Occam Gradient Descent

Abstract: Deep learning neural network models must be large enough to adapt to their problem domain, while small enough to avoid overfitting training data during gradient descent. To balance these competing demands, overprovisioned deep learning models such as transformers are trained for a single epoch on large data sets, and hence inefficient with both computing resources and training data. In response to these inefficiencies, we exploit learning theory to derive Occam Gradient Descent, an algorithm that interleaves adaptive reduction of model size to minimize generalization error, with gradient descent on model weights to minimize fitting error. In contrast, traditional gradient descent greedily minimizes fitting error without regard to generalization error. Our algorithm simultaneously descends the space of weights and topological size of any neural network without modification. With respect to loss, compute and model size, our experiments show (a) on image classification benchmarks, linear and convolutional neural networks trained with Occam Gradient Descent outperform traditional gradient descent with or without post-train pruning; (b) on a range of tabular data classification tasks, neural networks trained with Occam Gradient Descent outperform traditional gradient descent, as well as Random Forests; (c) on natural language transformers, Occam Gradient Descent outperforms traditional gradient descent.