We address the unsupervised learning of several interconnected problems in low-level vision: single view depth prediction, camera motion estimation, optical flow, and segmentation of a video into the static scene and moving regions. Our key insight is that these four fundamental vision problems are coupled through geometric constraints. Consequently, learning to solve them together simplifies the problem because the solutions can reinforce each other. We go beyond previous work by exploiting geometry more explicitly and segmenting the scene into static and moving regions. To that end, we introduce Competitive Collaboration, a framework that facilitates the coordinated training of multiple specialized neural networks to solve complex problems. Competitive Collaboration works much like expectation-maximization, but with neural networks that act as both competitors to explain pixels that correspond to static or moving regions, and as collaborators through a moderator that assigns pixels to be either static or independently moving. Our novel method integrates all these problems in a common framework and simultaneously reasons about the segmentation of the scene into moving objects and the static background, the camera motion, depth of the static scene structure, and the optical flow of moving objects. Our model is trained without any supervision and achieves state-of-the-art performance among joint unsupervised methods on all sub-problems. .

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Early stopping is a widely used technique to prevent poor generalization performance when training an over-expressive model by means of gradient-based optimization. To find a good point to halt the optimizer, a common practice is to split the dataset into a training and a smaller validation set to obtain an ongoing estimate of the generalization performance. We propose a novel early stopping criterion based on fast-to-compute local statistics of the computed gradients and entirely removes the need for a held-out validation set. Our experiments show that this is a viable approach in the setting of least-squares and logistic regression, as well as neural networks.

Mini-batch stochastic gradient descent and variants thereof have become standard for large-scale empirical risk minimization like the training of neural networks. These methods are usually used with a constant batch size chosen by simple empirical inspection. The batch size significantly influences the behavior of the stochastic optimization algorithm, though, since it determines the variance of the gradient estimates. This variance also changes over the optimization process; when using a constant batch size, stability and convergence is thus often enforced by means of a (manually tuned) decreasing learning rate schedule.We propose a practical method for dynamic batch size adaptation. It estimates the variance of the stochastic gradients and adapts the batch size to decrease the variance proportionally to the value of the objective function, removing the need for the aforementioned learning rate decrease. In contrast to recent related work, our algorithm couples the batch size to the learning rate, directly reflecting the known relationship between the two. On popular image classification benchmarks, our batch size adaptation yields faster optimization convergence, while simultaneously simplifying learning rate tuning. A TensorFlow implementation is available.

Standard first-order stochastic optimization algorithms base their updates solely on the average mini-batch gradient, and it has been shown that tracking additional quantities such as the curvature can help de-sensitize common hyperparameters. Based on this intuition, we explore the use of exact per-sample Hessian-vector products and gradients to construct optimizers that are self-tuning and hyperparameter-free. Based on a dynamics model of the gradient, we derive a process which leads to a curvature-corrected, noise-adaptive online gradient estimate. The smoothness of our updates makes it more amenable to simple step size selection schemes, which we also base off of our estimates quantities. We prove that our model-based procedure converges in the noisy quadratic setting. Though we do not see similar gains in deep learning tasks, we can match the performance of well-tuned optimizers and ultimately, this is an interesting step for constructing self-tuning optimizers.