Lie Group Approach to Riemannian Batch Normalization

Khái niệm cốt lõi

Establishing a unified framework for Riemannian Batch Normalization on Lie groups.

Tóm tắt

This paper introduces a novel approach, LieBN, for batch normalization over Lie groups. It generalizes existing Lie groups on SPD manifolds and demonstrates its effectiveness through experiments in radar recognition, human action recognition, and EEG classification. The LieBN framework offers control over both the Riemannian mean and variance, showcasing improvements in various applications. By extending the concept of deformation to parameterized Lie groups on SPD manifolds, the paper presents a comprehensive solution for normalizing data efficiently.

Thống kê

Empirically, we focus on Symmetric Positive Definite (SPD) manifolds.
The code is available at https://github.com/GitZH-Chen/LieBN.git.
The architectures used are {20, 16, 8}, {93, 30}, and {63, 33} for different datasets.
The experiments were conducted with a learning rate of 5e−3 and a batch size of 30.
For the Hinss2021 dataset, a learning rate of 1e−3 with weight decay of 1e−4 was used.

Trích dẫn

"Extensive experiments demonstrate the advantage of our LieBN."
"Our LieBN achieves comparable or even better efficiency than SPDNetBN."
"The choice of metrics significantly impacts the performance of LieBN."

Thông tin chi tiết chính được chắt lọc từ

A Lie Group Approach to Riemannian Batch Normalization

by Ziheng Chen,... lúc arxiv.org 03-19-2024

https://arxiv.org/pdf/2403.11261.pdf

Yêu cầu sâu hơn

How can the concept of deformation be further explored in other applications beyond SPD manifolds

The concept of deformation, as applied to SPD manifolds in the LieBN framework, can be further explored in various applications beyond just SPD manifolds. One potential avenue for exploration is in the field of computer graphics and animation. Deformation techniques are commonly used to manipulate and transform shapes and objects in animations. By applying the principles of Lie groups and deformation, it may be possible to develop more efficient and accurate methods for animating complex shapes or characters.
Another area where deformation could be beneficial is in medical imaging. Deforming anatomical structures or tissues to better align with a standard template or model could improve diagnostic accuracy and treatment planning. This approach could help account for variations in anatomy across different individuals while maintaining important geometric properties.
Furthermore, exploring deformation concepts in natural language processing (NLP) tasks could lead to advancements in text generation models. By deforming word embeddings or sentence representations based on contextual information, it may be possible to enhance the coherence and semantic relevance of generated text.

What potential challenges may arise when extending LieBN to other types of Lie groups

Extending LieBN to other types of Lie groups may present several challenges that need careful consideration. One challenge is ensuring compatibility between the normalization operations defined for specific Lie groups and their corresponding metrics. Different Lie groups have distinct geometric structures, requiring tailored approaches for centering, biasing, and scaling operations within each group's metric space.
Another challenge lies in generalizing the concept of controlling mean and variance across diverse types of Lie groups. Each group may exhibit unique characteristics that impact how statistical moments are controlled during normalization processes. Adapting these control mechanisms effectively across various group structures will require a deep understanding of their intrinsic properties.
Additionally, scalability issues may arise when extending LieBN to high-dimensional or complex Lie groups with intricate geometries. Efficient computation methods must be developed to handle the increased computational complexity associated with larger group spaces while maintaining accuracy and performance.

How can the efficiency gains observed in EEG classification tasks be translated to other domains

The efficiency gains observed in EEG classification tasks using DSMLieBN can potentially be translated into other domains by leveraging its advantages such as improved performance with reduced training time.
One way this efficiency can benefit other domains is through faster model training cycles without compromising accuracy.
By implementing DSMLieBN into neural network architectures for image recognition tasks like object detection or segmentation,
it might accelerate model convergence rates leading
to quicker deployment times.
Moreover,
the enhanced performance achieved by DSMLieBN
could translate into higher prediction accuracies
in various applications such as healthcare diagnostics,
financial forecasting,
or natural language processing tasks.
Overall,
the efficiency gains demonstrated by DSMLieBN
in EEG classification highlight its potential utility
across diverse domains where rapid model development
and superior predictive capabilities are essential requirements.