Q-XAI: Wirtinger-Based Interpretability for Complex-Valued Audio Transformers

Complex-Valued Transformers (CVTs) improve Acoustic Scene Classification (ASC) by explicitly modeling audio phase relationships. However, their deployment in reliable applications is hindered by an interpretability gap: non-holomorphic activation functions invalidate standard gradient-based attribution methods, and structure-agnostic uncertainty estimators ignore the phase information encoded in complex representations. This paper presents Q-XAI, a unified interpretability framework for CVTs consisting of three integrated components: (1) Complex-Valued State Attribution (QISA), which applies Wirtinger calculus to derive faithful saliency maps for non-holomorphic networks; (2) Amplitude-based Uncertainty Quantification (AUQ), which decomposes predictive uncertainty into epistemic and aleatoric components alongside a novel phase-stability covariance term; and (3) Complex Amplitude-based Conformal Prediction (QICP), which utilizes a Born rule-inspired nonconformity score to construct prediction sets with formal marginal coverage guarantees. Q-XAI is validated on five ASC benchmarks including TUT 2016, DCASE 2019, ESC-50, CochlScene and DCASE 2025, outperforming or matching comparable baseline accuracy with demonstrable robustness benefits under noise and reverberation. Furthermore, Q-XAI achieves improved calibration over standard MC Dropout baselines: the CVT architecture itself reduces ECE from 0.157 to 0.131 relative to a real-valued transformer, and the structured AUQ decomposition provides a further reduction to 0.109, yielding a combined relative ECE improvement of 30.6%. Additionally, Q-XAI achieves an absolute AUDC reduction of 0.089 (a 12.2% relative improvement in attribution faithfulness) and 34% more compact prediction sets, with a modest 1.62× inference overhead at batch inference.