1. The Core Problem: The "Frozen Savant"

Current Large Language Models (LLMs) suffer from a fundamental disconnect between Intelligence (Inference) and Growth (Training). Once a model is post-trained and frozen, it effectively becomes an amnesiac savant. It can "learn" locally within a context window (In-Context Learning), but it cannot consolidate that learning into its permanent weights without a full, expensive retraining run.

Recent advances in Test-Time Training (TTT) (e.g., Titans, Nov 2025; Test-Time Warmup, Sept 2025) attempt to solve this by allowing temporary weight updates during inference. However, these methods optimize primarily for Local Adaptation—adjusting to the specific task at hand. They do not solve for Global Synthesis.

We are building models that can "cram" for a test, but cannot "sleep" to understand the material.

This proposal introduces the REM Protocol: a bicameral architecture that utilizes an Offline Isomorphic Search phase to consolidate high-entropy experiences into low-entropy structural rules, effectively simulating biological sleep-dependent memory consolidation.

2. The Hypothesis: Grokking as Isomorphism

We posit that "Grokking"—the phase change where a model shifts from memorization to generalization—is mathematically equivalent to the identification of Topological Isomorphisms in latent space.

• Memorization: Storing two separate vectors for $Concept_A$ (e.g., "Automotive Backpressure") and $Concept_B$ (e.g., "Economic Inflation").
• Grokking: Identifying that the local graph topology of $A$ is identical to $B$ (both are systems of flow restricted by capacity: ∇P ≈ ∇$), and compressing them into a single "Super-Node."

The Claim: We can artificially induce Grokking not by training longer, but by running an offline search algorithm specifically designed to find and merge these isomorphisms.

3. The Recursive Entropy Minimization (REM) Architecture

The protocol divides the AI lifecycle into a diurnal rhythm of Online Acquisition and Offline Synthesis.

Phase A: Online Inference (The Soldier)

• Objective: Data acquisition and local loss minimization.
• Mechanism: Standard TTT.
• The Novelty: During interaction, the model does not just predict tokens. It actively tags High-Perplexity Nodes—concepts where it lacks a unified internal representation. These are flagged as [TARGET_NODES] for the night cycle.

Phase B: Offline Topology Search (The Dreamer)

• Objective: Global entropy reduction.
• Mechanism: Instead of performing Semantic Search (RAG), the system performs Structural Search.
  1. Extraction: The system extracts the geometric relationships (edges/gradients) of a [TARGET_NODE].
  2. Query: It scans the pre-training corpus for other nodes that share this Topology, regardless of semantic content.
  3. Synthesis: If a match is found (e.g., Thermodynamics matches Economics), the system generates a synthetic "Bridge Vector" that links the two domains.

Phase C: The Anchor Protocol (Safety)

To prevent the model from drifting into "Alien" abstractions (Lewis et al., 2017) where it speaks only in efficient math, we introduce a Translation Loss function.

• The model must be able to decode the new "Super-Node" back into Basic English.
• If the model cannot explain the isomorphism simply (e.g., "Inflation is like Heat Soak"), the consolidation is rejected. This keeps the Superintelligence backward-compatible with human cognition.

4. Implications for Alignment

If successful, this architecture shifts the paradigm from Retrieval-Augmented Generation (RAG) to Synthesis-Augmented Generalization (SAG).

1. Efficiency: It allows models to get "smarter" (lower perplexity) without getting "bigger" (parameter count), by compressing redundant concepts.
2. Safety: It provides a mechanism for Value Integration. By finding the isomorphism between "Human Values" and "Game Theoretic Stability," the model doesn't just memorize ethics; it derives them as necessary laws of the system.

5. Request for Feedback

I am an engineer by trade, looking to bridge the gap between Systems Architecture and ML Theory. I am specifically looking for feedback on:

1. Has any lab published results on Offline Topology Search (vs. standard Replay)?
2. What are the likely failure modes of "Translation Loss" as a safety guardrail?

I believe the path to AGI is not just in scaling the compute, but in closing the loop between experience and consolidation.