17 papers
Asymptotic Semantic Collapse in Hierarchical Optimization
Faruk Alpay, Bugra Kilictas
Multi-agent language systems can exhibit a failure mode where a shared dominant context progressively absorbs individual semantics, yielding near-uniform behavior across agents. We…
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…
Bare-Metal Tensor Virtualization: Overcoming the Memory Wall in Edge-AI Inference on ARM64
Bugra Kilictas, Faruk Alpay
The deployment of Large Language Models (LLMs) on edge devices is fundamentally constrained by the "Memory Wall" the bottleneck where data movement latency outstrips arithmetic thr…
Rate-Distortion Analysis of Compressed Query Delegation with Low-Rank Riemannian Updates
Faruk Alpay, Bugra Kilictas
Bounded-context agents fail when intermediate reasoning exceeds an effective working-memory budget. We study compressed query delegation (CQD): (i) compress a high-dimensional late…
The phi-Process: Operator-Algebraic Embeddings of Possibilities, Transfinite Stabilization, and a Quantitative Application to Sensory Depletion
Bugra Kilictas, Faruk Alpay
We formalize a transfinite Phi process that treats all possibility embeddings as operators on structured state spaces including complete lattices, Banach and Hilbert spaces, and or…
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…