A²M: Approximate Algebraic Memory Using Polynomials Rings

Emerging applications today operate on increasingly larger data sets, and as a result, the memory subsystem is prone to be a bottleneck in bandwidth and capacity. Many of these applications store data based on real world phenomena which often have continuity properties and can be approximated by mathematical functions. In this work, we view computer memory abstractly as a set of functions that map each address input to a data output. We propose Approximate Algebraic Memory (A²M), a specialized memory model that uses finite degree polynomials to approximate ranges of memory content with the desired properties. Specifically, A²M uses dedicated hardware to derive and store polynomial coefficients rather than memory data. In error resilient workloads, the benefits of this design is threefold: (1) high ratio memory compression, (2) high bandwidth accesses, and (3) direct computation on memory. We evaluate A²M's potential as an on-chip structure for general-purpose processors, and as a specialized read-only memory for neural network accelerators. Our results show that for CPU workloads, A²M yields minimal error (< 1%) at a fixed compression ratio of 16, and improves performance by 11.3% on average.