Backpropagation of Approximate Gradients for Stochastic Lattice Models

Abstract

Stochastic lattice models (s-LMs) are efficient computational tools for simulating non-equilibrium and morphogenetic systems. Yet, to date, no efficient method for fitting s-LM parameters to a set of objectives has been devised. The current state-of-the-art method for fitting s-LMs is Approximate- Bayesian Computation, a gradient-free general-purpose Bayesian inference method for estimating posterior distributions. While powerful, it is computationally expensive and quickly becomes intractable for high-dimensional parameter spaces. Gradient-based methods, particularly gradient descent algorithms making use of backpropagation could be significantly more efficient by directly fitting the parameters without needing to estimate the posterior. However, s-LMs are non-differentiable due to stochasticity and discreteness, preventing the use of backpropagation. Recent advances in Artificial Intelligence have introduced methods to circumvent this issue. The reparameterization trick re-enables backpropagation for stochastic models. Straight-through Estimation, on the other hand, enables backpropagation of approximate gradients for discrete models. We investigate the application of these methods for fitting four different s-LMs with respect to four common types of objectives. The results are promising, showing that backpropagation of approximate gradients can successfully be applied to various s-LM tasks. However, some challenges remain that will require further investigation.