Mixup Barcodes for Topology-Aware Financial Decision Making

2026-10-08

AI Summary

This study addresses the topological insensitivity of conventional trend indicators and their inability to capture market structural shifts by proposing a hybrid barcode framework grounded in persistent homology and Takens embedding. We introduce a novel Hybrid Barcode Perturbation Index that integrates the 1-Wasserstein distance with persistent entropy divergence to quantify market regime transitions. This approach transforms binary crossover signals into continuous stress scores, enabling dynamic position sizing. Empirical evaluations on the S&P 500 and Bitcoin demonstrate that the proposed method achieves Sharpe ratios of 1.116 and 1.238, respectively, while significantly reducing maximum drawdowns compared to buy-and-hold and standard benchmark strategies.

Abstract

We present a topology-aware system based on mixup barcodes and persistent homology for financial decision making. The suggested approach uses topological summaries obtained from Takens delay embeddings of a univariate price series to quantify structural changes between reference and current market regimes. The 1-Wasserstein distance between persistence diagrams, a mixup barcode disruption index, and persistence entropy divergence are combined to provide a novel stress score. A Golden Cross trading method is dynamically modulated by this score, which transforms a binary buy/sell signal into a continuous position-sizing process. At embedding settings chosen by maximizing in-sample Sharpe over a 72-point grid, in-sample assessment on the S&P 500 and Bitcoin yields Sharpe ratios of 1.116 and 1.238, respectively, with much lower maximum drawdown compared with both Buy-and-Hold and the standard Golden Cross baseline. Our findings imply that topological summaries of market geometry include useful information that goes beyond traditional trend markers.

Problem

• Financial Decision Making
• Persistent Homology
• Market Regime
• Position Sizing
• Maximum Drawdown

Innovation

• Persistent Homology
• Mixup Barcodes
• Takens Delay Embeddings
• Topology-Aware Trading
• Position Sizing