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This research demonstrates a transformer architecture utilizing linear self-attention that learns the analytical least squares solution for regression tasks via layer normalization, rather than relying on standard gradient descent approximations. The study provides empirical evidence of how in-context learning can acquire closed-form mathematical solutions through specific architectural choices and regularization techniques like L1 constraints.
In-context learning of closed form solution to simple linear regression task using transformer with linear self-attention
arXiv:2607.15819v1 Announce Type: cross 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 solver 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 construct a transformer with 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 approximately obtained by using layer normalization rather than an approximate solution based on gradient descent algorithm. Then, we show an experimental example, in which our implementation is mainly used in the transformer trained with l1 regularization when the target output is the least squares estimate.
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 solver 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 construct a transformer with 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 approximately obtained by using layer normalization rather than an approximate solution based on gradient descent algorithm. Then, we show an experimental example, in which our implementation is mainly used in the transformer trained with l1 regularization when the target output is the least squares estimate.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
arXiv:2607.15819 [cs.LG]
(or arXiv:2607.15819v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2607.15819 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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