Non-convex optimization with neural networks

  • Can I use neural network for optimization?

    The optimization process is conducted by the neural network's built-in backpropagation algorithm.
    The NOM solves optimization problems by extending the architecture of the NN objective function model.
    This is achieved by appropriately designing the NOM's structure, activation function, and loss function..

  • What does non convex mean?

    A polygon is convex if all the interior angles are less than 180 degrees.
    If one or more of the interior angles is more than 180 degrees the polygon is non-convex (or concave)..

  • What is non convex optimization for deep networks?

    A NCO is any problem where the objective or any of the constraints are non-convex.
    Even simple looking problems with as few as ten variables can be extremely challenging, while problems with a few hundreds of variables can be intractable.Jul 27, 2020.

  • What is optimization of non convex function?

    A non-convex optimization problem is any problem where the objective or any of the constraints are non-convex, as pictured below.
    Such a problem may have multiple feasible regions and multiple locally optimal points within each region..

  • Why do we need the deep neural network to be convex non-convex?

    Convex and non-convex functions are important concepts in machine learning, particularly in optimization problems.
    Convex functions have a unique global minimum, making optimization easier and more reliable.
    Non-convex functions, on the other hand, can have multiple local minima, making optimization more challenging..

  • A common optimization technique in neural networks is stochastic gradient descent.
    To alleviate the computational burden, training the neural network is carried out though mini-batches of the total training data.
    In each epoch, the training data are used in a mini-batch manner until all the data are used.

Can optimization algorithms solve neural network problems?

These tricks need to be combined with an optimization algorithm such as SGD and are largely orthogonal to optimization algorithms

In this section, we discuss optimization algorithms used to solve neural network problems, which are often generic and can be applied to other optimization problems as well

Does a neural network have a convex optimization?

Neural networks with linear activation functions and square loss will yield convex optimization (if my memory serves me right also for radial basis function networks with fixed variances)

However neural networks are mostly used with non-linear activation functions (i

e sigmoid), hence the optimization becomes non-convex

What is non-convex optimization?

Non-convex optimizationinvolves 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

The cost function of a neural network is in general neither convex nor concave. This means that the matrix of all second partial derivatives (the H...Best answer · 46

If you permute the neurons in the hidden layer and do the same permutation on the weights of the adjacent layers then the loss doesn't change. Henc...28

Whether the objective function is convex or not depends on the details of the network. In the case where multiple local minima exist, you ask wheth...11

Some answers for your updates: Yes, there are in general multiple local minima. (If there was only one, it would be called the global minimum.) The...6

You will have one global minimum if problem is convex or quasiconvex. About convex "building blocks" during building neural networks (Computer Scie...4

The composition of multiple layers is what makes the cross-entropy or least-squares loss function of multi-layer neural networks non-convex with re...1

By definition, a function $f(x)$ is convex over a convex set $S$ if for all $x, y \in S$ and $t \in [0, 1]$ , $tf(x) + (1-t)f(y) \geq f(tx...0


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