Transformers Can Implement Preconditioned Richardson Iteration for In-Context Gaussian Kernel Regression

arXiv:2605.08475 · cs.LG, cs.AI, cs.NA, math.NA, math.OC · Submitted 2026-05-08 · Read on arXiv

cs.LG, cs.AI, cs.NA, math.NA, math.OC

Submitted: 2026-05-08

Updated: 2026-09-25

Terminology

• Transformer — 213× in this paper · explained in 2 episodes
• In-Context Learning — 17× in this paper · explained in 4 episodes
• Ablation — 16× in this paper · explained in 1 episode
• Accuracy — 7× in this paper · explained in 1 episode
• Transformer Architecture — 7× in this paper · explained in 2 episodes
• Alignment — 6× in this paper · explained in 1 episode
• Regularization — 6× in this paper · explained in 3 episodes
• Ablation Studies — 4× in this paper · explained in 1 episode
• Cosine Similarity — 4× in this paper · explained in 3 episodes
• In-Context Learning (ICL) — 3× in this paper · explained in 5 episodes
• Linear probe — 3× in this paper · explained in 2 episodes
• Core — 2× in this paper · explained in 2 episodes
• Curse of Dimensionality — 2× in this paper · explained in 6 episodes
• Hilbert Space — 2× in this paper · explained in 2 episodes
• Linear Probing — 2× in this paper · explained in 2 episodes
• Approximation Bound — 1× in this paper · explained in 1 episode
• Bayesian Inference — 1× in this paper · explained in 5 episodes
• Convergence Guarantees — 1× in this paper · explained in 3 episodes
• Embeddings — 1× in this paper · explained in 2 episodes
• Generalization — 1× in this paper · explained in 13 episodes
• Generalization Bounds — 1× in this paper · explained in 2 episodes
• Neural Network Approximation — 1× in this paper · explained in 2 episodes
• Reproducing Kernel Hilbert Space — 1× in this paper
• Reproducing Kernel Hilbert Space (RKHS) — 1× in this paper · explained in 3 episodes
• Robustness — 1× in this paper · explained in 5 episodes
• Standard Gradient Descent — 1× in this paper
• Trace — 1× in this paper · explained in 2 episodes

Sources

• Softmax $\geq$ Linear: Transformers may learn to classify in-context by kernel gradient descent
• Towards Understanding the Universality of Transformers for Next-Token Prediction
• Understanding In-Context Learning on Structured Manifolds: Bridging Attention to Kernel Methods
• LLaMA: Open and Efficient Foundation Language Models
• Training Dynamics of In-Context Learning in Linear Attention

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