Abstract

I will talk about how modelling assumptions manifest themselves as algebraic structure in a variety of settings, including optimization, attention, and network parameters, and how we can algorithmically exploit that structure for better scaling laws with transformers. As part of this effort, I will present a unifying framework that enables searching among all linear operators expressible via an Einstein summation. This framework encompasses previously proposed structures, such as low-rank, Kronecker, Tensor-Train, and Monarch, along with many novel structures. We develop a taxonomy of all such operators based on their computational and algebraic properties, which provides insights into their compute-optimal scaling laws. Combining these insights with empirical evaluation, we identify a subset of structures that achieve better performance than dense layers as a function of training compute, which we then develop into a high-performance sparse mixture-of-experts layer.