# Forecasting Generative Amplification

arXiv: https://arxiv.org/abs/2509.08048 · HTML: https://mlsanity.com/paper/2509.08048/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 92 references that are in the map.
- First posted on arXiv 9 Sep 2025.

## Builds on (most cited first, 30 of 34)

- [Repulsive Deep Ensembles are Bayesian](https://mlsanity.com/paper/2106.11642/) (2021)
- [CaloGAN: Simulating 3D High Energy Particle Showers in Multi-Layer Electromagnetic Calorimeters with Generative Adversarial Networks](https://mlsanity.com/paper/1712.10321/) (2017)
- [Accelerating Science with Generative Adversarial Networks: An Application to 3D Particle Showers in Multi-Layer Calorimeters](https://mlsanity.com/paper/1705.02355/) (2017)
- [Score-based Generative Models for Calorimeter Shower Simulation](https://mlsanity.com/paper/2206.11898/) (2022)
- [CaloFlow: Fast and Accurate Generation of Calorimeter Showers with Normalizing Flows](https://mlsanity.com/paper/2106.05285/) (2021)
- [Calorimetry with Deep Learning: Particle Simulation and Reconstruction for Collider Physics](https://mlsanity.com/paper/1912.06794/) (2019)
- [Lorentz-Equivariant Geometric Algebra Transformers for High-Energy Physics](https://mlsanity.com/paper/2405.14806/) (2024)
- [CaloChallenge 2022: A Community Challenge for Fast Calorimeter Simulation](https://mlsanity.com/paper/2410.21611/) (2024)
- [CaloFlow II: Even Faster and Still Accurate Generation of Calorimeter Showers with Normalizing Flows](https://mlsanity.com/paper/2110.11377/) (2021)
- [CaloClouds: Fast Geometry-Independent Highly-Granular Calorimeter Simulation](https://mlsanity.com/paper/2305.04847/) (2023)
- [GANplifying Event Samples](https://mlsanity.com/paper/2008.06545/) (2020)
- [CaloMan: Fast generation of calorimeter showers with density estimation on learned manifolds](https://mlsanity.com/paper/2211.15380/) (2022)
- [A Lorentz-Equivariant Transformer for All of the LHC](https://mlsanity.com/paper/2411.00446/) (2024)
- [LHC analysis-specific datasets with Generative Adversarial Networks](https://mlsanity.com/paper/1901.05282/) (2019)
- [Ultra-High-Resolution Detector Simulation with Intra-Event Aware GAN and Self-Supervised Relational Reasoning](https://mlsanity.com/paper/2303.08046/) (2023)
- [DCTRGAN: Improving the Precision of Generative Models with Reweighting](https://mlsanity.com/paper/2009.03796/) (2020)
- [Inductive Simulation of Calorimeter Showers with Normalizing Flows](https://mlsanity.com/paper/2305.11934/) (2023)
- [Generative Networks for Precision Enthusiasts](https://mlsanity.com/paper/2110.13632/) (2021)
- [Simulation of electron-proton scattering events by a Feature-Augmented and Transformed Generative Adversarial Network (FAT-GAN)](https://mlsanity.com/paper/2001.11103/) (2020)
- [Understanding Event-Generation Networks via Uncertainties](https://mlsanity.com/paper/2104.04543/) (2021)
- [Convolutional L2LFlows: Generating Accurate Showers in Highly Granular Calorimeters Using Convolutional Normalizing Flows](https://mlsanity.com/paper/2405.20407/) (2024)
- [Lorentz Local Canonicalization: How to Make Any Network Lorentz-Equivariant](https://mlsanity.com/paper/2505.20280/) (2025)
- [Goodness of fit by Neyman-Pearson testing](https://mlsanity.com/paper/2305.14137/) (2023)
- [Optimising simulations for diphoton production at hadron colliders using amplitude neural networks](https://mlsanity.com/paper/2106.09474/) (2021)
- [Refereeing the Referees: Evaluating Two-Sample Tests for Validating Generators in Precision Sciences](https://mlsanity.com/paper/2409.16336/) (2024)
- [CaloHadronic: a diffusion model for the generation of hadronic showers](https://mlsanity.com/paper/2506.21720/) (2025)
- [PIPPIN: Generating variable length full events from partons](https://mlsanity.com/paper/2406.13074/) (2024)
- [Calibrating Bayesian Generative Machine Learning for Bayesiamplification](https://mlsanity.com/paper/2408.00838/) (2024)
- [Optimal Equivariant Architectures from the Symmetries of Matrix-Element Likelihoods](https://mlsanity.com/paper/2410.18553/) (2024)
- [Conditioned quantum-assisted deep generative surrogate for particle-calorimeter interactions](https://mlsanity.com/paper/2410.22870/) (2024)

## Built on by (most cited first, 3 of 3)

- [Scaling laws for amplitude surrogates](https://mlsanity.com/paper/2601.13308/) (2026)
- [Generative Models and Statistical Validation](https://mlsanity.com/paper/2605.30453/) (2026)
- [CaloTrilogy: Toward a Breakthrough in One-Step, End-to-End, Physics-Guided Shower Generation for Modern Calorimeters](https://mlsanity.com/paper/2606.04165/) (2026)

## Abstract (arXiv)

Generative networks are perfect tools to enhance the speed and precision of LHC simulations. Especially when generating events beyond the size of the training dataset, it is important to understand their statistical precision. We present two complementary methods to estimate the amplification factor without large holdout datasets. Averaging amplification uses Bayesian networks or ensembling to estimate amplification from the precision of integrals over given phase-space volumes. Differential amplification uses hypothesis testing to quantify amplification without any resolution loss. Applied to state-of-the-art event generators, both methods indicate that amplification is already possible in specific regions of phase space.