3 papers
cs.CL2026
Attention Meets Reachability: Structural Equivalence and Efficiency in Grammar-Constrained LLM Decoding
Faruk Alpay, Bilge Senturk
We study grammar-constrained decoding (GCD) as a coupling between an autoregressive next-token distribution and a reachability oracle over a pushdown system compiled from a context…
cs.DB2026
Topological Relational Theory: A Simplicial-Complex View of Functional Dependencies, Lossless Decomposition, and Acyclicity
Bilge Senturk, Faruk Alpay
We develop a topological lens on relational schema design by encoding functional dependencies (FDs) as simplices of an abstract simplicial complex. This dependency complex exposes…
cs.LG2026
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-p…