What is error surface in neural network?

What is error surface in neural network?

With a fixed training set the error is a function of the weights: the error surface. In the backpropagation algorithm the error in the output is reduced by changing the weight vector in the direction opposite to the gradient of the error with respect to the weights.

Is neural network a convex optimization problem?

Despite being non-convex, deep neural networks are surprisingly amenable to optimization by gradient descent. In this note, we use a deep neural network with D parameters to parametrize the input space of a generic d-dimensional nonconvex optimization problem.

Is neural network loss 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.

Can any neural network be made convex?

We show that many existing neural network architectures can be made input- convex with a minor modification, and develop specialized optimization algorithms tailored to this setting.

Which model error surface can have multiple local minima?

Accepted Answers: A) ANN error surface has multiple local minima while SVM error surface has only one minima B) After training, an ANN might land on a different minimum each time, when initialized with random weights during each run.

Is gradient descent an optimizer?

Gradient descent is an optimization algorithm that’s used when training a machine learning model. It’s based on a convex function and tweaks its parameters iteratively to minimize a given function to its local minimum.

Are CNNs convex?

Convolutional neural networks (CNNs) are a special kind of deep learning method, and it is particularly useful in field of computer vision. Despite deep learning’s great success on performance, there are always criticisms and concerns about this method. One of them are that it is not a convex problem.

What is a convex cost function?

A convex function: given any two points on the curve there will be no intersection with any other points, for non convex function there will be at least one intersection. In terms of cost function with a convex type you are always guaranteed to have a global minimum, whilst for a non convex only local minima.

Why neural networks are non convex?

1 Answer. Basically since weights are permutable across layers there are multiple solutions for any minima that will achieve the same results, and thus the function cannot be convex (or concave either).

Why neural networks is not convex?

Can a function have two local mins?

If a function of one variable has two local maxima, it must have a local minimum in between. It’s clear that the function is zero at (-1, 0) and (1, 2), and that the function is negative otherwise.

Can a function have multiple local maximums?

The maximum or minimum over the entire function is called an “Absolute” or “Global” maximum or minimum. There is only one global maximum (and one global minimum) but there can be more than one local maximum or minimum.

Why are error function surface and non convexity useless?

They end up being very very complicated multidimensional non convex shapes with lots and lots of local minimum. It is impossible for a human to imagine something in more than three dimensions let alone in thousands of dimensions. So trying to visualize why a cost function of a few thousands weight values is non-convex is just useless.

Is it hard to find the global minimum in a non convex function?

Actually the problem of finding the global minimum in a non convex function is NP-Hard. Not only that we might end up in a local minimum there is an even worse possibility. And that is to end up in a saddle point instead. As some results show, there is an exponential number of saddle points on the error surface, and that’s very bad news.

Which is the mean squared error function in neural net?

We know the mean squared error function which will sum up all the errors distances between the desired output the the actual output of the neural net. The desired output is obviously 1 and the actual output or the feed-forward values of the net is w1 * w2.

Why are the cost functions of neural nets so complicated?

Cost function for real neural nets are very very complicated. The reason for this is that most neural networks are using non linear sigmoid or tanh functions in their neurons and the have several layers each with hundreds or thousands of neurons, and this is translated into tens or thousands or even millions of parameters (weights and biases).