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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 is loss not convex?

Hence if the loss function is not convex, it is not guaranteed that we will always reach the global minima, rather we might get stuck at local minima. … f is convex if and only if f ”(x) ≥ 0 for all x. Hence if we can show that the double derivative of our loss function is ≥ 0 then we can claim it to be convex.

## Why do neural networks require non-convex optimization?

In fact, neural networks (NN)are universal function approximators. … To approximate them, convex functions cannot be good enough. Hence, the importance of using NCO. The freedom to express the learning problem as a non-convex optimization problem gives immense modeling power to the algorithm designer.

## Is the loss function of neural network convex?

No, it’s not convex unless it’s a one-layer network.

## 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 losses convex?

We should always use a convex loss function so that gradient descent can converge to the global minima (local optima free). Neural Networks are very complex non-linear mathematical functions and the loss function most often is non-convex, thus it is usual to stuck in a local minima.

## Is loss function always convex?

Fortunately, hinge loss, logistic loss and square loss are all convex functions. Convexity ensures global minimum and it’s computationally appleaing.

## What is convex and non convex problems?

A convex optimization problem is a problem where all of the constraints are convex functions, and the objective is a convex function if minimizing, or a concave function if maximizing. … A non-convex optimization problem is any problem where the objective or any of the constraints are non-convex, as pictured below.

## What is the difference between a convex function and non convex?

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.

## What is convex and non convex?

Non-convex. 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).

## How do neural networks reduce loss?

Solutions to this are to decrease your network size, or to increase dropout. For example you could try dropout of 0.5 and so on. If your training/validation loss are about equal then your model is underfitting. Increase the size of your model (either number of layers or the raw number of neurons per layer)

## What does loss mean in neural network?

Loss is the quantitative measure of deviation or difference between the predicted output and the actual output in anticipation. It gives us the measure of mistakes made by the network in predicting the output.

## What does loss function do in neural network?

A loss function is used to optimize the parameter values in a neural network model. Loss functions map a set of parameter values for the network onto a scalar value that indicates how well those parameter accomplish the task the network is intended to do.

## 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.

## Is cross entropy loss convex?

Since the Cross Entropy cost function is convex a variety of local optimization schemes can be more easily used to properly minimize it. For this reason the Cross Entropy cost is used more often in practice for logistic regression than is the logistic Least Squares cost.

## 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.