Prediction Is Not a Sufficient Memory State
A memory that reproduces every current prediction may still have forgotten how to learn from the next observation. We characterize this distinction for exact cumulative learning and attention. For smooth convex residual losses with unrestricted real features and labels, a continuous recurrent state of fixed dimension exists exactly when the loss is polynomial. With ordinary, unweighted observations, degree $D$ requires precisely $r=\binom{d+D}{D}-1$ coordinates; even among histories with one fixed current predictor, exactly $r-d$ coordinates can remain necessary for continuation. Nonpolynomial losses have unbounded requirements on such equal-prediction histories. Bounded scalar logistic e...
| Authors | Robert Jenkinson Alvarez |
|---|---|
| Primary category | cs.LG |
| Published | 9 October 2026 |
| Last updated at source | 9 October 2026 |
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