Accelerating Training of Convolutional Neural Networks With Hessian-Free Optimization for Detecting Alzheimer’s Disease in Brain MRI

Convolutional neural network (CNN) classifiers, which perform feature extraction from brain magnetic resonance imaging (MRI) data and classify them as healthy or diseased, are very promising in aiding the diagnosis of neurological disorders. CNN models are usually optimized with first-order algorithms, e.g. stochastic gradient descent (SGD) and adaptive momentum (Adam), which are susceptible to pathological curvature of the objective function. Hessian-free optimization (HFO), a second-order algorithm, overcomes this problem and thus is expected to converge faster. Here, we investigated whether HFO can increase the training speed of CNN models for brain MRI classification into cognitively normal or Alzheimer’s disease using data from the Alzheimer’s Disease Neuroimaging Initiative. We trained two naive CNN classifiers with either HFO, SGD or Adam and compared their performance. Our results show that HFO converged at least two to four times faster than Adam and SGD. The cross-validation accuracy of the models optimized with HFO was comparable or better than those optimized with SGD or Adam. In addition, HFO was more robust to hyperparameter changes. These results comply with theory and act as a proof of concept that second-order algorithms have an advantage over first-order methods in training CNN models for MRI classification.