---
license: cc-by-4.0
task_categories:
  - feature-extraction
language:
  - en
tags:
  - transformer
  - attention
  - rope
  - power-law
  - scaling-laws
  - interpretability
  - llm
  - benchmark
pretty_name: TAF Attention-Decay Measurements
size_categories:
  - n<1K
configs:
  - config_name: default
    data_files:
      - split: train
        path: taf-attention-decay.jsonl
---

# 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](https://doi.org/10.5281/zenodo.19826343) — *Predicting How Transformers Attend*
> - Paper II: [10.5281/zenodo.19960573](https://doi.org/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:

```json
{
  "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

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

```python
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](https://github.com/karlesmarin/tafagent))
- **Underlying model weights**: respective HuggingFace licenses (consult each model's card)

## Citation

```bibtex
@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](https://github.com/karlesmarin/tafagent), `cli/diagnose_model.py`
- Browser tool: [karlesmarin.github.io/tafagent](https://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](https://doi.org/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:

```bash
# 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](https://github.com/karlesmarin/tafagent) (when uploaded)
- Lean code: `lean_taf/taf/Taf/Identities.lean`
- Paper 2 appendix A.4: step-by-step proofs of all 15 identities