Mean-Field Microcanonical Gradient Descent

ArXiv ID: 2403.08362 “View on arXiv”

Authors: Unknown

Abstract

Microcanonical gradient descent is a sampling procedure for energy-based models allowing for efficient sampling of distributions in high dimension. It works by transporting samples from a high-entropy distribution, such as Gaussian white noise, to a low-energy region using gradient descent. We put this model in the framework of normalizing flows, showing how it can often overfit by losing an unnecessary amount of entropy in the descent. As a remedy, we propose a mean-field microcanonical gradient descent that samples several weakly coupled data points simultaneously, allowing for better control of the entropy loss while paying little in terms of likelihood fit. We study these models in the context of financial time series, illustrating the improvements on both synthetic and real data.

Keywords: Normalizing Flows, Energy-Based Models, Generative Models, Microcanonical Descent, Time Series Modeling

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper introduces and analyzes a novel generative model (MF-MGDM) with substantial theoretical derivation and entropy bounds, indicating high mathematical complexity, while also evaluating the method on synthetic and real financial data, demonstrating practical implementation and validation.

  flowchart TD
    A["Research Goal<br>Efficient Sampling for EBM"] --> B{"Methodology<br>Microcanonical Gradient Descent"}
    B --> C["Input: High-Entropy Data<br>Gaussian White Noise"]
    C --> D["Process: Mean-Field Optimization<br>Simultaneous weakly coupled descent"]
    D --> E["Output: Low-Energy Distribution<br>Sampled Time Series"]
    E --> F["Key Findings"]
    subgraph F ["Outcomes"]
        F1["Better entropy control<br>Less loss than normalizing flows"]
        F2["Efficient likelihood fit<br>in high dimensions"]
        F3["Effective on Financial Data<br>Synthetic & Real"]
    end