Neural posterior estimation of the neutrino direction in IceCube using transformer-encoded normalizing flows on the sphere
Authors: R. Abbasi, M. Ackermann, J. Adams, J. A. Aguilar, M. Ahlers, J. M. Alameddine, S. Ali, N. M. Amin, +406 more
Abstract
IceCube is a cubic-kilometer-scale neutrino detector located at the geographic South Pole. A precise directional reconstruction of IceCube neutrinos is vital for associations with astronomical objects. In this context, we discuss neural posterior estimation of the neutrino direction via a transformer encoder that maps to a normalizing flow on the 2-sphere. It achieves a new state-of-the-art angular resolution for the two main event morphologies in IceCube - tracks and showers - while being significantly faster than traditional B-spline-based likelihood reconstructions. All-sky scans can be performed within seconds rather than hours, and take constant computation time, regardless of whether the posterior extent is arc-minutes or spans the whole sky. We utilize a combination of C2-smooth rational-quadratic splines, scale transformations and rotations to define a novel spherical normalizing-flow distribution whose parameters are predicted as a whole as the output of the transformer encoder. We test several structural choices diverting from the vanilla transformer architecture. In particular, we find dual residual streams, nonlinear QKV projection and a separate class token with its own cross-attention processing to boost test-time performance. The angular resolution for both showers and tracks improves substantially over the whole trained energy range from 100 GeV to 100 PeV. At 100 TeV deposited energy, for example, the median angular resolution improves by a factor of 1.3 for throughgoing tracks, by a factor of 1.7 for showers and by a factor of 2.5 for starting tracks compared to state-of-the art likelihood reconstructions based on B-splines. While previous machine-learning (ML) efforts have managed to obtain competitive shower resolutions, this is the first time an ML-based method outperforms likelihood-based muon reconstructions above 100 GeV.
Reconstructing the direction of incoming neutrinos in the IceCube Neutrino Observatory is an important problem in astrophysics. The public IceCube--Neutrinos in Deep Ice Kaggle competition provided 140 million simulated events to benchmark reconstruction techniques. To address this challenge from a novel perspective we introduce neutrino fingerprints compact 72×72×3 images in which each pixel represents a single detector, with pulse timing and charge statistics encoded as color channels. This representation transforms sparse, irregular pulse data into dense images suitable for convolutional processing. Our ResNet18 model achieves a mean angular error of 1.10 rad, indicating that convolutional networks trained on fingerprints rival more complex architectures while offering an effective, interpretable baseline for IceCube event reconstruction.
Charged-particle tracking -- reconstructing trajectories from sparse detector measurements -- is a fundamental high-energy-physics inference problem and a canonical example of learning under extreme combinatorial ambiguity. At the High-Luminosity Large Hadron Collider (HL-LHC), tracking must remain accurate and efficient despite unprecedented collision densities. Graph neural networks perform strongly, but incur substantial costs from graph construction and processing, while transformer-based approaches rely on auxiliary stages that prevent end-to-end optimization. To address this, we present HEPTv2, an end-to-end point-transformer architecture that reconstructs tracks from detector hits in one trainable pipeline. HEPTv2 combines a locality-aware point encoder with a track decoder that predicts complete trajectories without graph-building, clustering, or filtering. The encoder uses locality-sensitive hashing in detector coordinate space to preserve tracking-relevant geometry while enabling efficient local attention. The decoder resolves ambiguities through sectorized decoding and direct hit-to-track prediction under joint encoder-decoder supervision, allowing the full pipeline to be optimized end-to-end. On TrackML, HEPTv2 achieves 98.6% double-majority tracking efficiency at a 0.8% fake rate, while requiring only ∼15ms inference time and 0.4GB peak memory per event on a NVIDIA A100 GPU. Latency and memory scale approximately linearly for events with up to 5×105 hits. HEPTv2 establishes a new state of the art in the accuracy-latency trade-off, improving efficiency by 4.5% over the strongest prior transformer and by 1.1--2.2% over optimized graph-based pipelines, while reducing latency by factors of 7 and 38--52, respectively. These results show end-to-end transformers can deliver the accuracy and efficiency required for real-time particle reconstruction at the HL-LHC.
We present a neural-network-based data processing pipeline for Baikal-GVD, designed to improve event reconstruction quality and accelerate neutrino candidates selection. The pipeline comprises three stages: fast suppression of extensive air shower events, suppression of noise optical modules activations, and extraction of high confidence neutrino candidates. All three networks employ a transformer architecture that exploits inter-hit correlations through the attention mechanism. Applied sequentially, the pipeline achieves orders-of-magnitude speedup over the standard reconstruction chain. Moreover, noise suppression neural network surpasses the accuracy of algorithmic noise suppression algorithms and provides estimate for time residuals of the signal hits, which is crucial for identification of track-like hits. We address the domain shift between Monte Carlo simulations and experimental data by incorporating a domain adaptation technique, demonstrating improved agreement between the two domains. The resulting framework enables near-real-time event classification, with direct applications to multi-messenger alert systems and diffuse neutrino flux measurements.