Contents
What is orthogonal initialization?
Orthogonal initialization is a simple yet relatively effective way of combatting exploding and vanishing gradients, especially when paired with other methods such as gradient clipping and more advanced architectures.
Why is Xavier initialization used?
The goal of Xavier Initialization is to initialize the weights such that the variance of the activations are the same across every layer. This constant variance helps prevent the gradient from exploding or vanishing.
What is orthogonal regularization?
Introduced by Brock et al. in Neural Photo Editing with Introspective Adversarial Networks. Orthogonal Regularization is a regularization technique for convolutional neural networks, introduced with generative modelling as the task in mind.
How do you know if a matrix is orthogonal?
To determine if a matrix is orthogonal, we need to multiply the matrix by it’s transpose, and see if we get the identity matrix. Since we get the identity matrix, then we know that is an orthogonal matrix.
What is meant by orthogonal?
1a : intersecting or lying at right angles In orthogonal cutting, the cutting edge is perpendicular to the direction of tool travel. b : having perpendicular slopes or tangents at the point of intersection orthogonal curves.
Can we gain more from orthogonality Regularizations?
Can We Gain More from Orthogonality Regularizations in Training Deep CNNs? We observe consistent performance gains after applying those proposed regularizations, in terms of both the final accuracies achieved, and faster and more stable convergences.
How does orthogonal weight normalization work in training?
Particularly, it constructs orthogonal transformation over proxy parameters to ensure the weight matrix is orthogonal and back-propagates gradient information through the transformation during training. To guarantee stability, we minimize the distortions between proxy parameters and canonical weights over all tractable orthogonal transformations.
Can a weight matrix be initialized to an orthogonal matrix?
In practice, initializing the weight matrix of a dense layer to a random orthogonal matrix is fairly straightforward. For the convolutional layer, where the weight matrix isn’t strictly a matrix, we need to think more carefully about what this means.
Why is orthogonal initialization used in convolutional layers?
Orthogonal initialization has shown to provide numerous benefits for training deep neural networks. It is easy to see which vectors should be orthogonal to one another in a dense layer, but less straightforward to see where this orthogonality should happen in a convolutional layer, because the weight matrix is no longer really a matrix.
What happens when weight initialization is too large?
During the course of the above hypothetical forward pass, the activation outputs completely vanished. To sum it up, if weights are initialized too large, the network won’t learn well. The same happens when weights are initialized too small. How can we find the sweet spot?
https://www.youtube.com/watch?v=vQ_ifavFBkI