The Anatomy of a Truth Direction: knowledge-dependent dimensionality, a relational law, and a convergent category geometry in small language models.
A training-free truth axis, read from the SVD of hidden-state minimal pairs: label-free up to one sign bit, evaluated held-out against permutation nulls, at a reading cost of two dot products per token. The axis is followed across four base models and two families, opened into a semantically signed mixture of per-category directions, and stress-tested at three scales under a declared spectral sign gauge.
Paper/The Anatomy of a Truth Direction.pdf
(Part I: the axis on one model; Part II: mechanics and geometry across
two families; stress tests and the knowledge-gated arrangement law)index.html)| path | content |
|---|---|
Paper/ |
the consolidated manuscript (tex + pdf) and its figures |
src/ |
every measurement tool: one command per reported number, no automatic verdicts |
Data/dictionaries/ |
exported truth dictionaries per model, at three scales (K=8 n=60 with six extra seeds, K=8 n=888, K=33 n=60), with consensus-gauge signed matrices (*_gauge.json) |
Data/know_rates/ |
behavioral per-relation know-rates (greedy string-match lower bound) |
Data/predictions/ |
predictions registered on file before the runs, confirmed and falsified alike |
drafts/ |
the paper trail: earlier versions, kept append-only |
Every exported artifact carries its identity (model, K, pairs, seed,
dataset revision) inside the file and in the filename; provenance tools
(src/inventario_dizionari.py, src/confronta_json.py,
src/identikit_pt.py) verify content by hash and cosine fingerprint.
Names can lie; axes cannot.
See REPRODUCING.md: golden rules, per-model landmark
table, and the exact command for every number in the paper.
pip install torch transformers datasets
python src/truth_probe.py signal --dataset builtin --with-2d --baseline --perm 200
The code was generated using an LLM, subject to my full decision-making and review, and to refine specific terminology necessitated by the translation from Italian to English.
Francesco Karim Vicidomini, The Anatomy of a Truth Direction, 2026. Code and data: doi:10.5281/zenodo.20938285. License: CC BY 4.0.