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, aiming to automate the design of SPD neural architectures. To address this problem, 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 with 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 state-of-the-art SPD networks and traditional NAS algorithms. Empirical results show that our algorithm excels in discovering better performing SPD network design and provides models that are more than three times lighter than searched by the state-of-the-art NAS algorithms.

Riemannian Local Mechanism for SPD Neural Networks

“…These approaches include Lie Group (Vemulapalli, Arrate, and Chellappa 2014), Hierarchical Recurrent Neural Network (HBRNN) (Du, Wang, and Wang 2015), Jointly Learning Heterogeneous Features (JOULE) (Hu et al 2015), Convolutional Two-Stream Network (Two stream) (Feichtenhofer, Pinz, and Zisserman 2016), Novel View (Rahmani and Mian 2016), Transition Forests (TF) (Garcia-Hernando and Kim 2017), Temporal Convolutional Network (TCN) (Kim and Reiter 2017), LSTM (Garcia-Hernando et al 2018) and Unified Hand and Object Model (Tekin, Bogo, and Pollefeys 2019). Besides, we also compare our approach against Euclidean network searching methods, DARTS (Liu, Simonyan, and Yang 2018) and FairDARTS (Chu et al 2020), following the setting in (Sukthanker et al 2021) by viewing SPD logarithm maps as Euclidean data.…”

A Gyrovector Space Approach for Symmetric Positive Semi-definite Matrix Learning

“…SPSD matrices are computational objects that are commonly encountered in various applied areas such as medical imaging [2,35], shape analysis [42], drone classification [6], image recognition [10], and human behavior analysis [9,14,15,17,32,41]. Due to the non-Euclidean nature of SPSD matrices, traditional machine learning algorithms usually fail to obtain good results when it comes to analyzing such data.…”