NEURAL ARCHITECTURE SEARCH OF SPD MANIFOLD NETWORKS

Abstract

In this paper, we propose a new neural architecture search (NAS) problem of Symmetric Positive Definite (SPD) manifold networks. Unlike the conventional NAS problem, our problem requires to search for a unique computational cell called the SPD cell. This SPD cell serves as a basic building block of SPD neural architectures. An efficient solution to our problem is important to minimize the extraneous manual effort in the SPD neural architecture design. To accomplish this goal, we first introduce a geometrically rich and diverse SPD neural architecture search space for an efficient SPD cell design. Further, we model our new NAS problem using the supernet strategy, which models the architecture search problem as a one-shot training process of a single supernet. Based on the supernet modeling, we exploit a differentiable NAS algorithm on our relaxed continuous search space for SPD neural architecture search. Statistical evaluation of our method on drone, action, and emotion recognition tasks mostly provides better results than the stateof-the-art SPD networks and NAS algorithms. Empirical results show that our algorithm excels in discovering better SPD network design and providing models that are more than 3 times lighter than searched by state-of-the-art NAS algorithms.

1. INTRODUCTION

Designing a favorable neural network architecture for a given application requires a lot of time, effort, and domain expertise. To mitigate this issue, researchers in the recent years have started developing algorithms to automate the design process of neural network architectures (Zoph & Le, 2016; Zoph et al., 2018; Liu et al., 2017; 2018a; Real et al., 2019; Liu et al., 2018b; Tian et al., 2020) . Although these neural architecture search (NAS) algorithms have shown great potential to provide an optimal architecture for a given application, it is limited to handle architectures with Euclidean operations and representation. To deal with non-euclidean data representation and corresponding set of operations, researchers have barely proposed any NAS algorithms -to the best of our knowledge. It is well-known that manifold-valued data representation such as symmetric positive definite (SPD) matrices have shown overwhelming accomplishments in many real-world applications such as pedestrian detection (Tuzel et al., 2006; 2008) , magnetic resonance imaging analysis (Pennec et al., 2006) , action recognition (Harandi et al., 2014) , face recognition (Huang et al., 2014; 2015) , braincomputer interfaces (Barachant et al., 2011) , structure from motion (Kumar et al., 2018; Kumar, 2019) , etc. Also, in applications like diffusion tensor imaging of the brain, drone imaging, samples are collected directly as SPD's. As a result, neural network usage based on Euclidean data representation becomes inefficient for those applications. Consequently, this has led to the development of the SPD neural network (SPDNet) architectures for further improvements in these areas of research (Huang & Van Gool, 2017; Brooks et al., 2019) . However, these architectures are handcrafted, so the operations or the parameters defined for these networks generally change as per the application. This motivated us to propose a new NAS problem of SPD manifold networks. A solution to this problem can reduce unwanted efforts in SPDNet design. Compared to the traditional NAS problem, our NAS problem requires a new definition of computation cell and proposal for diverse SPD candidate operation set. In particular, we model the basic architecture cell with a specific directed acyclic graph (DAG), where each node is a latent SPD representation, and each edge corresponds to a SPD candidate operation. Here, the intermediate transformations between nodes respect the geometry of the SPD manifolds. For solving the suggested NAS problem, we exploit a supernet search strategy which models the architecture search problem as a one-shot training process of a supernet that comprises of a mixture 1

