1,361 research outputs found
Bottom-Up and Top-Down Reasoning with Hierarchical Rectified Gaussians
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.Comment: To appear in CVPR 201
Application of Sparse Identification of Nonlinear Dynamics for Physics-Informed Learning
Advances in machine learning and deep neural networks has enabled complex engineering tasks like image recognition, anomaly detection, regression, and multi-objective optimization, to name but a few. The complexity of the algorithm architecture, e.g., the number of hidden layers in a deep neural network, typically grows with the complexity of the problems they are required to solve, leaving little room for interpreting (or explaining) the path that results in a specific solution. This drawback is particularly relevant for autonomous aerospace and aviation systems, where certifications require a complete understanding of the algorithm behavior in all possible scenarios. Including physics knowledge in such data-driven tools may improve the interpretability of the algorithms, thus enhancing model validation against events with low probability but relevant for system certification. Such events include, for example, spacecraft or aircraft sub-system failures, for which data may not be available in the training phase. This paper investigates a recent physics-informed learning algorithm for identification of system dynamics, and shows how the governing equations of a system can be extracted from data using sparse regression. The learned relationships can be utilized as a surrogate model which, unlike typical data-driven surrogate models, relies on the learned underlying dynamics of the system rather than large number of fitting parameters. The work shows that the algorithm can reconstruct the differential equations underlying the observed dynamics using a single trajectory when no uncertainty is involved. However, the training set size must increase when dealing with stochastic systems, e.g., nonlinear dynamics with random initial conditions
- …