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Yuling Yan

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8 papers

2 author rows

TMLR Journal 2025 Journal Article

Gaussian mixture layers for neural networks

Sinho Chewi
Philippe Rigollet
Yuling Yan

The mean-field theory for two-layer neural networks considers infinitely wide networks that are linearly parameterized by a probability measure over the parameter space. This nonparametric perspective has significantly advanced both the theoretical and conceptual understanding of neural networks, with substantial efforts made to validate its applicability to networks of moderate width. In this work, we explore the opposite direction, investigating whether dynamics can be directly implemented over probability measures. Specifically, we employ Gaussian mixture models as a flexible and expressive parametric family of distributions together with the theory of Wasserstein gradient flows to derive training dynamics for such measures. Our approach introduces a new type of layer—the Gaussian mixture (GM) layer—that can be integrated into neural network architectures. As a proof of concept, we validate our proposal through experiments on simple classification tasks, where a GM layer achieves test performance comparable to that of a two-layer fully connected network. Furthermore, we examine the behavior of these dynamics and demonstrate numerically that GM layers exhibit markedly different behavior compared to classical fully connected layers, even when the latter are large enough to be considered in the mean-field regime.

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JMLR Journal 2025 Journal Article

O(d/T) Convergence Theory for Diffusion Probabilistic Models under Minimal Assumptions

Gen Li
Yuling Yan

Score-based diffusion models, which generate new data by learning to reverse a diffusion process that perturbs data from the target distribution into noise, have achieved remarkable success across various generative tasks. Despite their superior empirical performance, existing theoretical guarantees are often constrained by stringent assumptions or suboptimal convergence rates. In this paper, we establish a fast convergence theory for the denoising diffusion probabilistic model (DDPM), a widely used SDE-based sampler, under minimal assumptions. Our analysis shows that, provided $\ell_{2}$-accurate estimates of the score functions, the total variation distance between the target and generated distributions is upper bounded by $O(d/T)$ (ignoring logarithmic factors), where $d$ is the data dimensionality and $T$ is the number of steps. This result holds for any target distribution with finite first-order moment. Moreover, we show that with careful coefficient design, the convergence rate improves to $O(k/T)$, where $k$ is the intrinsic dimension of the target data distribution. This highlights the ability of DDPM to automatically adapt to unknown low-dimensional structures, a common feature of natural image distributions. These results are achieved through a novel set of analytical tools that provides a fine-grained characterization of how the error propagates at each step of the reverse process. [abs] [ pdf ][ bib ] &copy JMLR 2025. ( edit, beta )

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ICLR Conference 2025 Conference Paper

O(d/T) Convergence Theory for Diffusion Probabilistic Models under Minimal Assumptions

Gen Li 0005
Yuling Yan

Score-based diffusion models, which generate new data by learning to reverse a diffusion process that perturbs data from the target distribution into noise, have achieved remarkable success across various generative tasks. Despite their superior empirical performance, existing theoretical guarantees are often constrained by stringent assumptions or suboptimal convergence rates. In this paper, we establish a fast convergence theory for the denoising diffusion probabilistic model (DDPM), a widely used SDE-based sampler, under minimal assumptions. Our analysis shows that, provided $\ell_{2}$-accurate estimates of the score functions, the total variation distance between the target and generated distributions is upper bounded by $O(d/T)$ (ignoring logarithmic factors), where $d$ is the data dimensionality and $T$ is the number of steps. This result holds for any target distribution with finite first-order moment. To our knowledge, this improves upon existing convergence theory for the DDPM sampler, while imposing minimal assumptions on the target data distribution and score estimates. This is achieved through a novel set of analytical tools that provides a fine-grained characterization of how the error propagates at each step of the reverse process.

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NeurIPS Conference 2024 Conference Paper

Adapting to Unknown Low-Dimensional Structures in Score-Based Diffusion Models

Gen Li
Yuling Yan

This paper investigates score-based diffusion models when the underlying target distribution is concentrated on or near low-dimensional manifolds within the higher-dimensional space in which they formally reside, a common characteristic of natural image distributions. Despite previous efforts to understand the data generation process of diffusion models, existing theoretical support remains highly suboptimal in the presence of low-dimensional structure, which we strengthen in this paper. For the popular Denoising Diffusion Probabilistic Model (DDPM), we find that the dependency of the error incurred within each denoising step on the ambient dimension $d$ is in general unavoidable. We further identify a unique design of coefficients that yields a converges rate at the order of $O(k^{2}/\sqrt{T})$ (up to log factors), where $k$ is the intrinsic dimension of the target distribution and $T$ is the number of steps. This represents the first theoretical demonstration that the DDPM sampler can adapt to unknown low-dimensional structures in the target distribution, highlighting the critical importance of coefficient design. All of this is achieved by a novel set of analysis tools that characterize the algorithmic dynamics in a more deterministic manner.

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NeurIPS Conference 2021 Conference Paper

Sample-Efficient Reinforcement Learning for Linearly-Parameterized MDPs with a Generative Model

Bingyan Wang
Yuling Yan
Jianqing Fan

The curse of dimensionality is a widely known issue in reinforcement learning (RL). In the tabular setting where the state space $\mathcal{S}$ and the action space $\mathcal{A}$ are both finite, to obtain a near optimal policy with sampling access to a generative model, the minimax optimal sample complexity scales linearly with $|\mathcal{S}|\times|\mathcal{A}|$, which can be prohibitively large when $\mathcal{S}$ or $\mathcal{A}$ is large. This paper considers a Markov decision process (MDP) that admits a set of state-action features, which can linearly express (or approximate) its probability transition kernel. We show that a model-based approach (resp. $~$Q-learning) provably learns an $\varepsilon$-optimal policy (resp. $~$Q-function) with high probability as soon as the sample size exceeds the order of $\frac{K}{(1-\gamma)^{3}\varepsilon^{2}}$ (resp. $~$$\frac{K}{(1-\gamma)^{4}\varepsilon^{2}}$), up to some logarithmic factor. Here $K$ is the feature dimension and $\gamma\in(0, 1)$ is the discount factor of the MDP. Both sample complexity bounds are provably tight, and our result for the model-based approach matches the minimax lower bound. Our results show that for arbitrarily large-scale MDP, both the model-based approach and Q-learning are sample-efficient when $K$ is relatively small, and hence the title of this paper.

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NeurIPS Conference 2020 Conference Paper

Efficient Clustering for Stretched Mixtures: Landscape and Optimality

Kaizheng Wang
Yuling Yan
Mateo Diaz

This paper considers a canonical clustering problem where one receives unlabeled samples drawn from a balanced mixture of two elliptical distributions and aims for a classifier to estimate the labels. Many popular methods including PCA and k-means require individual components of the mixture to be somewhat spherical, and perform poorly when they are stretched. To overcome this issue, we propose a non-convex program seeking for an affine transform to turn the data into a one-dimensional point cloud concentrating around -1 and 1, after which clustering becomes easy. Our theoretical contributions are two-fold: (1) we show that the non-convex loss function exhibits desirable geometric properties when the sample size exceeds some constant multiple of the dimension, and (2) we leverage this to prove that an efficient first-order algorithm achieves near-optimal statistical precision without good initialization. We also propose a general methodology for clustering with flexible choices of feature transforms and loss objectives.

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ICRA Conference 2017 Conference Paper

Estimation of EMG signal for shoulder joint based on EEG signals for the control of upper-limb power assistance devices

Hongbo Liang
Chi Zhu 0001
Masataka Yoshioka
Naoya Ueda
Ye Tian
Yu Iwata
Haoyong Yu
Feng Duan 0006

Brain-Machine Interface (BMI) has emerged as a powerful tool for assisting disabled people and for augmenting human performance. Up so far, no studies have succeeded in the power augmentation for the multi-DOFs robot based on EEG signals, especially for the complex shoulder joint. In this work, we propose an electromyography (EMG) estimation method based on electroencephalography (EEG) signals to realize the power assistance. The positions of the electrodes where the motion information of shoulder joint is effectively and exactly extracted are discussed, and a linear model that correlates the EMG to the EEG signal is constructed utilizing motion-related features extracted from multi-location EEG measurements. The constructed model is used to estimate the human muscular activity of shoulder joint from EEG using Principal Component Analysis (PCA) method. The proposed approach is experimentally verified, and an average correlation coefficients are as high as about 0. 90 for different subjects are obtained between the estimated and the actually measured EMG signal. Our results suggest that the estimation of EMG based on EEG is feasible. This demonstrates the potential of using EEG signals to support human activities via brain-machine interface.

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IROS Conference 2010 Conference Paper

A new type of omnidirectional wheelchair robot for walking support and power assistance

Chi Zhu 0001
Masashi Oda
Masayuki Suzuki
Xiang Luo 0001
Hideomi Watanabe
Yuling Yan

Up to now, many robotic aids for the elderly's walking support or the disabled's walking rehabilitation are reported, and numerous electrical-powered wheelchairs are developed. In this paper, a new kind of omnidirectional wheelchair typed robot is developed. The robot not only can accomplish the walking support or walking rehabilitation as the elderly or the disabled walk, but also can realize the power assistance for a caregiver when he/she pushes the robot to move. The basic structure of the robot is described, and the omnidirectional mobility of the robot is analyzed. Further, an admittance based human-machine interaction controller is introduced for power assistance. Experiments are implemented, and the experimental results show that the pushing force can be reduced and well controlled arbitrarily as designed. The development purposes of the robot for walking support and power assistance are achieved.

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