Spectrum of non-Hermitian deep-Hebbian neural networks

Neural networks with recurrent asymmetric couplings are important to understand how episodic memories are encoded in the brain. Here, we integrate the experimental observation of wide synaptic integration window into our model of sequence retrieval in the continuous time dynamics. The model with non-normal neuron-interactions is theoretically studied by deriving a random matrix theory of the Jacobian matrix in neural dynamics. The spectra bears several distinct features, such as breaking rotational symmetry about the origin, and the emergence of nested voids within the spectrum boundary. The spectral density is thus highly non-uniformly distributed in the complex plane. The random matrix theory also predicts a transition to chaos. In particular, the edge of chaos provides computational benefits for the sequential retrieval of memories. Our work provides a systematic study of time-lagged correlations with arbitrary time delays, and thus can inspire future studies of a broad class of memory models, and even big data analysis of biological time series.

SideRT: A Real-time Pure Transformer Architecture for Single Image Depth Estimation

Since context modeling is critical for estimating depth from a single image, researchers put tremendous effort into obtaining global context. Many global manipulations are designed for traditional CNN-based architectures to overcome the locality of convolutions. Attention mechanisms or transformers originally designed for capturing long-range dependencies might be a better choice, but usually complicates architectures and could lead to a decrease in inference speed. In this work, we propose a pure transformer architecture called SideRT that can attain excellent predictions in real-time. In order to capture better global context, Cross-Scale Attention (CSA) and Multi-Scale Refinement (MSR) modules are designed to work collaboratively to fuse features of different scales efficiently. CSA modules focus on fusing features of high semantic similarities, while MSR modules aim to fuse features at corresponding positions. These two modules contain a few learnable parameters without convolutions, based on which a lightweight yet effective model is built. This architecture achieves state-of-the-art performances in real-time (51.3 FPS) and becomes much faster with a reasonable performance drop on a smaller backbone Swin-T (83.1 FPS). Furthermore, its performance surpasses the previous state-of-the-art by a large margin, improving AbsRel metric 6.9% on KITTI and 9.7% on NYU. To the best of our knowledge, this is the first work to show that transformer-based networks can attain state-of-the-art performance in real-time in the single image depth estimation field. Code will be made available soon.