2 citations · 2 across the 93 of their papers we have counts for
6 papers · 1 filter
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…
Latent Object Permanence: Topological Phase Transitions, Free-Energy Principles, and Renormalization Group Flows in Deep Transformer Manifolds
Faruk Alpay, Bugra Kilictas
We study the emergence of multi-step reasoning in deep Transformer language models through a geometric and statistical-physics lens. Treating the hidden-state trajectory as a flow…
The Geometry of Thought: Disclosing the Transformer as a Tropical Polynomial Circuit
Faruk Alpay, Bilge Senturk
We prove that the Transformer self-attention mechanism in the high-confidence regime (, where is an inverse temperature) operates in the tropical semiring (max-plu…
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…
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…
Stable and Convexified Information Bottleneck Optimization via Symbolic Continuation and Entropy-Regularized Trajectories
Faruk Alpay
The Information Bottleneck (IB) method frequently suffers from unstable optimization, characterized by abrupt representation shifts near critical points of the IB trade-off paramet…