fraqtl-diagnostic 0.1.3

Fingerprint any transformer's compression potential in 30 minutes.

fraQtl Diagnostic

Fingerprint any transformer's compression potential — fast.

Measures per-layer:

• γ (stretched-exponential decay shape of the Hessian spectrum)
• knee (spectrum cutoff index)
• k95 (directions needed for 95% of eigenvalue energy)
• depth-law (how decay shape evolves across layers)
• compression potential + suggested bit budgets (Shannon-based)

Works on any HuggingFace-compatible transformer. ~3 min for a 0.5B model on A100, ~5 min for 1B, ~10 min for 7B.

---

Install

pip install fraqtl-diagnostic           # (once v0.1 lands on PyPI)
pip install -e /path/to/diagnostic-public  # editable install from source

Use

fraqtl analyze meta-llama/Llama-3.2-1B-Instruct

from fraqtl_diagnostic import analyze

report = analyze("meta-llama/Llama-3.2-1B-Instruct")
print(report.summary())
report.to_html("llama-1b_fingerprint.html")
report.to_png("llama-1b_fingerprint.png")

Try it on your GPU in one command (Modal)

If you don't want to fight Python-env dependencies locally, the fastest way to try the tool on a real model is via Modal (free tier gives you an A100):

# one-time: `pip install modal && modal setup`
# assumes a Modal secret named `huggingface` with an HF token

cd diagnostic-public/
modal run tests/modal_try.py --model-id Qwen/Qwen2.5-0.5B
modal run tests/modal_try.py --model-id TinyLlama/TinyLlama-1.1B-Chat-v1.0
modal run tests/modal_try.py --model-id mistralai/Mistral-7B-v0.1 --n-seqs 32 --seq-len 512

# pull the report back:
modal volume get fraqtl-hf-cache fraqtl-results/diagnostic-smoke ./reports/

---

What you get

Three outputs, same data, different framings:

• *.json — machine-readable per-layer fingerprint (feed into other tools)
• *.html — human-readable report with tables + embedded figure
• *.png — 4-panel figure: spectrum overlay, γ depth-law, k95/layer, summary

---

How to read the output

γ (stretched-exponential shape parameter)

The Hessian input-covariance spectrum λ_i of each linear projection is fit against λ_i ≈ exp(−β · i^γ + c). γ is the shape of the decay:

γ range	interpretation
γ ≈ 0.3	Stretched: fast head decay, long tail → compressible
γ ≈ 0.5	Typical for attention o_proj on Llama/Qwen/Mistral
γ ≈ 0.8	Typical for MLP down_proj on Llama/Qwen/Mistral
γ ≈ 1.0	Pure exponential decay — harder to compress aggressively
γ > 1.0	Super-exponential (flat head, sharp crash) — limited

Lower γ = more compression headroom.

k95 / dim

Fraction of eigendirections needed to capture 95% of eigenvalue energy. A value of 0.1 means "95% of the Hessian mass lives in the top 10% of directions" — prime territory for rank-preserving compression. Values typical on production transformers:

k95/dim range	implication
< 10%	very compressible, low-rank friendly
10–30%	common; most dense transformers fall here
30–50%	harder to compress without structured loss
> 50%	spectrum is near-uniform, limited headroom

Depth-law

Linear fit of γ across layer depth. A negative slope is the common case (shallow layers exponential, deep layers more stretched). The magnitude of the slope × R² tells you whether the shape is a stable architecture property or noisy per-layer.

Suggested bit budget

Shannon-derived bits-per-weight that the information-theoretic ceiling can tolerate at three conservatism tiers. This is a ceiling, not a prediction. Real PPL loss from compression depends on the recipe (sign correction, rank protection, per-model calibration). The diagnostic tells you how much room the math leaves; the actual compression run tells you how close to the ceiling you got.

---

Status

v0.1 (current): diagnostic metrics + suggested bit budgets. v1.0 (coming with Paper 3, ~4 weeks): adds Shannon-efficiency grading — "your model is at X% of the theoretical ceiling vs competitors at Y%."

Same pip install fraqtl-diagnostic — grading is a layer on top of diagnostic v0.1, not a separate tool.

---

How it works (one-paragraph summary)

For each target projection W : ℝ^d_in → ℝ^d_out, we capture the input covariance H = E[x^T x] on wikitext-2 calibration, then eigendecompose it. The spectrum λ_i encodes how much of the layer's Jacobian mass lives along each eigendirection of the input distribution. Tight universal shape (fixed γ across layers) implies compressible redundancy; a fat-tailed spectrum (high k95/dim) implies less. Shannon rate-distortion gives the information-theoretic floor D*(R) = geomean(λ) · 2^(−2R) at any bit budget R, which the diagnostic reports.

Full derivation + universality data across 8 architectures is in the forthcoming Paper 3.

---

Want to actually compress your model?

The diagnostic tells you the ceiling. The compression engine — sign correction, per-model calibration, fused MoE experts — is the closed part of the product:

fraqtl.ai/compress

---

License

Apache 2.0.