10 papers
Truth-Aware Decoding: A Program-Logic Approach to Factual Language Generation
Faruk Alpay, Hamdi Alakkad
This paper introduces Truth-Aware Decoding (TAD), a verification-oriented decoding scheme that aligns neural language generation with knowledge bases. Situated in the tradition of…
A Riemannian Variational and Spectral Framework for High-Dimensional Sphere Packing: Barrier-Dynamics Reconciliation, Periodic Rigidity, and Discrete-Time Guarantees
Faruk Alpay, Hamdi Alakkad
We develop a unified framework that reconciles a barrier based geometric model of periodic sphere packings with a provably convergent discrete time dynamics. First, we introduce a…
Glass-Box Analysis for Computer Systems: Transparency Index, Shapley Attribution, and Markov Models of Branch Prediction
Faruk Alpay, Hamdi Alakkad
We formalize glass-box analysis for computer systems and introduce three principled tools. First, the Glass-Box Transparency Index (GTI) quantifies the fraction of performance vari…
On the Fixed Point Property in Reflexive Banach Spaces
Faruk Alpay, Hamdi Alakkad
Fixed point theory studies conditions under which nonexpansive maps on Banach spaces have fixed points. This paper examines the open question of whether every reflexive Banach spac…
Quantization Errors, Human--AI Interaction, and Approximate Fixed Points in
Faruk Alpay, Hamdi Alakkad
We develop a rigorous measure-theoretic framework for the analysis of fixed points of nonexpansive maps in the space , with explicit consideration of quantization errors ar…
New Approaches to the Fixed Point Property in L^1 Spaces
Faruk Alpay, Hamdi Alakkad
This paper presents new approaches to the fixed point property for nonexpansive mappings in L^1 spaces. While it is well-known that L^1 fails the fixed point property in general, w…