Author name cluster

Lingshen He

Possible papers associated with this exact author name in Arrow. This page groups case-insensitive exact name matches and is not a full identity disambiguation profile.

6 papers

2 author rows

NeurIPS Conference 2025 Conference Paper

Projective Equivariant Networks via Second-order Fundamental Differential Invariants

Yikang Li
Yeqing Qiu
Yuxuan Chen
Lingshen He
Lexiang Hu
Zhouchen Lin

Equivariant networks enhance model efficiency and generalization by embedding symmetry priors into their architectures. However, most existing methods, primarily based on group convolutions and steerable convolutions, face significant limitations when dealing with complex transformation groups, particularly the projective group, which plays a crucial role in vision. In this work, we tackle the challenge by constructing projective equivariant networks based on differential invariants. Using the moving frame method with a carefully selected cross section tailored for multi-dimensional functions, we derive a complete and concise set of second-order fundamental differential invariants of the projective group. We provide a rigorous analysis of the properties and transformation relationships of their underlying components, yielding a further simplified and unified set of fundamental differential invariants, which facilitates both theoretical analysis and practical applications. Building on this foundation, we develop PDINet, the first framework for deep projective equivariant networks, achieving full projective equivariance without discretizing or sampling the group. Empirical results on the projectively transformed STL-10 and Imagenette datasets show that PDINet achieves improvements of 11. 39\% and 5. 66\% in accuracy over the respective standard baselines under out-of-distribution settings, demonstrating its strong generalization to complex geometric transformations.

PDF Details

ICLR Conference 2023 Conference Paper

Neural ePDOs: Spatially Adaptive Equivariant Partial Differential Operator Based Networks

Lingshen He
Yuxuan Chen
Zhengyang Shen
Yibo Yang
Zhouchen Lin

Endowing deep learning models with symmetry priors can lead to a considerable performance improvement. As an interesting bridge between physics and deep learning, the equivariant partial differential operators (PDOs) have drawn much researchers' attention recently. However, to ensure the PDOs translation equivariance, previous works have to require coefficient matrices to be constant and spatially shared for their linearity, which could lead to the sub-optimal feature learning at each position. In this work, we propose a novel nonlinear PDOs scheme that is both spatially adaptive and translation equivariant. The coefficient matrices are obtained by local features through a generator rather than spatially shared. Besides, we establish a new theory on incorporating more equivariance like rotations for such PDOs. Based on our theoretical results, we efficiently implement the generator with an equivariant multilayer perceptron (EMLP). As such equivariant PDOs are generated by neural networks, we call them Neural ePDOs. In experiments, we show that our method can significantly improve previous works with smaller model size in various datasets. Especially, we achieve the state-of-the-art performance on the MNIST-rot dataset with only half parameters of the previous best model.

Details

NeurIPS Conference 2021 Conference Paper

Efficient Equivariant Network

Lingshen He
Yuxuan Chen
Zhengyang Shen
Yiming Dong
Yisen Wang
Zhouchen Lin

Convolutional neural networks (CNNs) have dominated the field of Computer Vision and achieved great success due to their built-in translation equivariance. Group equivariant CNNs (G-CNNs) that incorporate more equivariance can significantly improve the performance of conventional CNNs. However, G-CNNs are faced with two major challenges: \emph{spatial-agnostic problem} and \emph{expensive computational cost}. In this work, we propose a general framework of previous equivariant models, which includes G-CNNs and equivariant self-attention layers as special cases. Under this framework, we explicitly decompose the feature aggregation operation into a kernel generator and an encoder, and decouple the spatial and extra geometric dimensions in the computation. Therefore, our filters are essentially dynamic rather than being spatial-agnostic. We further show that our \emph{E}quivariant model is parameter \emph{E}fficient and computation \emph{E}fficient by complexity analysis, and also data \emph{E}fficient by experiments, so we call our model $E^4$-Net. Extensive experiments verify that our model can significantly improve previous works with smaller model size. Especially, under the setting of training on $1/5$ data of CIFAR10, our model improves G-CNNs by $5\%+$ accuracy, while using only $56\%$ parameters and $68\%$ FLOPs.

PDF Details

NeurIPS Conference 2021 Conference Paper

Gauge Equivariant Transformer

Lingshen He
Yiming Dong
Yisen Wang
Dacheng Tao
Zhouchen Lin

Attention mechanism has shown great performance and efficiency in a lot of deep learning models, in which relative position encoding plays a crucial role. However, when introducing attention to manifolds, there is no canonical local coordinate system to parameterize neighborhoods. To address this issue, we propose an equivariant transformer to make our model agnostic to the orientation of local coordinate systems (\textit{i. e. }, gauge equivariant), which employs multi-head self-attention to jointly incorporate both position-based and content-based information. To enhance expressive ability, we adopt regular field of cyclic groups as feature fields in intermediate layers, and propose a novel method to parallel transport the feature vectors in these fields. In addition, we project the position vector of each point onto its local coordinate system to disentangle the orientation of the coordinate system in ambient space (\textit{i. e. }, global coordinate system), achieving rotation invariance. To the best of our knowledge, we are the first to introduce gauge equivariance to self-attention, thus name our model Gauge Equivariant Transformer (GET), which can be efficiently implemented on triangle meshes. Extensive experiments show that GET achieves state-of-the-art performance on two common recognition tasks.

PDF Details

ICML Conference 2020 Conference Paper

Implicit Euler Skip Connections: Enhancing Adversarial Robustness via Numerical Stability

Mingjie Li 0007
Lingshen He
Zhouchen Lin

Deep neural networks have achieved great success in various areas, but recent works have found that neural networks are vulnerable to adversarial attacks, which leads to a hot topic nowadays. Although many approaches have been proposed to enhance the robustness of neural networks, few of them explored robust architectures for neural networks. On this account, we try to address such an issue from the perspective of dynamic system in this work. By viewing ResNet as an explicit Euler discretization of an ordinary differential equation (ODE), for the first time, we find that the adversarial robustness of ResNet is connected to the numerical stability of the corresponding dynamic system, i. e. , more stable numerical schemes may correspond to more robust deep networks. Furthermore, inspired by the implicit Euler method for solving numerical ODE problems, we propose Implicit Euler skip connections (IE-Skips) by modifying the original skip connection in ResNet or its variants. Then we theoretically prove its advantages under the adversarial attack and the experimental results show that our ResNet with IE-Skips can largely improve the robustness and the generalization ability under adversarial attacks when compared with the vanilla ResNet of the same parameter size.

Details

ICML Conference 2020 Conference Paper

PDO-eConvs: Partial Differential Operator Based Equivariant Convolutions

Zhengyang Shen
Lingshen He
Zhouchen Lin
Jinwen Ma

Recent research has shown that incorporating equivariance into neural network architectures is very helpful, and there have been some works investigating the equivariance of networks under group actions. However, as digital images and feature maps are on the discrete meshgrid, corresponding equivariance-preserving transformation groups are very limited. In this work, we deal with this issue from the connection between convolutions and partial differential operators (PDOs). In theory, assuming inputs to be smooth, we transform PDOs and propose a system which is equivariant to a much more general continuous group, the $n$-dimension Euclidean group. In implementation, we discretize the system using the numerical schemes of PDOs, deriving approximately equivariant convolutions (PDO-eConvs). Theoretically, the approximation error of PDO-eConvs is of the quadratic order. It is the first time that the error analysis is provided when the equivariance is approximate. Extensive experiments on rotated MNIST and natural image classification show that PDO-eConvs perform competitively yet use parameters much more efficiently. Particularly, compared with Wide ResNets, our methods result in better results using only 12. 6% parameters.

Details