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Ruofeng Yang

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6 papers

2 author rows

ICML Conference 2025 Conference Paper

Improved Discretization Complexity Analysis of Consistency Models: Variance Exploding Forward Process and Decay Discretization Scheme

Ruofeng Yang
Bo Jiang
Cheng Chen 0015
Shuai Li 0010

Consistency models, a new class of one-step generative models, have shown competitive performance with multi-step diffusion models. The most challenging part of consistency models is the training process, which discretizes the continuous diffusion process into $K$ steps and trains a one-step mapping function on these discretized timepoints. Despite the empirical success, only a few works focus on the discretization complexity $K$, and their setting is far from that of empirical works. More specifically, the current theoretical works analyze the variance preserving (VP) diffusion process with a uniform stepsize, while empirical works adopt a variance exploding (VE) process with a decay discretization stepsize. As a result, these works suffer from large discretization complexity and fail to explain the empirical success of consistency models. To close the gap between theory and application, we analyze consistency models with (1) VE process and (2) decay stepsize and prove the state-of-the-art discretization complexity for consistency models. This result is competitive with the results of diffusion models and shows the potential of consistency models. To balance the computation and performance, previous empirical work further proposes a $2$-step consistency algorithm. In this work, we also analyze the role of $2$-step sampling and show that it improves the discretization complexity compared with one-step generation.

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NeurIPS Conference 2024 Conference Paper

Few-Shot Diffusion Models Escape the Curse of Dimensionality

Ruofeng Yang
Bo Jiang
Cheng Chen
Ruinan Jin
Baoxiang Wang
Shuai Li

While diffusion models have demonstrated impressive performance, there is a growing need for generating samples tailored to specific user-defined concepts. The customized requirements promote the development of few-shot diffusion models, which use limited $n_{ta}$ target samples to fine-tune a pre-trained diffusion model trained on $n_s$ source samples. Despite the empirical success, no theoretical work specifically analyzes few-shot diffusion models. Moreover, the existing results for diffusion models without a fine-tuning phase can not explain why few-shot models generate great samples due to the curse of dimensionality. In this work, we analyze few-shot diffusion models under a linear structure distribution with a latent dimension $d$. From the approximation perspective, we prove that few-shot models have a $\widetilde{O}(n_s^{-2/d}+n_{ta}^{-1/2})$ bound to approximate the target score function, which is better than $n_{ta}^{-2/d}$ results. From the optimization perspective, we consider a latent Gaussian special case and prove that the optimization problem has a closed-form minimizer. This means few-shot models can directly obtain an approximated minimizer without a complex optimization process. Furthermore, we also provide the accuracy bound $\widetilde{O}(1/n_{ta}+1/\sqrt{n_s})$ for the empirical solution, which still has better dependence on $n_{ta}$ compared to $n_s$. The results of the real-world experiments also show that the models obtained by only fine-tuning the encoder and decoder specific to the target distribution can produce novel images with the target feature, which supports our theoretical results.

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NeurIPS Conference 2024 Conference Paper

Leveraging Drift to Improve Sample Complexity of Variance Exploding Diffusion Models

Ruofeng Yang
Zhijie Wang
Bo Jiang
Shuai Li

Variance exploding (VE) based diffusion models, an important class of diffusion models, have shown state-of-the-art (SOTA) performance. However, only a few theoretical works analyze VE-based models, and those works suffer from a worse forward convergence rate $1/\text{poly}(T)$ than the $\exp{(-T)}$ of variance preserving (VP) based models, where $T$ is the forward diffusion time and the rate measures the distance between forward marginal distribution $q_T$ and pure Gaussian noise. The slow rate is due to the Brownian Motion without a drift term. In this work, we design a new drifted VESDE forward process, which allows a faster $\exp{(-T)}$ forward convergence rate. With this process, we achieve the first efficient polynomial sample complexity for a series of VE-based models with reverse SDE under the manifold hypothesis. Furthermore, unlike previous works, we allow the diffusion coefficient to be unbounded instead of a constant, which is closer to the SOTA models. Besides the reverse SDE, the other common reverse process is the probability flow ODE (PFODE) process, which is deterministic and enjoys faster sample speed. To deepen the understanding of VE-based models, we consider a more general setting considering reverse SDE and PFODE simultaneously, propose a unified tangent-based analysis framework, and prove the first quantitative convergence guarantee for SOTA VE-based models with reverse PFODE. We also show that the drifted VESDE can balance different error terms and improve generated samples without training through synthetic and real-world experiments.

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ICLR Conference 2023 Conference Paper

Learning Adversarial Linear Mixture Markov Decision Processes with Bandit Feedback and Unknown Transition

Canzhe Zhao
Ruofeng Yang
Baoxiang Wang 0001
Shuai Li 0010

We study reinforcement learning (RL) with linear function approximation, unknown transition, and adversarial losses in the bandit feedback setting. Specifically, the unknown transition probability function is a linear mixture model \citep{AyoubJSWY20,ZhouGS21,HeZG22} with a given feature mapping, and the learner only observes the losses of the experienced state-action pairs instead of the whole loss function. We propose an efficient algorithm LSUOB-REPS which achieves $\widetilde{O}(dS^2\sqrt{K}+\sqrt{HSAK})$ regret guarantee with high probability, where $d$ is the ambient dimension of the feature mapping, $S$ is the size of the state space, $A$ is the size of the action space, $H$ is the episode length and $K$ is the number of episodes. Furthermore, we also prove a lower bound of order $\Omega(dH\sqrt{K}+\sqrt{HSAK})$ for this setting. To the best of our knowledge, we make the first step to establish a provably efficient algorithm with a sublinear regret guarantee in this challenging setting and solve the open problem of \citet{HeZG22}.

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NeurIPS Conference 2023 Conference Paper

Learning Adversarial Low-rank Markov Decision Processes with Unknown Transition and Full-information Feedback

Canzhe Zhao
Ruofeng Yang
Baoxiang Wang
Xuezhou Zhang
Shuai Li

In this work, we study the low-rank MDPs with adversarially changed losses in the full-information feedback setting. In particular, the unknown transition probability kernel admits a low-rank matrix decomposition \citep{REPUCB22}, and the loss functions may change adversarially but are revealed to the learner at the end of each episode. We propose a policy optimization-based algorithm POLO, and we prove that it attains the $\widetilde{O}(K^{\frac{5}{6}}A^{\frac{1}{2}}d\ln(1+M)/(1-\gamma)^2)$ regret guarantee, where $d$ is rank of the transition kernel (and hence the dimension of the unknown representations), $A$ is the cardinality of the action space, $M$ is the cardinality of the model class that contains all the plausible representations, and $\gamma$ is the discounted factor. Notably, our algorithm is oracle-efficient and has a regret guarantee with no dependence on the size of potentially arbitrarily large state space. Furthermore, we also prove an $\Omega(\frac{\gamma^2}{1-\gamma} \sqrt{d A K})$ regret lower bound for this problem, showing that low-rank MDPs are statistically more difficult to learn than linear MDPs in the regret minimization setting. To the best of our knowledge, we present the first algorithm that interleaves representation learning, exploration, and exploitation to achieve the sublinear regret guarantee for RL with nonlinear function approximation and adversarial losses.

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AAAI Conference 2023 Conference Paper

Understanding Representation Learnability of Nonlinear Self-Supervised Learning

Ruofeng Yang
Xiangyuan Li
Bo Jiang
Shuai Li

Self-supervised learning (SSL) has empirically shown its data representation learnability in many downstream tasks. There are only a few theoretical works on data representation learnability, and many of those focus on final data representation, treating the nonlinear neural network as a ``black box". However, the accurate learning results of neural networks are crucial for describing the data distribution features learned by SSL models. Our paper is the first to analyze the learning results of the nonlinear SSL model accurately. We consider a toy data distribution that contains two features: the label-related feature and the hidden feature. Unlike previous linear setting work that depends on closed-form solutions, we use the gradient descent algorithm to train a 1-layer nonlinear SSL model with a certain initialization region and prove that the model converges to a local minimum. Furthermore, different from the complex iterative analysis, we propose a new analysis process which uses the exact version of Inverse Function Theorem to accurately describe the features learned by the local minimum. With this local minimum, we prove that the nonlinear SSL model can capture the label-related feature and hidden feature at the same time. In contrast, the nonlinear supervised learning (SL) model can only learn the label-related feature. We also present the learning processes and results of the nonlinear SSL and SL model via simulation experiments.

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