GPT-2 XL: a cut Lk is the residual stream entering block k, at the last token of the host prompt. L0 is the embedding; the stream after the last block is the final readout, not a cut. The host's other positions are held at their own values at the same depth.GPT-2 XL block: pre-layer-norm, attention then MLP, each with its own addition. The cut is the raw stream before ln_1.
Architecture
GPT-2 XL: 48 blocks, residual width 1600, 1.5B parameters. Plain-torch forward from the cached weights, outside inference_mode, so the rate-of-change estimates can differentiate through it. Cuts: the residual stream before each block, L0–L47.
Site convention
State = the residual vector at the final token of a ten-token prompt. An injection replaces that position only, and causal masking confines its effect to that position onwards. A block needs a whole sequence rather than one vector, so the surrounding prompt is part of the measurement: it is a fixed host drawn from the bank by a declared rule and named in the bank line below.
Readouts
L2 at every cut deeper than the injection, L2 on the stream after the last block (final), and the forward KL of the perturbed logits to the base logits. Depth is what the plateau grows with, so the readout is a control rather than a fixed choice: 50 of them on this network.
The median radius is the sphere a rotation rides on and the median norm is what relative displacement is divided by, so both sit in the denominators of every panel below. Centre over spread says how far the activations sit from the origin relative to their own scatter: where it is large, rotating about the origin and about the bank mean are materially different measurements.
Provenance
Weights
Public gpt2-xl, final weights only. One checkpoint, so the training axis every other page in this family will carry is absent here by construction rather than by omission.
Sweep
Every one of the 48 cuts × %%SEED_COUNT%% seeds (%%SEED_LIST%%) × two rotation frames (about the origin, about the bank mean) × two base families, %%SCANS%% scans each over %%ANGLES%% angles from 0° to 90°: %%ENSEMBLES%% ensembles. The seed redraws the base and every direction, so the spread across seeds is what says whether a depth trend is real or is one unlucky base repeated down the network.
Analysis
cells_developmental.experiments.scan_1d; perturbation geometry executed from the vendored Heimersheim gist rather than transcribed (77ee738d4c66…). Conventions: docs/conventions.md.
Arora, Ge, Neyshabur and Zhang’s Figure 1 construction: a perturbation of a fixed fraction of a state’s norm is added at one cut, and each line shows how much of it survives at every deeper readout, relative to what that readout carries. Each point is a mean over bases and directions, and the band is the tenth to ninetieth percentile across bases — an attenuation every base agrees on and an average over disagreement are different findings, and the mean alone cannot tell them apart.