Prime-Anchored Agentic AI: Solving Catastrophic Forgetting with DeepSeek-V2-Lite

Overview

This research introduces a production-ready agentic AI system designed to mitigate catastrophic forgetting in Large Language Models (LLMs). By anchoring six prime-indexed embedding rows $\{2, 3, 5, 7, 11, 13\}$ as fixed reference points, the system maintains historical knowledge with near-zero forgetting while requiring minimal memory overhead.

Key Technical Contributions

The Core Innovation: Prime Anchoring

• Topological Invariant: Utilizes the first six primes to create stable reference points.

• Mechanism: Anchor rows are snapshotted after initial training; gradient updates are blocked for these specific rows during subsequent tasks.

• Sparsity & Memory: Only 6 out of ~50,000 rows (0.01% of parameters) are used, resulting in an O(1) memory overhead of only 48–96 KB.

Mathematical Foundation

• Euler Attenuation Product: These six primes account for 97.85% of total spectral weight, defined by:

  $$\Lambda = 1 - \prod_{p\in \{2,3,5,7,11,13\}}(1 - p^{-0.5}) \approx 0.9785$$

• Spectral Trap: The anchors create a spectral peak at $\sigma = 0.5$, aligning with the critical line of the Riemann Hypothesis.

• Green-Tao Quantification: Establishes a decay law for coherence:

  $$\text{coherence}(k) = 2.1546\times k^{-0.8186} + 0.1218$$

Performance Metrics (Selected Models)

Multi-Agent System Architecture

The system employs four specialized agents to manage task routing and classification:

1. Classifier Agent: Routes documents based on keywords.

2. Topic Agent: Performs unsupervised domain topic extraction.

3. Sentiment Agent: Conducts autonomous tone analysis.

4. Decision Agent: Acts as the final arbiter for task approval and routing.

• Efficiency: Achieves 96–100% classification accuracy with inference times between 252–446ms.

Comparative Analysis

The topological approach outperforms traditional methods by balancing plasticity and stability:

Biological and Theoretical Insights

• Biological Analogy: The system treats 0% forgetting as a pathology. By allowing 99.99% of embedding rows to remain plastic, the model mimics biological brains that prioritize selective forgetting to facilitate adaptation.

• Riemann Hypothesis Connection: The research posits that the specific selection of the first six primes creates a unique "spectral trap" at $\sigma = 0.5$. Including any prime $\geq 17$ disrupts this trap and destroys the stability condition.

Production Readiness and Certification

• TOPO-2026 Track II: The system passed all rigorous benchmarks, including Task C accuracy ($\geq 80\%$), Combined Forgetting ($\leq 10\%$), and O(1) memory overhead.

• Deployment: Fully compatible with commodity hardware, specifically tested on NVIDIA RTX PRO 6000 Blackwell GPUs.

• Resources: Implementation code, technical reports, and proof documents are available via the project's GitHub and Zenodo repositories.