Optimization plays a key role in the training of deep neural networks. Deciding when to stop training can have a substantial impact on the performance of the network during inference. Under certain conditions, the generalization error can display a double descent pattern during training: the learning curve is non-monotonic and seemingly diverges before converging again after additional epochs. This optimization pattern can lead to early stopping procedures to stop training before the second convergence and consequently select a suboptimal set of parameters for the network, with worse performance during inference. In this work, in addition to confirming that double descent occurs with small datasets and noisy labels as evidenced by others, we show that noisy labels must be present both in the training and generalization sets to observe a double descent pattern. We also show that the learning rate has an influence on double descent, and study how different optimizers and optimizer parameters influence the apparition of double descent. Finally, we show that increasing the learning rate can create an aliasing effect that masks the double descent pattern without suppressing it. We study this phenomenon through extensive experiments on variants of CIFAR-10 and show that they translate to a real world application: the forecast of seizure events in epileptic patients from continuous electroencephalographic recordings.
Machine learning and quantum computing are two technologies that are causing a paradigm shift in the performance and behavior of certain algorithms, achieving previously unattainable results. Machine learning (kernel classification) has become ubiquitous as the forefront method for pattern recognition and has been shown to have numerous societal applications. While not yet fault-tolerant, Quantum computing is an entirely new method of computation due to its exploitation of quantum phenomena such as superposition and entanglement. While current machine learning classifiers like the Support Vector Machine are seeing gradual improvements in performance, there are still severe limitations on the efficiency and scalability of such algorithms due to a limited feature space which makes the kernel functions computationally expensive to estimate. By integrating quantum circuits into traditional ML, we may solve this problem through the use of quantum feature space, a technique that improves existing Machine Learning algorithms through the use of parallelization and the reduction of the storage space from exponential to linear. This research expands on this concept of the Hilbert space and applies it for classical machine learning by implementing the quantum-enhanced version of the K nearest neighbors algorithm. This paper first understands the mathematical intuition for the implementation of quantum feature space and successfully simulates quantum properties and algorithms like Fidelity and Grover's Algorithm via the Qiskit python library and the IBM Quantum Experience platform. The primary experiment of this research is to build a noisy variational quantum circuit KNN (QKNN) which mimics the classification methods of a traditional KNN classifier. The QKNN utilizes the distance metric of Hamming Distance and is able to outperform the existing KNN on a 10-dimensional Breast Cancer dataset.