Vectorized Adjoint Sensitivity Method for Graph Convolutional Neural Ordinary Differential Equations

This document, as the title stated, is meant to provide a vectorized implementation of adjoint dynamics calculation for Graph Convolutional Neural Ordinary Differential Equations (GCDE). The adjoint sensitivity method is the gradient approximation method for neural ODEs that replaces the back propagation. When implemented on libraries such as PyTorch or Tensorflow, the adjoint can be calculated by autograd functions without the need for a hand-derived formula. In applications such as edge computing and in memristor crossbars, however, autograds are not available, and therefore we need a vectorized derivation of adjoint dynamics to efficiently map the system on hardware. This document will go over the basics, then move on to derive the vectorized adjoint dynamics for GCDE.

HYPERLOCK: In-Memory Hyperdimensional Encryption in Memristor Crossbar Array

We present a novel cryptography architecture based on memristor crossbar array, binary hypervectors, and neural network. Utilizing the stochastic and unclonable nature of memristor crossbar and error tolerance of binary hypervectors and neural network, implementation of the algorithm on memristor crossbar simulation is made possible. We demonstrate that with an increasing dimension of the binary hypervectors, the non-idealities in the memristor circuit can be effectively controlled. At the fine level of controlled crossbar non-ideality, noise from memristor circuit can be used to encrypt data while being sufficiently interpretable by neural network for decryption. We applied our algorithm on image cryptography for proof of concept, and to text en/decryption with 100% decryption accuracy despite crossbar noises. Our work shows the potential and feasibility of using memristor crossbars as an unclonable stochastic encoder unit of cryptography on top of their existing functionality as a vector-matrix multiplication acceleration device.