A lying group approach to normalizing pomegranate payments

Links table

Abstract and 1 introduction

2 introductory

3. Reconsidering normalization

3.1 Reconsidering the normalization

3.2 Reconsidering the current RBN

4 Rimani’s normalization of lying groups

5 Liebn on lying groups of SPD and 5.1 distorted lying groups from SPD

5.2 Liebn on SPD

6 experiments

6.1 Experimental results

7 conclusions, recognition, and references

The contents of the appendix

Symbols

B Kyes Basic in SPDNET and TSMNET

C statistical results for expanding in Liben

D Liebn as a natural generalization component for Euclidean Bn

The field momentum for the field to classify EEG

And BackProPagation is a matrix function

G details and experiences Liebn on the SPD terrifying

H preliminary experiences on spin matrix

I am evidence of Limas and theories in the main paper

a summary

There are multiple value measurements in many applications within computer vision and machine learning. Recently neuropathic studies have been extended to distress, simultaneously, normalization techniques have also been adapted to several districts, referred to as Riemannian normalization. However, most of the current Riemannian normalization methods have been derived in a dedicated way and applied only to specific distress. This paper creates a unified framework for RBN’s normalization techniques on lying groups.

Our framework provides a theoretical guarantee of the control of both the Mediterranean and the contrast in Riemannian. Experimental, we focus on identical, similar and similar ramifications (SPD), which have three distinct types of lying group structures. Using the concept of deformation, we generalize the current lying groups to the SPD terribly into three families of the parameter lying groups. Then the specific normalization layers caused by these lying groups are proposed to the SPD. We explain the effectiveness of our approaches through three groups of experiments: recognition of the radar, identifying human work, and classifying electrical classification (EEG). The symbol is available on https://github.com/gitzh-chen/liebn.git.

1 introduction

Over the past decade or so, deep nerve networks (DNNS) have made remarkable progress in various scientific fields (Hochreiter & Schmidhuber, 1997; Krizhevsky et al., 2012; He et al., 2016; Vaswani et al Traditionally, the DNNS was developed with the main assumption of the Euclidean engineering inherent in the input data. However, there are a large number of applications in which the inherent spaces are defined by non -sophisticated structures such as BronStein et al., 2017.

To address this issue, the researchers tried to extend different types of DNNS to the distress based on the theories of Riemannian (Huang & Van Gool, 2017; Huang et al., 2017; 2018; Ganea et al Al.

Motivated by the great success of normalization techniques within DNNS (IFFE & Szegedy, 2015; Ba et al., 2016; ulyanov et al For multiple value data. Brooks and others. (2019B) Riemannian (RBN) is specially designed for SPD, with the ability to organize Riemannian average. This approach has been more improved in Kobler et al. (2022b) to expand the scope of control of the contrast. However, the above -mentioned methods are restricted within the changing scale (AIM) on the SPD, which limits the ability to apply and generally.

On the other hand, Chakraborty (2020) suggested two distinct Riemannian normalization frameworks, one designed for Riemannian homogeneous spaces and other restaurants for Lie Matrix groups. However, the normalization designed for the homogeneous spaces cannot regulate the average or contrast, while the normalization approach to the lies of the matrix is ​​limited to a specific type of distance (Chakraborty, 2020, SEC. 3.2). The initial Riemannian normalization frame remains able to control both the average and contrast.

Given that the normalization of the IOFFE & Szegedy, 2015 is the primary model of different types of normalization, our paper only focuses on RBN currently and can be easily extended to other normalization techniques. Since many multi -value measurements, including SPD, SO, SO, and private Euclidean groups (SE), we direct our attention to lying groups. We suggest a general framework for RBN on lying groups, referred to as Liebn, and verifying the validity of our approach to normalizing both the Mediterranean and contrast in Riemannian.

On the experimental side, we focus on the SPD, where three distinct types of lying groups have been identified in literature. We generalize these current lying groups in parameter forms through the concept of deformation. Next, we display our LIEBN framework on the SPD manifolds under these lying groups and suggest specific normalization layers. Intensive experiences conducted on the widely used SPD standards show the effectiveness of our framework. We highlight that our work is completely different in theory from Brooks et al. (2019B); Kobler et al. (2022A); If and others. (2020), more general than Chakraborty (2020). Previous RBN styles are designed either for a specific meter or scale (Brooks et al., 2019b; Kobler et al Liebn we have medium normalization and contrast to general lying groups.

In short, our main contributions are as follows: (a) The framework of normalization of a general lie group with statistics of the first and second degree statistics that can be controlled, and (B) the building specified for the Liebn layers on the SPD is based on three distorted groups and applied to SPD networks Nervousness. Because of the page limits, all proofs are placed in the application. I.