Transformer solves simple regression exactly using new attention method
In-context learning of solution to simple linear regression task using transformer with masked linear self-attention
Machine Learning
Summary
Solving math problems like finding the best line to fit points can be done with computers in many ways. The paper shows that a special kind of computer model called a transformer can learn to solve simple line-fitting exactly, using a neat trick with its attention method. Instead of the usual way of gradually improving guesses, it finds the perfect answer directly. The authors also tested their method and showed it works well under certain conditions.
What this means in practice
- •For machine learning engineers: Design transformer-based models that exactly solve simple linear regression tasks for improved model interpretability and efficiency.
- •For data scientists: Build more accurate in-context solvers for regression problems without relying on iterative gradient methods, improving model training outcomes.
Authors
Katsuyuki Hagiwara
Abstract
In-context learning is a remarkable property of transformers and has recently received a lot of interest. In many studies of in-context learning, it has been shown that transformers are capable of implementing solvers for linear and non-linear regression problems, in which the most of them implement gradient descent algorithm. However, it is still unclear whether those implementations have actually been acquired through training. In this paper, we constructed a transformer with masked linear self-attention, which in-context learns the least squares estimate in a simple regression task. The point here is that the closed form (analytical) solution is obtained by using layer normalization rather than an approximate solution based on the gradient descent algorithm. Then, we showed an experimental example, in which, by taking the non-uniqueness of the transformer representation into account, our implementation for a closed form solution is used in the transformer trained with the l1 regularization when the target output is the least squares estimate.