Abstract: The brain maintains stable cognition despite continuously changing neural activity. How to extract stable cognitive states from variable neural observations remains a central problem in neural decoding. Existing neural decoding methods map neural observations to predefined external labels based on the stimulus-response principle, often capturing recording-specific spurious correlations. Inspired by how the brain infers the world, and specifically by Bayesian brain theory, we recast neural decoding as cognitive inference constrained by brain-intrinsic priors, yielding high-level meta-neural semantic representations. In decoding experiments spanning five neural recording modalities and three cognitive domains (motor, perception and internal mentation), our cognitive inference method reorganized the geometry of neural observation representations, yielding meta-neural semantic representations that exhibited consistent geometric relationships across cognitive tasks and enabled the recovery of stable cognitive states from variable neural observations. Our work provides an account of how the brain maintains relatively stable cognition despite continual changes in the external environment. Cognitive stability is sustained through cognitive inference from changing neural activity, without requiring fixed neural activity patterns.