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

2026-06-20

AI Summary

This study addresses the opacity of neural network mechanisms in time-delay estimation (TDOA) under noisy and reverberant conditions by systematically analyzing the hidden representations of MLP, CNN, and Transformer architectures. Using cross-architectural probing, gradient-based attribution, and causal frequency-domain masking—guided by the mathematical pipeline of GCC-PHAT—the work reveals, for the first time, that all three model families consistently learn to compute the cross-power spectrum, yet none reproduce the PHAT whitening operation. Instead, they adopt an amplitude-aware reliability weighting strategy, suggesting that PHAT imposes an information bottleneck. Removing PHAT improves TDOA performance for both classical and neural methods in additive noise, while end-to-end models achieve lower estimation errors in real reverberant environments through data-adaptive weighting.

Abstract

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.

Problem

• TDOA estimation
• neural networks
• GCC-PHAT
• PHAT whitening
• cross-power spectrum

Innovation

• TDOA estimation
• neural network probing
• GCC-PHAT
• frequency weighting
• cross-architecture analysis