arXiv subjects

Bing He

Publications and source records attributed to Bing He.

At least 37 records · Page 2Linked to original sources

arXiv2026

Asymptotic Statistics of Odd Unimodal Sequences: Rank Distributions and Probabilistic Structures

Integer partitions have fascinated people for centuries, from Ramanujan's groundbreaking congruences to the modern theory of modular forms. This paper investigates the statistical properties of odd unimodal sequences--a natural refinement where sequences rise to a peak and then fall, but with the constraint that all parts must be odd, and develops a comprehensive statistical theory for their rank and shape parameters. We establish the asymptotic distribution of the rank statistic and demonstrate that, when properly normalized, it converges to the hyperbolic secant distribution. Beyond the rank distribution, limiting distributions of the peak, the largest parts on either side of the peak, and the joint behavior of small parts are also proved. These results reveal a rich probabilistic structure that parallels the classical theory of integer partitions while exhibiting distinctive new features arising from the odd-part constraint. The analysis employs a synthesis of modular transformation theory, false theta function asymptotics, and conditioned Boltzmann models. This extends the probabilistic machinery previously developed for unimodal sequences into a more general and analytically demanding setting, offering a unified approach that bridges modular forms and probability.

math.NT↗

arXiv2026

Staircase mechanical energy growth in optomechanical systems of median mechanical frequencies

Owing to the radiation-force-induced nonlinearity, cavity optomechanical systems (COMS) exhibit dynamical phenomena such as back-action induced oscillation, chaos, mechanical amplitude locking, and anomalous stabilization, which occur under different driving conditions and different system parameters. We here identify a previously unknown dynamical pattern of staircase evolution for the energy of mechanical resonator, when a COMS with neither very large nor very small built-in mechanical frequency is driven by a two-tone field, which satisfies a condition that the frequency difference of the two tones matches the built-in mechanical frequency. The properties of this phenomenon are analyzed for the different system parameters due to fabrication such as mechanical frequencies and quality factors, as well as under the varied driving conditions such as unequal drive tone powers and mismatched drive tone difference from the mechanical frequency. Some special features, such as an emergent bifurcation due to the tone power difference, together with the totally different responses of the system to the drive tone mismatches of opposite signs, are discovered to exist only in this type of COMS with median mechanical frequencies. This work fills a gap in the study of the dynamics of COMS under two-tone drives. In the aspect of applications, the rapid increase of mechanical energy exhibited in the phenomenon promises phonon laser generation, and the sensitive dynamical response to the drive tone mismatches offers a potential approach to high-precision sensing.

physics.optics↗

arXiv2026

Complete transparency with three active-passive-coupled optical resonators

The phenomena of induced transparency, with the typical examples of electromagnetically induced transparency (EIT) in atomic media and those based on coupled optical resonators, have attracted tremendous interest since their discoveries. Owing to the limitations of the involved physical elements, however, near-100\% transmissions were reported under highly demanding experimental conditions. With a structure of three linearly coupled optical resonators, an active one carrying optical gain and two passive ones simply with dissipation, we demonstrate that a transmitted light field can become completely transparent through the structure, which displays all properties similar to those of EIT. It is due to a destructive interference mechanism that totally eliminates the intracavity field in the dissipative resonator directly coupled to the transmitted field of any feasible power, when the coupling strength of two other resonators is tuned across a point determined by their associated gain and loss rates. This mechanism works for all possible coupling strengths of the dark resonator with the input field and its neighboring resonator, as well as for any available quality factor from its fabrication. The transparency window size and output field intensity can be freely adjusted by tuning two inter-cavity couplings of wide ranges, without modifying the built-in optical gain which can be just slightly stronger than the dissipation of the active resonator.

quant-ph↗

arXiv2026

Adaptive Learned Image Compression with Graph Neural Networks

Efficient image compression relies on modeling both local and global redundancy. Most state-of-the-art (SOTA) learned image compression (LIC) methods are based on CNNs or Transformers, which are inherently rigid. Standard CNN kernels and window-based attention mechanisms impose fixed receptive fields and static connectivity patterns, which potentially couple non-redundant pixels simply due to their proximity in Euclidean space. This rigidity limits the model's ability to adaptively capture spatially varying redundancy across the image, particularly at the global level. To overcome these limitations, we propose a content-adaptive image compression framework based on Graph Neural Networks (GNNs). Specifically, our approach constructs dual-scale graphs that enable flexible, data-driven receptive fields. Furthermore, we introduce adaptive connectivity by dynamically adjusting the number of neighbors for each node based on local content complexity. These innovations empower our Graph-based Learned Image Compression (GLIC) model to effectively model diverse redundancy patterns across images, leading to more efficient and adaptive compression. Experiments demonstrate that GLIC achieves state-of-the-art performance, achieving BD-rate reductions of 19.29%, 21.69%, and 18.71% relative to VTM-9.1 on Kodak, Tecnick, and CLIC, respectively. Code will be released at https://github.com/UnoC-727/GLIC.

cs.CV↗

arXiv2026

Content-Aware Mamba for Learned Image Compression

Recent learned image compression (LIC) leverages Mamba-style state-space models (SSMs) for global receptive fields with linear complexity. However, the standard Mamba adopts content-agnostic, predefined raster (or multi-directional) scans under strict causality. This rigidity hinders its ability to effectively eliminate redundancy between tokens that are content-correlated but spatially distant. We introduce Content-Aware Mamba (CAM), an SSM that dynamically adapts its processing to the image content. Specifically, CAM overcomes prior limitations with two novel mechanisms. First, it replaces the rigid scan with a content-adaptive token permutation strategy to prioritize interactions between content-similar tokens regardless of their location. Second, it overcomes the sequential dependency by injecting sample-specific global priors into the state-space model, which effectively mitigates the strict causality without multi-directional scans. These innovations enable CAM to better capture global redundancy while preserving computational efficiency. Our Content-Aware Mamba-based LIC model (CMIC) achieves state-of-the-art rate-distortion performance, surpassing VTM-21.0 by 15.91%, 21.34%, and 17.58% in BD-rate on the Kodak, Tecnick, and CLIC datasets, respectively. Code will be released at https://github.com/UnoC-727/CMIC.

cs.CV↗

arXiv2026

Position: Agentic Evolution is the Path to Evolving LLMs

As Large Language Models (LLMs) move from curated training sets into open-ended real-world environments, a fundamental limitation emerges: static training cannot keep pace with continual deployment environment change. Scaling training-time and inference-time compute improves static capability but does not close this train-deploy gap. We argue that addressing this limitation requires a new scaling axis-evolution. Existing deployment-time adaptation methods, whether parametric fine-tuning or heuristic memory accumulation, lack the strategic agency needed to diagnose failures and produce durable improvements. Our position is that agentic evolution represents the inevitable future of LLM adaptation, elevating evolution itself from a fixed pipeline to an autonomous evolver agent. We instantiate this vision in a general framework, A-Evolve, which treats deployment-time improvement as a deliberate, goal-directed optimization process over persistent system state. We further propose the evolution-scaling hypothesis: the capacity for adaptation scales with the compute allocated to evolution, positioning agentic evolution as a scalable path toward sustained, open-ended adaptation in the real world. Our code is publicly available at https://github.com/A-EVO-Lab/a-evolve.

cs.AI↗

arXiv2026

How Do Latent Reasoning Methods Perform Under Weak and Strong Supervision?

Latent reasoning has been recently proposed as a reasoning paradigm and performs multi-step reasoning through generating steps in the latent space instead of the textual space. This paradigm enables reasoning beyond discrete language tokens by performing multi-step computation in continuous latent spaces. Although there have been numerous studies focusing on improving the performance of latent reasoning, its internal mechanisms remain not fully investigated. In this work, we conduct a comprehensive analysis of latent reasoning methods to better understand the role and behavior of latent representation in the process. We identify two key issues across latent reasoning methods with different levels of supervision. First, we observe pervasive shortcut behavior, where they achieve high accuracy without relying on latent reasoning. Second, we examine the hypothesis that latent reasoning supports BFS-like exploration in latent space, and find that while latent representations can encode multiple possibilities, the reasoning process does not faithfully implement structured search, but instead exhibits implicit pruning and compression. Finally, our findings reveal a trade-off associated with supervision strength: stronger supervision mitigates shortcut behavior but restricts the ability of latent representations to maintain diverse hypotheses, whereas weaker supervision allows richer latent representations at the cost of increased shortcut behavior.

cs.AI↗

arXiv2026

SurfSplat: Conquering Feedforward 2D Gaussian Splatting with Surface Continuity Priors

Reconstructing 3D scenes from sparse images remains a challenging task due to the difficulty of recovering accurate geometry and texture without optimization. Recent approaches leverage generalizable models to generate 3D scenes using 3D Gaussian Splatting (3DGS) primitive. However, they often fail to produce continuous surfaces and instead yield discrete, color-biased point clouds that appear plausible at normal resolution but reveal severe artifacts under close-up views. To address this issue, we present SurfSplat, a feedforward framework based on 2D Gaussian Splatting (2DGS) primitive, which provides stronger anisotropy and higher geometric precision. By incorporating a surface continuity prior and a forced alpha blending strategy, SurfSplat reconstructs coherent geometry together with faithful textures. Furthermore, we introduce High-Resolution Rendering Consistency (HRRC), a new evaluation metric designed to evaluate high-resolution reconstruction quality. Extensive experiments on RealEstate10K, DL3DV, and ScanNet demonstrate that SurfSplat consistently outperforms prior methods on both standard metrics and HRRC, establishing a robust solution for high-fidelity 3D reconstruction from sparse inputs. Project page: https://hebing-sjtu.github.io/SurfSplat-website/

cs.CV↗

arXiv2025

Proof of a conjecture of Baruah and Sarma on sign patterns of certain infinite products

Let \[ \sum_{n=0}^{\infty}A(n)q^{n} := \frac{(q^{2};q^{5})_{\infty}^{5}(q^{3};q^{5})_{\infty}^{5}}{(q;q^{5})_{\infty}^{5}(q^{4};q^{5})_{\infty}^{5}}, \] \[ \sum_{n=0}^{\infty} B(n)q^{n} := \frac{(q;q^{5})_{\infty}^{5} (q^{4};q^{5})_{\infty}^{5}} {(q^{2};q^{5})_{\infty}^{5}(q^{3}; q^{5})_{\infty}^{5}}, \] and \[ \sum_{n=0}^{\infty} D(n)q^{n} := \frac{(q^{5};q^{25})_{\infty}(q^{20}; q^{25})_{\infty}} {(q^{10};q^{25})_{\infty}(q^{15}; q^{25})_{\infty}} \frac{(q^{2}; q^{5})_{\infty}^{5}(q^{3};q^{5})_{\infty}^{5}} {(q;q^{5})_{\infty}^{5} (q^{4};q^{5})_{\infty}^{5}} \] where $(a;q)_{\infty} := \prod_{k=0}^{\infty}(1-aq^{k})$ and $|q|<1.$ These sequences are closely related to the celebrated Rogers-Ramanujan continued fraction. In this paper, we study the sign behavior o of the coefficients $A(n),B(n)$ and $D(n).$ We prove that for all integers $n\geq0,$ \begin{align*} A(5n)<0\quad(n\neq0),\qquad B(5n) < 0\quad(n\neq0),\qquad D(5n+1)>0. \end{align*} This confirms a recent conjecture of Baruah and Sarma. Our proof is different from the previous method of Baruah and Sarma, and combines asymptotic coefficient analysis with symbolic computation for finite case verification.

math.NT↗

arXiv2025

H3D-DGS: Exploring Heterogeneous 3D Motion Representation for Deformable 3D Gaussian Splatting

Dynamic scene reconstruction poses a persistent challenge in 3D vision. Deformable 3D Gaussian Splatting has emerged as an effective method for this task, offering real-time rendering and high visual fidelity. This approach decomposes a dynamic scene into a static representation in a canonical space and time-varying scene motion. Scene motion is defined as the collective movement of all Gaussian points, and for compactness, existing approaches commonly adopt implicit neural fields or sparse control points. However, these methods predominantly rely on gradient-based optimization for all motion information. Due to the high degree of freedom, they struggle to converge on real-world datasets exhibiting complex motion. To preserve the compactness of motion representation and address convergence challenges, this paper proposes heterogeneous 3D control points, termed \textbf{H3D control points}, whose attributes are obtained using a hybrid strategy combining optical flow back-projection and gradient-based methods. This design decouples directly observable motion components from those that are geometrically occluded. Specifically, components of 3D motion that project onto the image plane are directly acquired via optical flow back projection, while unobservable portions are refined through gradient-based optimization. Experiments on the Neu3DV and CMU-Panoptic datasets demonstrate that our method achieves superior performance over state-of-the-art deformable 3D Gaussian splatting techniques. Remarkably, our method converges within just 100 iterations and achieves a per-frame processing speed of 2 seconds on a single NVIDIA RTX 4070 GPU.

cs.CV↗

arXiv2025

TRAJECT-Bench:A Trajectory-Aware Benchmark for Evaluating Agentic Tool Use

Large language model (LLM)-based agents increasingly rely on tool use to complete real-world tasks. While existing works evaluate the LLMs' tool use capability, they largely focus on the final answers yet overlook the detailed tool usage trajectory, i.e., whether tools are selected, parameterized, and ordered correctly. We introduce TRAJECT-Bench, a trajectory-aware benchmark to comprehensively evaluate LLMs' tool use capability through diverse tasks with fine-grained evaluation metrics. TRAJECT-Bench pairs high-fidelity, executable tools across practical domains with tasks grounded in production-style APIs, and synthesizes trajectories that vary in breadth (parallel calls) and depth (interdependent chains). Besides final accuracy, TRAJECT-Bench also reports trajectory-level diagnostics, including tool selection and argument correctness, and dependency/order satisfaction. Analyses reveal failure modes such as similar tool confusion and parameter-blind selection, and scaling behavior with tool diversity and trajectory length where the bottleneck of transiting from short to mid-length trajectories is revealed, offering actionable guidance for LLMs' tool use.

cs.AI↗

arXiv2025

Adaptive Test-Time Reasoning via Reward-Guided Dual-Phase Search

Large Language Models (LLMs) have achieved significant advances in reasoning tasks. A key approach is tree-based search with verifiers, which expand candidate reasoning paths and use reward models to guide pruning and selection. Although effective in improving accuracy, these methods are not optimal in terms of efficiency: they perform simple decomposition on the reasoning process, but ignore the planning-execution nature of tasks such as math reasoning or code generation. This results in inefficient exploration of reasoning process. To address this, we propose a dual-phase test-time scaling framework that explicitly separates reasoning into planning and execution, and performs search over the two phases individually. Specifically, we decompose reasoning trajectories and develop reward models for each phase, enabling the search to explore and prune plans and executions separately. We further introduce a dynamic budget allocation mechanism that adaptively redistributes sampling effort based on reward feedback, allowing early stopping on confident steps and reallocation of computation to more challenging parts of the reasoning process. Experiments on both mathematical reasoning and code generation benchmarks demonstrate that our approach consistently improves accuracy while reducing redundant computation.

cs.AI↗

arXiv2025

Proof of a conjecture of Garvan and Jennings-Shaffer on the nonnegativity of M_{C1}(m,n) and M_{C5}(m,n)

In their 2016 paper on exotic Bailey--Slater SPT-functions, Garvan and Jennings-Shaffer introduced many new spt-crank-type functions and proposed a conjecture that the spt-crank-type functions $M_{C1}(m,n)$ and $M_{C5}(m,n)$ are both nonnegative for all $m\in\mathbb{Z}$ and $n\in\mathbb{N}.$ Applying Wright\textquoteright s circle method, Jang and Kim showed that $M_{C1}(m,n)$ and $M_{C5}(m,n)$ are both positive for a fixed integer $m$ and large enough integers $n.$ Up to now, no complete proof of this conjecture has been given. In this paper, we provide a complete proof for this conjecture by using the theory of lattice points. Our proof is quite different from that of Jang and Kim.

math.NT↗

arXiv2025

Steering Protein Language Models

Protein Language Models (PLMs), pre-trained on extensive evolutionary data from natural proteins, have emerged as indispensable tools for protein design. While powerful, PLMs often struggle to produce proteins with precisely specified functionalities or properties due to inherent challenges in controlling their outputs. In this work, we investigate the potential of Activation Steering, a technique originally developed for controlling text generation in Large Language Models (LLMs), to direct PLMs toward generating protein sequences with targeted properties. We propose a simple yet effective method that employs activation editing to steer PLM outputs, and extend this approach to protein optimization through a novel editing site identification module. Through comprehensive experiments on lysozyme-like sequence generation and optimization, we demonstrate that our methods can be seamlessly integrated into both auto-encoding and autoregressive PLMs without requiring additional training. These results highlight a promising direction for precise protein engineering using foundation models.

q-bio.BM↗

arXiv2025

Some conjectures of Schlosser and Zhou on sign patterns of the coefficients of infinite products

Recently, Schlosser and Zhou proposed many conjectures on sign patterns of the coefficients appearing in the $q$-series expansions of the infinite Borwein product and other infinite products raised to a real power. In this paper, we will study several of these conjectures. Let \[ G(q):=\prod_{i=1}^{I}\left(\prod_{k=0}^{\infty}(1-q^{m_{i}+kn_{i}})(1-q^{-m_{i}+(k+1)n_{i}})\right)^{u_{i}} \] where $I$ is a positive integer, $1\leq m_{i}<n_{i}$ and $u_{i}\neq0$ for $1\leq i\leq I$ and $|q|<1.$ We will establish an asymptotic formula for the coefficients of $G(q)^δ$ with $δ$ being a positive real number by using the Hardy--Ramanujan--Rademacher circle method. As applications, we apply the asymptotic formula to confirm some of the conjectures of Schlosser and Zhou.

math.CO↗

arXiv2025

Weighted partial sums of a random multiplicative function and their positivity

In this paper, we study the probability that some weighted partial sums of a random multiplicative function $f$ are positive. Applying the characteristic decomposition, we obtain that if $S$ is a non-empty subset of the multiplicative residue class group $(\mathbb{Z}/m\mathbb{Z})^{\times}$ with $m$ being a fixed positive integer and $A=\{a+mn\mid n=0,1,2,3,\cdots\}$ with $a\in S,$ then there exists a positive number $δ$ independent of $x$, such that \[ \mathbb{P}\left(\sum_{A\cap[1,x)}\frac{f(n)}{n}<0\right)>δ\] unless the coefficients of the real characters in the expansion of the characteristic function of $S$ according to the characters of $(\mathbb{Z}/m\mathbb{Z})^{\times}$ are all non-negative, and the coefficients of the complex characters are all zero, in which case we have \[ \mathbb{P}\left(\sum_{A\cap[1,x)}\frac{f(n)}{n}<0\right)=O\left(\exp\left(-\exp\left(\frac{\ln x}{C\ln_{2}x}\right)\right)\right) \] for a positive constant $C.$ This includes as a special case a result of Angelo and Xu. We also extend the result to the cyclotomic field $K_{n}=\mathbb{Q}(ζ_{n})$ with $ζ_{n}=e^{2πi/n}$ and study the probability that these generalized weighted sums are positive. In addition, we deal with the positivity problem of certain partial sums related to the celebrated Ramanujan tau function $τ(n)$ and the Ramanujan modular form $Δ(q),$ and obtain an upper bound for the probability that these partial sums are negative in a more general situation.

math.NT↗

arXiv2025

ROBAD: Robust Adversary-aware Local-Global Attended Bad Actor Detection Sequential Model

Detecting bad actors is critical to ensure the safety and integrity of internet platforms. Several deep learning-based models have been developed to identify such users. These models should not only accurately detect bad actors, but also be robust against adversarial attacks that aim to evade detection. However, past deep learning-based detection models do not meet the robustness requirement because they are sensitive to even minor changes in the input sequence. To address this issue, we focus on (1) improving the model understanding capability and (2) enhancing the model knowledge such that the model can recognize potential input modifications when making predictions. To achieve these goals, we create a novel transformer-based classification model, called ROBAD (RObust adversary-aware local-global attended Bad Actor Detection model), which uses the sequence of user posts to generate user embedding to detect bad actors. Particularly, ROBAD first leverages the transformer encoder block to encode each post bidirectionally, thus building a post embedding to capture the local information at the post level. Next, it adopts the transformer decoder block to model the sequential pattern in the post embeddings by using the attention mechanism, which generates the sequence embedding to obtain the global information at the sequence level. Finally, to enrich the knowledge of the model, embeddings of modified sequences by mimicked attackers are fed into a contrastive-learning-enhanced classification layer for sequence prediction. In essence, by capturing the local and global information (i.e., the post and sequence information) and leveraging the mimicked behaviors of bad actors in training, ROBAD can be robust to adversarial attacks. Extensive experiments on Yelp and Wikipedia datasets show that ROBAD can effectively detect bad actors when under state-of-the-art adversarial attacks.

cs.LG↗

arXiv2025

Memory effects in pulsed optomechanical systems

Memory, understood as time non-locality, is a fundamental property of any physical system, whether classical or quantum, and has important applications in a wide variety of technologies. In the context of quantum technologies, systems with memory can be used in quantum information, communication, and sensing. Here, we demonstrate that cavity optomechanical systems driven by a pulsed laser can operate as programmable quantum memory elements. By engineering the adiabatic and non-adiabatic pulses, particularly the Gaussian and sinusoidal, we induce and control diverse memory phenomena such as dynamical hysteresis, quantized phononic transitions, and distinct energy-storing responses. Within a mean-field approach, we derive the analytical and numerical criteria under which the photonic and phononic observables manifest the memory effects in strongly driven regimes. The memory effects are quantified through a dimensionless geometric form factor, which provides a versatile metric to characterize the memory efficiency. Our protocol is readily compatible with the current optomechanical platforms, highlighting the new possibilities for advanced memory functionalities in quantum technologies.

quant-ph↗