12.6 A small language-model test

The Penn Treebank (PTB-small) study uses a word-level causal KET. Pretraining fits next-token prediction; LINCS then repairs only the incidence and route adapters. A deterministic 512-token vocabulary, context length eight, 512 training windows, 32 frozen repair-validation windows, and 128 test windows make the study deliberately small. The three seeds share five repair steps and four fixed train and validation tangent probes; embeddings, backbone, normalization, and vocabulary decoder remain frozen during repair.

Experiment: PTB-small registered result

Across three held-out seeds, base Kan RMS falls \(2.35\% \) and tangent Kan RMS falls \(2.32\% \). Overall test cross-entropy changes by \(+0.11\% \), perplexity by \(+0.48\% \), and non-<unk> cross-entropy by \(-0.41\% \). Every seed improves both structural blocks, so the registered criterion passes.

The vocabulary is truncated to 512 tokens and the test target <unk> rate is \(32.62\% \). The reported perplexity is therefore not comparable to standard full-vocabulary PTB. The experiment supports post-training structural repair with nearly preserved language behavior; it does not show an overall language-modeling improvement.