Temporal Anchoring in Deepening Embedding Spaces: Event-Indexed Projections, Drift, Convergence, and an Internal Computational Architecture
Alpay, Faruk, Kilictas, Bugra, Alakkad, Hamdi
We develop an operator-theoretic framework for temporal anchoring in embedding spaces, modeled as drift maps interleaved with event-indexed blocks culminating in affine projections. We provide complete proofs for a variable-block contraction lemma (products of Lipschitz factors), a drift--projection convergence theorem with explicit uniform-gap envelopes, and ontological convergence under nested affine anchors with a robustness variant. We formalize an internal Manuscript Computer (MC) whose computations are defined purely by these operators and prove a rigorous finite-run equivalence theorem (with perturbation bounds). For attention layers, we give a self-contained proof that softmax is $1/2$-Lipschitz in $\ell_2$ and derive sufficient layer-contraction conditions (orthogonal/non-orthogonal heads). All floats are placed exactly where written; the manuscript uses only in-paper pseudocode and appendix figures.
Aug-14-2025
- Country:
- Asia > Russia (0.04)
- Europe
- Hungary > Csongrád-Csanád County
- Szeged (0.04)
- Russia (0.04)
- United Kingdom > England
- Cambridgeshire > Cambridge (0.04)
- Hungary > Csongrád-Csanád County
- Genre:
- Research Report (0.50)
- Technology: