Krzysztof Geras

Umang Sharma, Jungkyu Park, Laura Heacock et al.

Full Field Digital Mammograms (FFDMs) and Digital Breast Tomosynthesis (DBT) are the two most widely used imaging modalities for breast cancer screening. Although DBT has increased cancer detection compared to FFDM, its widespread adoption in clinical practice has been slowed by increased interpretation times and a perceived decrease in the conspicuity of specific lesion types. Specifically, the non-inferiority of DBT for microcalcifications remains under debate. Due to concerns about the decrease in visual acuity, combined DBT-FFDM acquisitions remain popular, leading to overall increased exam times and radiation dosage. Enabling DBT to provide diagnostic information present in both FFDM and DBT would reduce reliance on FFDM, resulting in a reduction in both quantities. We propose a machine learning methodology that learns high-level representations leveraging the complementary diagnostic signal from both DBT and FFDM. Experiments on a large-scale data set validate our claims and show that our representations enable more accurate breast lesion detection than any DBT- or FFDM-based model.

Stanislaw Jastrzebski, Devansh Arpit, Oliver Astrand et al.

The early phase of training a deep neural network has a dramatic effect on the local curvature of the loss function. For instance, using a small learning rate does not guarantee stable optimization because the optimization trajectory has a tendency to steer towards regions of the loss surface with increasing local curvature. We ask whether this tendency is connected to the widely observed phenomenon that the choice of the learning rate strongly influences generalization. We first show that stochastic gradient descent (SGD) implicitly penalizes the trace of the Fisher Information Matrix (FIM), a measure of the local curvature, from the start of training. We argue it is an implicit regularizer in SGD by showing that explicitly penalizing the trace of the FIM can significantly improve generalization. We highlight that poor final generalization coincides with the trace of the FIM attaining a large value early in training, to which we refer as catastrophic Fisher explosion. Finally, to gain insight into the regularization effect of penalizing the trace of the FIM, we show that it limits memorization by reducing the learning speed of examples with noisy labels more than that of the examples with clean labels.

Stanislaw Jastrzebski, Maciej Szymczak, Stanislav Fort et al.

The early phase of training of deep neural networks is critical for their final performance. In this work, we study how the hyperparameters of stochastic gradient descent (SGD) used in the early phase of training affect the rest of the optimization trajectory. We argue for the existence of the "break-even" point on this trajectory, beyond which the curvature of the loss surface and noise in the gradient are implicitly regularized by SGD. In particular, we demonstrate on multiple classification tasks that using a large learning rate in the initial phase of training reduces the variance of the gradient, and improves the conditioning of the covariance of gradients. These effects are beneficial from the optimization perspective and become visible after the break-even point. Complementing prior work, we also show that using a low learning rate results in bad conditioning of the loss surface even for a neural network with batch normalization layers. In short, our work shows that key properties of the loss surface are strongly influenced by SGD in the early phase of training. We argue that studying the impact of the identified effects on generalization is a promising future direction.

Amos Storkey, Jono Millin, Krzysztof Geras

Recently, prediction markets have shown considerable promise for developing flexible mechanisms for machine learning. In this paper, agents with isoelastic utilities are considered. It is shown that the costs associated with homogeneous markets of agents with isoelastic utilities produce equilibrium prices corresponding to alpha-mixtures, with a particular form of mixing component relating to each agent's wealth. We also demonstrate that wealth accumulation for logarithmic and other isoelastic agents (through payoffs on prediction of training targets) can implement both Bayesian model updates and mixture weight updates by imposing different market payoff structures. An iterative algorithm is given for market equilibrium computation. We demonstrate that inhomogeneous markets of agents with isoelastic utilities outperform state of the art aggregate classifiers such as random forests, as well as single classifiers (neural networks, decision trees) on a number of machine learning benchmarks, and show that isoelastic combination methods are generally better than their logarithmic counterparts.