Hyun‐Su Kim

Hyunsu Kim, Jonggeon Park, Joan Bruna et al.

The advent of foundation models in AI has significantly advanced general-purpose learning, enabling remarkable capabilities in zero-shot inference and in-context learning. However, training such models on physics data, including solutions to partial differential equations (PDEs), poses a unique challenge due to varying dimensionalities across different systems. Traditional approaches either fix a maximum dimension or employ separate encoders for different dimensionalities, resulting in inefficiencies. To address this, we propose a dimension-agnostic neural network architecture, the Axial Neural Network (XNN), inspired by parameter-sharing structures such as Deep Sets and Graph Neural Networks. XNN generalizes across varying tensor dimensions while maintaining computational efficiency. We convert existing PDE foundation models into axial neural networks and evaluate their performance across three training scenarios: training from scratch, pretraining on multiple PDEs, and fine-tuning on a single PDE. Our experiments show that XNNs perform competitively with original models and exhibit superior generalization to unseen dimensions, highlighting the importance of multidimensional pretraining for foundation models.

Hyunsu Kim

This paper introduces a potential application of deep learning and artificial intelligence in finance, particularly its application in hedging. The major goal encompasses two objectives. First, we present a framework of a direct policy search reinforcement agent replicating a simple vanilla European call option and use the agent for the model-free delta hedging. Through the first part of this paper, we demonstrate how the RNN-based direct policy search RL agents can perform delta hedging better than the classic Black-Scholes model in Q-world based on parametrically generated underlying scenarios, particularly minimizing tail exposures at higher values of the risk aversion parameter. In the second part of this paper, with the non-parametric paths generated by time-series GANs from multi-variate temporal space, we illustrate its delta hedging performance on various values of the risk aversion parameter via the basic RNN-based RL agent introduced in the first part of the paper, showing that we can potentially achieve higher average profits with a rather evident risk-return trade-off. We believe that this RL-based hedging framework is a more efficient way of performing hedging in practice, addressing some of the inherent issues with the classic models, providing promising/intuitive hedging results, and rendering a flexible framework that can be easily paired with other AI-based models for many other purposes.