machine_learning

Low-rank approximations scale Gaussian-process regression, but they are typically judged by kernel accuracy rather than posterior-solve safety; this paper introduces a noise-floor rule for certified low-rank GP linear solves.

The companion core paper establishes, and machine-checks, a single identity: a transformer's forward pass can implement one gradient-descent step on an implicit least-squares objective (the ICL=GD mechanism).

The companion core paper establishes, and machine-checks, a single identity: a transformer's forward pass can implement one gradient-descent step on an implicit least-squares objective (the ICL=GD mechanism). This satellite asks what that verified identity forces to be true about *representational capacity and scaling*.

The companion core paper establishes, and machine-checks, a single identity: a transformer's forward pass can implement one gradient-descent step on an implicit least-squares objective (the ICL=GD mechanism).

We turn the gradient-descent account of in-context learning (ICL) into machine-checked mathematics and falsifiable predictions about real transformers. The formal target is the linear-attention regression identity: a forward pass can implement one gradient-descent step on an implicit least-squares objective.