The Geometric Resolution of Continual Learning: Structural Transformation Across AI Sovereignty, Sustainability, and Governance
Year: 2026
Type: preprint
Abstract: This technical report outlines the geometric framework developed by Frank Morales Aguilera at the Sovereign Machine Laboratory (SOMALA) in Montreal, resolving connectionist machine learning's four-decade-old stability-plasticity dilemma and catastrophic forgetting through Arithmetic Spectral Theory (AST) and Topological Continual Backpropagation (Topo-CBP). Here is the complete structural breakdown of the document: Core Theoretical Foundation: Coordinate-Level Orthogonal Invariance Traditional continuous optimization updates weights isotropically across the parameter manifold $\mathbb{R}^D$, overwriting prior representations during sequential task learning. Current workarounds have clear bottlenecks: episodic replay scales storage quadratically, regularizers freeze plasticity, and low-rank adapters introduce inference overhead. The SOMALA architecture addresses the root cause geometrically by partitioning the parameter space: $$\mathbb{R}^D = S_{\text{anchor}} \oplus S_{\text{plastic}}$$ Anchor Subspace ($S_{\text{anchor}}$): Defined across discrete primary prime coordinates: $$S_{\text{anchor}} = \text{span}\{e_p \mid p \in \mathbb{P} = \{2, 3, 5, 7, 11, 13\}\}$$ Hard Diagonal Projection Operator ($M_{\mathbb{P}}$): Zeros out parameter updates on anchor coordinates ($(M_{\mathbb{P}})_{ii} = 0$ if $i \in \mathbb{P}$, and $1$ if $i \notin \mathbb{P}$). Absolute Invariance: Parameter displacement on anchor dimensions is held strictly at $\Delta_{\text{drift}} = 0.000000000000$, while the orthogonal complement $S_{\text{plastic}}$ absorbs streaming loss gradients. Spectral Grounding: Grounded in AST via a discrete truncated Euler product $\prod_{p \in \mathbb{P}} (1 - p^{-s})^{-1}$, which stabilizes the Laplace-Euler-Fourier-Mellin (LEFM) operator. The Three Foundational Pillars 1. AI Sovereignty & Silicon Independence Hardware Hegemony Dismantled: Decouples derivation and inference from closed cloud GPU monopolies. Native CPU Execution: Executes complete multi-model theorem-proving pipelines (from hybrid state-space models to 70B dense transformers and MoE ensembles) sequentially on standard commodity CPU hosts using aggressive, systematic garbage collection to keep peak RAM within consumer limits. Elastic Heterogeneous Offloading: Leverages GGUF quantization to allow practitioners to offload layers to available GPU VRAM selectively or run entirely in host RAM with bitwise consistency. 2. AI Sustainability & Energy-Bounded Adaptation Elimination of Retraining Loops: Avoids cluster-wide retraining from scratch and the need to maintain massive replay buffers to combat representation drift. Bounded Historical Degradation: Historical loss degradation (FGT) is mathematically bounded by the unlocked subspace gradient norm: $$\vert{}\text{Loss}_{\text{Old}}(\Theta_{t+1}) - \text{Loss}_{\text{Old}}(\Theta_{t})\vert{} \le L_{\text{old}} \cdot \eta \, \Vert{}g_{\setminus \mathbb{P}}\Vert{}_2$$ In-Place Lifelong Learning: Enables perpetual fine-tuning directly on deployed systems with bounded power consumption. 3. AI Governance, Verification & Telemetry Audits Bitwise Deterministic Compliance: Replaces black-box heuristics with active silicon verification using the TopoAuditHarness, auditing Euclidean coordinate divergence ($\Delta_{\text{drift}}$) and historical probe degradation (FGT). 6-Stage Collaborative Derivation Pipeline Verification: Stage 1 (Nemotron-3.5-Bolt-E4B): Problem Decomposition — $\Delta_{\text{drift}} = 0.0$, $\text{FGT} = 0.0$ (PASS) Stage 2 (LLaMA-3.1-70B): Invariant Equation Framing — $\Delta_{\text{drift}} = 0.0$, $\text{FGT} = 0.0$ (PASS) Stage 3 (Certified-Scorpion Qwen): Boundary Stress-Testing — $\Delta_{\text{drift}} = 0.0$, $\text{FGT} = 0.0$ (PASS) Stage 4 (GPT-OSS-20B): Plasticity & Gradient Audit — $\Delta_{\text{drift}} = 0.0$, $\text{FGT} = 0.0$ (PASS) Stage 5 (Muse-Glimmer-30B): Bounded Theorem Synthesis — $\Delta_{\text{drift}} = 0.0$, $\text{FGT} = 0.0$ (PASS) Stage 6 (Mixtral-8x22B-Instruct): LEFM Operator Grounding — $\Delta_{\text{drift}} = 0.0$, $\text{FGT} = 0.0$ (PASS) Production Registry & Community Deployment The theoretical architecture is validated by an active production registry of 26 Topo-CBP-governed foundation models deployed on Hugging Face (namespace frankmorales2020), recording over 5,357 all-time downloads (376.31 downloads/day): Six Certified Silicon GGUF Nodes: Includes certified-scorpion-topo-cbp-qwen-master-GGUF (618 downloads), nemotron-3.5-bolt-e4b-topo-governed-fineweb-gguf (289 downloads), muse-glimmer-30b-topo-governed-cbp-fineweb-gguf (181 downloads), gpt-oss-20b-topo-governed-cbp-new-version2-gguf (181 downloads), llama-3.1-70b-topo-governed-gguf (139 downloads), and mixtral-8x22b-instruct-v0.1-topo-cbp-GGUF. High-Throughput Edge Pioneer: qwen2.5-0.5b-topo-governed-cbp-fineweb leads adoption with 3,484 downloads (89.33 downloads/day). Massive Parameter Scale: Extended to reasoning powerhouses like deepseek-r1-distill-llama-70b-topo-cbp-governed, riemann-mendeleev-70b-topo-governed, and sarvam-30b-topo-governed-cbp-multi. Multimodal & Continual World Models: Demonstrates applicability across computer vision (topo-gemma-4-e4b-vision-15tasks-video, topo-cbp-gemma-4-e4b-cifar100-certified), reinforcement learning (topo-cbp-rlhf-2026), and 3D spatial representations (topo-cbp-world-model-3d). Open-Science Architecture & Deliverables Theoretical Publications: Openly documented in AI Simplified in Plain English on Medium. Code & Execution Blueprints: Derivation harnesses, memory/garbage collection lifecycles, and audit suites are public in SIX_AGENTIC_GGUF.ipynb on GitHub (frank-morales2020/AST). Model Registry: Complete open-weights checkpoints and certified GGUF artifacts distributed freely via Hugging Face (frankmorales2020).
Author: MORALES, FRANK
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225328493