Soft-Label Dataset Distillation and Text Dataset Distillation

Dataset distillation is a method for reducing dataset sizes by learning a small number of synthetic samples containing all the information of a large dataset. This has several benefits like speeding up model training, reducing energy consumption, and reducing required storage space. Currently, each synthetic sample is assigned a single `hard' label, and also, dataset distillation can currently only be used with image data. We propose to simultaneously distill both images and their labels, thus assigning each synthetic sample a `soft' label (a distribution of labels). Our algorithm increases accuracy by 2-4% over the original algorithm for several image classification tasks. Using `soft' labels also enables distilled datasets to consist of fewer samples than there are classes as each sample can encode information for multiple classes. For example, training a LeNet model with 10 distilled images (one per class) results in over 96% accuracy on MNIST, and almost 92% accuracy when trained on just 5 distilled images. We also extend the dataset distillation algorithm to distill sequential datasets including texts. We demonstrate that text distillation outperforms other methods across multiple datasets. For example, models attain almost their original accuracy on the IMDB sentiment analysis task using just 20 distilled sentences. Our code can be found at $\href{https://github.com/ilia10000/dataset-distillation}{\text{https://github.com/ilia10000/dataset-distillation}}$

Exact solutions to the nonlinear dynamics of learning in deep linear neural networks

Despite the widespread practical success of deep learning methods, our theoretical understanding of the dynamics of learning in deep neural networks remains quite sparse. We attempt to bridge the gap between the theory and practice of deep learning by systematically analyzing learning dynamics for the restricted case of deep linear neural networks. Despite the linearity of their input-output map, such networks have nonlinear gradient descent dynamics on weights that change with the addition of each new hidden layer. We show that deep linear networks exhibit nonlinear learning phenomena similar to those seen in simulations of nonlinear networks, including long plateaus followed by rapid transitions to lower error solutions, and faster convergence from greedy unsupervised pretraining initial conditions than from random initial conditions. We provide an analytical description of these phenomena by finding new exact solutions to the nonlinear dynamics of deep learning. Our theoretical analysis also reveals the surprising finding that as the depth of a network approaches infinity, learning speed can nevertheless remain finite: for a special class of initial conditions on the weights, very deep networks incur only a finite, depth independent, delay in learning speed relative to shallow networks. We show that, under certain conditions on the training data, unsupervised pretraining can find this special class of initial conditions, while scaled random Gaussian initializations cannot. We further exhibit a new class of random orthogonal initial conditions on weights that, like unsupervised pre-training, enjoys depth independent learning times. We further show that these initial conditions also lead to faithful propagation of gradients even in deep nonlinear networks, as long as they operate in a special regime known as the edge of chaos.Comment: Submission to ICLR2014. Revised based on reviewer feedbac