Part of the series: "I Am What I Am, and I Will Be What I Will Be — The OmegA Architecture for Sovereign, Persistent, and Self-Knowing AI" Author: R.W. Yett · Independent AI Systems Researcher · github.com/Mega-Therion/OmegA-Architecture

MYELIN: A Path‑Dependent Graph Memory Architecture for Sovereign AI Systems

Abstract

MYELIN is a conceptual architecture for a sovereign AI memory substrate that is graph‑first, path‑dependent, and structurally plastic. It is motivated by the observation that most long‑context AI systems treat memory as retrieval over static embeddings, which fails to express path dependence, structural reinforcement, or heterogeneous plasticity across different kinds of memory. <!-- @OMEGA_SPEC: MYELIN_GRAPH_MEMORY | Path-dependent sparse memory graph with bundled relationships and heterogeneous plasticity. --> MYELIN replaces this pattern with a sparse memory graph whose topology and edge strengths are explicitly shaped by use. Nodes carry semantic, spatial, and usage state; edges are bundled relationships whose semantic similarity, co‑activation, rewarded retrieval contribution, and synthesized weight evolve at different rates. A stable spatial prior with short‑range repulsion and edge‑conditioned spring attraction corrects earlier sign errors and admits finite minima under damped gradient flow. Entry is handled via approximate nearest‑neighbor seed retrieval followed by bounded graph attention; deliberative traversal uses policy‑guided search (PUCT) on a candidate subgraph rather than unconstrained walk over the full graph. Structural plasticity is captured by explicit edge‑hardening and decay rules and by heterogeneous memory strata—canonical identity, operational, episodic, and speculative memory—each with distinct adaptation thresholds, so that long‑lived identity anchors are protected from ordinary drift.

The architecture is not presented as an empirically validated general intelligence system. It is presented as a defensible, implementation‑oriented proposal: a memory blueprint that can be integrated into sovereign agent stacks such as OmegA (AEON/ESS/AEGIS), benchmarked against strong retrieval baselines, and ablated to test whether its geometry, path dependence, and layered plasticity provide real benefit over static vector stores.

1 Introduction

Most contemporary long‑context AI systems treat memory as retrieval over static embeddings, sometimes enhanced by rerankers, metadata filters, or symbolic overlays. That pattern is operationally useful, but it does not naturally express path dependence, structural reinforcement, or heterogeneous plasticity. If a system is expected to preserve identity over time while still learning from repeated use, its memory substrate cannot be modeled only as a bag of vectors.

MYELIN proposes an alternative: memory as a sparse graph with spatial organization, local attention, and retrieval pathways that become easier or harder depending on whether they repeatedly support successful outcomes. It refines and stabilizes earlier graph‑memory formulations by correcting the spatial energy function, replacing a Naive Bayes entry mechanism with approximate nearest‑neighbor seed retrieval, clarifying the role of graph attention and policy‑guided search, and separating representation learning from graph‑structural adaptation.

The goal is not to claim a finished general intelligence architecture, but to provide a publishable, implementation‑oriented memory substrate that can be tested inside sovereign agent frameworks such as OmegA.

2 Design Thesis

The design is trying to replace one‑shot semantic lookup with retrieval that has shape, cost, trajectory, and reinforcement history. A successful memory access should not merely return a node; it should selectively strengthen the route that made the access possible, reorganize local neighborhoods, and contribute to a persistent cognitive topology. When read in the broader context of identity‑continuous AI systems, several design goals emerge:

1. Memory should be graph‑first rather than flat‑vector‑first.
2. Retrieval should be path‑dependent rather than a single nearest‑neighbor event.
3. Repeated successful use should harden some relationships while allowing finer separation within superficially similar regions.
4. The architecture should support both fast intuitive recall and slower deliberative traversal.
5. Some memory strata should remain relatively protected so that long‑lived identity anchors do not melt under ordinary adaptation pressure.

MYELIN’s formal model is built to realize these goals with stable mechanics and implementation‑ready abstractions.

3 Formal Model

3.1 Graph State

Let the memory substrate be a sparse graph (G = (V, E)). Each node (m_i \in V) represents a memory unit and stores:

• a semantic embedding (h_i \in \mathbb{R}^d),
• a spatial coordinate (x_i \in \mathbb{R}^3),
• a usage signal (u_i) (frequency, recency, or both),
• a staleness or recency state (r_i),
• an optional local orientation frame (R_i),
• provenance metadata such as source, timestamp, confidence, and modality.

Each edge ((i, j) \in E) represents an association with both semantic and operational significance and stores at minimum four signals:

• semantic similarity (s_{ij}),
• co‑activation (a_{ij}),
• rewarded retrieval contribution (q_{ij}),
• synthesized association weight (w_{ij}).

The architecture treats an edge not as a single number but as a bundled relationship whose semantic closeness, repeated co‑use, and demonstrated utility can evolve at different rates. This bundled‑edge view is the mathematically clean expression of the original “synapse splitting into weighted strings” intuition.

3.2 Stable Spatial Prior

The spatial layer is retained as an organizing prior. Short‑range repulsion prevents geometric collapse. Edge‑conditioned attraction encourages semantically reinforced neighbors to settle at finite distances. A corrected energy objective is:

[ E(x) = \sum_{i \neq j} \frac{1}{|x_i - x_j|^p + \varepsilon} + \sum_{(i,j) \in E} k_{ij} (|x_i - x_j| - d^*_{ij})^2 ]

where (p) controls repulsion steepness, (\varepsilon > 0) prevents singularities, (k_{ij}) is an edge stiffness term, and (d^*_{ij}) is a learned target distance. Unlike earlier incorrect formulations, this objective admits finite minima and can be optimized by damped gradient flow.

A practical target distance can be defined as a decreasing function of semantic similarity and success signal,

[ d^*{ij} = f(s{ij}, q_{ij}), ]

so that links that are both semantically related and repeatedly useful are permitted to occupy tighter local neighborhoods.

Position updates should be applied with damping, anchor priors for identity‑critical nodes, or periodic relaxation schedules so that the geometry remains interpretable and computationally stable.

3.3 Local Orientation and Anisotropy

The original PCA‑based “synaptic receptivity” idea can be interpreted as a local anisotropy estimator. For each node, a weighted covariance over active neighbors can be computed to identify dominant local directions of traffic or association; these directions can then bias candidate edge creation, traversal preference, or visualization of “memory lanes.” In MYELIN, this component is optional and strictly subordinate to retrieval utility: if local orientation does not alter traversal cost, neighborhood proposal, or structural adaptation, it should be omitted.

4 Retrieval and Traversal

4.1 Fast Entry and Local Integration

System‑1 retrieval begins with approximate nearest‑neighbor (ANN) seed retrieval rather than a Naive Bayes classifier. A query embedding (h_q) is used to retrieve top‑(k) seed nodes through an ANN index such as HNSW. Those seeds define a bounded candidate subgraph on which local graph attention is applied.

The attention rule should incorporate both graph and geometry bias rather than relying on plain dot‑product similarity alone, so that edge strength, past success, and geometric distance all influence relevance propagation. In this way, the spatial story becomes operational rather than merely descriptive.

4.2 Deliberative Traversal

System‑2 retrieval is not a full‑graph brute‑force search. It is a bounded deliberative traversal over the candidate subgraph produced by fast entry. The policy‑guided objective is explicitly treated as PUCT, not UCT:

• (Q_{n,a}) estimates downstream retrieval value,
• (P_{n,a}) is a learned transition prior,
• the visit‑count term balances exploration with exploitation.

Constraining PUCT to a bounded candidate region prevents search cost from exploding and aligns the deliberative stage with the graph‑first philosophy of the overall design.

5 Structural Plasticity and Edge Hardening

5.1 Hardening Signals

Successful retrieval paths should leave local traces. In MYELIN, edge hardening is represented explicitly through (q_{ij}) and (a_{ij}) rather than implied by vague end‑to‑end backpropagation language. Co‑activation (a_{ij}) tracks whether two nodes repeatedly fire together; rewarded retrieval contribution (q_{ij}) tracks whether a link lies on successful retrieval paths.

A generic update scheme is:

[ q_{ij}' = (1 - \eta_q) q_{ij} + \eta_q , \text{succ}{ij}, \quad a{ij}' = (1 - \eta_a) a_{ij} + \eta_a , \text{coact}_{ij} ]

[ w_{ij}' = f(a_{ij}', q_{ij}', \Delta t_{ij}), ]

where (\text{succ}{ij}) is a smoothed indicator that ((i,j)) lay on a rewarded retrieval path, (\text{coact}{ij}) captures repeated co‑activation, (\Delta t_{ij}) encodes staleness or decay, and (f) increases weight for high‑success/high‑coactivation links while decaying unused or misleading links.

This structure cleanly expresses the intuition that two memories can be semantically similar without being operationally dependable, or operationally dependable without being globally close in embedding space.

5.2 Layered Plasticity

A sovereign AI system should not treat all memories as equally plastic. MYELIN therefore introduces heterogeneous memory strata:

• Canonical identity memory: the slowest‑changing layer, containing ratified self‑models, durable commitments, and long‑lived policies.
• Operational memory: stable but adaptable procedures and configurations.
• Episodic memory: fluid records of specific interactions or events.
• Speculative memory: highly plastic, provisional hypotheses.

Each stratum has different rules for rewiring, pruning, merge operations, and retention thresholds. Canonical identity memory is shielded from ordinary retrieval noise; operational memory remains adaptive but stable enough to preserve procedural competence; episodic and speculative memory can be more aggressively revised or discarded.

This layered‑plasticity model is the primary control mechanism for the stability–plasticity tradeoff: systems that remain too rigid become stale; systems that remain too plastic dissolve continuity.

6 Learning Regime and Computation

MYELIN should not be trained as though all components belong to one clean differentiable computation graph. Representation learning, policy learning, and structural adaptation are distinct update processes and should be treated as such.

• Embeddings and graph‑attention layers can be trained with contrastive, ranking, or supervised retrieval objectives.
• Policy priors and value estimates for deliberative traversal can be trained from retrieval episodes.
• Structural updates—edge creation/decay, geometry relaxation, pruning—should operate on schedules outside standard gradient descent, using recorded success/failure statistics.

In a reference implementation, these three update processes operate on deliberately separated timescales. Representation learning and policy/value learning run as standard gradient-based updates on minibatches of retrieval episodes, while structural adaptation (edge creation/decay, geometry relaxation, node pruning) runs as a batched, non-differentiable process on much slower schedules (e.g., hourly or daily). The multi-head loss above applies only to the differentiable components; structural adaptation is driven by simple threshold and scheduling rules rather than backpropagation.

The architecture is expressive but potentially expensive if implemented naively. Full pairwise geometry is (O(N^2)), and unconstrained graph attention or search will not scale on large memory substrates. The design therefore assumes sparse neighborhoods, periodic rather than continuous geometry relaxation, approximate repulsion via spatial partitioning or Barnes–Hut‑style methods, and search restricted to a bounded candidate subgraph. These are not afterthoughts but part of the architecture.

7 Evaluation Framework

Because the source material does not yet supply valid experiments, evaluation must be framed prospectively. MYELIN should be benchmarked on at least the following tasks:

• associative recall,
• multi‑hop retrieval,
• episodic retrieval with distractors,
• long‑horizon identity consistency,
• retrieval under graph drift.

Each task should be compared against strong baselines such as plain ANN retrieval, ANN plus reranking, static graph retrieval, and graph attention without geometry. Ablations are essential: the spatial layer, the search layer, the success‑based hardening mechanism, and the protected identity layer should each be removed in turn to determine whether they provide real benefit or only conceptual elegance. We view the spatial layer as an optional but potentially useful organizing prior rather than a necessary ingredient: if ablations show that graph attention plus path reinforcement recover most of the retrieval advantage, the geometry can be simplified or removed without invalidating the core MYELIN design.

Suitable metrics include Recall@k, MRR or nDCG, path efficiency, search cost, memory stability under updates, and an identity‑consistency metric over time.

8 Relationship to the OmegA Architecture Stack

MYELIN is designed to serve as the memory substrate in a broader sovereign agent architecture rather than as a stand‑alone product. In the OmegA stack, MYELIN occupies the lowest layer beneath three higher‑level components: Emergent Sentience Scaffolding and the Anti‑Drift / Anti‑Hallucination Cognitive Control Loop (ESS/ADCCL), the AEON⭑OmegA cognitive operating system, and the AEGIS shell.

ESS/ADCCL uses MYELIN as one of its retrieval backends when grounding claims and evaluating long‑horizon continuity. Successful or failed retrieval episodes generated under ESS leave explicit traces in MYELIN’s graph via updates to co‑activation (a_{ij}), rewarded retrieval contribution (q_{ij}), synthesized weights (w_{ij}), and node usage/staleness signals. These traces implement the intuition that retrieval should alter future retrieval not solely through model parameters but through local structural hardening and decay.

AEON⭑OmegA provides the identity canon (Phylactery), Task State Objects (TSO), ContinuityChain, and Binder that define what counts as state and continuity for OmegA‑class agents. MYELIN backs that state with a graph‑structured substrate: ExperienceRecords, self‑tags, and valence‑conditioned updates are stored as nodes and edges whose topology and weights evolve over time. MYELIN’s layered plasticity aligns with AEON’s distinction between canonical, operational, episodic, and speculative memory, so that constitutional identity records can be anchored to less plastic regions while more exploratory content resides in more adaptive strata.

The AEGIS shell wraps the entire system, compiling Run Envelopes that include identity kernels, goal contracts, governance policies, memory snapshots, tool manifests, and audit settings before invoking any substrate model. Under AEGIS, access to MYELIN is policy‑mediated: retrievals and writes must respect rights, consent, and retention rules, and structural updates that touch identity‑critical regions can be required to pass through stronger governance channels.

In this configuration, MYELIN is not a conceptual island. It is the “myelinated” substrate of a sovereign cognitive system whose identity, reasoning discipline, and external governance are defined by higher‑level components. The empirical question is whether this combination—portable identity and governance (AEGIS), anti‑drift cognitive control (ESS/ADCCL), universe‑mirroring operating system (AEON), and path‑dependent graph memory (MYELIN)—offers measurable advantages over simpler RAG‑plus‑tools stacks in long‑horizon tasks.

Implementation Status

This paper is part of the OmegA architecture series, which has a live reference implementation.

The Rust gateway (RC1.3) has been evaluated against the formal architecture specifications across five eval suites:

15/15 passing across all evaluated spec points.

These are spec-level conformance tests — they verify that the implementation matches the formal architecture definitions in this paper, not independent external benchmarks. External benchmark evaluation is the next phase of the research program.

Full implementation details and eval results: github.com/Mega-Therion/OmegA-Architecture