Abstract & Diagnostic Summary: This 53-page manuscript documents an 18-run diagnostic program (Runs A–AA) analyzing the retrieval bottlenecks of externalized topological memory structures for frozen neural networks. The architecture projects compressed, low-dimensional memory keys ("roots") onto a 2D physical grid ("the scalp") with neighborhood leakage, keeping uncompressed targets in deep "shaft" vectors. Key Findings & Metrics: Squeezing & Layouts: High-dimensional 64-element keys are projected via rᵢ = normalize (P * kᵢ) onto competing layouts: a deterministic Fermat Spiral vs. a uniform random baseline. The Coverage vs. Selection Crisis: Transitioning to Multi-Root Overlapping Retrieval (top-k=10 neighborhoods across k=3 roots) eliminated candidate access bottlenecks, pushing Oracle Union candidate coverage up to ~0. 90. The End-to-End Ceiling: Despite 90% candidate exposure, end-to-end accuracy strictly stalled at 0. 76–0. 77, failing to beat a flat content-addressed baseline (0. 78–0. 80). Standard neural selectors and soft-voting judges failed, proving the system bottleneck is within-pool judgment, not spatial search layouts. Spiral PCA Correction: The baseline Fermat Spiral suffered from hyper-dense central mass concentration. A Principal Component Analysis Aligned Spiral Map ("spiral pca") successfully restored spatial entropy and candidate coverage, though it could not decisively defeat the random baseline due to intrinsic geometric redundancy. Conclusion: Geometric surface-mapped memory routing yields efficient candidate shortlist generation (~0. 90). To surpass standard flat key-value lookups, future work must pivot from spatial placement optimization toward engineering high-fidelity, ambiguity-aware selection policies to harden noisy candidate pools. LLM Transparency & Provenance: ChatGPT, Gemini, and Grok assisted with code scaffolding and LaTeX formatting under strict author verification. Live Google Colab code repository and conversation verification logs are explicitly detailed on page 1.
Sohan Poudel (Tue,) studied this question.