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Zixiang Chen

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23 papers

2 author rows

ICLR Conference 2025 Conference Paper

Convergence of Score-Based Discrete Diffusion Models: A Discrete-Time Analysis

Zikun Zhang
Zixiang Chen
Quanquan Gu

Diffusion models have achieved great success in generating high-dimensional samples across various applications. While the theoretical guarantees for continuous-state diffusion models have been extensively studied, the convergence analysis of the discrete-state counterparts remains under-explored. In this paper, we study the theoretical aspects of score-based discrete diffusion models under the Continuous Time Markov Chain (CTMC) framework. We introduce a discrete-time sampling algorithm in the general state space $[S]^d$ that utilizes score estimators at predefined time points. We derive convergence bounds for the Kullback-Leibler (KL) divergence and total variation (TV) distance between the generated sample distribution and the data distribution, considering both scenarios with and without early stopping under reasonable assumptions. Notably, our KL divergence bounds are nearly linear in the dimension $d$, aligning with state-of-the-art results for diffusion models. Our convergence analysis employs a Girsanov-based method and establishes key properties of the discrete score function, which are essential for characterizing the discrete-time sampling process.

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ICML Conference 2025 Conference Paper

Global Convergence and Rich Feature Learning in L-Layer Infinite-Width Neural Networks under μ Parametrization

Zixiang Chen
Greg Yang
Qingyue Zhao 0001
Quanquan Gu

Despite deep neural networks’ powerful representation learning capabilities, theoretical understanding of how networks can simultaneously achieve meaningful feature learning and global convergence remains elusive. Existing approaches like the neural tangent kernel (NTK) are limited because features stay close to their initialization in this parametrization, leaving open questions about feature properties during substantial evolution. In this paper, we investigate the training dynamics of infinitely wide, $L$-layer neural networks using the tensor program (TP) framework. Specifically, we show that, when trained with stochastic gradient descent (SGD) under the Maximal Update parametrization ($\mu$P) and mild conditions on the activation function, SGD enables these networks to learn linearly independent features that substantially deviate from their initial values. This rich feature space captures relevant data information and ensures that any convergent point of the training process is a global minimum. Our analysis leverages both the interactions among features across layers and the properties of Gaussian random variables, providing new insights into deep representation learning. We further validate our theoretical findings through experiments on real-world datasets.

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TMLR Journal 2025 Journal Article

Guided Discrete Diffusion for Electronic Health Record Generation

Jun Han
Zixiang Chen
Yongqian Li
Yiwen Kou
Eran Halperin
Robert E. Tillman
Quanquan Gu

Electronic health records (EHRs) are a pivotal data source that enables numerous applications in computational medicine, e.g., disease progression prediction, clinical trial design, and health economics and outcomes research. Despite wide usability, their sensitive nature raises privacy and confidentially concerns, which limit potential use cases. To tackle these challenges, we explore the use of generative models to synthesize artificial, yet realistic EHRs. While diffusion-based methods have recently demonstrated state-of-the-art performance in generating other data modalities and overcome the training instability and mode collapse issues that plague previous GAN-based approaches, their applications in EHR generation remain underexplored. The discrete nature of tabular medical code data in EHRs poses challenges for high-quality data generation, especially for continuous diffusion models. To this end, we introduce a novel tabular EHR generation method, EHR-D3PM, which enables both unconditional and conditional generation using the discrete diffusion model. Our experiments demonstrate that EHR-D3PM significantly outperforms existing generative baselines on comprehensive fidelity and utility metrics while maintaining less attribute and membership vulnerability risks. Furthermore, we show EHR-D3PM is effective as a data augmentation method and enhances performance on downstream tasks when combined with real data.

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NeurIPS Conference 2024 Conference Paper

Fast Sampling via Discrete Non-Markov Diffusion Models with Predetermined Transition Time

Zixiang Chen
Huizhuo Yuan
Yongqian Li
Yiwen Kou
Junkai Zhang
Quanquan Gu

Discrete diffusion models have emerged as powerful tools for high-quality data generation. Despite their success in discrete spaces, such as text generation tasks, the acceleration of discrete diffusion models remains under-explored. In this paper, we propose discrete non-Markov diffusion models (DNDM), which naturally induce the predetermined transition time set. This enables a training-free sampling algorithm that significantly reduces the number of function evaluations (i. e. , calls to the neural network), making the sampling process much faster. Furthermore, we study the transition from finite to infinite step sampling, offering new insights into bridging the gap between discrete and continuous-time processes for discrete diffusion models. Extensive experiments on natural language generation and machine translation tasks demonstrate the superior performance of our method in terms of both generation speed and sample quality compared to existing methods for discrete diffusion models. Codes are available at \url{https: //github. com/uclaml/DNDM}.

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ICLR Conference 2024 Conference Paper

How Many Pretraining Tasks Are Needed for In-Context Learning of Linear Regression?

Jingfeng Wu
Difan Zou
Zixiang Chen
Vladimir Braverman
Quanquan Gu
Peter L. Bartlett

Transformers pretrained on diverse tasks exhibit remarkable in-context learning (ICL) capabilities, enabling them to solve unseen tasks solely based on input contexts without adjusting model parameters. In this paper, we study ICL in one of its simplest setups: pretraining a single-layer linear attention model for linear regression with a Gaussian prior. We establish a statistical task complexity bound for the attention model pretraining, showing that effective pretraining only requires a small number of independent tasks. Furthermore, we prove that the pretrained model closely matches the Bayes optimal algorithm, i.e., optimally tuned ridge regression, by achieving nearly Bayes optimal risk on unseen tasks under a fixed context length. These theoretical findings complement prior experimental research and shed light on the statistical foundations of ICL.

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NeurIPS Conference 2024 Conference Paper

Matching the Statistical Query Lower Bound for $k$-Sparse Parity Problems with Sign Stochastic Gradient Descent

Yiwen Kou
Zixiang Chen
Quanquan Gu
Sham M. Kakade

The $k$-sparse parity problem is a classical problem in computational complexity and algorithmic theory, serving as a key benchmark for understanding computational classes. In this paper, we solve the $k$-sparse parity problem with sign stochastic gradient descent, a variant of stochastic gradient descent (SGD) on two-layer fully-connected neural networks. We demonstrate that this approach can efficiently solve the $k$-sparse parity problem on a $d$-dimensional hypercube ($k\le O(\sqrt{d})$) with a sample complexity of $\tilde{O}(d^{k-1})$ using $2^{\Theta(k)}$ neurons, matching the established $\Omega(d^{k})$ lower bounds of Statistical Query (SQ) models. Our theoretical analysis begins by constructing a good neural network capable of correctly solving the $k$-parity problem. We then demonstrate how a trained neural network with sign SGD can effectively approximate this good network, solving the $k$-parity problem with small statistical errors. To the best of our knowledge, this is the first result that matches the SQ lower bound for solving $k$-sparse parity problem using gradient-based methods.

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ICML Conference 2024 Conference Paper

Self-Play Fine-Tuning Converts Weak Language Models to Strong Language Models

Zixiang Chen
Yihe Deng
Huizhuo Yuan
Kaixuan Ji
Quanquan Gu

Harnessing the power of human-annotated data through Supervised Fine-Tuning (SFT) is pivotal for advancing Large Language Models (LLMs). In this paper, we delve into the prospect of growing a strong LLM out of a weak one without the need for acquiring additional human-annotated data. We propose a new fine-tuning method called Self-Play fIne-tuNing (SPIN), which starts from a supervised fine-tuned model. At the heart of SPIN lies a self-play mechanism, where the LLM refines its capability by playing against instances of itself. More specifically, the LLM generates its own training data from its previous iterations, refining its policy by discerning these self-generated responses from those obtained from human-annotated data. Our method progressively elevates the LLM from a nascent model to a formidable one, unlocking the full potential of human-annotated demonstration data for SFT. Theoretically, we prove that the global optimum to the training objective function of our method is achieved only when the LLM policy aligns with the target data distribution. Empirically, we evaluate our method on several benchmark datasets including the HuggingFace Open LLM Leaderboard, MT-Bench, and datasets from Big-Bench. Our results show that SPIN can significantly improve the LLM’s performance across a variety of benchmarks and even outperform models trained through direct preference optimization (DPO) supplemented with extra GPT-4 preference data. This sheds light on the promise of self-play, enabling the achievement of human-level performance in LLMs without the need for expert opponents.

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NeurIPS Conference 2024 Conference Paper

Self-Play Fine-tuning of Diffusion Models for Text-to-image Generation

Huizhuo Yuan
Zixiang Chen
Kaixuan Ji
Quanquan Gu

Fine-tuning Diffusion Models remains an underexplored frontier in generative artificial intelligence (GenAI), especially when compared with the remarkable progress made in fine-tuning Large Language Models (LLMs). While cutting-edge diffusion models such as Stable Diffusion (SD) and SDXL rely on supervised fine-tuning, their performance inevitably plateaus after seeing a certain volume of data. Recently, reinforcement learning (RL) has been employed to fine-tune diffusion models with human preference data, but it requires at least two images ( winner'' and loser'' images) for each text prompt. In this paper, we introduce an innovative technique called self-play fine-tuning for diffusion models (SPIN-Diffusion), where the diffusion model engages in competition with its earlier versions, facilitating an iterative self-improvement process. Our approach offers an alternative to conventional supervised fine-tuning and RL strategies, significantly improving both model performance and alignment. Our experiments on the Pick-a-Pic dataset reveal that SPIN-Diffusion outperforms the existing supervised fine-tuning method in aspects of human preference alignment and visual appeal right from its first iteration. By the second iteration, it exceeds the performance of RLHF-based methods across all metrics, achieving these results with less data. Codes are available at \url{https: //github. com/uclaml/SPIN-Diffusion/}.

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ICLR Conference 2024 Conference Paper

Understanding Transferable Representation Learning and Zero-shot Transfer in CLIP

Zixiang Chen
Yihe Deng
Yuanzhi Li
Quanquan Gu

Multi-modal learning has become increasingly popular due to its ability to leverage information from different data sources (e.g., text and images) to improve the model performance. Recently, CLIP has emerged as an effective approach that employs vision-language contrastive pretraining to learn joint image and text representations and exhibits remarkable performance in zero-shot learning and text-guided natural image generation. Despite the substantial practical success of CLIP, its theoretical understanding remains elusive. In this paper, we formally study transferrable representation learning underlying CLIP and demonstrate how features from different modalities get aligned. We also analyze its zero-shot transfer performance on the downstream tasks. In addition, we conduct empirical evaluations on real data to back up our theory. Inspired by our analysis, we propose a new CLIP-type approach, which achieves better performance than CLIP and other state-of-the-art methods on benchmark datasets.

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ICLR Conference 2023 Conference Paper

A General Framework for Sample-Efficient Function Approximation in Reinforcement Learning

Zixiang Chen
Chris Junchi Li
Huizhuo Yuan
Quanquan Gu
Michael I. Jordan

With the increasing need for handling large state and action spaces, general function approximation has become a key technique in reinforcement learning (RL). In this paper, we propose a general framework that unifies model-based and model-free RL, and an Admissible Bellman Characterization (ABC) class that subsumes nearly all Markov decision process (MDP) models in the literature for tractable RL. We propose a novel estimation function with decomposable structural properties for optimization-based exploration and the functional Eluder dimension as a complexity measure of the ABC class. Under our framework, a new sample-efficient algorithm namely OPtimization-based ExploRation with Approximation (OPERA) is proposed, achieving regret bounds that match or improve over the best-known results for a variety of MDP models. In particular, for MDPs with low Witness rank, under a slightly stronger assumption, OPERA improves the state-of-the-art sample complexity results by a factor of $dH$. Our framework provides a generic interface to design and analyze new RL models and algorithms.

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ICML Conference 2023 Conference Paper

Benign Overfitting in Two-layer ReLU Convolutional Neural Networks

Yiwen Kou
Zixiang Chen
Yuanzhou Chen
Quanquan Gu

Modern deep learning models with great expressive power can be trained to overfit the training data but still generalize well. This phenomenon is referred to as benign overfitting. Recently, a few studies have attempted to theoretically understand benign overfitting in neural networks. However, these works are either limited to neural networks with smooth activation functions or to the neural tangent kernel regime. How and when benign overfitting can occur in ReLU neural networks remains an open problem. In this work, we seek to answer this question by establishing algorithm-dependent risk bounds for learning two-layer ReLU convolutional neural networks with label-flipping noise. We show that, under mild conditions, the neural network trained by gradient descent can achieve near-zero training loss and Bayes optimal test risk. Our result also reveals a sharp transition between benign and harmful overfitting under different conditions on data distribution in terms of test risk. Experiments on synthetic data back up our theory.

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ICML Conference 2023 Conference Paper

Finite-Sample Analysis of Learning High-Dimensional Single ReLU Neuron

Jingfeng Wu
Difan Zou
Zixiang Chen
Vladimir Braverman
Quanquan Gu
Sham M. Kakade

This paper considers the problem of learning single ReLU neuron with squared loss (a. k. a. , ReLU regression) in the overparameterized regime, where the input dimension can exceed the number of samples. We analyze a Perceptron-type algorithm called GLM-tron [Kakade et al. 2011], and provide its dimension-free risk upper bounds for high-dimensional ReLU regression in both well-specified and misspecified settings. Our risk bounds recover several existing results as special cases. Moreover, in the well-specified setting, we also provide an instance-wise matching risk lower bound for GLM-tron. Our upper and lower risk bounds provide a sharp characterization of the high-dimensional ReLU regression problems that can be learned via GLM-tron. On the other hand, we provide some negative results for stochastic gradient descent (SGD) for ReLU regression with symmetric Bernoulli data: if the model is well-specified, the excess risk of SGD is provably no better than that of GLM-tron ignoring constant factors, for each problem instance; and in the noiseless case, GLM-tron can achieve a small risk while SGD unavoidably suffers from a constant risk in expectation. These results together suggest that GLM-tron might be more preferable than SGD for high-dimensional ReLU regression.

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ICLR Conference 2023 Conference Paper

How Does Semi-supervised Learning with Pseudo-labelers Work? A Case Study

Yiwen Kou
Zixiang Chen
Yuan Cao 0006
Quanquan Gu

Semi-supervised learning is a popular machine learning paradigm that utilizes a large amount of unlabeled data as well as a small amount of labeled data to facilitate learning tasks. While semi-supervised learning has achieved great success in training neural networks, its theoretical understanding remains largely open. In this paper, we aim to theoretically understand a semi-supervised learning approach based on pre-training and linear probing. In particular, the semi-supervised learning approach we consider first trains a two-layer neural network based on the unlabeled data with the help of pseudo-labelers. Then it linearly probes the pre-trained network on a small amount of labeled data. We prove that, under a certain toy data generation model and two-layer convolutional neural network, the semisupervised learning approach can achieve nearly zero test loss, while a neural network directly trained by supervised learning on the same amount of labeled data can only achieve constant test loss. Through this case study, we demonstrate a separation between semi-supervised learning and supervised learning in terms of test loss provided the same amount of labeled data.

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NeurIPS Conference 2023 Conference Paper

Implicit Bias of Gradient Descent for Two-layer ReLU and Leaky ReLU Networks on Nearly-orthogonal Data

Yiwen Kou
Zixiang Chen
Quanquan Gu

The implicit bias towards solutions with favorable properties is believed to be a key reason why neural networks trained by gradient-based optimization can generalize well. While the implicit bias of gradient flow has been widely studied for homogeneous neural networks (including ReLU and leaky ReLU networks), the implicit bias of gradient descent is currently only understood for smooth neural networks. Therefore, implicit bias in non-smooth neural networks trained by gradient descent remains an open question. In this paper, we aim to answer this question by studying the implicit bias of gradient descent for training two-layer fully connected (leaky) ReLU neural networks. We showed that when the training data are nearly-orthogonal, for leaky ReLU activation function, gradient descent will find a network with a stable rank that converges to $1$, whereas for ReLU activation function, gradient descent will find a neural network with a stable rank that is upper bounded by a constant. Additionally, we show that gradient descent will find a neural network such that all the training data points have the same normalized margin asymptotically. Experiments on both synthetic and real data backup our theoretical findings.

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ICLR Conference 2023 Conference Paper

Understanding Train-Validation Split in Meta-Learning with Neural Networks

Xinzhe Zuo
Zixiang Chen
Huaxiu Yao
Yuan Cao 0006
Quanquan Gu

The goal of meta-learning is to learn a good prior model from a collection of tasks such that the learned prior is able to adapt quickly to new tasks without accessing many data from the new tasks. A common practice in meta-learning is to perform a train-validation split on each task, where the training set is used for adapting the model parameter to that specific task and the validation set is used for learning a prior model that is shared across all tasks. Despite its success and popularity in multitask learning and few-shot learning, the understanding of the train-validation split is still limited, especially when the neural network models are used. In this paper, we study the benefit of train-validation split for classification problems with neural network models trained by gradient descent. We prove that the train-validation split is necessary to learn a good prior model when the noise in the training sample is large, while the train-train method fails. We validate our theory by conducting experiment on both synthetic and real datasets. To the best of our knowledge, this is the first work towards the theoretical understanding of train-validation split in meta-learning with neural networks.

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NeurIPS Conference 2023 Conference Paper

Why Does Sharpness-Aware Minimization Generalize Better Than SGD?

Zixiang Chen
Junkai Zhang
Yiwen Kou
Xiangning Chen
Cho-Jui Hsieh
Quanquan Gu

The challenge of overfitting, in which the model memorizes the training data and fails to generalize to test data, has become increasingly significant in the training of large neural networks. To tackle this challenge, Sharpness-Aware Minimization (SAM) has emerged as a promising training method, which can improve the generalization of neural networks even in the presence of label noise. However, a deep understanding of how SAM works, especially in the setting of nonlinear neural networks and classification tasks, remains largely missing. This paper fills this gap by demonstrating why SAM generalizes better than Stochastic Gradient Descent (SGD) for a certain data model and two-layer convolutional ReLU networks. The loss landscape of our studied problem is nonsmooth, thus current explanations for the success of SAM based on the Hessian information are insufficient. Our result explains the benefits of SAM, particularly its ability to prevent noise learning in the early stages, thereby facilitating more effective learning of features. Experiments on both synthetic and real data corroborate our theory.

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NeurIPS Conference 2022 Conference Paper

Benign Overfitting in Two-layer Convolutional Neural Networks

Yuan Cao
Zixiang Chen
Misha Belkin
Quanquan Gu

Modern neural networks often have great expressive power and can be trained to overfit the training data, while still achieving a good test performance. This phenomenon is referred to as “benign overfitting”. Recently, there emerges a line of works studying “benign overfitting” from the theoretical perspective. However, they are limited to linear models or kernel/random feature models, and there is still a lack of theoretical understanding about when and how benign overfitting occurs in neural networks. In this paper, we study the benign overfitting phenomenon in training a two-layer convolutional neural network (CNN). We show that when the signal-to-noise ratio satisfies a certain condition, a two-layer CNN trained by gradient descent can achieve arbitrarily small training and test loss. On the other hand, when this condition does not hold, overfitting becomes harmful and the obtained CNN can only achieve a constant level test loss. These together demonstrate a sharp phase transition between benign overfitting and harmful overfitting, driven by the signal-to-noise ratio. To the best of our knowledge, this is the first work that precisely characterizes the conditions under which benign overfitting can occur in training convolutional neural networks.

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NeurIPS Conference 2022 Conference Paper

Towards Understanding the Mixture-of-Experts Layer in Deep Learning

Zixiang Chen
Yihe Deng
Yue Wu
Quanquan Gu
Yuanzhi Li

The Mixture-of-Experts (MoE) layer, a sparsely-activated model controlled by a router, has achieved great success in deep learning. However, the understanding of such architecture remains elusive. In this paper, we formally study how the MoE layer improves the performance of neural network learning and why the mixture model will not collapse into a single model. Our empirical results suggest that the cluster structure of the underlying problem and the non-linearity of the expert are pivotal to the success of MoE. This motivates us to consider a challenging classification problem with intrinsic cluster structures. Theoretically, we proved that this problem is hard to solve by a single expert such as a two-layer convolutional neural network (CNN). Yet with the MoE layer with each expert being a two-layer CNN, the problem can be solved successfully. In particular, our theory shows that the router can learn the cluster-center features, which helps divide the input complex problem into simpler classification sub-problems that individual experts can conquer. To our knowledge, this is the first theoretical result toward formally understanding the mechanism of the MoE layer for deep learning.

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ICLR Conference 2021 Conference Paper

How Much Over-parameterization Is Sufficient to Learn Deep ReLU Networks?

Zixiang Chen
Yuan Cao 0006
Difan Zou
Quanquan Gu

A recent line of research on deep learning focuses on the extremely over-parameterized setting, and shows that when the network width is larger than a high degree polynomial of the training sample size $n$ and the inverse of the target error $\epsilon^{-1}$, deep neural networks learned by (stochastic) gradient descent enjoy nice optimization and generalization guarantees. Very recently, it is shown that under certain margin assumptions on the training data, a polylogarithmic width condition suffices for two-layer ReLU networks to converge and generalize (Ji and Telgarsky, 2020). However, whether deep neural networks can be learned with such a mild over-parameterization is still an open question. In this work, we answer this question affirmatively and establish sharper learning guarantees for deep ReLU networks trained by (stochastic) gradient descent. In specific, under certain assumptions made in previous work, our optimization and generalization guarantees hold with network width polylogarithmic in $n$ and $\epsilon^{-1}$. Our results push the study of over-parameterized deep neural networks towards more practical settings.

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JBHI Journal 2021 Journal Article

Learning a Deep CNN Denoising Approach Using Anatomical Prior Information Implemented With Attention Mechanism for Low-Dose CT Imaging on Clinical Patient Data From Multiple Anatomical Sites

Zhenxing Huang
Xinfeng Liu
Rongpin Wang
Zixiang Chen
Yongfeng Yang
Xin Liu
Hairong Zheng
Dong Liang

Dose reduction in computed tomography (CT) has gained considerable attention in clinical applications because it decreases radiation risks. However, a lower dose generates noise in low-dose computed tomography (LDCT) images. Previous deep learning (DL)-based works have investigated ways to improve diagnostic performance to address this ill-posed problem. However, most of them disregard the anatomical differences among different human body sites in constructing the mapping function between LDCT images and their high-resolution normal-dose CT (NDCT) counterparts. In this article, we propose a novel deep convolutional neural network (CNN) denoising approach by introducing information of the anatomical prior. Instead of designing multiple networks for each independent human body anatomical site, a unified network framework is employed to process anatomical information. The anatomical prior is represented as a pattern of weights of the features extracted from the corresponding LDCT image in an anatomical prior fusion module. To promote diversity in the contextual information, a spatial attention fusion mechanism is introduced to capture many local regions of interest in the attention fusion module. Although many network parameters are saved, the experimental results demonstrate that our method, which incorporates anatomical prior information, is effective in denoising LDCT images. Furthermore, the anatomical prior fusion module could be conveniently integrated into other DL-based methods and avails the performance improvement on multiple anatomical data.

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NeurIPS Conference 2020 Conference Paper

A Generalized Neural Tangent Kernel Analysis for Two-layer Neural Networks

Zixiang Chen
Yuan Cao
Quanquan Gu
Tong Zhang

A recent breakthrough in deep learning theory shows that the training of over-parameterized deep neural networks can be characterized by a kernel function called \textit{neural tangent kernel} (NTK). However, it is known that this type of results does not perfectly match the practice, as NTK-based analysis requires the network weights to stay very close to their initialization throughout training, and cannot handle regularizers or gradient noises. In this paper, we provide a generalized neural tangent kernel analysis and show that noisy gradient descent with weight decay can still exhibit a ``kernel-like'' behavior. This implies that the training loss converges linearly up to a certain accuracy. We also establish a novel generalization error bound for two-layer neural networks trained by noisy gradient descent with weight decay.

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EAAI Journal 2014 Journal Article

Hybrid biogeography-based evolutionary algorithms

Haiping Ma
Dan Simon
Minrui Fei
Xinzhan Shu
Zixiang Chen

Hybrid evolutionary algorithms (EAs) are effective optimization methods that combine multiple EAs. We propose several hybrid EAs by combining some recently-developed EAs with a biogeography-based hybridization strategy. We test our hybrid EAs on the continuous optimization benchmarks from the 2013 Congress on Evolutionary Computation (CEC) and on some real-world traveling salesman problems. The new hybrid EAs include two approaches to hybridization: (1) iteration-level hybridization, in which various EAs and BBO are executed in sequence; and (2) algorithm-level hybridization, which runs various EAs independently and then exchanges information between them using ideas from biogeography. Our empirical study shows that the new hybrid EAs significantly outperforms their constituent algorithms with the selected tuning parameters and generation limits, and algorithm-level hybridization is generally better than iteration-level hybridization. Results also show that the best new hybrid algorithm in this paper is competitive with the algorithms from the 2013 CEC competition. In addition, we show that the new hybrid EAs are generally robust to tuning parameters. In summary, the contribution of this paper is the introduction of biogeography-based hybridization strategies to the EA community.

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EAAI Journal 2013 Journal Article

On the equivalences and differences of evolutionary algorithms

Haiping Ma
Dan Simon
Minrui Fei
Zixiang Chen

Evolutionary algorithms (EAs) are fast and robust computation methods for global optimization, and have been widely used in many real-world applications. We first conceptually discuss the equivalences of various popular EAs including genetic algorithm (GA), biogeography-based optimization (BBO), differential evolution (DE), evolution strategy (ES) and particle swarm optimization (PSO). We find that the basic versions of BBO, DE, ES and PSO are equal to the GA with global uniform recombination (GA/GUR) under certain conditions. Then we discuss their differences based on biological motivations and implementation details, and point out that their distinctions enhance the diversity of EA research and applications. To further study the characteristics of various EAs, we compare the basic versions and advanced versions of GA, BBO, DE, ES and PSO to explore their optimization ability on a set of real-world continuous optimization problems. Empirical results show that among the basic versions of the algorithms, BBO performs best on the benchmarks that we studied. Among the advanced versions of the algorithms, DE and ES perform best on the benchmarks that we studied. However, our main conclusion is that the conceptual equivalence of the algorithms is supported by the fact that algorithmic modifications result in very different performance levels.

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