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Wenlian Lu

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10 papers

2 author rows

ICML Conference 2025 Conference Paper

One Example Shown, Many Concepts Known! Counterexample-Driven Conceptual Reasoning in Mathematical LLMs

Yinghui Li
Jiayi Kuang
Haojing Huang 0001
Zhikun Xu
Xinnian Liang
Yi Yu
Wenlian Lu
Yangning Li

Leveraging mathematical Large Language Models (LLMs) for proof generation is a fundamental topic in LLMs research. We argue that the ability of current LLMs to prove statements largely depends on whether they have encountered the relevant proof process during training. This reliance limits their deeper understanding of mathematical theorems and related concepts. Inspired by the pedagogical method of "proof by counterexamples" commonly used in human mathematics education, our work aims to enhance LLMs’ ability to conduct mathematical reasoning and proof through counterexamples. Specifically, we manually create a high-quality, university-level mathematical benchmark, COUNTERMATH, which requires LLMs to prove mathematical statements by providing counterexamples, thereby assessing their grasp of mathematical concepts. Additionally, we develop a data engineering framework to automatically obtain training data for further model improvement. Extensive experiments and detailed analyses demonstrate that COUNTERMATH is challenging, indicating that LLMs, such as OpenAI o1, have insufficient counterexample-driven proof capabilities. Moreover, our exploration into model training reveals that strengthening LLMs’ counterexample-driven conceptual reasoning abilities is crucial for improving their overall mathematical capabilities. We believe that our work offers new perspectives on the community of mathematical LLMs.

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NeurIPS Conference 2025 Conference Paper

Stochastic Forward-Forward Learning through Representational Dimensionality Compression

Zhichao Zhu
Yang Qi
Hengyuan Ma
Wenlian Lu
Jianfeng Feng

The Forward-Forward (FF) learning algorithm provides a bottom-up alternative to backpropagation (BP) for training neural networks, relying on a layer-wise "goodness" function with well-designed negative samples for contrastive learning. Existing goodness functions are typically defined as the sum of squared postsynaptic activations, neglecting correlated variability between neurons. In this work, we propose a novel goodness function termed dimensionality compression that uses the effective dimensionality (ED) of fluctuating neural responses to incorporate second-order statistical structure. Our objective minimizes ED for noisy copies of individual inputs while maximizing it across the sample distribution, promoting structured representations without the need to prepare negative samples. We demonstrate that this formulation achieves competitive performance compared to other non-BP methods. Moreover, we show that noise plays a constructive role that can enhance generalization and improve inference when predictions are derived from the mean of squared output, which is equivalent to making predictions based on an energy term. Our findings contribute to the development of more biologically plausible learning algorithms and suggest a natural fit for neuromorphic computing, where stochasticity is a computational resource rather than a nuisance. The code is available at https: //github. com/ZhichaoZhu/StochasticForwardForward.

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NeurIPS Conference 2024 Conference Paper

Efficient Combinatorial Optimization via Heat Diffusion

Hengyuan Ma
Wenlian Lu
Jianfeng Feng

Combinatorial optimization problems are widespread but inherently challenging due to their discrete nature. The primary limitation of existing methods is that they can only access a small fraction of the solution space at each iteration, resulting in limited efficiency for searching the global optimal. To overcome this challenge, diverging from conventional efforts of expanding the solver's search scope, we focus on enabling information to actively propagate to the solver through heat diffusion. By transforming the target function while preserving its optima, heat diffusion facilitates information flow from distant regions to the solver, providing more efficient navigation. Utilizing heat diffusion, we propose a framework for solving general combinatorial optimization problems. The proposed methodology demonstrates superior performance across a range of the most challenging and widely encountered combinatorial optimizations. Echoing recent advancements in harnessing thermodynamics for generative artificial intelligence, our study further reveals its significant potential in advancing combinatorial optimization.

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YNIMG Journal 2021 Journal Article

Sensory, somatomotor and internal mentation networks emerge dynamically in the resting brain with internal mentation predominating in older age

Lu Zhang
Jiajia Zhao
Qunjie Zhou
ZhaoWen Liu
Yi Zhang
Wei Cheng
Weikang Gong
Xiaoping Hu

Age-related changes in the brain are associated with a decline in functional flexibility. Intrinsic functional flexibility is evident in the brain's dynamic ability to switch between alternative spatiotemporal states during resting state. However, the relationship between brain connectivity states, associated psychological functions during resting state, and the changes in normal aging remain poorly understood. In this study, we analyzed resting-state functional magnetic resonance imaging (rsfMRI) data from the Human Connectome Project (HCP; N = 812) and the UK Biobank (UKB; N = 6,716). Using signed community clustering to identify distinct states of dynamic functional connectivity, and text-mining of a large existing literature for functional annotation of each state, our findings from the HCP dataset indicated that the resting brain spontaneously transitions between three functionally specialized states: sensory, somatomotor, and internal mentation networks. The occurrence, transition-rate, and persistence-time parameters for each state were correlated with behavioural scores using canonical correlation analysis. We estimated the same brain states and parameters in the UKB dataset, subdivided into three distinct age ranges: 50-55, 56-67, and 68-78 years. We found that the internal mentation network was more frequently expressed in people aged 71 and older, whereas people younger than 55 more frequently expressed sensory and somatomotor networks. Furthermore, analysis of the functional entropy - a measure of uncertainty of functional connectivity - also supported this finding across the three age ranges. Our study demonstrates that dynamic functional connectivity analysis can expose the time-varying patterns of transition between functionally specialized brain states, which are strongly tied to increasing age.

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IROS Conference 2020 Conference Paper

On a videoing control system based on object detection and tracking

Yanhao Ren
Yi Wang
Qi Tang
Haijun Jiang
Wenlian Lu

In this paper, we propose a camera control system towards occasionally videoing preassigned objects. Based on the technique of real-time visual detection and tracking, using the Kalman filter and re-identification (ReID), we propose continuous composition of lens, based on the atomic rules of shots, and give the trajectory planning of the camera, to generate the PID controller to the pan-tilt. By both simulation and emulation by frame-wise cropping of video clips, we illustrate the efficiency of this method. Based on this model, we design and produce an AI automatic camera for lively photography and clip videoing.

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NeurIPS Conference 2019 Conference Paper

On Fenchel Mini-Max Learning

Chenyang Tao
Liqun Chen
Shuyang Dai
Junya Chen
Ke Bai
Dong Wang
Jianfeng Feng
Wenlian Lu

Inference, estimation, sampling and likelihood evaluation are four primary goals of probabilistic modeling. Practical considerations often force modeling approaches to make compromises between these objectives. We present a novel probabilistic learning framework, called Fenchel Mini-Max Learning (FML), that accommodates all four desiderata in a flexible and scalable manner. Our derivation is rooted in classical maximum likelihood estimation, and it overcomes a longstanding challenge that prevents unbiased estimation of unnormalized statistical models. By reformulating MLE as a mini-max game, FML enjoys an unbiased training objective that (i) does not explicitly involve the intractable normalizing constant and (ii) is directly amendable to stochastic gradient descent optimization. To demonstrate the utility of the proposed approach, we consider learning unnormalized statistical models, nonparametric density estimation and training generative models, with encouraging empirical results presented.

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TAAS Journal 2014 Journal Article

Adaptive Epidemic Dynamics in Networks

Shouhuai Xu
Wenlian Lu
Li Xu
Zhenxin Zhan

Theoretical modeling of computer virus/worm epidemic dynamics is an important problem that has attracted many studies. However, most existing models are adapted from biological epidemic ones. Although biological epidemic models can certainly be adapted to capture some computer virus spreading scenarios (especially when the so-called homogeneity assumption holds), the problem of computer virus spreading is not well understood because it has many important perspectives that are not necessarily accommodated in the biological epidemic models. In this article, we initiate the study of such a perspective, namely that of adaptive defense against epidemic spreading in arbitrary networks. More specifically, we investigate a nonhomogeneous Susceptible-Infectious-Susceptible (SIS) model where the model parameters may vary with respect to time. In particular, we focus on two scenarios we call semi-adaptive defense and fully adaptive defense, which accommodate implicit and explicit dependency relationships between the model parameters, respectively. In the semi-adaptive defense scenario, the model’s input parameters are given; the defense is semi-adaptive because the adjustment is implicitly dependent upon the outcome of virus spreading. For this scenario, we present a set of sufficient conditions (some are more general or succinct than others) under which the virus spreading will die out; such sufficient conditions are also known as epidemic thresholds in the literature. In the fully adaptive defense scenario, some input parameters are not known (i.e., the aforementioned sufficient conditions are not applicable) but the defender can observe the outcome of virus spreading. For this scenario, we present adaptive control strategies under which the virus spreading will die out or will be contained to a desired level.

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YNIMG Journal 2013 Journal Article

Spatio-temporal Granger causality: A new framework

Qiang Luo
Wenlian Lu
Wei Cheng
Pedro A. Valdes-Sosa
Xiaotong Wen
Mingzhou Ding
Jianfeng Feng

That physiological oscillations of various frequencies are present in fMRI signals is the rule, not the exception. Herein, we propose a novel theoretical framework, spatio-temporal Granger causality, which allows us to more reliably and precisely estimate the Granger causality from experimental datasets possessing time-varying properties caused by physiological oscillations. Within this framework, Granger causality is redefined as a global index measuring the directed information flow between two time series with time-varying properties. Both theoretical analyses and numerical examples demonstrate that Granger causality is a monotonically increasing function of the temporal resolution used in the estimation. This is consistent with the general principle of coarse graining, which causes information loss by smoothing out very fine-scale details in time and space. Our results confirm that the Granger causality at the finer spatio-temporal scales considerably outperforms the traditional approach in terms of an improved consistency between two resting-state scans of the same subject. To optimally estimate the Granger causality, the proposed theoretical framework is implemented through a combination of several approaches, such as dividing the optimal time window and estimating the parameters at the fine temporal and spatial scales. Taken together, our approach provides a novel and robust framework for estimating the Granger causality from fMRI, EEG, and other related data.

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TAAS Journal 2012 Journal Article

Push- and pull-based epidemic spreading in networks

Shouhuai Xu
Wenlian Lu
Li Xu

Understanding the dynamics of computer virus (malware, worm) in cyberspace is an important problem that has attracted a fair amount of attention. Early investigations for this purpose adapted biological epidemic models, and thus inherited the so-called homogeneity assumption that each node is equally connected to others. Later studies relaxed this often unrealistic homogeneity assumption, but still focused on certain power-law networks. Recently, researchers investigated epidemic models in arbitrary networks (i.e., no restrictions on network topology). However, all these models only capture push-based infection, namely that an infectious node always actively attempts to infect its neighboring nodes. Very recently, the concept of pull-based infection was introduced but was not treated rigorously. Along this line of research, the present article investigates push- and pull-based epidemic spreading dynamics in arbitrary networks, using a nonlinear dynamical systems approach. The article advances the state-of-the-art as follows: (1) It presents a more general and powerful sufficient condition (also known as epidemic threshold in the literature) under which the spreading will become stable. (2) It gives both upper and lower bounds on the global mean infection rate, regardless of the stability of the spreading. (3) It offers insights into, among other things, the estimation of the global mean infection rate through localized monitoring of a small constant number of nodes, without knowing the values of the parameters.

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YNIMG Journal 2010 Journal Article

On a Gaussian neuronal field model

Wenlian Lu
Enrico Rossoni
Jianfeng Feng

Can we understand the dynamic behaviour of leaky integrate-and-fire (LIF) networks, which present the major, and possibly the only, analytically tractable tool we employ in computational neuroscience? To answer this question, here we present a theoretical framework on the spike activities of LIF networks by including the first order moment (mean firing rate) and the second order moment statistics (variance and correlation), based on a moment neuronal network (MNN) approach. The spike activity of a LIF network is approximated as a Gaussian random field and can reduce to the classical Wilson–Cowan–Amari (WCA) neural field if the variances vanish. Our analyses reveal several interesting phenomena of LIF networks. With a small clamped correlation and strong inhibition, the firing rate response function could be non-monotonic (not sigmoidal type), which can lead to interesting dynamics. For a feedforward and recurrent neuronal network, our setup allows us to prove that all neuronal spike activities rapidly synchronize, a well-known fact observed in both experiments and numerical simulations. We also present several examples of wave propagations in this field model. Finally, we test our MNN with the content-dependent working memory setting. The potential application of this random neuronal field idea to account for many experimental data is also discussed.

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