Chan Li

Chan Li

Statistical physics, computational neuroscience and machine learning.

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Learning credit assignment

Published in Physical Review Letters, 2020

Deep learning has achieved impressive prediction accuracies in a variety of scientific and industrial domains. However, the nested non-linear feature of deep learning makes the learning highly nontransparent, i.e., it is still unknown how the learning coordinates a huge number of parameters to achieve a decision making. To explain this hierarchical credit assignment, we propose a mean-field learning model by assuming that an ensemble of sub-networks, rather than a single network, are trained for a classification task. Surprisingly, our model reveals that apart from some deterministic synaptic weights connecting two neurons at neighboring layers, there exist a large number of connections that can be absent, and other connections can allow for a broad distribution of their weight values. Therefore, synaptic connections can be classified into three categories: very important ones, unimportant ones, and those of variability that may partially encode nuisance factors. Therefore, our model learns the credit assignment leading to the decision, and predicts an ensemble of subnetworks that can accomplish the same task, thereby providing insights toward understanding the macroscopic behavior of deep learning through the lens of distinct roles of synaptic weights.

Recommended citation: Chan Li,Haiping Huang. (2020). "Learning credit assignment." Physical Review Letters. https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.125.178301

Ensemble perspective for understanding temporal credit assignment

Published in Physical Review E, 2023

Recurrent neural networks are widely used for modeling spatiotemporal sequences in both nature language processing and neural population dynamics. However, understanding the temporal credit assignment is hard. Here, we propose that each individual connection in the recurrent computation is modeled by a spike and slab distribution, rather than a precise weight value. We then derive the mean-field algorithm to train the network at the ensemble level. The method is then applied to classify handwritten digits when pixels are read in sequence, and to the multisensory integration task that is a fundamental cognitive function of animals. Our model reveals important connections that determine the overall performance of the network. The model also shows how spatiotemporal information is processed through the hyperparameters of the distribution, and moreover reveals distinct types of emergent neural selectivity. To provide a mechanistic analysis of the ensemble learning, we first derive an analytic solution of the learning at the infinitely large network limit. We then carry out a low-dimensional projection of both neural and synaptic dynamics, analyze symmetry breaking in the parameter space, and finally demonstrate the role of stochastic plasticity in the recurrent computation. Therefore, our study sheds light on mechanisms of how weight uncertainty impacts the temporal credit assignment in recurrent neural networks from the ensemble perspective..

Recommended citation: Wenxuan Zou1,*, Chan Li1,*, and Haiping Huang. (2023). "Ensemble perspective for understanding temporal credit assignment." Physical Review E. https://journals.aps.org/pre/abstract/10.1103/PhysRevE.107.024307

Emergence of hierarchical modes from deep learning

Published in Physical Review Research, 2023

Large-scale deep neural networks consume expensive training costs, but the training results in less-interpretable weight matrices constructing the networks. Here, we propose a mode decomposition learning that can interpret the weight matrices as a hierarchy of latent modes. These modes are akin to patterns in physics studies of memory networks, but the least number of modes increases only logarithmically with the network width and even becomes a constant when the width grows further. The mode decomposition learning not only saves a significant large amount of training costs but also explains the network performance with the leading modes, displaying a striking piecewise power-law behavior. The modes specify a progressively compact latent space across the network hierarchy, making a more disentangled subspace compared to standard training. Our mode decomposition learning is also studied in an analytic online learning setting, which reveals multiple stages of learning dynamics with a continuous specialization of hidden nodes. Therefore the proposed mode decomposition learning points to a cheap and interpretable route towards the magical deep learning.

Recommended citation: Chan Li,Haiping Huang. (2023). "Emergence of hierarchical modes from deep learning." Physical Review Research. https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.5.L022011

Statistical mechanics of continual learning: Variational principle and mean-field potential

Published in Physical Review E, 2023

An obstacle to artificial general intelligence is set by continual learning of multiple tasks of a different nature. Recently, various heuristic tricks, both from machine learning and from neuroscience angles, were proposed, but they lack a unified theory foundation. Here, we focus on continual learning in single-layered and multilayered neural networks of binary weights. A variational Bayesian learning setting is thus proposed in which the neural networks are trained in a field-space, rather than a gradient-ill-defined discrete-weight space, and furthermore, weight uncertainty is naturally incorporated, and it modulates synaptic resources among tasks. From a physics perspective, we translate variational continual learning into a Franz-Parisi thermodynamic potential framework, where previous task knowledge serves as a prior probability and a reference as well. We thus interpret the continual learning of the binary perceptron in a teacher-student setting as a Franz-Parisi potential computation. The learning performance can then be analytically studied with mean-field order parameters, whose predictions coincide with numerical experiments using stochastic gradient descent methods. Based on the variational principle and Gaussian field approximation of internal preactivations in hidden layers, we also derive the learning algorithm considering weight uncertainty, which solves the continual learning with binary weights using multilayered neural networks, and performs better than the currently available metaplasticity algorithm in which binary synapses bear hidden continuous states and the synaptic plasticity is modulated by a heuristic regularization function. Our proposed principled frameworks also connect to elastic weight consolidation, weight-uncertainty modulated learning, and neuroscience-inspired metaplasticity, providing a theoretically grounded method for real-world multitask learning with deep networks..

Recommended citation: Chan Li1,*, Zhenye Huang2,*, Wenxuan Zou1,*, and Haiping Huang. (2023). "Statistical mechanics of continual learning: Variational principle and mean-field potential." Physical Review E. https://journals.aps.org/pre/abstract/10.1103/PhysRevE.108.014309

Meta predictive learning model of languages in neural circuits

Published in Physical Review E, 2024

Large language models based on self-attention mechanisms have achieved astonishing performances, not only in natural language itself, but also in a variety of tasks of different nature. However, regarding processing language, our human brain may not operate using the same principle. Then, a debate is established on the connection between brain computation and artificial self-supervision adopted in large language models. One of most influential hypotheses in brain computation is the predictive coding framework, which proposes to minimize the prediction error by local learning. However, the role of predictive coding and the associated credit assignment in language processing remains unknown. Here, we propose a mean-field learning model within the predictive coding framework, assuming that the synaptic weight of each connection follows a spike and slab distribution, and only the distribution, rather than specific weights, is trained. This meta predictive learning is successfully validated on classifying handwritten digits where pixels are input to the network in sequence, and moreover, on the toy and real language corpus. Our model reveals that most of the connections become deterministic after learning, while the output connections have a higher level of variability. The performance of the resulting network ensemble changes continuously with data load, further improving with more training data, in analogy with the emergent behavior of large language models. Therefore, our model provides a starting point to investigate the connection among brain computation, next-token prediction, and general intelligence.

Recommended citation: Chan Li1 and Haiping Huang. (2024). "Meta predictive learning model of languages in neural circuits." Physical Review E. https://journals.aps.org/pre/abstract/10.1103/PhysRevE.109.044309

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