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Guoqiang Wu

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13 papers

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ICML Conference 2025 Conference Paper

A Theory for Conditional Generative Modeling on Multiple Data Sources

Rongzhen Wang
Yan Zhang
Chenyu Zheng
Chongxuan Li
Guoqiang Wu

The success of large generative models has driven a paradigm shift, leveraging massive multi-source data to enhance model capabilities. However, the interaction among these sources remains theoretically underexplored. This paper provides a first attempt to fill this gap by rigorously analyzing multi-source training in conditional generative modeling, where each condition represents a distinct data source. Specifically, we establish a general distribution estimation error bound in average total variation distance for conditional maximum likelihood estimation based on the bracketing number. Our result shows that when source distributions share certain similarities and the model is expressive enough, multi-source training guarantees a sharper bound than single-source training. We further instantiate the general theory on conditional Gaussian estimation and deep generative models including autoregressive and flexible energy-based models, by characterizing their bracketing numbers. The results highlight that the number of sources and similarity among source distributions improve the advantage of multi-source training. Simulations and real-world experiments validate our theory.

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AAAI Conference 2025 Conference Paper

Towards Macro-AUC Oriented Imbalanced Multi-Label Continual Learning

Yan Zhang
Guoqiang Wu
Bingzheng Wang
Teng Pang
Haoliang Sun
Yilong Yin

In Continual Learning (CL), while existing work primarily focuses on the multi-class classification task, there has been limited research on Multi-Label Learning (MLL). In practice, MLL datasets are often class-imbalanced, making it inherently challenging, a problem that is even more acute in CL. Due to its sensitivity to imbalance, Macro-AUC is an appropriate and widely used measure in MLL. However, there is no research to optimize Macro-AUC in MLCL specifically. To fill this gap, in this paper, we propose a new memory replay-based method to tackle the imbalance issue for Macro-AUC-oriented MLCL. Specifically, inspired by recent theory work, we propose a new Reweighted Label-Distribution-Aware Margin (RLDAM) loss. Furthermore, to be compatible with the RLDAM loss, a new memory-updating strategy named Weight Retain Updating (WRU) is proposed to maintain the numbers of positive and negative instances of the original dataset in memory. Theoretically, we provide superior generalization analyses of the RLDAM-based algorithm in terms of Macro-AUC, separately in batch MLL and MLCL settings. This is the first work to offer theoretical generalization analyses in MLCL to our knowledge. Finally, a series of experimental results illustrate the effectiveness of our method over several baselines.

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TMLR Journal 2024 Journal Article

Calibrating Deep Ensemble through Functional Variational Inference

Zhijie Deng
Feng Zhou
Jianfei Chen
Guoqiang Wu
Jun Zhu

Deep Ensemble (DE) is an effective and practical uncertainty quantification approach in deep learning. The uncertainty of DE is usually manifested by the functional inconsistency among the ensemble members, which, yet, originates from unmanageable randomness in the initialization and optimization of neural networks (NNs), and may easily collapse in specific cases. To tackle this issue, we advocate characterizing the functional inconsistency with the empirical covariance of the functions dictated by the ensemble members, and defining a Gaussian process (GP) with it. We perform functional variational inference to tune such a probabilistic model w.r.t. training data and specific prior beliefs. This way, we can explicitly manage the uncertainty of the ensemble of NNs. We further provide strategies to make the training efficient. The proposed approach achieves better uncertainty quantification than DE and its variants across diverse scenarios, while consuming only marginally added training cost compared to standard DE. The code is available at https://github.com/thudzj/DE-GP.

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AAAI Conference 2024 Conference Paper

DiffAIL: Diffusion Adversarial Imitation Learning

Bingzheng Wang
Guoqiang Wu
Teng Pang
Yan Zhang
Yilong Yin

Imitation learning aims to solve the problem of defining reward functions in real-world decision-making tasks. The current popular approach is the Adversarial Imitation Learning (AIL) framework, which matches expert state-action occupancy measures to obtain a surrogate reward for forward reinforcement learning. However, the traditional discriminator is a simple binary classifier and doesn't learn an accurate distribution, which may result in failing to identify expert-level state-action pairs induced by the policy interacting with the environment. To address this issue, we propose a method named diffusion adversarial imitation learning (DiffAIL), which introduces the diffusion model into the AIL framework. Specifically, DiffAIL models the state-action pairs as unconditional diffusion models and uses diffusion loss as part of the discriminator's learning objective, which enables the discriminator to capture better expert demonstrations and improve generalization. Experimentally, the results show that our method achieves state-of-the-art performance and significantly surpasses expert demonstration on two benchmark tasks, including the standard state-action setting and state-only settings.

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NeurIPS Conference 2024 Conference Paper

Lower Bounds of Uniform Stability in Gradient-Based Bilevel Algorithms for Hyperparameter Optimization

Rongzhen Wang
Chenyu Zheng
Guoqiang Wu
Xu Min
Xiaolu Zhang
Jun Zhou
Chongxuan Li

Gradient-based bilevel programming leverages unrolling differentiation (UD) or implicit function theorem (IFT) to solve hyperparameter optimization (HO) problems, and is proven effective and scalable in practice. To understand their generalization behavior, existing works establish upper bounds on the uniform stability of these algorithms, while their tightness is still unclear. To this end, this paper attempts to establish stability lower bounds for UD-based and IFT-based algorithms. A central technical challenge arises from the dependency of each outer-level update on the concurrent stage of inner optimization in bilevel programming. To address this problem, we introduce lower-bounded expansion properties to characterize the instability in update rules which can serve as general tools for lower-bound analysis. These properties guarantee the hyperparameter divergence at the outer level and the Lipschitz constant of inner output at the inner level in the context of HO. Guided by these insights, we construct a quadratic example that yields tight lower bounds for the UD-based algorithm and meaningful bounds for a representative IFT-based algorithm. Our tight result indicates that uniform stability has reached its limit in stability analysis for the UD-based algorithm.

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NeurIPS Conference 2024 Conference Paper

On Mesa-Optimization in Autoregressively Trained Transformers: Emergence and Capability

Chenyu Zheng
Wei Huang
Rongzhen Wang
Guoqiang Wu
Jun Zhu
Chongxuan Li

Autoregressively trained transformers have brought a profound revolution to the world, especially with their in-context learning (ICL) ability to address downstream tasks. Recently, several studies suggest that transformers learn a mesa-optimizer during autoregressive (AR) pretraining to implement ICL. Namely, the forward pass of the trained transformer is equivalent to optimizing an inner objective function in-context. However, whether the practical non-convex training dynamics will converge to the ideal mesa-optimizer is still unclear. Towards filling this gap, we investigate the non-convex dynamics of a one-layer linear causal self-attention model autoregressively trained by gradient flow, where the sequences are generated by an AR process $x_{t+1} = W x_t$. First, under a certain condition of data distribution, we prove that an autoregressively trained transformer learns $W$ by implementing one step of gradient descent to minimize an ordinary least squares (OLS) problem in-context. It then applies the learned $\widehat{W}$ for next-token prediction, thereby verifying the mesa-optimization hypothesis. Next, under the same data conditions, we explore the capability limitations of the obtained mesa-optimizer. We show that a stronger assumption related to the moments of data is the sufficient and necessary condition that the learned mesa-optimizer recovers the distribution. Besides, we conduct exploratory analyses beyond the first data condition and prove that generally, the trained transformer will not perform vanilla gradient descent for the OLS problem. Finally, our simulation results verify the theoretical results.

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ICML Conference 2023 Conference Paper

Revisiting Discriminative vs. Generative Classifiers: Theory and Implications

Chenyu Zheng
Guoqiang Wu
Fan Bao
Yue Cao
Chongxuan Li
Jun Zhu 0001

A large-scale deep model pre-trained on massive labeled or unlabeled data transfers well to downstream tasks. Linear evaluation freezes parameters in the pre-trained model and trains a linear classifier separately, which is efficient and attractive for transfer. However, little work has investigated the classifier in linear evaluation except for the default logistic regression. Inspired by the statistical efficiency of naive Bayes, the paper revisits the classical topic on discriminative vs. generative classifiers. Theoretically, the paper considers the surrogate loss instead of the zero-one loss in analyses and generalizes the classical results from binary cases to multiclass ones. We show that, under mild assumptions, multiclass naive Bayes requires $O(\log n)$ samples to approach its asymptotic error while the corresponding multiclass logistic regression requires $O(n)$ samples, where $n$ is the feature dimension. To establish it, we present a multiclass $\mathcal{H}$-consistency bound framework and an explicit bound for logistic loss, which are of independent interests. Simulation results on a mixture of Gaussian validate our theoretical findings. Experiments on various pre-trained deep vision models show that naive Bayes consistently converges faster as the number of data increases. Besides, naive Bayes shows promise in few-shot cases and we observe the "two regimes” phenomenon in pre-trained supervised models. Our code is available at https: //github. com/ML-GSAI/Revisiting-Dis-vs-Gen-Classifiers.

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NeurIPS Conference 2023 Conference Paper

Toward Understanding Generative Data Augmentation

Chenyu Zheng
Guoqiang Wu
Chongxuan Li

Generative data augmentation, which scales datasets by obtaining fake labeled examples from a trained conditional generative model, boosts classification performance in various learning tasks including (semi-)supervised learning, few-shot learning, and adversarially robust learning. However, little work has theoretically investigated the effect of generative data augmentation. To fill this gap, we establish a general stability bound in this not independently and identicallydistributed (non-i. i. d. ) setting, where the learned distribution is dependent on the original train set and generally not the same as the true distribution. Our theoretical result includes the divergence between the learned distribution and the true distribution. It shows that generative data augmentation can enjoy a faster learning rate when the order of divergence term is $o(\max\left( \log(m)\beta_m, 1 / \sqrt{m})\right)$, where $m$ is the train set size and $\beta_m$ is the corresponding stability constant. We further specify the learning setup to the Gaussian mixture model and generative adversarial nets. We prove that in both cases, though generative data augmentation does not enjoy a faster learning rate, it can improve the learning guarantees at a constant level when the train set is small, which is significant when the awful overfitting occurs. Simulation results on the Gaussian mixture model and empirical results on generative adversarial nets support our theoretical conclusions.

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ICML Conference 2023 Conference Paper

Towards Understanding Generalization of Macro-AUC in Multi-label Learning

Guoqiang Wu
Chongxuan Li
Yilong Yin

Macro-AUC is the arithmetic mean of the class-wise AUCs in multi-label learning and is commonly used in practice. However, its theoretical understanding is far lacking. Toward solving it, we characterize the generalization properties of various learning algorithms based on the corresponding surrogate losses w. r. t. Macro-AUC. We theoretically identify a critical factor of the dataset affecting the generalization bounds: the label-wise class imbalance. Our results on the imbalance-aware error bounds show that the widely-used univariate loss-based algorithm is more sensitive to the label-wise class imbalance than the proposed pairwise and reweighted loss-based ones, which probably implies its worse performance. Moreover, empirical results on various datasets corroborate our theory findings. To establish it, technically, we propose a new (and more general) McDiarmid-type concentration inequality, which may be of independent interest.

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NeurIPS Conference 2021 Conference Paper

On the Convergence of Prior-Guided Zeroth-Order Optimization Algorithms

Shuyu Cheng
Guoqiang Wu
Jun Zhu

Zeroth-order (ZO) optimization is widely used to handle challenging tasks, such as query-based black-box adversarial attacks and reinforcement learning. Various attempts have been made to integrate prior information into the gradient estimation procedure based on finite differences, with promising empirical results. However, their convergence properties are not well understood. This paper makes an attempt to fill up this gap by analyzing the convergence of prior-guided ZO algorithms under a greedy descent framework with various gradient estimators. We provide a convergence guarantee for the prior-guided random gradient-free (PRGF) algorithms. Moreover, to further accelerate over greedy descent methods, we present a new accelerated random search (ARS) algorithm that incorporates prior information, together with a convergence analysis. Finally, our theoretical results are confirmed by experiments on several numerical benchmarks as well as adversarial attacks.

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NeurIPS Conference 2021 Conference Paper

Rethinking and Reweighting the Univariate Losses for Multi-Label Ranking: Consistency and Generalization

Guoqiang Wu
Chongxuan Li
Kun Xu
Jun Zhu

The (partial) ranking loss is a commonly used evaluation measure for multi-label classification, which is usually optimized with convex surrogates for computational efficiency. Prior theoretical efforts on multi-label ranking mainly focus on (Fisher) consistency analyses. However, there is a gap between existing theory and practice --- some inconsistent pairwise losses can lead to promising performance, while some consistent univariate losses usually have no clear superiority in practice. To take a step towards filling up this gap, this paper presents a systematic study from two complementary perspectives of consistency and generalization error bounds of learning algorithms. We theoretically find two key factors of the distribution (or dataset) that affect the learning guarantees of algorithms: the instance-wise class imbalance and the label size $c$. Specifically, in an extremely imbalanced case, the algorithm with the consistent univariate loss has an error bound of $O(c)$, while the one with the inconsistent pairwise loss depends on $O(\sqrt{c})$ as shown in prior work. This may shed light on the superior performance of pairwise methods in practice, where real datasets are usually highly imbalanced. Moreover, we present an inconsistent reweighted univariate loss-based algorithm that enjoys an error bound of $O(\sqrt{c})$ for promising performance as well as the computational efficiency of univariate losses. Finally, experimental results confirm our theoretical findings.

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NeurIPS Conference 2021 Conference Paper

Stability and Generalization of Bilevel Programming in Hyperparameter Optimization

Fan Bao
Guoqiang Wu
Chongxuan Li
Jun Zhu
Bo Zhang

The (gradient-based) bilevel programming framework is widely used in hyperparameter optimization and has achieved excellent performance empirically. Previous theoretical work mainly focuses on its optimization properties, while leaving the analysis on generalization largely open. This paper attempts to address the issue by presenting an expectation bound w. r. t. the validation set based on uniform stability. Our results can explain some mysterious behaviours of the bilevel programming in practice, for instance, overfitting to the validation set. We also present an expectation bound for the classical cross-validation algorithm. Our results suggest that gradient-based algorithms can be better than cross-validation under certain conditions in a theoretical perspective. Furthermore, we prove that regularization terms in both the outer and inner levels can relieve the overfitting problem in gradient-based algorithms. In experiments on feature learning and data reweighting for noisy labels, we corroborate our theoretical findings.

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NeurIPS Conference 2020 Conference Paper

Multi-label classification: do Hamming loss and subset accuracy really conflict with each other?

Guoqiang Wu
Jun Zhu

Various evaluation measures have been developed for multi-label classification, including Hamming Loss (HL), Subset Accuracy (SA) and Ranking Loss (RL). However, there is a gap between empirical results and the existing theories: 1) an algorithm often empirically performs well on some measure(s) while poorly on others, while a formal theoretical analysis is lacking; and 2) in small label space cases, the algorithms optimizing HL often have comparable or even better performance on the SA measure than those optimizing SA directly, while existing theoretical results show that SA and HL are conflicting measures. This paper provides an attempt to fill up this gap by analyzing the learning guarantees of the corresponding learning algorithms on both SA and HL measures. We show that when a learning algorithm optimizes HL with its surrogate loss, it enjoys an error bound for the HL measure independent of $c$ (the number of labels), while the bound for the SA measure depends on at most $O(c)$. On the other hand, when directly optimizing SA with its surrogate loss, it has learning guarantees that depend on $O(\sqrt{c})$ for both HL and SA measures. This explains the observation that when the label space is not large, optimizing HL with its surrogate loss can have promising performance for SA. We further show that our techniques are applicable to analyze the learning guarantees of algorithms on other measures, such as RL. Finally, the theoretical analyses are supported by experimental results.

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