Catastrophic Fisher Explosion: Early Phase Fisher Matrix Impacts Generalization

The early phase of training has been shown to be important in two ways for deep neural networks. First, the degree of regularization in this phase significantly impacts the final generalization. Second, it is accompanied by a rapid change in the local loss curvature influenced by regularization choices. Connecting these two findings, we show that stochastic gradient descent (SGD) implicitly penalizes the trace of the Fisher Information Matrix (FIM) from the beginning 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 further show that the early value of the trace of the FIM correlates strongly with the final generalization. We highlight that in the absence of implicit or explicit regularization, the trace of the FIM can increase to 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 1) it limits memorization by reducing the learning speed of examples with noisy labels more than that of the clean examples, and 2) trajectories with a low initial trace of the FIM end in flat minima, which are commonly associated with good generalization.

Differences between human and machine perception in medical diagnosis

Deep neural networks (DNNs) show promise in image-based medical diagnosis, but cannot be fully trusted since their performance can be severely degraded by dataset shifts to which human perception remains invariant. If we can better understand the differences between human and machine perception, we can potentially characterize and mitigate this effect. We therefore propose a framework for comparing human and machine perception in medical diagnosis. The two are compared with respect to their sensitivity to the removal of clinically meaningful information, and to the regions of an image deemed most suspicious. Drawing inspiration from the natural image domain, we frame both comparisons in terms of perturbation robustness. The novelty of our framework is that separate analyses are performed for subgroups with clinically meaningful differences. We argue that this is necessary in order to avert Simpson's paradox and draw correct conclusions. We demonstrate our framework with a case study in breast cancer screening, and reveal significant differences between radiologists and DNNs. We compare the two with respect to their robustness to Gaussian low-pass filtering, performing a subgroup analysis on microcalcifications and soft tissue lesions. For microcalcifications, DNNs use a separate set of high frequency components than radiologists, some of which lie outside the image regions considered most suspicious by radiologists. These features run the risk of being spurious, but if not, could represent potential new biomarkers. For soft tissue lesions, the divergence between radiologists and DNNs is even starker, with DNNs relying heavily on spurious high frequency components ignored by radiologists. Importantly, this deviation in soft tissue lesions was only observable through subgroup analysis, which highlights the importance of incorporating medical domain knowledge into our comparison framework.

We Should at Least Be Able to Design Molecules That Dock Well

Designing compounds with desired properties is a key element of the drug discovery process. However, measuring progress in the field has been challenging due to the lack of realistic retrospective benchmarks, and the large cost of prospective validation. To close this gap, we propose a benchmark based on docking, a popular computational method for assessing molecule binding to a protein. Concretely, the goal is to generate drug-like molecules that are scored highly by SMINA, a popular docking software. We observe that popular graph-based generative models fail to generate molecules with a high docking score when trained using a realistically sized training set. This suggests a limitation of the current incarnation of models for de novo drug design. Finally, we propose a simplified version of the benchmark based on a simpler scoring function, and show that the tested models are able to partially solve it. We release the benchmark as an easy to use package available at https://github.com/cieplinski-tobiasz/smina-docking-benchmark. We hope that our benchmark will serve as a stepping stone towards the goal of automatically generating promising drug candidates.

The Break-Even Point on Optimization Trajectories of Deep Neural Networks

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.

Large Scale Structure of Neural Network Loss Landscapes

There are many surprising and perhaps counter-intuitive properties of optimization of deep neural networks. We propose and experimentally verify a unified phenomenological model of the loss landscape that incorporates many of them. High dimensionality plays a key role in our model. Our core idea is to model the loss landscape as a set of high dimensional \emph{wedges} that together form a large-scale, inter-connected structure and towards which optimization is drawn. We first show that hyperparameter choices such as learning rate, network width and $L_2$ regularization, affect the path optimizer takes through the landscape in a similar ways, influencing the large scale curvature of the regions the optimizer explores. Finally, we predict and demonstrate new counter-intuitive properties of the loss-landscape. We show an existence of low loss subspaces connecting a set (not only a pair) of solutions, and verify it experimentally. Finally, we analyze recently popular ensembling techniques for deep networks in the light of our model.

Parameter-Efficient Transfer Learning for NLP

Fine-tuning large pre-trained models is an effective transfer mechanism in NLP. However, in the presence of many downstream tasks, fine-tuning is parameter inefficient: an entire new model is required for every task. As an alternative, we propose transfer with adapter modules. Adapter modules yield a compact and extensible model; they add only a few trainable parameters per task, and new tasks can be added without revisiting previous ones. The parameters of the original network remain fixed, yielding a high degree of parameter sharing. To demonstrate adapter's effectiveness, we transfer the recently proposed BERT Transformer model to 26 diverse text classification tasks, including the GLUE benchmark. Adapters attain near state-of-the-art performance, whilst adding only a few parameters per task. On GLUE, we attain within 0.4% of the performance of full fine-tuning, adding only 3.6% parameters per task. By contrast, fine-tuning trains 100% of the parameters per task.