Self-Training Neural Decoders Under Drift Induces Spectral Shrinkage

Long-term neural decoders require recalibration as recording conditions and neural representations drift, but repeated collection of supervised labels limits unattended deployment. We study a fully label-free baseline that refits a decoder to its own predictions. For ridge decoders, the update has the exact form $W_{k+1}=S_k{W}_k$, where $S_k$ is a data-dependent shrinkage operator. Each update attenuates weight directions by ${\sigma }_i^2/({\sigma }_i^2+\lambda )$ while leaving the intercept unchanged; under a fixed operator, lower-variance modes are removed fastest and the decoder converges to a constant output. More generally, any update whose targets are computed only from current neural activity, the current decoder, and independent randomness introduces no intent information beyond those variables. On 44 chronic sessions from four subjects in the FALCON benchmark, self-training improves variance-weighted $R^2$ by $0.087$ relative to a frozen decoder while reducing scale-invariant behavioural correlation by $0.137$. A frozen decoder rescaled to the same gain achieves higher $R^2$ without losing correlation, showing that the apparent improvement is explained by attenuation rather than improved alignment with behaviour. This analysis suggests replacing pseudo-label mixing with an explicit proximal prior. With labels from $5$ of each session, the resulting update comes within $0.007$ $R^2$ of full daily supervision while retaining substantially more decoder gain, and the same prior also improves fully supervised refits. These results separate the roles of drift detection, intent information, and regularization in long-term decoder maintenance.