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Jiachen Yao

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7 papers

2 author rows

TMLR Journal 2025 Journal Article

A Theoretical Study of Neural Network Expressive Power via Manifold Topology

Jiachen Yao
Lingjie Yi
Mayank Goswami
Chao Chen

A prevalent assumption regarding real-world data is that it lies on or close to a low-dimensional manifold. When deploying a neural network on data manifolds, the required size, i.e., the number of neurons of the network, heavily depends on the intricacy of the underlying latent manifold. While significant advancements have been made in understanding the geometric attributes of manifolds, it's essential to recognize that topology, too, is a fundamental characteristic of manifolds. In this study, we investigate network expressive power in terms of the latent data manifold. Integrating both topological and geometric facets of the data manifold, we present a size upper bound of ReLU neural networks.

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ICLR Conference 2025 Conference Paper

Backdooring Vision-Language Models with Out-Of-Distribution Data

Weimin Lyu
Jiachen Yao
Saumya Gupta
Lu Pang 0006
Tao Sun 0009
Lingjie Yi
Lijie Hu
Haibin Ling

The emergence of Vision-Language Models (VLMs) represents a significant advancement in integrating computer vision with Large Language Models (LLMs) to generate detailed text descriptions from visual inputs. Despite their growing importance, the security of VLMs, particularly against backdoor attacks, is under explored. Moreover, prior works often assume attackers have access to the original training data, which is often unrealistic. In this paper, we address a more practical and challenging scenario where attackers must rely solely on Out-Of-Distribution (OOD) data. We introduce VLOOD (Backdoor Vision-Language Models using Out-of-Distribution Data), a novel approach with two key contributions: (1) demonstrating backdoor attacks on VLMs in complex image-to-text tasks while minimizing degradation of the original semantics under poisoned inputs, and (2) proposing innovative techniques for backdoor injection without requiring any access to the original training data. Our evaluation on image captioning and visual question answering (VQA) tasks confirms the effectiveness of VLOOD, revealing a critical security vulnerability in VLMs and laying the foundation for future research on securing multimodal models against sophisticated threats.

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ICLR Conference 2025 Conference Paper

Geometry of Long-Tailed Representation Learning: Rebalancing Features for Skewed Distributions

Lingjie Yi
Jiachen Yao
Weimin Lyu
Haibin Ling
Raphael Douady
Chao Chen 0012

Deep learning has achieved significant success by training on balanced datasets. However, real-world data often exhibit long-tailed distributions. Empirical studies have revealed that long-tailed data skew data representations, where head classes dominate the feature space. Many methods have been proposed to empirically rectify the skewed representations. However, a clear understanding of the underlying cause and extent of this skew remains lacking. In this study, we provide a comprehensive theoretical analysis to elucidate how long-tailed data affect feature distributions, deriving the conditions under which centers of tail classes shrink together or even collapse into a single point. This results in overlapping feature distributions of tail classes, making features in the overlapping regions inseparable. Moreover, we demonstrate that merely empirically correcting the skewed representations of the training data is insufficient to separate the overlapping features due to distribution shifts between the training and real data. To address these challenges, we propose a novel long-tailed representation learning method, FeatRecon. It reconstructs the feature space in order to arrange features from different classes into symmetricial and linearly separable regions. This, in turn, enhances the model’s robustness to long-tailed data. We validate the effectiveness of our method through extensive experiments on the CIFAR-10-LT, CIFAR-100-LT, ImageNet-LT, and iNaturalist 2018 datasets.

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NeurIPS Conference 2025 Conference Paper

Guided Diffusion Sampling on Function Spaces with Applications to PDEs

Jiachen Yao
Abbas Mammadov
Julius Berner
Gavin Kerrigan
Jong Chul Ye
Kamyar Azizzadenesheli
Animashree Anandkumar

We propose a general framework for conditional sampling in PDE-based inverse problems, targeting the recovery of whole solutions from extremely sparse or noisy measurements. This is accomplished by a function-space diffusion model and plug-and-play guidance for conditioning. Our method first trains an unconditional discretization-agnostic denoising model using neural operator architectures. At inference, we refine the samples to satisfy sparse observation data via a gradient-based guidance mechanism. Through rigorous mathematical analysis, we extend Tweedie's formula to infinite-dimensional Banach spaces, providing the theoretical foundation for our posterior sampling approach. Our method (FunDPS) accurately captures posterior distribution in function spaces under minimal supervision and severe data scarcity. Across five PDE tasks with only 3\% observation, our method achieves an average 32\% accuracy improvement over state-of-the-art fixed-resolution diffusion baselines while reducing sampling steps by 4x. Furthermore, multi-resolution fine-tuning ensures strong cross-resolution generalizability and speedup. To the best of our knowledge, this is the first diffusion-based framework to operate independently of discretization, offering a practical and flexible solution for forward and inverse problems in the context of PDEs. Code is available at https: //github. com/neuraloperator/FunDPS.

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NeurIPS Conference 2024 Conference Paper

PINNacle: A Comprehensive Benchmark of Physics-Informed Neural Networks for Solving PDEs

Zhongkai Hao
Jiachen Yao
Chang Su
Hang Su
Ziao Wang
Fanzhi Lu
Zeyu Xia
Yichi Zhang

While significant progress has been made on Physics-Informed Neural Networks (PINNs), a comprehensive comparison of these methods across a wide range of Partial Differential Equations (PDEs) is still lacking. This study introduces PINNacle, a benchmarking tool designed to fill this gap. PINNacle provides a diverse dataset, comprising over 20 distinct PDEs from various domains, including heat conduction, fluid dynamics, biology, and electromagnetics. These PDEs encapsulate key challenges inherent to real-world problems, such as complex geometry, multi-scale phenomena, nonlinearity, and high dimensionality. PINNacle also offers a user-friendly toolbox, incorporating about 10 state-of-the-art PINN methods for systematic evaluation and comparison. We have conducted extensive experiments with these methods, offering insights into their strengths and weaknesses. In addition to providing a standardized means of assessing performance, PINNacle also offers an in-depth analysis to guide future research, particularly in areas such as domain decomposition methods and loss reweighting for handling multi-scale problems and complex geometry. To the best of our knowledge, it is the largest benchmark with a diverse and comprehensive evaluation that will undoubtedly foster further research in PINNs.

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ICLR Conference 2023 Conference Paper

Learning to Segment from Noisy Annotations: A Spatial Correction Approach

Jiachen Yao
Yikai Zhang 0003
Songzhu Zheng
Mayank Goswami 0001
Prateek Prasanna
Chao Chen 0012

Noisy labels can significantly affect the performance of deep neural networks (DNNs). In medical image segmentation tasks, annotations are error-prone due to the high demand in annotation time and in the annotators' expertise. Existing methods mostly tackle label noise in classification tasks. Their independent-noise assumptions do not fit label noise in segmentation task. In this paper, we propose a novel noise model for segmentation problems that encodes spatial correlation and bias, which are prominent in segmentation annotations. Further, to mitigate such label noise, we propose a label correction method to recover true label progressively. We provide theoretical guarantees of the correctness of the proposed method. Experiments show that our approach outperforms current state-of-the-art methods on both synthetic and real-world noisy annotations.

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ICML Conference 2023 Conference Paper

MultiAdam: Parameter-wise Scale-invariant Optimizer for Multiscale Training of Physics-informed Neural Networks

Jiachen Yao
Chang Su
Zhongkai Hao
Songming Liu
Hang Su 0006
Jun Zhu 0001

Physics-informed Neural Networks (PINNs) have recently achieved remarkable progress in solving Partial Differential Equations (PDEs) in various fields by minimizing a weighted sum of PDE loss and boundary loss. However, there are several critical challenges in the training of PINNs, including the lack of theoretical frameworks and the imbalance between PDE loss and boundary loss. In this paper, we present an analysis of second-order non-homogeneous PDEs, which are classified into three categories and applicable to various common problems. We also characterize the connections between the training loss and actual error, guaranteeing convergence under mild conditions. The theoretical analysis inspires us to further propose MultiAdam, a scale-invariant optimizer that leverages gradient momentum to parameter-wisely balance the loss terms. Extensive experiment results on multiple problems from different physical domains demonstrate that our MultiAdam solver can improve the predictive accuracy by 1-2 orders of magnitude compared with strong baselines.

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