Bottom-Up and Top-Down Reasoning with Hierarchical Rectified Gaussians
This work addresses the need for improved spatial reasoning in AI, particularly for tasks like keypoint localization under occlusions, though it appears incremental as it builds on existing CNN and probabilistic model frameworks.
The paper tackles the problem of detailed spatial understanding in neural networks by introducing a bidirectional architecture that combines bottom-up and top-down reasoning using hierarchical Rectified Gaussians, achieving state-of-the-art results on keypoint localization under occlusions.
Convolutional neural nets (CNNs) have demonstrated remarkable performance in recent history. Such approaches tend to work in a unidirectional bottom-up feed-forward fashion. However, practical experience and biological evidence tells us that feedback plays a crucial role, particularly for detailed spatial understanding tasks. This work explores bidirectional architectures that also reason with top-down feedback: neural units are influenced by both lower and higher-level units. We do so by treating units as rectified latent variables in a quadratic energy function, which can be seen as a hierarchical Rectified Gaussian model (RGs). We show that RGs can be optimized with a quadratic program (QP), that can in turn be optimized with a recurrent neural network (with rectified linear units). This allows RGs to be trained with GPU-optimized gradient descent. From a theoretical perspective, RGs help establish a connection between CNNs and hierarchical probabilistic models. From a practical perspective, RGs are well suited for detailed spatial tasks that can benefit from top-down reasoning. We illustrate them on the challenging task of keypoint localization under occlusions, where local bottom-up evidence may be misleading. We demonstrate state-of-the-art results on challenging benchmarks.