While semi-supervised learning (SSL) algorithms provide an efficient way to make use of both labelled and unlabelled data, they generally struggle when the number of annotated samples is very small. In this work, we consider the problem of SSL multi-class classification with very few labelled instances. We introduce two key ideas. The first is a simple but effective one: we leverage the power of transfer learning among different tasks and self-supervision to initialize a good representation of the data without making use of any label. The second idea is a new algorithm for SSL that can exploit well such a pre-trained representation. The algorithm works by alternating two phases, one fitting the labelled points and one fitting the unlabelled ones, with carefully-controlled information flow between them. The benefits are greatly reducing overfitting of the labelled data and avoiding issue with balancing labelled and unlabelled losses during training. We show empirically that this method can successfully train competitive models with as few as 10 labelled data points per class. More in general, we show that the idea of bootstrapping features using self-supervised learning always improves SSL on standard benchmarks. We show that our algorithm works increasingly well compared to other methods when refining from other tasks or datasets.

We propose a fast second-order method that can be used as a drop-in replacement for current deep learning solvers. Compared to stochastic gradient descent (SGD), it only requires two additional forward-mode automatic differentiation operations per iteration, which has a computational cost comparable to two standard forward passes and is easy to implement. Our method addresses long-standing issues with current second-order solvers, which invert an approximate Hessian matrix every iteration exactly or by conjugate-gradient methods, a procedure that is both costly and sensitive to noise. Instead, we propose to keep a single estimate of the gradient projected by the inverse Hessian matrix, and update it once per iteration. This estimate has the same size and is similar to the momentum variable that is commonly used in SGD. No estimate of the Hessian is maintained. We first validate our method, called CurveBall, on small problems with known closed-form solutions (noisy Rosenbrock function and degenerate 2-layer linear networks), where current deep learning solvers seem to struggle. We then train several large models on CIFAR and ImageNet, including ResNet and VGG-f networks, where we demonstrate faster convergence with no hyperparameter tuning. Code is available.

While learning models of intuitive physics is an increasingly active area of research, current approaches still fall short of natural intelligences in one important regard: they require external supervision, such as explicit access to physical states, at training and sometimes even at test times. Some authors have relaxed such requirements by supplementing the model with an handcrafted physical simulator. Still, the resulting methods are unable to automatically learn new complex environments and to understand physical interactions within them. In this work, we demonstrated for the first time learning such predictors directly from raw visual observations and without relying on simulators. We do so in two steps: first, we learn to track mechanically-salient objects in videos using causality and equivariance, two unsupervised learning principles that do not require auto-encoding. Second, we demonstrate that the extracted positions are sufficient to successfully train visual motion predictors that can take the underlying environment into account. We validate our predictors on synthetic datasets; then, we introduce a new dataset, ROLL4REAL, consisting of real objects rolling on complex terrains (pool table, elliptical bowl, and random height-field). We show that in all such cases it is possible to learn reliable extrapolators of the object trajectories from raw videos alone, without any form of external supervision and with no more prior knowledge than the choice of a convolutional neural network architecture.