# nu-Flows: Conditional Neutrino Regression

arXiv: https://arxiv.org/abs/2207.00664 · HTML: https://mlsanity.com/paper/2207.00664/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 71 references that are in the map.
- First posted on arXiv 1 Jul 2022.

## Builds on (most cited first, 16 of 16)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Fast R-CNN](https://mlsanity.com/paper/1504.08083/) (2015)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [Guided Image Generation with Conditional Invertible Neural Networks](https://mlsanity.com/paper/1907.02392/) (2019)
- [Flows for simultaneous manifold learning and density estimation](https://mlsanity.com/paper/2003.13913/) (2020)
- [Anomaly Detection with Density Estimation](https://mlsanity.com/paper/2001.04990/) (2020)
- [CaloFlow: Fast and Accurate Generation of Calorimeter Showers with Normalizing Flows](https://mlsanity.com/paper/2106.05285/) (2021)
- [CaloFlow II: Even Faster and Still Accurate Generation of Calorimeter Showers with Normalizing Flows](https://mlsanity.com/paper/2110.11377/) (2021)
- [Tractable Density Estimation on Learned Manifolds with Conformal Embedding Flows](https://mlsanity.com/paper/2106.05275/) (2021)
- [Permutationless Many-Jet Event Reconstruction with Symmetry Preserving Attention Networks](https://mlsanity.com/paper/2010.09206/) (2020)
- [SPANet: Generalized Permutationless Set Assignment for Particle Physics using Symmetry Preserving Attention](https://mlsanity.com/paper/2106.03898/) (2021)

## Built on by (most cited first, 11 of 11)

- [The Landscape of Unfolding with Machine Learning](https://mlsanity.com/paper/2404.18807/) (2024)
- [CaloFlow for CaloChallenge Dataset 1](https://mlsanity.com/paper/2210.14245/) (2022)
- [nu2-Flows: Fast and improved neutrino reconstruction in multi-neutrino final states with conditional normalizing flows](https://mlsanity.com/paper/2307.02405/) (2023)
- [Calorimeter shower superresolution](https://mlsanity.com/paper/2308.11700/) (2023)
- [Reconstruction of Unstable Heavy Particles Using Deep Symmetry-Preserving Attention Networks](https://mlsanity.com/paper/2309.01886/) (2023)
- [Unifying Simulation and Inference with Normalizing Flows](https://mlsanity.com/paper/2404.18992/) (2024)
- [Simulation-Prior Independent Neural Unfolding Procedure](https://mlsanity.com/paper/2507.15084/) (2025)
- [Extrapolating Jet Radiation with Autoregressive Transformers](https://mlsanity.com/paper/2412.12074/) (2024)
- [Variational inference for pile-up removal at hadron colliders with diffusion models](https://mlsanity.com/paper/2410.22074/) (2024)
- [CaloTrilogy: Toward a Breakthrough in One-Step, End-to-End, Physics-Guided Shower Generation for Modern Calorimeters](https://mlsanity.com/paper/2606.04165/) (2026)
- [Comprehensive reconstruction of collider events with hypergraph representation learning and graph-conditioned diffusion](https://mlsanity.com/paper/2609.18928/) (2026)

## Abstract (arXiv)

We present nu-Flows, a novel method for restricting the likelihood space of neutrino kinematics in high energy collider experiments using conditional normalizing flows and deep invertible neural networks. This method allows the recovery of the full neutrino momentum which is usually left as a free parameter and permits one to sample neutrino values under a learned conditional likelihood given event observations. We demonstrate the success of nu-Flows in a case study by applying it to simulated semileptonic tbart events and show that it can lead to more accurate momentum reconstruction, particularly of the longitudinal coordinate. We also show that this has direct benefits in a downstream task of jet association, leading to an improvement of up to a factor of 1.41 compared to conventional methods.