# Scaling laws for amplitude surrogates

arXiv: https://arxiv.org/abs/2601.13308 · HTML: https://mlsanity.com/paper/2601.13308/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 65 of its 126 references that are in the map.
- First posted on arXiv 19 Jan 2026.

## Builds on (most cited first, 30 of 65)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [Wide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descent](https://mlsanity.com/paper/1902.06720/) (2019)
- [Deep Neural Networks as Gaussian Processes](https://mlsanity.com/paper/1711.00165/) (2017)
- [Deep Learning Scaling is Predictable, Empirically](https://mlsanity.com/paper/1712.00409/) (2017)
- [Scaling Laws for Autoregressive Generative Modeling](https://mlsanity.com/paper/2010.14701/) (2020)
- [The generalization error of random features regression: Precise asymptotics and double descent curve](https://mlsanity.com/paper/1908.05355/) (2019)
- [Scaling Data-Constrained Language Models](https://mlsanity.com/paper/2305.16264/) (2023)
- [Explaining Neural Scaling Laws](https://mlsanity.com/paper/2102.06701/) (2021)
- [Deep Evidential Regression](https://mlsanity.com/paper/1910.02600/) (2019)
- [Tensor Programs V: Tuning Large Neural Networks via Zero-Shot Hyperparameter Transfer](https://mlsanity.com/paper/2203.03466/) (2022)
- [Intrinsic dimension of data representations in deep neural networks](https://mlsanity.com/paper/1905.12784/) (2019)
- [Estimating the intrinsic dimension of datasets by a minimal neighborhood information](https://mlsanity.com/paper/1803.06992/) (2018)
- [A Constructive Prediction of the Generalization Error Across Scales](https://mlsanity.com/paper/1909.12673/) (2019)
- [Spectrum Dependent Learning Curves in Kernel Regression and Wide Neural Networks](https://mlsanity.com/paper/2002.02561/) (2020)
- [Feature Learning in Infinite-Width Neural Networks](https://mlsanity.com/paper/2011.14522/) (2020)
- [Scaling Laws and Compute-Optimal Training Beyond Fixed Training Durations](https://mlsanity.com/paper/2405.18392/) (2024)
- [A Dynamical Model of Neural Scaling Laws](https://mlsanity.com/paper/2402.01092/) (2024)
- [Repulsive Deep Ensembles are Bayesian](https://mlsanity.com/paper/2106.11642/) (2021)
- [Tensor Programs VI: Feature Learning in Infinite-Depth Neural Networks](https://mlsanity.com/paper/2310.02244/) (2023)
- [Getting ViT in Shape: Scaling Laws for Compute-Optimal Model Design](https://mlsanity.com/paper/2305.13035/) (2023)
- [Resolving Discrepancies in Compute-Optimal Scaling of Language Models](https://mlsanity.com/paper/2406.19146/) (2024)
- [CaloGAN: Simulating 3D High Energy Particle Showers in Multi-Layer Electromagnetic Calorimeters with Generative Adversarial Networks](https://mlsanity.com/paper/1712.10321/) (2017)
- [Depthwise Hyperparameter Transfer in Residual Networks: Dynamics and Scaling Limit](https://mlsanity.com/paper/2309.16620/) (2023)
- [Mining gold from implicit models to improve likelihood-free inference](https://mlsanity.com/paper/1805.12244/) (2018)
- [Accelerating Science with Generative Adversarial Networks: An Application to 3D Particle Showers in Multi-Layer Calorimeters](https://mlsanity.com/paper/1705.02355/) (2017)
- [A Neural Scaling Law from the Dimension of the Data Manifold](https://mlsanity.com/paper/2004.10802/) (2020)
- [Score-based Generative Models for Calorimeter Shower Simulation](https://mlsanity.com/paper/2206.11898/) (2022)

## Built on by (most cited first, 6 of 6)

- [Neural Scaling Laws for Boosted Jet Tagging](https://mlsanity.com/paper/2602.15781/) (2026)
- [Towards Engineering Scaling Laws with Pretraining Data Composition](https://mlsanity.com/paper/2606.19781/) (2026)
- [Prompting Particle Physics: Tokenized Multi-modal Foundation Models for Combinatorially Many Tasks](https://mlsanity.com/paper/2609.31862/) (2026)
- [Event Generation with Parallel Langevin Sampling and Learned Stein Diagnostics](https://mlsanity.com/paper/2606.14854/) (2026)
- [Machine learning for the LHC physics program: a 2025-2026 stocktake](https://mlsanity.com/paper/2609.32874/) (2026)
- [How to scale your HEP ML models: A recipe for robust architecture comparisons at scale](https://mlsanity.com/paper/2610.06784/) (2026)

## Abstract (arXiv)

Scaling laws describing the dependence of neural network performance on the amount of training data, the spent compute, and the network size have emerged across a huge variety of machine learning task and datasets. In this work, we systematically investigate these scaling laws in the context of amplitude surrogates for particle physics. We show that the scaling coefficients are connected to the number of external particles of the process. Our results demonstrate that scaling laws are a useful tool to achieve desired precision targets.