What Can a Recurrent State Safely Forget?
Recurrent models must preserve information that changes future behavior while suppressing hidden-state error. These objectives conflict: contraction improves stability, but contraction along a future-distinguishing direction destroys memory. We formalize this boundary through the predictive quotient of a recurrent state space. Two hidden states are equivalent when they induce the same conditional future; their equivalence classes form predictive fibers. Every exact semantics-preserving corrector acts as the identity on this quotient. At a regular point with hidden dimension d and predictive dimension k, it can eliminate at most d - k independent directions. This establishes a discrete-con...
| Authors | Linzhe Zhang, Changming Xu |
|---|---|
| Primary category | cs.LG |
| Published | 20 September 2026 |
| Last updated at source | 20 September 2026 |
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