Hongpeng Zhou

Yang Cui, Jingyuan Sun, Yizheng Sun et al.

How the brain supports language across different languages is a basic question in neuroscience and a useful test for multilingual artificial intelligence. Neuroimaging has identified language-responsive brain regions across languages, but it cannot by itself show whether the underlying processing is shared or language-specific. Here we use six multilingual large language models (LLMs) as controllable systems and create targeted ``computational lesions'' by zeroing small parameter sets that are important across languages or especially important for one language. We then compare intact and lesioned models in predicting functional magnetic resonance imaging (fMRI) responses during 100 minutes of naturalistic story listening in native English, Chinese and French (112 participants). Lesioning a compact shared core reduces whole-brain encoding correlation by 60.32% relative to intact models, whereas language-specific lesions preserve cross-language separation in embedding space but selectively weaken brain predictivity for the matched native language. These results support a shared backbone with embedded specializations and provide a causal framework for studying multilingual brain-model alignment.

Hongpeng Zhou, Wei Pan

Discovering governing equations from data is critical for diverse scientific disciplines as they can provide insights into the underlying phenomenon of dynamic systems. This work presents a new representation for governing equations by designing the Mathematical Operation Network (MathONet) with a deep neural network-like hierarchical structure. Specifically, the MathONet is stacked by several layers of unary operations (e.g., sin, cos, log) and binary operations (e.g., +,-), respectively. An initialized MathONet is typically regarded as a super-graph with a redundant structure, a sub-graph of which can yield the governing equation. We develop a sparse group Bayesian learning algorithm to extract the sub-graph by employing structurally constructed priors over the redundant mathematical operations. By demonstrating the chaotic Lorenz system, Lotka-Volterra system, and Kolmogorov-Petrovsky-Piskunov system, the proposed method can discover the ordinary differential equations (ODEs) and partial differential equations (PDEs) from the observations given limited mathematical operations, without any prior knowledge on possible expressions of the ODEs and PDEs.

Hongpeng Zhou, Chahine Ibrahim, Wei Xing Zheng et al.

This paper proposes a sparse Bayesian treatment of deep neural networks (DNNs) for system identification. Although DNNs show impressive approximation ability in various fields, several challenges still exist for system identification problems. First, DNNs are known to be too complex that they can easily overfit the training data. Second, the selection of the input regressors for system identification is nontrivial. Third, uncertainty quantification of the model parameters and predictions are necessary. The proposed Bayesian approach offers a principled way to alleviate the above challenges by marginal likelihood/model evidence approximation and structured group sparsity-inducing priors construction. The identification algorithm is derived as an iterative regularised optimisation procedure that can be solved as efficiently as training typical DNNs. Remarkably, an efficient and recursive Hessian calculation method for each layer of DNNs is developed, turning the intractable training/optimisation process into a tractable one. Furthermore, a practical calculation approach based on the Monte-Carlo integration method is derived to quantify the uncertainty of the parameters and predictions. The effectiveness of the proposed Bayesian approach is demonstrated on several linear and nonlinear system identification benchmarks by achieving good and competitive simulation accuracy. The code to reproduce the experimental results is open-sourced and available online.

Haiping Liu, Lijing Lin, Jingyuan Sun et al.

Rotary Position Embedding (RoPE) is widely adopted in large language models (LLMs) due to its efficient encoding of relative positions with strong extrapolation capabilities. However, while its application in higher-dimensional input domains, such as 2D images, have been explored in several attempts, a unified theoretical framework is still lacking. To address this, we propose a systematic mathematical framework for RoPE grounded in Lie group and Lie algebra theory. We derive the necessary and sufficient conditions for any valid $N$-dimensional RoPE based on two core properties of RoPE - relativity and reversibility. We demonstrate that RoPE can be characterized as a basis of a maximal abelian subalgebra (MASA) in the special orthogonal Lie algebra, and that the commonly used axis-aligned block-diagonal RoPE, where each input axis is encoded by an independent 2x2 rotation block, corresponds to the maximal toral subalgebra. Furthermore, we reduce spatial inter-dimensional interactions to a change of basis, resolved by learning an orthogonal transformation. Our experiment results suggest that inter-dimensional interactions should be balanced with local structure preservation. Overall, our framework unifies and explains existing RoPE designs while enabling principled extensions to higher-dimensional modalities and tasks.

Yizheng Sun, Hao Li, Chang Xu et al.

Vision-Language Models (VLMs) are powerful yet computationally intensive for widespread practical deployments. To address such challenge without costly re-training, post-training acceleration techniques like quantization and token reduction are extensively explored. However, current acceleration evaluations primarily target minimal overall performance degradation, overlooking a crucial question: does the accelerated model still give the same answers to the same questions as it did before acceleration? This is vital for stability-centered industrial applications where consistently correct answers for specific, known situations are paramount, such as in AI-based disease diagnosis. We systematically investigate this for accelerated VLMs, testing four leading models (LLaVA-1.5, LLaVA-Next, Qwen2-VL, Qwen2.5-VL) with eight acceleration methods on ten multi-modal benchmarks. Our findings are stark: despite minimal aggregate performance drops, accelerated models changed original answers up to 20% of the time. Critically, up to 6.5% of these changes converted correct answers to incorrect. Input perturbations magnified these inconsistencies, and the trend is confirmed by case studies with the medical VLM LLaVA-Med. This research reveals a significant oversight in VLM acceleration, stressing an urgent need for instance-level stability checks to ensure trustworthy real-world deployment.

Hongpeng Zhou, Chahine Ibrahim, Wei Pan

Nonlinear system identification is important with a wide range of applications. The typical approaches for nonlinear system identification include Volterra series models, nonlinear autoregressive with exogenous inputs models, block-structured models, state-space models and neural network models. Among them, neural networks (NN) is an important black-box method thanks to its universal approximation capability and less dependency on prior information. However, there are several challenges associated with NN. The first one lies in the design of a proper neural network structure. A relatively simple network cannot approximate the feature of the system, while a complex model may lead to overfitting. The second lies in the availability of data for some nonlinear systems. For some systems, it is difficult to collect enough data to train a neural network. This raises the challenge that how to train a neural network for system identification with a small dataset. In addition, if the uncertainty of the NN parameter could be obtained, it would be also beneficial for further analysis. In this paper, we propose a sparse Bayesian deep learning approach to address the above problems. Specifically, the Bayesian method can reinforce the regularization on neural networks by introducing introduced sparsity-inducing priors. The Bayesian method can also compute the uncertainty of the NN parameter. An efficient iterative re-weighted algorithm is presented in this paper. We also test the capacity of our method to identify the system on various ratios of the original dataset. The one-step-ahead prediction experiment on Cascaded Tank System shows the effectiveness of our method. Furthermore, we test our algorithm with more challenging simulation experiment on this benchmark, which also outperforms other methods.

Hongpeng Zhou, Minghao Yang, Jun Wang et al.

One-Shot Neural Architecture Search (NAS) is a promising method to significantly reduce search time without any separate training. It can be treated as a Network Compression problem on the architecture parameters from an over-parameterized network. However, there are two issues associated with most one-shot NAS methods. First, dependencies between a node and its predecessors and successors are often disregarded which result in improper treatment over zero operations. Second, architecture parameters pruning based on their magnitude is questionable. In this paper, we employ the classic Bayesian learning approach to alleviate these two issues by modeling architecture parameters using hierarchical automatic relevance determination (HARD) priors. Unlike other NAS methods, we train the over-parameterized network for only one epoch then update the architecture. Impressively, this enabled us to find the architecture on CIFAR-10 within only 0.2 GPU days using a single GPU. Competitive performance can be also achieved by transferring to ImageNet. As a byproduct, our approach can be applied directly to compress convolutional neural networks by enforcing structural sparsity which achieves extremely sparse networks without accuracy deterioration.