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> The brain is not predicting it's compressing

Compression requires prediction, therefore your brain requires prediction.

Some form of prediction being used by the higher-level neurons doesn't make the brain a prediction engine.

I'm not sure who claimed the brain was a "predictive engine" or what that means exactly. The OP specifically referenced predictive coding which describes precisely what is meant, and has empirical support.

If you meant this as a comparison to machine learning, then a predictive coding model closely matches.

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