Non-local methods exploiting the self-similarity of natural signals have been well studied, for example in image analysis and restoration. Existing approaches, however, rely on k-nearest neighbors (KNN) matching in a fixed feature space. The main hurdle in optimizing this feature space w.r.t. application performance is the non-differentiability of the KNN selection rule. To overcome this, we propose a continuous deterministic relaxation of KNN selection that maintains differentiability w.r.t. pairwise distances, but retains the original KNN as the limit of a temperature parameter approaching zero. To exploit our relaxation, we propose the neural nearest neighbors block (N3 block), a novel non-local processing layer that leverages the principle of self-similarity and can be used as building block in modern neural network architectures. We show its effectiveness for the set reasoning task of correspondence classification as well as for image restoration, including image denoising and single image super-resolution, where we outperform strong convolutional neural network (CNN) baselines and recent non-local models that rely on KNN selection in hand-chosen features spaces.

Non-local methods exploiting the self-similarity of natural signals have been well studied, for example in image analysis and restoration. Existing approaches, however, rely on k-nearest neighbors (KNN) matching in a fixed feature space. The main hurdle in optimizing this feature space w.r.t. application performance is the non-differentiability of the KNN selection rule. To overcome this, we propose a continuous deterministic relaxation of KNN selection that maintains differentiability w.r.t. pairwise distances, but retains the original KNN as the limit of a temperature parameter approaching zero. To exploit our relaxation, we propose the neural nearest neighbors block (N3 block), a novel non-local processing layer that leverages the principle of self-similarity and can be used as building block in modern neural network architectures. We show its effectiveness for the set reasoning task of correspondence classification as well as for image restoration, including image denoising and single image super-resolution, where we outperform strong convolutional neural network (CNN) baselines and recent non-local models that rely on KNN selection in hand-chosen features spaces.

Variational inference has experienced a recent surge in popularity owing to stochastic approaches, which have yielded practical tools for a wide range of model classes. A key benefit is that stochastic variational inference obviates the tedious process of deriving analytical expressions for closed-form variable updates. Instead, one simply needs to derive the gradient of the log-posterior, which is often much easier. Yet for certain model classes, the log-posterior itself is difficult to optimize using standard gradient techniques. One such example are random field models, where optimization based on gradient linearization has proven popular, since it speeds up convergence significantly and can avoid poor local optima. In this paper we propose stochastic variational inference with gradient linearization (SVIGL). It is similarly convenient as standard stochastic variational inference - all that is required is a local linearization of the energy gradient. Its benefit over stochastic variational inference with conventional gradient methods is a clear improvement in convergence speed, while yielding comparable or even better variational approximations in terms of KL divergence. We demonstrate the benefits of SVIGL in three applications: Optical flow estimation, Poisson-Gaussian denoising, and 3D surface reconstruction.