arXiv subjects

Lai Jiang

Publications and source records attributed to Lai Jiang.

At least 37 records · Page 2Linked to original sources

arXiv2026

Awakening the Sleeping Agent: Lean-Specific Agentic Data Reactivates General Tool Use in Goedel Prover

Heavy supervised fine-tuning on a target domain can strongly suppress capabilities that were present in the base model. We study this phenomenon in formal mathematics using Goedel-Prover-V2, an open-source model heavily trained on 1.8 million formal-math examples. After domain specialization, the model almost completely loses its ability to produce valid tool calls, even when explicitly instructed to use tools, dropping from 89.4% function-calling accuracy in the base model to nearly 0%. We ask whether this agentic collapse is permanent or instead reversible. To answer this question, we fine-tune the specialized model on a small amount of Lean-specific tool-use data. Remarkably, as few as 100 agentic traces are sufficient to restore strong tool-calling behavior. Importantly, this recovery is not the result of reward hacking or benchmark-specific optimization: the recovery data is entirely drawn from the Lean setting, where the model uses natural-language queries to search the Mathlib library for relevant theorems and lemmas, yet the regained capability transfers well beyond that domain. In particular, these same 100 Lean-specific traces improve performance on the Berkeley Function Calling Leaderboard from near zero to 83.8%, approaching the base model's 89.4% despite the mismatch in task distribution and protocol. The recovered capability is also practically useful in-domain. On ProofNet, pass@32 improves from 21.51% to 25.81%. Together, these results show that heavy domain supervised fine-tuning can suppress general tool-use ability without permanently erasing it, and that a small amount of domain-specific agentic data can awaken dormant tool-use capabilities.

cs.AI↗

arXiv2026

Local level sets of the Takagi-van der Waerden function

In this paper, we investigate the Takagi-van der Waerden function, $$ T_r(x) = \sum_{n=0}^{\infty} \frac{ϕ(r^n x)}{r^n} ,\quad x\in [0,1], \quad r \in \mathbb{Z}^+, $$ where $ϕ(x)={\rm dist}(x,\mathbb{Z})$ represents the distance from $x$ to the nearest integer. %We prove that for every even integer $r \geq 2$, the expected number of local level sets contained in the level set $L_r(y)$ is $1 + 1/r$, if $y$ is a random variable uniformly distributed over the range of $T_r$. Lagarias and Maddock [Level sets of the Takagi function: local level sets, \emph{Monatsh. Math.}, {\bf 166} (2012), No. 2, 201--238] introduced the notion of local level sets for the classical Takagi function $T_2$. They proved that if $y$ is a random variable uniformly distributed over the range of $T_2$, then the expected number of local level sets contained in the level set $L_2(y)$ equals $3/2$. We extend the study by defining an analogous concept of local level sets for all even integers $r$. Then we prove that, for every even integer $r\geq 2$, if $y$ is a random variable uniformly distributed, then the expected number of local level sets contained in the level set $L_r(y)$ equals $1 + 1/r$.

math.CA↗

arXiv2025

Representations of rational numbers and Minkowski dimension

In this paper, we investigate the representations of rational numbers via continued fraction, Egyptian fraction, and Engel fraction expansions. Given $m \in \mathbb{N}$, denote by $C_m, E_m, E_m^*$ the sets of rational numbers whose continued fraction, Egyptian fraction, and Engel fraction expansions have length $m$, respectively. We first establish the Minkowski dimensions of these sets, which implies that their global scaling properties are different. We also apply the results to sumsets of decreasing sequences.

math.CA↗

arXiv2025

SceneJailEval: A Scenario-Adaptive Multi-Dimensional Framework for Jailbreak Evaluation

Accurate jailbreak evaluation is critical for LLM red team testing and jailbreak research. Mainstream methods rely on binary classification (string matching, toxic text classifiers, and LLM-based methods), outputting only "yes/no" labels without quantifying harm severity. Emerged multi-dimensional frameworks (e.g., Security Violation, Relative Truthfulness and Informativeness) use unified evaluation standards across scenarios, leading to scenario-specific mismatches (e.g., "Relative Truthfulness" is irrelevant to "hate speech"), undermining evaluation accuracy. To address these, we propose SceneJailEval, with key contributions: (1) A pioneering scenario-adaptive multi-dimensional framework for jailbreak evaluation, overcoming the critical "one-size-fits-all" limitation of existing multi-dimensional methods, and boasting robust extensibility to seamlessly adapt to customized or emerging scenarios. (2) A novel 14-scenario dataset featuring rich jailbreak variants and regional cases, addressing the long-standing gap in high-quality, comprehensive benchmarks for scenario-adaptive evaluation. (3) SceneJailEval delivers state-of-the-art performance with an F1 score of 0.917 on our full-scenario dataset (+6% over SOTA) and 0.995 on JBB (+3% over SOTA), breaking through the accuracy bottleneck of existing evaluation methods in heterogeneous scenarios and solidifying its superiority.

cs.CL↗

arXiv2025

Burst Image Quality Assessment: A New Benchmark and Unified Framework for Multiple Downstream Tasks

In recent years, the development of burst imaging technology has improved the capture and processing capabilities of visual data, enabling a wide range of applications. However, the redundancy in burst images leads to the increased storage and transmission demands, as well as reduced efficiency of downstream tasks. To address this, we propose a new task of Burst Image Quality Assessment (BuIQA), to evaluate the task-driven quality of each frame within a burst sequence, providing reasonable cues for burst image selection. Specifically, we establish the first benchmark dataset for BuIQA, consisting of $7,346$ burst sequences with $45,827$ images and $191,572$ annotated quality scores for multiple downstream scenarios. Inspired by the data analysis, a unified BuIQA framework is proposed to achieve an efficient adaption for BuIQA under diverse downstream scenarios. Specifically, a task-driven prompt generation network is developed with heterogeneous knowledge distillation, to learn the priors of the downstream task. Then, the task-aware quality assessment network is introduced to assess the burst image quality based on the task prompt. Extensive experiments across 10 downstream scenarios demonstrate the impressive BuIQA performance of the proposed approach, outperforming the state-of-the-art. Furthermore, it can achieve $0.33$ dB PSNR improvement in the downstream tasks of denoising and super-resolution, by applying our approach to select the high-quality burst frames.

cs.CV↗

arXiv2025

Box dimension of the graphs of recurrent fractal interpolation functions

Let $f$ be a generalized affine recurrent fractal interpolation function with vertical scaling functions. In this paper, by introducing underlying local iterated function systems of $f$, we define restricted vertical scaling matrices. Then we prove the monotonicity of spectral radii of these matrices without additional conditions. We also prove the irreducibility of these matrices under the assumption that vertical scaling functions are positive. With these results, we estimate the upper and lower box dimensions of the graphs of $f$ by the limits of spectral radii of restricted vertical scaling matrices. In particular, we obtain an explicit formula of the box dimension of the graph of $f$ under certain constraint conditions.

math.CA↗

arXiv2025

Goedel-Prover-V2: Scaling Formal Theorem Proving with Scaffolded Data Synthesis and Self-Correction

We introduce Goedel-Prover-V2, a series of open-source language models that set a new state-of-the-art in automated theorem proving. Built on the standard expert iteration and reinforcement learning pipeline, our approach incorporates three key innovations: (1) Scaffolded data synthesis: We generate synthetic tasks of increasing difficulty to train the model to master increasingly complex theorems; (2) Verifier-guided self-correction: We enable the model to iteratively revise its proofs by leveraging feedback from the Lean compiler; (3) Model averaging: We merge model checkpoints to mitigate the decrease in model output diversity in later stages of training. Our small model, Goedel-Prover-V2-8B, reaches 84.6% pass@32 on MiniF2F and outperforms DeepSeek-Prover-V2-671B under the same metric, despite being 80X smaller. Our flagship model, Goedel-Prover-V2-32B, achieves 88.1% on MiniF2F at pass@32 in standard mode and 90.4% in self-correction mode, outperforming prior SOTA by a large margin. Additionally, our flagship model solves 86 problems on PutnamBench at pass@184, securing the first place among open-source models on the leaderboard, surpassing DeepSeek-Prover-V2-671B's record of solving 47 problems by pass@1024 with a significantly smaller model size and compute budget. At the time of its release (July-August 2025), Goedel-Prover-V2 achieves the strongest overall performance among all open-source theorem provers. It also ranks among the top-performing models--including closed-source systems with publicly reported performance--under a constrained test-time compute budget. Our models, code, and data are released at https://github.com/Goedel-LM/Goedel-Prover-V2.

cs.LG↗

arXiv2025

Flow of Reasoning: Training LLMs for Divergent Reasoning with Minimal Examples

The ability to generate diverse solutions to a given problem is a hallmark of human creativity. This divergent reasoning is also crucial for machines, enhancing their robustness and enabling them to assist humans in many applications such as scientific discovery. However, existing approaches to multi-step reasoning with large language models (LLMs) have mostly focused only on reasoning accuracy, without further discovering more diverse valid solutions. For example, supervised fine-tuning improves reasoning quality but requires vast labeled data, while reward-maximizing reinforcement learning finds top-reward solutions while neglecting the solution diversity. To fill this gap, we propose Flow of Reasoning (FoR), an efficient diversity-seeking LLM finetuning method aimed at improving reasoning quality and diversity with minimal data. FoR formulates multi-step LLM reasoning as a Markovian flow on a DAG-structured reasoning graph. This formulation allows us to incorporate and adapt principled GFlowNet approaches, for finetuning LLMs to sample divergent paths with probabilities proportional to the (unnormalized) reward of target problems. Extensive experiments show that, with limited training examples (e.g., 15 examples), FoR enables the discovery of diverse, creative, high-quality solutions, greatly outperforming a wide range of existing inference and training methods across six challenging reasoning tasks, including BlocksWorld (embodied reasoning), Game24 (math puzzle solving), Rubik's Cube (spatial reasoning), 1D-ARC (abstraction reasoning), GSM8k (math reasoning), and ProntoQA (logical reasoning). Code is available at https://github.com/Yu-Fangxu/FoR.

cs.AI↗

arXiv2025

PersuasiveToM: A Benchmark for Evaluating Machine Theory of Mind in Persuasive Dialogues

The ability to understand and predict the mental states of oneself and others, known as the Theory of Mind (ToM), is crucial for effective social scenarios. Although recent studies have evaluated ToM in Large Language Models (LLMs), existing benchmarks focus on simplified settings (e.g., Sally-Anne-style tasks) and overlook the complexity of real-world social interactions. To mitigate this gap, we propose PersuasiveToM, a benchmark designed to evaluate the ToM abilities of LLMs in persuasive dialogues. Our framework contains two core tasks: ToM Reasoning, which tests tracking of evolving desires, beliefs, and intentions; and ToM Application, which assesses the use of inferred mental states to predict and evaluate persuasion strategies. Experiments across eight leading LLMs reveal that while models excel on multiple questions, they struggle with the tasks that need tracking the dynamics and shifts of mental states and understanding the mental states in the whole dialogue comprehensively. Our aim with PersuasiveToM is to allow an effective evaluation of the ToM reasoning ability of LLMs with more focus on complex psychological activities. Our code is available at https://github.com/Yu-Fangxu/PersuasiveToM.

cs.CL↗

arXiv2025

Assouad dimension of the Takagi function

For any integer $b\geq2$ and real series $\{c_n\}$ such that $\sum_{n=0}^\infty|c_n|<\infty$, the generalized Takagi function $f_{{\mathbf c},b}(x)$ is defined by $$ f_{{\mathbf c},b}(x):=\sum_{n=0}^\infty c_nϕ(b^n x), \quad x\in [0,1], $$ where $ϕ(x)=dist(x,\mathbb{Z})$ is the distance from $x$ to the nearest integer. The collection of functions with the form are called the Takagi class. In this paper, we show that in the case that $\varlimsup_{n \to \infty} b^n |c_n|<\infty$, the Assouad dimension of the graph ${\mathcal G} f_{{\mathbf c},b}=\{(x,f_{{\mathbf c},b}(x)):x\in[0,1]\}$ for the generalized Takagi function $f_{{\mathbf c},b}(x)$ is equal to one, that is, $$ \dim_A {\mathcal G} f_{{\mathbf c},b}=1. $$ In particular, for each $0<a<1$ and integer $b \geq 2$, we define Takagi function $T_{a,b}$ as followed, $$ T_{a,b}(x):=\sum_{n=0}^\infty a^n ϕ(b^n x), \quad x\in [0,1]. $$ Then $ \dim_A {\mathcal G} T_{a,b}=1 $ if and only if $0<a \leq 1/b$.

math.CA↗

arXiv2025

Hierarchical Semantic Compression for Consistent Image Semantic Restoration

The emerging semantic compression has been receiving increasing research efforts most recently, capable of achieving high fidelity restoration during compression, even at extremely low bitrates. However, existing semantic compression methods typically combine standard pipelines with either pre-defined or high-dimensional semantics, thus suffering from deficiency in compression. To address this issue, we propose a novel hierarchical semantic compression (HSC) framework that purely operates within intrinsic semantic spaces from generative models, which is able to achieve efficient compression for consistent semantic restoration. More specifically, we first analyse the entropy models for the semantic compression, which motivates us to employ a hierarchical architecture based on a newly developed general inversion encoder. Then, we propose the feature compression network (FCN) and semantic compression network (SCN), such that the middle-level semantic feature and core semantics are hierarchically compressed to restore both accuracy and consistency of image semantics, via an entropy model progressively shared by channel-wise context. Experimental results demonstrate that the proposed HSC framework achieves the state-of-the-art performance on subjective quality and consistency for human vision, together with superior performances on machine vision tasks given compressed bitstreams. This essentially coincides with human visual system in understanding images, thus providing a new framework for future image/video compression paradigms. Our code shall be released upon acceptance.

cs.CV↗

arXiv2025

Federated Learning Strategies for Coordinated Beamforming in Multicell ISAC

We propose two cooperative beamforming frameworks based on federated learning (FL) for multi-cell integrated sensing and communications (ISAC) systems. Our objective is to address the following dilemma in multicell ISAC: 1) Beamforming strategies that rely solely on local channel information risk generating significant inter-cell interference (ICI), which degrades network performance for both communication users and sensing receivers in neighboring cells; 2) conversely centralized beamforming strategies can mitigate ICI by leveraging global channel information, but they come with substantial transmission overhead and latency that can be prohibitive for latency-sensitive and source-constrained applications. To tackle these challenges, we first propose a partially decentralized training framework motivated by the vertical federated learning (VFL) paradigm. In this framework, the participating base stations (BSs) collaboratively design beamforming matrices under the guidance of a central server. The central server aggregates local information from the BSs and provides feedback, allowing BSs to implicitly manage ICI without accessing the global channel information. To make the solution scalable for densely deployed wireless networks, we take further steps to reduce communication overhead by presenting a fully decentralized design based on the horizontal federated learning (HFL). Specifically, we develop a novel loss function to control the interference leakage power, enabling a more efficient training process by entirely eliminating local channel information exchange. Numerical results show that the proposed solutions can achieve significant performance improvements comparable to the benchmarks in terms of both communication and radar information rates.

eess.SP↗

arXiv2024

Noninvasive Extraction of Maternal and Fetal Electrocardiograms Using Progressive Periodic Source Peel-off

Abdominal electrocardiogram (AECG) gives a safe and non-invasive way to monitor fetal well-being during pregnancy using surface electrodes. However, it is challenging to extract weak fetal ECG (fECG) from the AECG recordings with larger maternal ECG (mECG) and external noises. In this study, we introduce a novel progressive periodic source peel-off (PPSP) method for extracting periodic ECG sources from multi-channel AECG recordings, including three main modules: 1) A periodic constrained FastICA (PCFICA) module with ECG physiology-informed constraints for extracting precise ECG spike trains, 2) A singular value decomposition module for estimating ECG waveforms, and 3) A peel-off strategy that facilitates to discern weak fECG source by eliminating previously separated sources or noises. The performance of the PPSP method was examined on two public databases, synthetic data and our clinical data. For extracting fECG spike trains, our PPSP method achieved an F1-scores of 99.59% on public data, 99.50% on synthetic data at the highest noise level. It further yielded the lowest RMSE of fetal heart rate of 6.20% on clinical data. It significantly outperformed other state-of-the-art methods on any set of data (p < 0.05). This study demonstrated effectiveness of the PPSP method for extracting and separating mECG and weak fECG signals, with high precision especially at high noise levels. Our study promotes noninvasive measurement and intelligent monitoring of both fetal and maternal heart activities towards advanced healthcare in perinatal medicine.

physics.med-ph↗

arXiv2024

Box dimension of generalized affine fractal interpolation functions (II)

Let $f$ be a generalized affine fractal interpolation function with vertical scaling functions. In this paper, we prove the monotonicity of spectral radii of vertical scaling matrices without additional assumptions. We also obtain the irreducibility of these matrices under certain conditions. By these results, we estimate $\mathrm{dim}_B Γf$, the box dimension of the graph of $f$, by the limits of spectral radii of vertical scaling matrices. We also estimate $\mathrm{dim}_B Γf$ directly by the sum function of vertical scaling functions. As an application, we study the box dimension of the graph of a generalized Weierstrass-type function.

math.CA↗

arXiv2024

From Role-Play to Drama-Interaction: An LLM Solution

Drama is a form of storytelling inspired by human creativity, proceeding with a predefined storyline, carrying emotions and thoughts. This paper introduces \emph{LLM-based interactive drama}, which endows traditional drama with an unprecedented immersion, where a person is allowed to walk into it and interact with the characters and scenes. We define this new artistic genre by 6 essential elements-plot, character, thought, diction, spectacle and interaction-and study the entire pipeline to forge a backbone \emph{drama LLM} to drive the playing process, which is challenged by limited drama resources, uncontrollable narrative development, and complicated instruction following. We propose \emph{Narrative Chain} to offer finer control over the narrative progression during interaction with players; \emph{Auto-Drama} to synthesize drama scripts given arbitrary stories; \emph{Sparse Instruction Tuning} to allow the model to follow sophisticated instructions. We manually craft 3 scripts, \emph{Detective Conan}, \emph{Harry Potter}, \emph{Romeo and Juliet}, and design a 5-dimension principle to evaluate the drama LLM comprehensively.

cs.CL↗

arXiv2024

Box dimension of fractal interpolation surfaces with vertical scaling function

In this paper, we first present a simple lemma which allows us to estimate the box dimension of graphs of given functions by the associated oscillation sums and oscillation vectors. Then we define vertical scaling matrices of generalized affine fractal interpolation surfaces (FISs). By using these matrices, we establish relationships between oscillation vectors of different levels, which enables us to obtain the box dimension of generalized affine FISs under certain constraints.

math.GT↗

arXiv2023

Uncertainty Guided Adaptive Warping for Robust and Efficient Stereo Matching

Correlation based stereo matching has achieved outstanding performance, which pursues cost volume between two feature maps. Unfortunately, current methods with a fixed model do not work uniformly well across various datasets, greatly limiting their real-world applicability. To tackle this issue, this paper proposes a new perspective to dynamically calculate correlation for robust stereo matching. A novel Uncertainty Guided Adaptive Correlation (UGAC) module is introduced to robustly adapt the same model for different scenarios. Specifically, a variance-based uncertainty estimation is employed to adaptively adjust the sampling area during warping operation. Additionally, we improve the traditional non-parametric warping with learnable parameters, such that the position-specific weights can be learned. We show that by empowering the recurrent network with the UGAC module, stereo matching can be exploited more robustly and effectively. Extensive experiments demonstrate that our method achieves state-of-the-art performance over the ETH3D, KITTI, and Middlebury datasets when employing the same fixed model over these datasets without any retraining procedure. To target real-time applications, we further design a lightweight model based on UGAC, which also outperforms other methods over KITTI benchmarks with only 0.6 M parameters.

cs.CV↗

arXiv2023

Lightweight wood panel defect detection method incorporating attention mechanism and feature fusion network

In recent years, deep learning has made significant progress in wood panel defect detection. However, there are still challenges such as low detection , slow detection speed, and difficulties in deploying embedded devices on wood panel surfaces. To overcome these issues, we propose a lightweight wood panel defect detection method called YOLOv5-LW, which incorporates attention mechanisms and a feature fusion network.Firstly, to enhance the detection capability of acceptable defects, we introduce the Multi-scale Bi-directional Feature Pyramid Network (MBiFPN) as a feature fusion network. The MBiFPN reduces feature loss, enriches local and detailed features, and improves the model's detection capability for acceptable defects.Secondly, to achieve a lightweight design, we reconstruct the ShuffleNetv2 network model as the backbone network. This reconstruction reduces the number of parameters and computational requirements while maintaining performance. We also introduce the Stem Block and Spatial Pyramid Pooling Fast (SPPF) models to compensate for any accuracy loss resulting from the lightweight design, ensuring the model's detection capabilities remain intact while being computationally efficient.Thirdly, we enhance the backbone network by incorporating Efficient Channel Attention (ECA), which improves the network's focus on key information relevant to defect detection. By attending to essential features, the model becomes more proficient in accurately identifying and localizing defects.We validate the proposed method using a self-developed wood panel defect dataset.The experimental results demonstrate the effectiveness of the improved YOLOv5-LW method. Compared to the original model, our approach achieves a 92.8\% accuracy rate, reduces the number of parameters by 27.78\%, compresses computational volume by 41.25\%, improves detection inference speed by 10.16\%

cs.CV↗