# What Do Neural Networks Learn for TDOA Estimation? A Cross-Architecture Probing Study

arXiv: https://arxiv.org/abs/2606.22020 · HTML: https://mlsanity.com/paper/2606.22020/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 29 references that are in the map.
- First posted on arXiv 20 Jun 2026.

## Builds on (most cited first, 18 of 18)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [Understanding intermediate layers using linear classifier probes](https://mlsanity.com/paper/1610.01644/) (2016)
- [Probing Classifiers: Promises, Shortcomings, and Advances](https://mlsanity.com/paper/2102.12452/) (2021)
- [Progress measures for grokking via mechanistic interpretability](https://mlsanity.com/paper/2301.05217/) (2023)
- [Designing and Interpreting Probes with Control Tasks](https://mlsanity.com/paper/1909.03368/) (2019)
- [What you can cram into a single vector: Probing sentence embeddings for linguistic properties](https://mlsanity.com/paper/1805.01070/) (2018)
- [Information-Theoretic Probing with Minimum Description Length](https://mlsanity.com/paper/2003.12298/) (2020)
- [Pyroomacoustics: A Python package for audio room simulations and array processing algorithms](https://mlsanity.com/paper/1710.04196/) (2017)
- [Self-Supervised Speech Representations are More Phonetic than Semantic](https://mlsanity.com/paper/2406.08619/) (2024)
- [A Survey of Sound Source Localization with Deep Learning Methods](https://mlsanity.com/paper/2109.03465/) (2021)
- [Overview and Evaluation of Sound Event Localization and Detection in DCASE 2019](https://mlsanity.com/paper/2009.02792/) (2020)
- [Evidence of Vocal Tract Articulation in Self-Supervised Learning of Speech](https://mlsanity.com/paper/2210.11723/) (2022)
- [Extending GCC-PHAT using Shift Equivariant Neural Networks](https://mlsanity.com/paper/2208.04654/) (2022)
- [PSELDNets: Pre-trained Neural Networks on a Large-scale Synthetic Dataset for Sound Event Localization and Detection](https://mlsanity.com/paper/2411.06399/) (2024)
- [Observability-Aware Active Calibration of Multi-Sensor Extrinsics for Ground Robots via Online Trajectory Optimization](https://mlsanity.com/paper/2506.13420/) (2025)
- [On the reliability of feature attribution methods for speech classification](https://mlsanity.com/paper/2505.16406/) (2025)

## Abstract (arXiv)

Neural networks outperform classical GCC-PHAT for Time-Difference-of-Arrival (TDOA) estimation in noise and reverberation, yet their internal strategy remains unexplored. To uncover it, we turn GCC-PHAT's mathematical steps into diagnostic targets, probing hidden layers of three architectures (MLP, CNN, Transformer) and complementing with gradient attribution and causal frequency masking. We find that cross-power computation consistently emerges across all architectures and conditions, while PHAT whitening, the defining step of GCC-PHAT, fails to emerge. Instead, networks learn a magnitude-aware frequency weighting that preserves per-frequency reliability information discarded by PHAT. This makes PHAT an information bottleneck: removing it from both classical and neural GCC pipelines improves performance under additive noise. On real-world reverberant data, PHAT remains the best classical weighting, but end-to-end networks achieve lower error by learning data-adaptive weighting.