Can a neural network be convex?

A new neural network architecture called the Input Convex Neural Networks (ICNNs) learn the output as a convex function of inputs thereby allowing the use of efficient convex optimization methods. …

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.

Why are neural nets not convex?

Thanks for the A2A. The non-convexity is due to the use of a non-linear activation function in one of the layers. So it is not a function of how many layers the network has.

Can any neural network training objective be made 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).

Is Deep neural network convex?

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.

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Is neural network optimization convex?

Are Neural Network Convex? The answer is No. You might want to argue that convex optimization shouldn’t be that interesting for machine learning since we often encounter loss surfaces like image below, that are far from convex. … However, Neural Network is also known as Differentiable Problems.

Is MLP convex?

MLP with hidden layers have a non-convex loss function where there exists more than one local minimum. … MLP requires tuning a number of hyperparameters such as the number of hidden neurons, layers, and iterations. MLP is sensitive to feature scaling.

Is the composition of convex functions convex?

prove that the composition of g(f) is convex on Ω. … Under what conditions is g(f) strictly convex.

Is sigmoid convex?

In general, a sigmoid function is monotonic, and has a first derivative which is bell shaped. … A sigmoid function is convex for values less than a particular point, and it is concave for values greater than that point: in many of the examples here, that point is 0.

What is convex and non-convex function?

Convex Functions

Geometrically, a function is convex if a line segment drawn from any point (x, f(x)) to another point (y, f(y)) — called the chord from x to y — lies on or above the graph of f, as in the picture below: … A non-convex function “curves up and down” — it is neither convex nor concave.

Is the cost function always convex?

The log likelihood function of a logistic regression function is concave , so if you define the cost function as the negative log likelihood function then indeed the cost function is convex.

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Is ReLU function convex?

We develop a convex analytic framework for ReLU neural networks which elucidates the inner workings of hidden neurons and their function space characteristics. … Our results show that the hidden neurons of a ReLU net- work can be interpreted as convex autoen- coders of the input layer.

Which cost function is convex?

The cost function is convex if its Second Order Derivative is positive semidefinite (i.e. ≥0 ). But this definition depends on the function with respect to which you take the derivative.

Does loss function have to be convex?

Popular loss functions are convex because a local minimum of a convex function is a global minimum. Also, a strictly convex function has a single global minimum. Therefore, we can use a local optimization algorithm, such as gradient descent, to find the best parameters globally.

Is CNN convex?

CNNs have achieved state of the art performance on many challenging computer vision contests, which brings CNNs a lot of attention. 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.

Is Softmax convex?

Since the Softmax cost function is convex a variety of local optimization schemes can be used to properly minimize it properly. For these reasons the Softmax cost is used more often in practice for logistic regression than is the logistic Least Squares cost for linear classification.

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