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An Zhang

An Zhang contributes to research discovery and scholarly infrastructure.

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Artificial Intelligence Computer Vision Machine Learning math.PR math.ST q-fin.MF Statistics Theory

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preprint2026arXiv

Central limit theorem for a partially observed interacting system of Hawkes processes I: subcritical case

We consider a system of $N$ Hawkes processes and observe the actions of a subpopulation of size $K \le N$ up to time $t$, where $K$ is large. The influence relationships between each pair of individuals are modeled by i.i.d.Bernoulli($p$) random variables, where $p \in [0,1]$ is an unknown parameter. Each individual acts at a {\it baseline} rate $μ> 0$ and, additionally, at an {\it excitation} rate of the form $N^{-1} \sum_{j=1}^{N} θ_{ij} \int_{0}^{t} ϕ(t-s)\,dZ_s^{j,N}$, which depends on the past actions of all individuals that influence it, scaled by $N^{-1}$ (i.e. the mean-field type), with the influence of older actions discounted through a memory kernel $ϕ\colon \mathbb{R}{+} \to \mathbb{R}{+}$. Here, $μ$ and $ϕ$ are treated as nuisance parameters. The aim of this paper is to establish a central limit theorem for the estimator of $p$ proposed in \cite{D}, under the subcritical condition $Λp < 1$.

preprint2026arXiv

Debiased Orthogonal Boundary-Driven Efficient Noise Mitigation

Mitigating the detrimental effects of noisy labels on the training process has become increasingly critical, as obtaining entirely clean or human-annotated samples for large-scale pre-training tasks is often impractical. Nonetheless, existing noise mitigation methods often encounter limitations in practical applications due to their task-specific design, model dependency, and significant computational overhead. In this work, we exploit the properties of high-dimensional orthogonality to identify a robust and effective boundary in cone space for separating clean and noisy samples. Building on this, we propose One-Step Anti-noise (OSA), a model-agnostic noisy label mitigation paradigm that employs an estimator model and a scoring function to assess the noise level of input pairs through just one-step inference. We empirically validate the superiority of OSA, demonstrating its enhanced training robustness, improved task transferability, streamlined deployment, and reduced computational overhead across diverse benchmarks, models, and tasks. Our code is released at https://github.com/leolee99/OSA.

preprint2026arXiv

GLT-PEFT: Gated Lie-Tucker Parameter-Efficient Fine-Tuning for Alzheimer's Disease Diagnosis with Hippocampal Segmentation Pretraining

Parameter-efficient fine-tuning (PEFT) has emerged as a promising paradigm for adapting pretrained models under limited data conditions. However, most existing PEFT methods are designed for matrix-structured parameters and are not well suited for high-dimensional convolutional kernels in medical imaging models. Moreover, they typically rely on additive updates and lack mechanisms to preserve the geometric structure of pretrained parameters, while multiplicative (geometry-aware) updates are difficult to integrate within a unified framework. To address this issue, this paper proposes GLT-PEFT, a gated Lie-Tucker parameter-efficient fine-tuning framework for Alzheimer's disease (AD) diagnosis. The proposed approach transfers a hippocampal segmentation pretrained model to a downstream classification task. Tucker decomposition enables tensor-aware low-rank adaptation of 3D convolutional kernels, while Lie group-based transformations provide structure-preserving multiplicative updates. A gating mechanism further reconciles additive and multiplicative update forms, resulting in a unified and more stable fine-tuning strategy. Extensive experiments demonstrate that GLT-PEFT achieves effective cross-task transfer while significantly reducing trainable parameters, highlighting its effectiveness for efficient and robust adaptation in medical imaging models.

preprint2026arXiv

Reasoning Can Be Restored by Correcting a Few Decision Tokens

Large reasoning models (LRMs) substantially outperform their base LLM counterparts on challenging reasoning benchmarks, yet it remains poorly understood where base models go wrong during token-by-token generation and how to narrow this gap efficiently. We study the base-reasoning gap through quantifying token-level distributional disagreement between a base model and a stronger reasoning model using likelihood-based divergences. Across benchmarks, we find that the reasoning advantage is highly sparse and concentrates on a small set of early, planning-related decision tokens. For instance, on Qwen3-0.6B, only ~8% of generated tokens account for the salient disagreement, and these tokens concentrate early in the response, are strongly enriched in planning-related decisions (17x), and coincide with high base-model uncertainty -- suggesting that base models fail mainly at early planning points that steer the subsequent reasoning trajectory. Building on these findings, we propose disagreement-guided token intervention, a simple inference-time delegation scheme that performs a one-token takeover by the reasoning model only at high-disagreement positions and immediately switches back to the base model. With a small intervention budget, this sparse delegation substantially recovers and can even surpass the performance of a same-size reasoning model on challenging reasoning tasks. Code is available at https://github.com/AlphaLab-USTC/RRTokenIntervention.

preprint2026arXiv

Self-ReSET: Learning to Self-Recover from Unsafe Reasoning Trajectories

Large Reasoning Models possess remarkable capabilities for self-correction in general domain; however, they frequently struggle to recover from unsafe reasoning trajectories under adversarial attacks. Existing alignment methods attempt to mitigate this vulnerability by fine-tuning the model on expert data including reflection traces or adversarial prefixes. Crucially, these approaches are often hindered by static training data which inevitably deviate from model's dynamic, on-policy reasoning traces, resulting in model hardly covering its vast generation space and learning to recover from its own failures. To bridge this gap, we propose Self-ReSET, a pure reinforcement learning framework designed to equip LRMs with the intrinsic capacity to recover from their own safety error trajectories, which are subsequently reused as an initial state for reinforcement learning. Extensive experiments across various LRMs and benchmarks demonstrate that Self-ReSET significantly enhances robustness against adversarial attacks especially out-of-distribution (OOD) jailbreak prompts while maintaining general utility, along with efficient data utilization. Further analysis reveals that our method effectively fosters self-recovery patterns, enabling models to better identify and recover from unsafe intermediate error states back to benign paths. Our codes and data are available at https://github.com/Ing1024/Self-ReSET.

preprint2024arXiv

Scaling limits for supercritical nearly unstable Hawkes processes

In this paper, we investigate the asymptotic behavior of nearly unstable Hawkes processes whose regression kernel has $L^1$ norm strictly greater than one and close to one as time goes to infinity. We find that,the scaling size determines the scaling behavior of the processes like in \cite{MR3313750}. Specifically,after suitable rescaling, the limit of the sequence of Hawkes processes is deterministic.And also with another appropriate rescaling, the sequence converges in law to an integrated Cox Ingersoll Ross like process. This theoretical result may apply to model the recent COVID19 in epidemiology and in social network.

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