karlexmarin/taf-attention-decay

TAF Attention-Decay Measurements

First public dataset of attention-decay exponent γ measurements across transformer LLMs. Companion to the Thermodynamic Attention Framework (TAF) papers by Carles Marín (2026):

• Paper I: 10.5281/zenodo.19826343 — Predicting How Transformers Attend
• Paper II: 10.5281/zenodo.19960573 — A Six-Axis Decomposition with the Learned Imprint, Sink-Dominated Precision Boundaries, Bimodal Phase Structure, and Honest Revisions

What it is

Each record is one γ measurement on one (model, corpus, precision) tuple. γ is the exponent of the power-law decay of attention weights at distance d:

A(d) ∝ d^(-γ)

predicted from RoPE geometry by the closed-form Padé formula

γ_padé = (2θ - T√2) / (2θ + T√2)

where θ is the RoPE base frequency and T is the evaluation context length.

Coverage

• 35 models across 13 families (Pythia, Qwen, Llama, Mistral, Gemma, Phi, OLMo, OLMoE, DeepSeek, StarCoder2, CodeLlama, GPT-J, SmolLM2, Falcon, Yi)
• 88 records total
• 2 corpora: real text (real_text, MongoDB English episodes) + random tokens (random_tokens)
• 2 precisions: 4-bit NF4 (BitsAndBytes) + bfloat16
• Includes random-init controls (E2 falsifier on Pythia 70M/410M/1B with random Gaussian init, no pretraining) — establishes that the slope ν = ∂γ/∂log₁₀(P) ≈ −1/(2π) is genuinely a training imprint, not architecture artifact.
• Pythia-70M training trajectory (9 checkpoints × 2 corpora = 18 records, sesion 32) — within-model γ across step1000 → step143000. Honest null result: trajectory does NOT converge to ν = −1/(2π); imprint constant emerges across-models, not within-model.
• Pythia-31m high-n robustness (n=60 prompts × 2 corpora = 2 records) — tightens CI on smallest pythia anchor.
• Yi-9B random_tokens (n=30) — fills 9B class gap in family panel.
• R²-direction rule extension (sesion 32 v2, 2026-05-02): 6 new bf16/4-bit paired measurements (Pythia-410M, Pythia-1.4B, StarCoder2-3B, Mistral-7B base + Instruct, Qwen2.5-7B base). Brings R²-direction rule panel from $n=5$ to $n=8$ paired (7/8 sign-correct; StarCoder2-3B is the new outlier).

Schema

Each JSONL row:

{
  "model_id": "EleutherAI/pythia-2.8b",
  "revision": "main",
  "arch": {
    "d_model": 2560, "n_heads": 32, "n_layers": 32, "d_head": 80,
    "n_kv_heads": 32, "n_params_M": 2800, "rope_theta": 10000,
    "T_train": 2048, "family": "pythia",
    "is_instruct": false, "is_moe": false
  },
  "measurement": {
    "gamma": 0.674,
    "gamma_ci95_lo": 0.65, "gamma_ci95_hi": 0.70,
    "method": "pade_d_alias_T",
    "fit": {"log_A": -3.21, "R2": 0.987, "n_points": 9, "delta_R2_power_minus_exp": 0.42},
    "T_eval": 2048,
    "corpus": "real_text",
    "n_prompts_per_distance": 150,
    "seeds": [42, 123, 7],
    "distances": [10, 20, 30, 50, 100, 200, 500, 1000, 2000],
    "precision": "4-bit-NF4"
  },
  "predictions": {
    "gamma_pade": 0.747,
    "gamma_random_pred": null,
    "imprint_constant_nu": -0.1592
  },
  "decision": "MED gamma=0.674 (R²=0.987)",
  "provenance": {
    "taf_version": "0.4",
    "paper_doi": "10.5281/zenodo.19826343",
    "source_file": "EleutherAI--pythia-2.8b_mongo.json",
    "tool": "tafagent/cli/diagnose_model.py + e4_extended_gamma.py",
    "license_data": "CC-BY-4.0",
    "license_code": "Apache-2.0"
  }
}

Usage

from datasets import load_dataset
ds = load_dataset("karlexmarin/taf-attention-decay")
print(ds["train"][0])

import pandas as pd
df = pd.read_json("taf-attention-decay.jsonl", lines=True)
df_text = df[df["measurement"].apply(lambda m: m["corpus"] == "real_text")]
df_text["gamma"] = df_text["measurement"].apply(lambda m: m["gamma"])
print(df_text.groupby("arch")["gamma"].describe())

Why this dataset exists

The attention-decay exponent γ is a single-number diagnostic of how "locally" or "globally" a transformer attends. It connects RoPE geometry to long-context behavior, KV-cache compression, NIAH retrieval, and hallucination rates — see the companion paper for details.

Until now, no public dataset of γ measurements existed across LLMs. This release closes that gap.

What's NOT in this dataset

• Raw attention tensors (TB-scale, redundant with model weights)
• Per-layer per-head γ-fields (separate dataset planned)
• Training-trajectory γ over checkpoints (Pythia-70M trajectory now INCLUDED as of sesion 32; broader panel still planned)
• Downstream task scores (use RULER, LongBench-v2, HELM separately)

License

• Data (this dataset): CC-BY-4.0
• Measurement code: Apache-2.0 (github.com/karlesmarin/tafagent)
• Underlying model weights: respective HuggingFace licenses (consult each model's card)

Citation

@dataset{marin2026taf_attention_decay,
  author    = {Mar{\'\i}n, Carles},
  title     = {TAF Attention-Decay Measurements},
  year      = {2026},
  publisher = {HuggingFace},
  url       = {https://huggingface.co/datasets/karlexmarin/taf-attention-decay},
  license   = {CC-BY-4.0}
}

@article{marin2026predicting,
  author    = {Mar{\'\i}n, Carles},
  title     = {Predicting How Transformers Attend: Analytic Power-Law Theory,
               Phase Transitions, and Practical Compression Tools},
  year      = {2026},
  doi       = {10.5281/zenodo.19826343},
  url       = {https://zenodo.org/records/19826343}
}

@article{marin2026taf2,
  author    = {Mar{\'\i}n, Carles},
  title     = {Predicting How Transformers Attend, Part II: A Six-Axis
               Decomposition with the Learned Imprint $\nu = -1/(2\pi)$,
               Sink-Dominated Precision Boundaries, Bimodal Phase Structure,
               and Honest Revisions},
  year      = {2026},
  publisher = {Zenodo},
  doi       = {10.5281/zenodo.19960573},
  url       = {https://doi.org/10.5281/zenodo.19960573}
}

Acknowledgements

This dataset would not exist without:

• EleutherAI for the Pythia panel (8 sizes from 14M to 2.8B), the primary scientific anchor of the framework.
• AI2 for OLMo / OLMoE.
• Meta, Mistral AI, Qwen team / Alibaba, Google DeepMind, Microsoft, HuggingFace SmolLM team, DeepSeek-AI, TII (Falcon), and BigScience (BLOOM) for releasing weights publicly.
• The HuggingFace Hub for free hosting that made the measurements possible.

Reproducibility

The measurement protocol is fully open:

• Tool: github.com/karlesmarin/tafagent, cli/diagnose_model.py
• Browser tool: karlesmarin.github.io/tafagent

Each row in this dataset can be reproduced from the original model weights via the open tool. If you find a discrepancy, please open an issue at the GitHub repo — refutations are welcome.

Updates

• 2026-04-29: Initial release (58 records, 32 models, 2 corpora, 2 precisions)
• 2026-04-30: Added analysis/games/game_O_results.json + game_P_results.json (hyperscaling identities + recursive derivations)
• 2026-05-01: ★ Sesion 32 paper 2 strengthening — +21 records (79 total):
  • Pythia-70M ν trajectory (9 ckpts × 2 corpora = 18) — within-model null documented
  • Yi-9B random_tokens (1) — 9B class gap filled
  • Pythia-31m high-n robustness (2, n=60 each) — tightened CI on smallest anchor
• 2026-05-02: ★ Paper II released on Zenodo (DOI 10.5281/zenodo.19960573) + 9 new records (88 total):
  • 3 bf16/4-bit pairs (Pythia-410M, Pythia-1.4B, StarCoder2-3B) — R²-direction rule extension
  • Mistral-7B base + Instruct (4-bit) — F9 RLHF pair, finds Δγ_RLHF = −0.133
  • Qwen2.5-7B base (4-bit) — completes the Qwen GQA RLHF pair
• 2026-05-01: ★ TAF v0.5 machine-verified consistency — 15 algebraic identities of TAF critical exponents formally proven via dual-tool approach:
  • Sage Groebner basis (algebraic decision in PolynomialRing(ℚ))
  • Lean Mathlib4 (dependent type theory, 1973/1973 jobs build success)
  • Including ★★ D-SAGE-1: 2η² + η·γ_χ + 1 = 0 quadratic identity
  • Paper 1 erratum: η = 2γ refuted algebraically; correct η = γ−1
  • First transformer-attention framework with formal machine-proof backing
• Future: training-trajectory data (Pythia checkpoint γ-flow), per-layer γ-fields, fp16 anchor measurements (DeepSeek-chat verification, Llama-3-8B cross-paper anchor)

Machine-verification artifacts

For independent verification of TAF critical exponent identities:

# Sage verification (~30s)
docker run --rm -v "$(pwd)/analysis:/work" sagemath/sagemath:latest \
    sage /work/sage_recursive_sweep_2026-04-30.sage

# Lean Mathlib4 verification (~10min first time, cached)
docker run --rm -v "$(pwd)/lean_taf:/work" \
    leanprovercommunity/lean:latest \
    -c "cd /work/taf && lake build"

• Sage results: analysis/sage_recursive_sweep_results.json
• Sage script: tafagent repo (when uploaded)
• Lean code: lean_taf/taf/Taf/Identities.lean
• Paper 2 appendix A.4: step-by-step proofs of all 15 identities