mechanisms to capture both structural and appearance-based facial cues. Complementing this, global context and iden-tity features are extracted using pretrained ResNet18 and VGGFace back-bones. To capture temporal dynamics, frame-level features are processed by a BiGRU enhanced with temporal attention modules. Meanwhile, audio representations are derived from the VGGish network, and linguistic se-mantics are captured via the XLM-Roberta transformer. To achieve effective multimodal integration, we propose a Channel Attention-based Fusion module, followed by a Multi-Layer Perceptron (MLP) regression head for predicting personality traits. Extensive experiments show that GAME con-sistently outperforms existing methods across multiple benchmarks, vali-dating its effectiveness and generalizability.

cs.CV↗