The Thermodynamic Costs of Simple Linear Regression
For researchers concerned with the energetic costs of machine learning, this work provides foundational thermodynamic bounds for a basic modeling algorithm.
This paper derives thermodynamic lower bounds on the energy costs of simple linear regression, both exact and via stochastic gradient descent, and uses these to obtain energy-cost-aware scaling laws for optimal dataset size given a generalization error demand.
The construction of models from data is a significant contributor to the energetic costs of computation. Because of this, understanding how foundational thermodynamic bounds apply to modeling algorithms will be increasingly important. Here, we study the thermodynamic costs of a basic and fundamental modeling algorithm: simple linear regression. Following Landauer, we approximate the thermodynamic lower bound on irreversibly performing both exact linear regression and linear regression via stochastic gradient descent as implemented on floating-point numbers. From this, we derive energycost aware scaling laws for the optimal dataset size for training a linear regression model given a generalization error dependent demand for inference. Additionally, we discuss a method to lower bound the entropy production from the mismatch cost for algorithms with continuous input variables.