A single-head softmax transformer with O(log(1/ε)) blocks and O(√(N/ε)) MLP width implements preconditioned Richardson iteration to achieve ε-accurate Gaussian KRR predictions on length-N prompts under bounded data.
In-context language learning: Architectures and algorithms
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Transformers Can Implement Preconditioned Richardson Iteration for In-Context Gaussian Kernel Regression
A single-head softmax transformer with O(log(1/ε)) blocks and O(√(N/ε)) MLP width implements preconditioned Richardson iteration to achieve ε-accurate Gaussian KRR predictions on length-N prompts under bounded data.