Position: Beyond Prediction: Toward Verifiable Physiological Waveform Reasoning with Foundation Models and Agentic LLMs

Physiological waveforms (e.g., ECG, PPG, EEG) encode clinically meaningful information in fine-grained morphology, precise timing, and cross-channel dynamics, yet most machine learning systems still treat them as generic time series and optimize end-to-end prediction. In this position paper, we argue for verifiable physiological waveform reasoning: extracting localized, measurable signal evidence from raw signals, interpreting that evidence into physiological semantics, and supporting clinically grounded decisions. Waveform reasoning is challenging due to acquisition heterogeneity, signal fidelity, complex semantics and cross-channel coupled dynamics. We analyze why existing model families remain insufficient: physiological foundation models learn strong perceptual representations but remain weak at verifiable reasoning, while LLM-based adaptations have limited waveform understanding. To bridge this gap, we advocate verifiable, closed-loop systems that unify waveform semantics with language intelligence. Concretely, we propose a dual-process architecture that System 1 aligns physiological waveforms with language, and System 2 provides agentic reasoning via a Plan--Act--Verify loop, together enabling verifiable physiological waveform reasoning. We further propose evaluations beyond accuracy, emphasizing traceability, replayability, counterfactual robustness, and calibrated abstention.