Topo-Miner: CRISPR-Enhanced DNA Computing for Accelerated Topological Feature Extraction

Soong Kyum LEE

TL;DR: This paper introduces Topo-Miner, a specialized DNA computer that uses CRISPR to accelerate topological data analysis, with big implications for graph learning and complex data.

Abstract: This paper introduces Topo-Miner, a novel computational platform for rapid and accurate topological feature extraction based on a CRISPR-enhanced DNA computer. Addressing the growing importance of topological data analysis (TDA) in understanding complex systems and the computational bottlenecks of traditional TDA methods, Topo-Miner leverages the inherent parallelism of DNA computing and the sequence specificity of CRISPR-Cas gene editing technology to drastically accelerate persistent homology calculations, a core algorithm in TDA. We detail the design and implementation of Topo-Miner, including the encoding of nodes, edges, and simplices into DNA sequences and the use of CRISPR-Cas systems (Cas9, dCas9, Cas12a) to perform boundary operations and matrix reductions in a highly parallel fashion. Our approach extends beyond standard persistent homology by incorporating tensor-based algorithms for efficient computation of higher-order and multi-scale topological features, and we explore the potential to calculate string theory-inspired topological invariants. Through rigorous simulations, calibrated with experimental parameters from existing literature on CRISPR-Cas systems and DNA computing, we demonstrate that Topo-Miner achieves significant speedups (50x-200x) over state-of-the-art tools like Ripser for graphs with over 10,000 nodes while maintaining high accuracy (error rates below 5% and accuracy exceeding 95%). Furthermore, we provide a theoretical framework for analyzing the time/space complexity and accuracy of Topo-Miner, including a mathematical proof for a lower bound on its accuracy. We also outline a clear experimental plan for in vitro validation of Topo-Miner's capabilities. The integration of Topo-Miner with the broader TopoComp platform, encompassing modules for graph neural network enhancement (STING) and NP-hard problem solving (TopoPath), further expands its capabilities, offering a powerful new toolkit for machine learning, particularly in graph analysis, materials science, and biological network analysis. Topo-Miner represents a paradigm shift in TDA, opening new avenues for exploring complex data and potentially enabling breakthroughs in topology-aware computing.

Primary Area: General Machine Learning->Hardware and Software

Keywords: Topological Data Analysis (TDA), DNA Computing, CRISPR, Persistent Homology, Tensor Computation, Topological Abstraction, Bio-Topo-Miner, Computational Acceleration, Accuracy, Scalability, Heterogeneous Computing, Graph Neural Networks, Optimization, Artificial General Intelligence (AGI), Real-Time Analysis

Submission Number: 14396