2025/08/13 by Alpay, Faruk, Kilictas, Bugra, Alakkad, Hamdi · 1 citation
#47H09 #47H10 #65K10 #68T07 #90C25 #F.1.1 #FOS: Computer and information sciences #FOS: Mathematics #Functional Analysis (math.FA) #G.1.2 #G.1.6 #I.2.6 #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2508.09693
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 ℓ2 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.