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.