Manuscript Psy03-C@1 · Psy03-C-v1.tex · proposition · d3380b90

Proposition: Zero recurrent weights do not remove all recurrence

Gate-aware recurrent stability › Why simple recurrent summaries are insufficient · lines 716–729 · proof included or linked

Psy03-C@1#prop:carry

If $B_{r} = B_{ζ} = B_{n} = 0$ , the GRU can still depend on its preceding hidden state:

F_{θ} (u, h) = (1 - ζ (u)) \circ n (u) + ζ (u) \circ h .

Thus deletion of every stored recurrent weight does not delete the update-gate carry path.

Proof. Substitute the zero recurrent blocks into (eq:cell).

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