arXiv:2601.11618v3 Announce Type: replace-cross
Abstract: Neural architecture is often identified by module syntax, computation graphs, or the composite functions they realize. These descriptions answer different identity questions. We study the represented process available at a receiver: an actual factorization $B_j=G_jQ_j$ in which $Q_j(x)$ is the intermediate state supplied for further computation. Forgetting the presentation and retaining only $\ker Q_j$ yields the predecessor distinctions preserved at that cut. For a fixed branch, this extensional shadow exactly classifies unmarked surjective factorizations up to unique carrier re-presentation, but it does not determine marked receiver organization or the accessibility of retained information to restricted continuations. Under composition the relevant interface is $Q_{j,\theta}A$, so downstream architectural distinctions depend on the states produced upstream. An exact two-token construction shows that local and attention schemas are distinction-equivalent after one injective prefix and inequivalent after another, even though neither prefix loses predecessor information. The result exposes a context dependence hidden by modular architecture labels and motivates architecture comparison at the represented-process level.
Abstract: Neural architecture is often identified by module syntax, computation graphs, or the composite functions they realize. These descriptions answer different identity questions. We study the represented process available at a receiver: an actual factorization $B_j=G_jQ_j$ in which $Q_j(x)$ is the intermediate state supplied for further computation. Forgetting the presentation and retaining only $\ker Q_j$ yields the predecessor distinctions preserved at that cut. For a fixed branch, this extensional shadow exactly classifies unmarked surjective factorizations up to unique carrier re-presentation, but it does not determine marked receiver organization or the accessibility of retained information to restricted continuations. Under composition the relevant interface is $Q_{j,\theta}A$, so downstream architectural distinctions depend on the states produced upstream. An exact two-token construction shows that local and attention schemas are distinction-equivalent after one injective prefix and inequivalent after another, even though neither prefix loses predecessor information. The result exposes a context dependence hidden by modular architecture labels and motivates architecture comparison at the represented-process level.
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