Smooth input preparation for quantum and quantum-inspired machine learning

Machine learning has recently emerged as a fruitful area for finding potential quantum computational advantage. Many of the quantum-enhanced machine learning algorithms critically hinge upon the ability to efficiently produce states proportional to high-dimensional data points stored in a quantum accessible memory. Even given query access to exponentially many entries stored in a database, the construction of which is considered a one-off overhead, it has been argued that the cost of preparing such amplitude-encoded states may offset any exponential quantum advantage. Here we prove using smoothed analysis that if the data analysis algorithm is robust against small entry-wise input perturbation, state preparation can always be achieved with constant queries. This criterion is typically satisfied in realistic machine learning applications, where input data is subjective to moderate noise. Our results are equally applicable to the recent seminal progress in quantum-inspired algorithms, where specially constructed databases suffice for polylogarithmic classical algorithm in low-rank cases. The consequence of our finding is that for the purpose of practical machine learning, polylogarithmic processing time is possible under a general and flexible input model with quantum algorithms or quantum-inspired classical algorithms in the low-rank cases.

Adversarial Transformations for Semi-Supervised Learning

We propose a Regularization framework based on Adversarial Transformations (RAT) for semi-supervised learning. RAT is designed to enhance robustness of the output distribution of class prediction for a given data against input perturbation. RAT is an extension of Virtual Adversarial Training (VAT) in such a way that RAT adversraialy transforms data along the underlying data distribution by a rich set of data transformation functions that leave class label invariant, whereas VAT simply produces adversarial additive noises. In addition, we verified that a technique of gradually increasing of perturbation region further improves the robustness. In experiments, we show that RAT significantly improves classification performance on CIFAR-10 and SVHN compared to existing regularization methods under standard semi-supervised image classification settings.

Smooth Deep Image Generator from Noises

Generative Adversarial Networks (GANs) have demonstrated a strong ability to fit complex distributions since they were presented, especially in the field of generating natural images. Linear interpolation in the noise space produces a continuously changing in the image space, which is an impressive property of GANs. However, there is no special consideration on this property in the objective function of GANs or its derived models. This paper analyzes the perturbation on the input of the generator and its influence on the generated images. A smooth generator is then developed by investigating the tolerable input perturbation. We further integrate this smooth generator with a gradient penalized discriminator, and design smooth GAN that generates stable and high-quality images. Experiments on real-world image datasets demonstrate the necessity of studying smooth generator and the effectiveness of the proposed algorithm.