A Compute and Communication Runtime Model for Loihi 2

Neuromorphic computers hold the potential to vastly improve the speed and efficiency of a wide range of computational kernels with their asynchronous, compute-memory co-located, spatially distributed, and scalable nature. However, performance models that are simple yet sufficiently expressive to predict runtime on actual neuromorphic hardware are lacking, posing a challenge for researchers and developers who strive to design fast algorithms and kernels. As breaking the memory bandwidth wall of conventional von-Neumann architectures is a primary neuromorphic advantage, modeling communication time is especially important. At the same time, modeling communication time is difficult, as complex congestion patterns arise in a heavily-loaded Network-on-Chip. In this work, we introduce the first max-affine lower-bound runtime model -- a multi-dimensional roofline model -- for Intel's Loihi 2 neuromorphic chip that quantitatively accounts for both compute and communication based on a suite of microbenchmarks. Despite being a lower-bound model, we observe a tight correspondence (Pearson correlation coefficient greater than or equal to 0.97) between our model's estimated runtime and the measured runtime on Loihi 2 for a neural network linear layer, i.e., matrix-vector multiplication, and for an example application, a Quadratic Unconstrained Binary Optimization solver. Furthermore, we derive analytical expressions for communication-bottlenecked runtime to study scalability of the linear layer, revealing an area-runtime tradeoff for different spatial workload configurations with linear to superlinear runtime scaling in layer size with a variety of constant factors. Our max-affine runtime model helps empower the design of high-speed algorithms and kernels for Loihi 2.