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Can any neural network training objective be made convex?
No, it’s not convex unless it’s a one-layer network. In the general multiple-layer case, the parameters of the later layers (the weights and activation parameters) can be highly recursive functions of the parameters in previous layers.
How do you optimize a neural network model?
Optimizing Neural Networks — Where to Start?
- Start with learning rate;
- Then try number of hidden units, mini-batch size and momentum term;
- Lastly, tune number of layers and learning rate decay.
What are convex loss functions?
Fortunately, hinge loss, logistic loss and square loss are all convex functions. Convexity ensures global minimum and it’s computationally appleaing.
How is non convex optimization used in neural network optimization?
Non-convex optimization involves a function which has multiple optima, only one of which is the global optima. Depending on the loss surface, it can be very difficult to locate the global optima For a neural network, the curve or surface that we are talking about is the loss surface.
Why are the popular loss functions not convex?
As others pointed out, deep nets’ loss functions are mostly not convex. The easiest way to see this is to realize the symmetry of two hidden nodes in the same layer. Machine learning is faster when you collaborate with your team. Our servers make that possible.
Are there local optima for convex optimization problems?
Convex optimization involves a function in which there is only one optimum, corresponding to the global optimum (maximum or minimum). There is no concept of local optima for convex optimization problems, making them relatively easy to solve — these are common introductory topics in undergraduate and graduate optimization classes.
How are loss functions used in neural networks?
Neural networks are trained using stochastic gradient descent and require that you choose a loss function when designing and configuring your model. There are many loss functions to choose from and it can be challenging to know what to choose, or even what a loss function is and the role it plays when training a neural network.