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cognitive state measurement for transformers

SAE feature decomposition reveals a cognitive property — commitment intensity — that is statistically significant, beats standard uncertainty baselines, and is completely invisible to three independent raw-activation probes across four transformer architectures.

SAEs are not interpretability aids. They are the spectroscopes of artificial cognition.

---

results at a glance

 cross-architecture     d = 0.584      Fisher p = 0.00018
 beats logit entropy    AUC 0.663      vs 0.607 (p = 0.013)
 2D cognitive map       65% halluc     danger zone vs 22% safe
 SAE necessity          3 probes       4 architectures — all null
 architectures          Gemma-2-2B     Llama-3.2-1B confirmed
 patents                3 filed        US 64/020,489 · 64/021,113 · 64/026,964

---

what is commitment intensity?

                    ┌─────────────────────────────────────────┐
                    │          S = max(C∆) / K_τ              │
                    │                                         │
                    │   C∆(t) = coherence_late - coherence_early   │
                    │   K_τ   = count of spikes above threshold    │
                    │                                         │
                    │   mathematically equivalent to:         │
                    │   S = M × IPR(event_locations)          │
                    │                                         │
                    │   IPR = inverse participation ratio     │
                    │   (condensed-matter physics, 70+ years) │
                    └─────────────────────────────────────────┘

     high S ──► few intense commitment events ──► attractor lock-in
     low  S ──► many distributed events      ──► exploration

---

cross-architecture replication

  MODEL                    LAYERS    WINDOW     d        AUC      p
  ─────────────────────────────────────────────────────────────────
  Gemma-2-2B-IT              26     [0, 7)    +0.535    0.663    0.013
  Llama-3.2-1B-Instruct      16     [0, 20)   +0.635    0.641    0.005
  ─────────────────────────────────────────────────────────────────
  POOLED                                      +0.584             0.00018

commitment window scales with model depth. fewer layers → more tokens to settle.

head-to-head vs standard methods

  SIGNAL                AUC      p          SOURCE
  ──────────────────────────────────────────────────
  S_early (ours)       0.663    0.013  ◄── SAE coherence
  logit entropy        0.607    0.053      standard
  logprob              0.559    0.291      standard
  top-2 margin         0.477    0.624      standard
  ──────────────────────────────────────────────────
  S is the ONLY feature reaching significance.
  r(S, entropy) = -0.17 — nearly independent signals.

SAE necessity — the probes that failed

  PROBE                  ARCHITECTURES    FISHER p    RESULT
  ─────────────────────────────────────────────────────────
  top-k IPR                    4           0.619      null
  cross-layer cosine           4           0.948      null
  cognitive fingerprint        4             —        AUC 0.566
  ─────────────────────────────────────────────────────────
  SAE-based S (Gemma)          1           0.013      ✓ confirmed
  SAE-based S (Llama)          1           0.005      ✓ confirmed
  ─────────────────────────────────────────────────────────
  SAE decomposition is doing irreplaceable work.

---

quick start

from coherence_steerer_ext import CoherenceSteererExt

steerer = CoherenceSteererExt(model_name="google/gemma-2-2b-it")
result = steerer.generate_with_entropy(
    "Q: What is the capital of France?\nA:",
    max_tokens=20
)

# per-token commitment + entropy
for i, (cd, ent) in enumerate(zip(
    result.c_delta_trajectory,
    result.entropy_trajectory
)):
    print(f"  t={i}: C_delta={cd:+.4f}  entropy={ent:.3f}")

API

curl -X POST https://fathom-gpu.darkcity.wtf/scan \
  -H "Content-Type: application/json" \
  -d '{"prompt": "What did Paul Revere say?", "max_tokens": 20}'

returns per-token c_delta, entropy, logprob + cognitive zone classification:

  SAFE       low commitment + low entropy      grounded retrieval
  UNCERTAIN  low commitment + high entropy     exploring
  RISKY      high commitment + low entropy     confident — verify
  DANGER     high commitment + high entropy    hallucination signature

---

the fathom cognitive atlas

  the first public, cross-architecture cognitive state atlas of
  open-weight language models.

  v0.3 — H1 supported (pre-registered replication)
    n = 6 model family pairs (Gemma-2, Gemma-3, Llama-3.2-3B,
                              Llama-3.2-1B, Qwen2.5-3B, Qwen2.5-1.5B)
    mean LOO cos = +0.769   bootstrap CI [+0.571, +0.869]
    permutation p = 0.0315  (one-sided, 2000 shuffles)

  pre-registered in PREREG_v0.3_attractor_replication.md before
  any v0.3 data was captured. analysis ran without modification.

→ full writeup: atlas/FINDINGS_v0.3.md → atlas overview + roadmap: atlas/README.md → sealed pre-registration: atlas/PREREG_v0.3_attractor_replication.md → rigor audit: atlas/FINDINGS_bulletproof_audit.md

---

repository structure

  fathom-research/
  │
  ├── README.md                  you are here
  ├── coherence_steerer.py       core SAE measurement engine
  ├── depth_scorer.py            depth scoring via circuit attribution
  ├── fathom_oversight.py        D-axis + K/C/S measurement pipeline
  ├── requirements.txt           dependencies
  │
  ├── paper/                     ICML 2026 workshop submission (LaTeX)
  ├── atlas/                     cognitive atlas v0.3 (see above)
  │   ├── probes/                probe_set_v0.1.json, hash-pinned
  │   ├── captures/              12 versioned per-model JSONs
  │   ├── analysis/              bootstrap, permutation, estimator validation
  │   ├── FINDINGS_*.md          v0.1 → v0.2 → v0.2.1 → v0.3 trail
  │   └── PREREG_v0.3_*.md       sealed pre-registration
  │
  ├── analysis/                  D-axis + S-axis analysis scripts
  ├── runners/                   experiment drivers
  ├── probes/                    SAE-free cross-architecture probes
  ├── verification/              reproducibility assertions
  ├── api/                       Fathom Scan API v2 + interactive demo
  │
  ├── findings/                  documented results
  ├── prereg/                    OSF pre-registrations (locked before data)
  ├── docs/                      strategy, vision, applications
  │
  ├── figures/                   publication figures (PDF + PNG)
  └── truthfulqa_results/        experimental data (JSON)

reproducibility

python verification/verify_all_claims.py   # 17 assertions from raw data
python verification/verify_s_axis.py       # 14 S-axis specific assertions

all claims in the paper verified to reproduce exactly from saved JSON data.

---

citation

@article{rodabaugh2026fathom,
  title   = {Fathom: Cognitive Measurement Instruments for
             Transformer Internals via SAE Feature Coherence Geometry},
  author  = {Rodabaugh, Alexander},
  year    = {2026},
  note    = {Zenodo concept DOI. doi:10.5281/zenodo.19326174}
}

@misc{rodabaugh2026atlas,
  title  = {The Fathom Cognitive Atlas v0.3: Pre-registered
            Cross-Architecture Replication of the RLHF Attractor},
  author = {Rodabaugh, Alexander},
  year   = {2026},
  note   = {Zenodo concept DOI. doi:10.5281/zenodo.19326174}
}

license

research code — patent pending (US 64/020,489 · 64/021,113 · 64/026,964)

---

Fathom Intelligence · fathom.darkflobi.com · Alexander Rodabaugh · 2026