Geometric Dynamics of Consumer Credit Cycles: A Multivector-based Linear-Attention Framework for Explanatory Economic Analysis

Paper: arXiv 2510.15892

Authors: Agus Sudjianto, Sandi Setiawan

Abstract

This study introduces geometric algebra to decompose credit system relationships into their projective (correlation-like) and rotational (feedback-spiral) components. We represent economic states as multi-vectors in Clifford algebra, where bivector elements capture the rotational coupling between unemployment, consumption, savings, and credit utilization. This mathematical framework reveals interaction patterns invisible to conventional analysis: when unemployment and credit contraction enter simultaneous feedback loops, their geometric relationship shifts from simple correlation to dangerous rotational dynamics that characterize systemic crises.

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 6.5/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This paper presents a highly original integration of Geometric (Clifford) Algebra and linear attention mechanisms to model macroeconomic feedback loops and consumer credit cycles. It bridges advanced mathematical concepts with empirical time-series data from 1980 to 2024, providing strong explanatory power and novel regime-detection capabilities.

Research Flowchart

  flowchart TD
    A[Goal: Decompose Credit Cycles into Correlation & Feedback Dynamics] --> B[Input Data: Unemployment, Consumption, Savings, & Credit Utilization]
    B --> C[Map Economic States as Multi-vectors in Clifford Algebra]
    C --> D[Apply Linear-Attention Framework to Compute Geometric Relationships]
    D --> E[Decompose Dynamics into Projective & Rotational Components]
    E --> F[Outcome: Uncovered Hidden Feedback Spirals & Rotational Shifts Signalling Crises]