Invariant Representations with Stochastically Quantized Neural Networks

Representation learning algorithms offer the opportunity to learn invariant representations of the input data with regard to nuisance factors. Many authors have leveraged such strategies to learn fair representations, i.e., vectors where information about sensitive attributes is removed. These methods are attractive as they may be interpreted as minimizing the mutual information between a neural layer's activations and a sensitive attribute. However, the theoretical grounding of such methods relies either on the computation of infinitely accurate adversaries or on minimizing a variational upper bound of a mutual information estimate. In this paper, we propose a methodology for direct computation of the mutual information between a neural layer and a sensitive attribute. We employ stochastically-activated binary neural networks, which lets us treat neurons as random variables. We are then able to compute (not bound) the mutual information between a layer and a sensitive attribute and use this information as a regularization factor during gradient descent. We show that this method compares favorably with the state of the art in fair representation learning and that the learned representations display a higher level of invariance compared to full-precision neural networks

Mutual Information Maximizing Quantum Generative Adversarial Network and Its Applications in Finance

One of the most promising applications in the era of NISQ (Noisy Intermediate-Scale Quantum) computing is quantum machine learning. Quantum machine learning offers significant quantum advantages over classical machine learning across various domains. Specifically, generative adversarial networks have been recognized for their potential utility in diverse fields such as image generation, finance, and probability distribution modeling. However, these networks necessitate solutions for inherent challenges like mode collapse. In this study, we capitalize on the concept that the estimation of mutual information between high-dimensional continuous random variables can be achieved through gradient descent using neural networks. We introduce a novel approach named InfoQGAN, which employs the Mutual Information Neural Estimator (MINE) within the framework of quantum generative adversarial networks to tackle the mode collapse issue. Furthermore, we elaborate on how this approach can be applied to a financial scenario, specifically addressing the problem of generating portfolio return distributions through dynamic asset allocation. This illustrates the potential practical applicability of InfoQGAN in real-world contexts.Comment: 15 pages, 15 figure