Inferring genotype-phenotype maps using attention models

Predicting phenotype from genotype is a central challenge in genetics. Traditional approaches in quantitative genetics typically analyze this problem using methods based on linear regression. These methods generally assume that the genetic architecture of complex traits can be parameterized in terms of an additive model, where the effects of loci are independent, plus (in some cases) pairwise epistatic interactions between loci. However, these models struggle to analyze more complex patterns of epistasis or subtle gene-environment interactions. Recent advances in machine learning, particularly attention-based models, offer a promising alternative. Initially developed for natural language processing, attention-based models excel at capturing context-dependent interactions and have shown exceptional performance in predicting protein structure and function. Here, we apply attention-based models to quantitative genetics. We analyze the performance of this attention-based approach in predicting phenotype from genotype using simulated data across a range of models with increasing epistatic complexity, and using experimental data from a recent quantitative trait locus mapping study in budding yeast. We find that our model demonstrates superior out-of-sample predictions in epistatic regimes compared to standard methods. We also explore a more general multi-environment attention-based model to jointly analyze genotype-phenotype maps across multiple environments and show that such architectures can be used for "transfer learning" - predicting phenotypes in novel environments with limited training data.

Cortical Computation via Iterative Constructions

We study Boolean functions of an arbitrary number of input variables that can be realized by simple iterative constructions based on constant-size primitives. This restricted type of construction needs little global coordination or control and thus is a candidate for neurally feasible computation. Valiant's construction of a majority function can be realized in this manner and, as we show, can be generalized to any uniform threshold function. We study the rate of convergence, finding that while linear convergence to the correct function can be achieved for any threshold using a fixed set of primitives, for quadratic convergence, the size of the primitives must grow as the threshold approaches 0 or 1. We also study finite realizations of this process and the learnability of the functions realized. We show that the constructions realized are accurate outside a small interval near the target threshold, where the size of the construction grows as the inverse square of the interval width. This phenomenon, that errors are higher closer to thresholds (and thresholds closer to the boundary are harder to represent), is a well-known cognitive finding.