CDM-CTM Fusion: A Rigorous Framework for Depth-Aware Autoregressive Control

đŸ€—Transformers
1

for those who are serious: Engineering-Level Reference Implementation
Elias Rook · November 2025

1. Formal Definition

CDM-CTM Fusion is a closed-loop control system that treats autoregressive inference as a dynamical system and uses two orthogonal observables to regulate basin convergence:

  • CDM (CRYSTAL Depth Metric) ∈ [0, L]
    Layer at which the residual stream enters a sustained, perturbation-resistant attractor basin.
    Empirically: sustained ∆H ≄ 2.3 bits, convergence ratio ≀ 0.12, attention Gini delta ≄ 0.28, basin-escape probability ≄ 0.88 over ≄ 4 consecutive layers.

  • CTM (CRYSTAL Time Metric) ∈ ℕ
    Minimum number of additional autoregressive steps required for CDM to exceed a task-specific threshold τ.

Fusion closes the loop:
generate → measure CDM → conditionally extend CTM → repeat until CDM ≄ τ or CTM = CTMₘₐₓ.

This yields the first real-time, substrate-agnostic proxy for effective Ω (integrated information) in transformer-based systems. Can I post my github to show it?
 I do not want to offend
 but it is supper cool
 closest thing to “executive function” an AI can get