The Bioelectrical Information Theory: Investigating the theoretical compression limit of bioelectrical signals under artificial intelligence

Bioelectrical signals are increasingly acquired at scales that challenge the bandwidth of brain-computer interfaces. However, their compression is still often framed as a problem of waveform preservation, limited by the entropy of the raw signal. Here we propose an information-theoretic framework in which the effective information of bioelectrical data is determined not only by signal fidelity, but also by physiological structure, model capacity and downstream task requirements. We formulate bioelectrical compression as a three-level hierarchy. At the signal level, noise is reduced to the information they carry about latent physiological sources. At the physiological level, parametric encoders map purified signals into compact, structured and quantized representations. At the semantic level, task-irrelevant information is discarded, while deep learning models exploit causal dependencies to replace marginal entropy with conditional entropy. This perspective reframes the compression limit of bioelectrical signals as a model- and task-conditioned quantity rather than a fixed property of the waveform. As increasingly expressive models become integrated with neural and physiological interfaces, bioelectrical compression may shift from transmitting signals to transmitting only the residual information required for task-level interpretation.