Loop Amplitude Regression Eval

---
name: loop-amplitude-regression-eval
description: Evaluates a model's ability to accurately regress one-loop scattering amplitudes across a high-dimensional kinematic phase space. It specifically probes precision in challenging regions and the reliability of uncertainty quantification inherent to Bayesian neural networks. Use when the user wants to benchmark on One-loop gg→γγg(g) amplitudes, or asks about evaluating this task. Reports Δ (relative amplitude error).
metadata:
  skill_kind: dataset_eval
  source_arxiv: 2206.14831
  bibtex_key: [REDACTED]
  confidence: high
---

# loop-amplitude-regression-eval

> Loop Amplitudes from Precision Networks — Badger et al. (2022) (arXiv:2206.14831, 2022)

## What this evaluates

Evaluates a model's ability to accurately regress one-loop scattering amplitudes across a high-dimensional kinematic phase space. It specifically probes precision in challenging regions and the reliability of uncertainty quantification inherent to Bayesian neural networks.

## Datasets

- **One-loop gg→γγg(g) amplitudes** — total 960000; splits: train (90000), test (870000)

## Metrics

- `Δ (relative amplitude error)` **(primary)** — range: other
  - Δ_j = (A_{j,NN} / A_{j,true}) - 1. The evaluation focuses on the width/distribution of Δ across the dataset rather than a single scalar.

## Input / output format

**Input**: External 4-momenta of final-state partons, defining a 20-dimensional phase space subject to detector-inspired kinematic cuts.

**Output**: Predicted real-valued one-loop scattering amplitude.

## Scoring recipe

```python
def compute_delta(nn_pred, true_amp):
    return (nn_pred / true_amp) - 1.0
# Report distribution width (e.g., std or percentile range) of delta across test set
```

## Common pitfalls

- The metric Δ is a relative error, so its scale depends on the magnitude of the true amplitude; reporting only mean/median Δ can mask large errors in low-amplitude regions.
- The paper emphasizes the distribution width of Δ as the figure of merit, not a standard point-estimate metric like MSE or MAE.
- High precision (per-mille level) is required, making standard regression benchmarks insufficient without careful outlier handling or boosting strategies.

## Evidence (verbatim from paper)

> The main figure of merit compares the true and the NN-amplitudes for a set of training or test data points, Δ_j^(train) = A_{j,NN}/A_{j,train} - 1 or Δ_j^(test) = A_{j,NN}/A_{j,test} - 1, where j runs over amplitude data points and we subtract 1 compared with the original paper [8].

## Citation

```bibtex
@misc{badger2022loopamplitudes,
  title={Loop Amplitudes from Precision Networks},
  author={Badger et al. (2022)},
  year={2022},
  note={arXiv:2206.14831}
}
```

- arXiv: 2206.14831