This project evaluated the use of emerging spintronic memory devices for robust and efficient variational inference schemes. Variational inference (VI) schemes, which constrain the distribution for each weight to be a Gaussian distribution with a mean and standard deviation, are a tractable method for calculating posterior distributions of weights in a Bayesian neural network such that this neural network can also be trained using the powerful backpropagation algorithm. Our project focuses on domain-wall magnetic tunnel junctions (DW-MTJs), a powerful multi-functional spintronic synapse design that can achieve low power switching while also opening the pathway towards repeatable, analog operation using fabricated notches. Our initial efforts to employ DW-MTJs as an all-in-one stochastic synapse with both a mean and standard deviation didn’t end up meeting the quality metrics for hardware-friendly VI. In the future, new device stacks and methods for expressive anisotropy modification may make this idea still possible. However, as a fall back that immediately satisfies our requirements, we invented and detailed how the combination of a DW-MTJ synapse encoding the mean and a probabilistic Bayes-MTJ device, programmed via a ferroelectric or ionically modifiable layer, can robustly and expressively implement VI. This design includes a physics-informed small circuit model, that was scaled up to perform and demonstrate rigorous uncertainty quantification applications, up to and including small convolutional networks on a grayscale image classification task, and larger (Residual) networks implementing multi-channel image classification. Lastly, as these results and ideas all depend upon the idea of an inference application where weights (spintronic memory states) remain non-volatile, the retention of these synapses for the notched case was further interrogated. These investigations revealed and emphasized the importance of both notch geometry and anisotropy modification in order to further enhance the endurance of written spintronic states. In the near future, these results will be mapped to effective predictions for room temperature and elevated operation DW-MTJ memory retention, and experimentally verified when devices become available.
Neural networks are largely based on matrix computations. During forward inference, the most heavily used compute kernel is the matrix-vector multiplication (MVM): $W \vec{x} $. Inference is a first frontier for the deployment of next-generation hardware for neural network applications, as it is more readily deployed in edge devices, such as mobile devices or embedded processors with size, weight, and power constraints. Inference is also easier to implement in analog systems than training, which has more stringent device requirements. The main processing kernel used during inference is the MVM.
This presentation concludes in situ computation enables new approaches to linear algebra problems which can be both more effective and more efficient as compared to conventional digital systems. Preconditioning is well-suited to analog computation due to the tolerance for approximate solutions. When combined with prior work on in situ MVM for scientific computing, analog preconditioning can enable significant speedups for important linear algebra applications.