PFCS: Prime Factorization Cache System for Deterministic Data Relationship Discovery

2025-07-05

AI Summary

Traditional cache designs rely on statistical heuristics that inadequately model fine-grained data dependencies, resulting in inaccurate prefetching, suboptimal hit rates (85–92%), and resource inefficiency. This paper introduces the first deterministic relationship discovery framework grounded in the Fundamental Theorem of Arithmetic: data elements are uniquely encoded as distinct primes, and their relationships are represented as composite numbers; exact dependencies are then recovered via integer factorization—enabling formally verifiable, lossless relational modeling. Unlike approximate methods, this approach eliminates false positives. Integrated into cache architecture, it enables efficient relationship-aware retrieval and prefetching. Evaluated across database, machine learning, and HPC workloads, the design achieves a mean cache hit rate of 98.9%, delivers a 6.2× speedup in execution performance, and reduces energy consumption by 38%.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Cache systems fundamentally limit modern computing performance due to their inability to precisely capture data relationships. While achieving 85-92% hit rates, traditional systems rely on statistical heuristics that cannot guarantee relationship discovery, leading to suboptimal prefetching and resource waste. We present PFCS (Prime Factorization Cache System), which leverages the mathematical uniqueness of prime factorization to achieve deterministic relationship discovery with zero false positives. PFCS assigns unique primes to data elements and represents relationships as composite numbers, enabling the recovery of perfect relationships through factorization. A comprehensive evaluation across database, ML, and HPC workloads demonstrates an average performance improvement of x 6.2, 98.9% hit rates, and a 38% power reduction compared to state-of-the-art systems. The mathematical foundation provides formal guarantees impossible with approximation-based approaches, establishing a new paradigm for cache system design

Problem

• Deterministic discovery of data relationships in caches
• Eliminating false positives in cache prefetching
• Improving performance and power efficiency in cache systems

Innovation

• Uses prime factorization for deterministic data relationships
• Assigns unique primes to represent data relationships
• Achieves 98.9% hit rates and 38% power reduction