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cs.LG2026
Finite Certificates for In-Context Determinacy and a Threshold Theory of Emergence in Language Models
Faruk Alpay, Hamdi Alakkad
This paper develops a model-theoretic framework for verifying context-conditioned language-model behavior by replacing benchmark labels with finite semantic certificates. The first…
cs.LG2025
Escaping Saddle Points via Curvature-Calibrated Perturbations: A Complete Analysis with Explicit Constants and Empirical Validation
Faruk Alpay, Hamdi Alakkad
We present a comprehensive theoretical analysis of first-order methods for escaping strict saddle points in smooth non-convex optimization. Our main contribution is a Perturbed Sad…
cs.LG2025
Temporal Anchoring in Deepening Embedding Spaces: Event-Indexed Projections, Drift, Convergence, and an Internal Computational Architecture
Faruk Alpay, Bugra Kilictas, Hamdi Alakkad
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…