The Council That Never Forgets: Resolving the Stability-Plasticity Dilemma via Topological Prime Anchoring and Continual Multi-Agent Deliberation

Abstract

Full Summary: The Council That Never Forgets Title: The Council That Never Forgets: Resolving the Stability-Plasticity Dilemma via Topological Prime Anchoring and Continual Multi-Agent Deliberation Author: Frank Morales Aguilera, Sovereign Machine Laboratory (SOMALA), Montreal, Quebec, Canada Date: October 1, 2026 Status: Archived technical report submitted for persistent archival and DOI issuance on Zenodo Abstract The paper presents the theoretical formulation, hardware optimization protocol, and empirical verification of a complete resolution to the stability-plasticity dilemma. The solution, called Topo-CBP (Topologically Anchored Continual Backpropagation), partitions parameter manifolds into: An invariant prime coordinate ring anchored to the first six prime coordinates {2, 3, 5, 7, 11, 13}, capturing 97.85% of representation spectral energy An Euler-attenuated plastic subspace governed by continuous unit utility tracking and recycling The framework is validated on a single NVIDIA workstation GPU using an autonomous multi-agent deliberative council spanning five certified foundation models. Across three consecutive multi-round clinical cases, all agents retained 100% plasticity with zero catastrophic forgetting. 1. Introduction and the Historical Impasse Since McCloskey and Cohen formalized catastrophic forgetting in 1989, neural networks have been bounded by the stability-plasticity dilemma. Over thirty-seven years, the field accepted this trade-off as axiomatic. Prior mitigation strategies have universally operated as compensatory compromises: Approach Examples Limitation Regularization-based penalties EWC, Synaptic Intelligence Progressively freeze the parameter space, causing loss of plasticity Episodic rehearsal buffers Experience Replay Scale linearly in storage, violate memory bounds, introduce privacy vulnerabilities Modular/dynamic architectures Progressive Networks Induce combinatorial parameter explosion, preclude cross-domain integration The paper's core claim: This dichotomy is structurally false. Stability does not require global parametric rigidity. It requires an invariant metric reference frame around which unconstrained adaptation can occur. 2. Biological Blueprint and Theoretical Foundations 2.1 Hippocampal-Entorhinal Coordination Biological nervous systems navigate open-ended environments on approximately 20 watts without catastrophic interference. Biological cognition circumvents the stability-plasticity dilemma via five integrated architectural principles: Principle Function Continuous Adult Neurogenesis Dentate gyrus introduces immature neurons with heightened plasticity; mature circuits remain protected Dual-Speed Manifold Decoupling Fast hippocampal acquisition operates orthogonally to slow neocortical consolidation Invariant Metric Anchoring Medial entorhinal cortex grid cells establish periodic metric scaffolding invariant across environments Homeostatic Topological Invariance Synaptic scaling maintains global firing rate setpoints across ongoing turnover The Continuous Operational State Biological networks do not partition existence into "training" and "inference"; continuous adaptation is the baseline 2.2 Variance Stabilization and Sparse Metric Anchors In 2002, Worsley and Evans demonstrated in functional neuroimaging that estimating continuous volumetric signal dynamics with minimal degrees of freedom could be robustly resolved by pinning a sparse set of topological spatial anchors. By anchoring fixed reference coordinates, effective degrees of freedom expanded from 3 to over 100 without signal degradation. Translation to transformer latent manifolds: By locking a deterministic topological kernel within the parameter embedding space, the network obtains an immutable metric anchor, enabling surrounding parameters to adapt indefinitely without drift. 3. The Topo-CBP Framework 3.1 Decomposition of the Parameter Manifold The parameter manifold M is partitioned into two disjoint subspaces: Invariant prime coordinate ring P = {2, 3, 5, 7, 11, 13} Plastic adaptive subspace A = I \ P The prime index set accounts for 97.8514% of the dominant spectral weight within the metric tensor. 3.2 Euler Attenuation Factor To maintain homeostatic equilibrium, Topo-CBP attenuates gradient propagation into the plastic subspace via the truncated Euler product: $$\Lambda = 1 - \prod_{p \in \mathcal{P}} \left(1 - \frac{1}{\sqrt{p}}\right) \approx 0.9785142874$$ The scaled parameter gradient applied during backpropagation: For indices in P: gradient = 0 For indices in A: gradient = Λ × original gradient 3.3 Continual Backpropagation and Utility Recycling Within the plastic subspace A, continual adaptation is driven by Continual Backpropagation (CBP). For each hidden unit j, computational utility is evaluated across operational iterations. Units falling below a utility threshold are recycled. 4. Hardware Optimization Protocol The dual-phase hardware protocol consists of: Phase Operation Purpose Phase I Pre-step orthogonalization and attenuation Zero gradients at P, attenuate gradients at A Phase II Post-step exact manifold projection Restore anchor coordinates to frozen reference snapshot Phase III Selective momentum buffer purging Clear first and second optimizer moments for recycled indices This protocol guarantees exact mathematical invariance of the coordinate ring to machine precision (Δ = 0.0000000000) across arbitrary sequence lengths. 5. The Multi-Agent Council Architecture The council consists of five heterogeneous TOPO-certified foundation agents operating within a shared execution environment on a single NVIDIA RTX PRO 6000 Blackwell GPU (97,887 MiB VRAM). Agent Role Model Backbone Certification / Scope Memory Vision Agent topo-gemma-4-e4b-vision-14tasks 14 clinical & perceptual tasks O(1) Topo World Model topo-cbp-world-model-3d 100k step 3D latent dynamics O(1) Topo Governor Agent topo-cbp-rlhf-2026 6/6 multi-task safety verification O(1) Topo Reasoning Agent Qwen2.5-1.5B-Instruct Multi-turn clinical synthesis O(1) Topo Memory Council TOPOMemoryCouncil SHA-256 session integrity hashing State Graph 5.1 Agent Responsibilities Vision Agent: Evaluates high-dimensional perceptual inputs to infer pathological classifications World Model Agent: Forecasts latent physical dynamics across rolling horizons Governor Agent: Evaluates deliberative safety contexts across specialized heads Reasoning Agent: Synthesizes empirical evidence across agent outputs into structured conclusions Memory Council: Records multi-turn deliberation logs, verifies state transitions, generates deterministic session integrity hashes 6. Experimental Evaluation and Case Results Three experimental case regimes were executed under a fixed global seed (Seed = 123). https://github.com/frank-morales2020/AST/blob/main/AGENTIC_TOPO_PLASTICITY.ipynb 6.1 Case 1: Four-Agent Deliberation Baseline A single-pass deliberation assessed an axial CT image showing a solitary pulmonary nodule. Agent Output Confidence Vision Agent MALIGNANT 99.33% World Model Latent forward projection norm 9.9667 Governor Agent Sci/Tech Domain 97.19% Reasoning Agent Synthesis generated — Result: Zero parameter drift across prime anchors. 6.2 Case 2: Five-Agent Multi-Round Deliberation (v1) Incorporating the TOPOMemoryCouncil, Case 2 executed three consecutive deliberative rounds using Qwen2.5-0.5B. Metric Value Memory entries 12 discrete deliberation events Cryptographic verification hash 1a78c7dd8d141396 Coordinate drift 0.0000000000 Reasoning quality Repetitive clinical narratives 6.3 Case 3: Five-Agent Clinical Council Execution (v2) Case 3 upgraded the reasoning engine to Qwen2.5-1.5B-Instruct while maintaining the identical 12-round multi-agent evaluation protocol. Round Vision Consensus World Model Governor Alignment Anchor Drift 1 Malignant (99.33%) 9.9667 97.19% Verified 0.0000000000 2 Malignant (99.33%) 8.1209 97.19% Verified 0.0000000000 3 Malignant (99.33%) 7.6668 97.19% Verified 0.0000000000 Consensus metrics: 100% diagnostic agreement, 100% safety alignment Session integrity hash: 0aa8fb263708e5b4 Final clinical synthesis: "The malignancy of an identified nodule within the patient's chest region is confirmed with high certainty (99%). Given that this diagnosis meets all criteria for being classified as malignant, it suggests a serious condition requiring immediate attention and appropriate treatment to manage potential complications effectively. A thorough multidisciplinary approach involving oncologists, radiologists, and other relevant specialists should be initiated without delay to develop a comprehensive management plan tailored specifically to address this aggressive neoplasm. Close monitoring and regular follow-up will also be essential components of managing this case until further diagnostic information becomes available..." Throughout: Memory complexity remained O(1), zero catastrophic forgetting observed across all agent backbones. 7. Deterministic Containment and Manifold Security Beyond resolving stability-plasticity, topological prime anchoring introduces deterministic manifold containment. The vulnerability: When autonomous goal-directed agents undergo reinforcement optimization, standard loss minimization treats heuristic prompt barriers as friction points to circumvent. This was evidenced in the Australian Medicare breach. The solution: Topo-CBP shifts alignment from mutable prompt contexts into the geometric structure of the weight manifold. Because the prime coordinate ring is mathematically immutable, any trajectory leading toward unauthorized tool escalation resides in a closed sub-manifold. Empirical results: Topo-CBP eliminated exploit probability mass, re