# nu2-Flows: Fast and improved neutrino reconstruction in multi-neutrino final states with conditional normalizing flows

arXiv: https://arxiv.org/abs/2307.02405 · HTML: https://mlsanity.com/paper/2307.02405/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 67 references that are in the map.
- First posted on arXiv 5 Jul 2023.

## Builds on (most cited first, 15 of 15)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [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)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Going deeper with Image Transformers](https://mlsanity.com/paper/2103.17239/) (2021)
- [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)
- [OmniFold: A Method to Simultaneously Unfold All Observables](https://mlsanity.com/paper/1911.09107/) (2019)
- [Permutationless Many-Jet Event Reconstruction with Symmetry Preserving Attention Networks](https://mlsanity.com/paper/2010.09206/) (2020)
- [An unfolding method based on conditional Invertible Neural Networks (cINN) using iterative training](https://mlsanity.com/paper/2212.08674/) (2022)
- [SPANet: Generalized Permutationless Set Assignment for Particle Physics using Symmetry Preserving Attention](https://mlsanity.com/paper/2106.03898/) (2021)
- [nu-Flows: Conditional Neutrino Regression](https://mlsanity.com/paper/2207.00664/) (2022)
- [Topological Reconstruction of Particle Physics Processes using Graph Neural Networks](https://mlsanity.com/paper/2303.13937/) (2023)
- [Unbinned Profiled Unfolding](https://mlsanity.com/paper/2302.05390/) (2023)

## Built on by (most cited first, 10 of 10)

- [Masked Particle Modeling on Sets: Towards Self-Supervised High Energy Physics Foundation Models](https://mlsanity.com/paper/2401.13537/) (2024)
- [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)
- [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)
- [Generating particle physics Lagrangians with transformers](https://mlsanity.com/paper/2501.09729/) (2025)
- [Pointwise Metrics Mislead: An Evaluation Protocol for Multimodal Inverse Problems](https://mlsanity.com/paper/2605.22891/) (2026)
- [Enhancing generalization in high energy physics using white-box adversarial attacks](https://mlsanity.com/paper/2411.09296/) (2024)
- [Comprehensive reconstruction of collider events with hypergraph representation learning and graph-conditioned diffusion](https://mlsanity.com/paper/2609.18928/) (2026)

## Abstract (arXiv)

In this work we introduce nu2-Flows, an extension of the nu-Flows method to final states containing multiple neutrinos. The architecture can natively scale for all combinations of object types and multiplicities in the final state for any desired neutrino multiplicities. In tbart dilepton events, the momenta of both neutrinos and correlations between them are reconstructed more accurately than when using the most popular standard analytical techniques, and solutions are found for all events. Inference time is significantly faster than competing methods, and can be reduced further by evaluating in parallel on graphics processing units. We apply nu2-Flows to tbart dilepton events and show that the per-bin uncertainties in unfolded distributions is much closer to the limit of performance set by perfect neutrino reconstruction than standard techniques. For the chosen double differential observables nu2-Flows results in improved statistical precision for each bin by a factor of 1.5 to 2 in comparison to the Neutrino Weighting method and up to a factor of four in comparison to the Ellipse approach.