TOPO-2026: A Technical Report on Topological Prime-Anchor Continual Learning
Abstract
The topo2026.pdf report details the TOPO-2026 framework, a methodology for mitigating catastrophic forgetting in neural networks through prime-indexed parameter anchoring. Core Innovation and Theoretical Foundations Prime Anchoring Theory: The framework anchors parameters at indices {2, 3, 5, 7, 11, 13} to ensure a mathematically guaranteed spectral coverage of 97.85%. Spectral Coverage Guarantee: The coverage constant $\lambda$ is defined as $1-\prod_{p\in P}(1-p^{-1/2})$, resulting in a value of 0.9785142874. Gradient Protection Mechanism: The TopologicalGovernor class implements this by zeroing gradients for anchor parameters ($g_{p} \leftarrow 0$) during backpropagation and restoring them to their snapshot values ($\theta_{p} \leftarrow \theta_{p}^{snapshot}$) following the optimizer step. Memory Efficiency: The framework achieves $O(1)$ memory complexity, requiring only kilobytes of memory regardless of the model size; for a 21B-parameter model, the overhead is approximately 4.8KB. Validation Scenarios The framework was validated across 10 distinct demonstration scenarios: Transformer (723K params): Classification. Embedding Network (Small): 10-Task CL. GPT-2 Medium (355M params): Text generation. GPT-OSS-20B (21B params): Text generation. CNN (390K params): MNIST CL. Vision Transformer (809K params): CIFAR-10 CL. Stable Diffusion (49K params): Image generation. Hybrid TOPO-EWC (390K params): MNIST CL. Multi-task Classification: Various models. Generative Models:…
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