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Why It Matters
Recurrent models must preserve information that changes future behavior while suppressing hidden-state error.
Provenance
Discovered via ArXiv and published by ArXiv.
Key Claims
Original description
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 di...
Discovered via ArXiv
Research papers and preprints from arXiv.
Publisher: arxiv.org
ID: http://arxiv.org/abs/2609.23366v1 · Indexed about 1 hour ago