Measuring computational regimes inside LLMs via attribution graph geometry.

We extract attribution graphs from model internals (via transcoders/SAEs) and compute metrics that characterize different computational patterns. Different task types produce measurably different geometric signatures.

Using inertia tensor analysis (adapted from AIDA-TNG galaxy morphology):

All task domains are prolate (cigar-shaped in metric space) — variance concentrates along a dominant axis rather than spreading uniformly.

Works:

• Task type classification (grammar vs reasoning)
• Computational complexity estimation
• Anomaly detection (out-of-distribution inputs)

Doesn't work:

• Hallucination detection
• Truthfulness detection (d=0.05)
• Output correctness prediction

The model processes hallucinations with the same internal geometry as truthful statements.

1. Dec 2025: Started with hallucination detection via feature spectroscopy
2. Jan 2026: Discovered most "signal" was text length confounding (r=0.98)
3. Feb 2026: Pivoted to task-type diagnostics with length control
4. Mar 2026: Added geometric analysis — domain shapes in metric space

See archive/disproved/ for early experiments with honest disclaimers.

notebooks/                    # START HERE - narrative series
  01_introduction.ipynb       # What this project discovers
  02_the_journey.ipynb        # From hallucination detection to task diagnostics
  03_methodology.ipynb        # How we extract and analyze metrics
  04_core_results.ipynb       # Main findings with visualizations
  05_negative_results.ipynb   # What doesn't work (and why)

experiments/
  core/                       # Main analyses (geometric_analysis.py, etc.)
  statistics/                 # Statistical tests
  visualization/              # Figure generation
  utilities/                  # Shared code
  _archive/                   # Historical experiments
  _runs/                      # Timestamped analysis outputs

figures/paper/                # Core figures
data/results/                 # Computed metrics (JSON)
scripts/                      # Modal GPU runners
archive/disproved/            # Early work with honest post-mortems

pip install -e .

# Run geometric analysis
python experiments/core/geometric_analysis.py --analyze

# Generate figures
python experiments/visualization/generate_figures.py

# Compute attribution metrics (GPU, parallel)
modal run scripts/modal_general_attribution.py \
  --input-file data/domain_analysis/domain_samples.json \
  --output-file data/results/domain_attribution_metrics.json

1. Attribution Graphs: Extract causal graphs via circuit-tracer showing feature→feature influence during inference

2. Metrics:

   • mean_influence: Average edge weight (causal strength)
   • concentration: Gini coefficient of influence distribution
   • mean_activation: Feature activation strength

3. Length Control: Residualize against text length (raw n_active correlates r=0.98 with tokens)

4. Geometric Analysis: Treat domain samples as point clouds in 6D metric space, compute shape via inertia tensor eigendecomposition (axis ratios, effective dimensionality)

• Requires model internals — SAE/transcoder access (currently Gemma 2 via Goodfire)
• Compute intensive — ~30 sec/sample on A100
• Measures structure, not correctness — can't detect hallucinations
• Length confounding — must residualize (raw n_active is artifact)

MIT