Linear Computation Coding

TL;DR

This paper introduces computation coding for linear functions, presenting an algorithm that reduces the computational cost of matrix-vector multiplication by decomposing matrices into codebook wiring matrices, significantly decreasing the number of addition units needed.

Contribution

It proposes a novel computation coding method for linear functions, enabling efficient matrix multiplication with minimal addition units, especially beneficial for deep neural network implementations.

Findings

Reduces the number of addition units required for matrix multiplication.

Achieves 16-bit signed integer accuracy with minimal hardware.

Decreases computational complexity in neural network matrix operations.

Abstract

We introduce the new concept of computation coding. Similar to how rate-distortion theory is concerned with the lossy compression of data, computation coding deals with the lossy computation of functions. Particularizing to linear functions, we present an algorithm to reduce the computational cost of multiplying an arbitrary given matrix with an unknown column vector. The algorithm decomposes the given matrix into the product of codebook wiring matrices whose entries are either zero or signed integer powers of two. For a typical implementation of deep neural networks, the proposed algorithm reduces the number of required addition units several times. To achieve the accuracy of 16-bit signed integer arithmetic for 4k-vectors, no multipliers and only 1.5 adders per matrix entry are needed.