Non-adversarial training of Neural SDEs with signature kernel scores

ArXiv ID: 2305.16274 “View on arXiv”

Authors: Unknown

Abstract

Neural SDEs are continuous-time generative models for sequential data. State-of-the-art performance for irregular time series generation has been previously obtained by training these models adversarially as GANs. However, as typical for GAN architectures, training is notoriously unstable, often suffers from mode collapse, and requires specialised techniques such as weight clipping and gradient penalty to mitigate these issues. In this paper, we introduce a novel class of scoring rules on pathspace based on signature kernels and use them as objective for training Neural SDEs non-adversarially. By showing strict properness of such kernel scores and consistency of the corresponding estimators, we provide existence and uniqueness guarantees for the minimiser. With this formulation, evaluating the generator-discriminator pair amounts to solving a system of linear path-dependent PDEs which allows for memory-efficient adjoint-based backpropagation. Moreover, because the proposed kernel scores are well-defined for paths with values in infinite dimensional spaces of functions, our framework can be easily extended to generate spatiotemporal data. Our procedure permits conditioning on a rich variety of market conditions and significantly outperforms alternative ways of training Neural SDEs on a variety of tasks including the simulation of rough volatility models, the conditional probabilistic forecasts of real-world forex pairs where the conditioning variable is an observed past trajectory, and the mesh-free generation of limit order book dynamics.

Keywords: Neural SDEs, Signature Kernels, Time Series Generation, Rough Volatility, Limit Order Book, General Financial Markets (Derivatives/Spot)

Complexity vs Empirical Score

• Math Complexity: 9.0/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats
• Why: The paper is highly theoretical, featuring advanced mathematics like signature kernels, infinite-dimensional pathspace analysis, and strict properness proofs, but it lacks any empirical implementation details such as code, backtests, or datasets, focusing instead on theoretical guarantees and high-level descriptions of applications.

  flowchart TD
    A["Research Goal: Non-adversarial<br>Training of Neural SDEs"] --> B{"Introduce Novel Scoring Rule<br>based on Signature Kernels"}
    B --> C["Derive Theoretical Guarantees<br>Strict Properness & Consistency"]
    C --> D["Formulate Generator-Discriminator<br>as Linear Path-Dependent PDEs"]
    D --> E["Apply Memory-Efficient<br>Adjoint Backpropagation"]
    E --> F["Key Outcomes"]
    
    subgraph F [" "]
        F1["Stable Training<br>No Mode Collapse"]
        F2["Spill-over to<br>Spatiotemporal Data"]
        F3["State-of-the-Art Performance<br>on Rough Volatility & LOB"]
    end