14 votes

What are the advantages of ReLU vs Leaky ReLU and Parametric ReLU (if any)?

Combining ReLU, the hyper-parameterized1 leaky variant, and variant with dynamic parametrization during learning confuses two distinct things: The comparison between ReLU with the leaky variant is ...
Douglas Daseeco's user avatar
5 votes
Accepted

How exactly can ReLUs approximate non-linear and curved functions?

The outputs of a ReLU network are always "linear" and discontinuous. They can approximate curves, but it could take a lot of ReLU units. However, at the same time, their outputs will often ...
Default picture's user avatar
5 votes

In deep learning, is it possible to use discontinuous activation functions?

Even the first artificial neural network - Rosenblatt's perceptron [1] had a discontinuous activation function. That network is in introductory chapters of many textbooks about AI. For example, ...
Vladislav Gladkikh's user avatar
4 votes
Accepted

Why is tf.abs non-differentiable in Tensorflow?

By convention, the $\mathrm{ReLU}$ activation is treated as if it is differentiable at zero (e.g. in [1]). Therefore it makes sense for TensorFlow to adopt this convention for ...
htl's user avatar
  • 1,010
4 votes

How does gradient descent work with relu if weights are negative?

The issue you have described is called the dying ReLU, which is basically about getting a gradient of zero when negative predicted values got thresholded to zero. In general this is only an issue when ...
Luca Anzalone's user avatar
3 votes

If features are always positives, why do we use RELU activation functions?

The fact that features are always positive values don't guarantee that outputs of hidden layers are positive too. Due to multiplication, output of an hidden layer could contain negative values, i.e., ...
SpiderRico's user avatar
  • 1,000
3 votes
Accepted

How does backpropagation with unbounded activation functions such as ReLU work?

Backprop through ReLU is easier than backprop through sigmoid activations. For positive activations, you just pass through the input gradients as they were. For negative activations you just set the ...
ssegvic's user avatar
  • 499
3 votes
Accepted

What happens when I mix activation functions?

The general answer to the behavior of combining common activation functions is that the laws of calculus must be applied, specifically differential calculus, the results must be obtained through ...
Douglas Daseeco's user avatar
3 votes
Accepted

Network doesn't converge with ReLU or Leaky ReLU, but works well with sigmoid/tanh

I don't think it is dead ReLU units as a main cause, although they may be happening as part of the NN failing. The NN architecture is too complex for the given task (too deep, too many neurons) and ...
Neil Slater's user avatar
  • 32.1k
3 votes

Is ReLU a non-linear activation function?

ReLU is non-linear by definition In calculus and related areas, a linear function is a function whose graph is a straight line, that is a polynomial function of degree one or zero. Since the graph ...
brazofuerte's user avatar
  • 1,031
3 votes
Accepted

Why cannot linear activation functions be used to approximate any function?

However I when thinking graphically I think that it is possible to approximate these nonlinear functions using lots of linear ( scaled and shifted) linear lines and I do not understand why this is ...
Chillston's user avatar
  • 1,703
2 votes

What is the derivative of the Leaky ReLU activation function?

Derivative gives the rate of change in $y$ for a small change in $x$ or the slope of a function at point $x$. In the above function, ...
Mahesh Nepal's user avatar
2 votes

Why do we prefer ReLU over linear activation functions?

A multi-layer network in which all units have linear activation functions can always be collapsed to an equivalent network with two layers of units. That is why it is essential to use nonlinear unit ...
James V Stone's user avatar
2 votes

Why do non-linear activation functions that produce values larger than 1 or smaller than 0 work?

Why wouldn't they work? Each neuron's output is equal to a function over the sum of all its weights multiplied by their corresponding neurons. If that function is the Sigmoid function, then the output ...
BlueMoon93's user avatar
2 votes
Accepted

Are ReLUs incapable of solving certain problems?

There are a variety of possible things that could be wrong, but let me give you some potentially useful information. Neural networks with ReLU activation functions are Turing complete for a ...
lahwran's user avatar
  • 136
2 votes

Is ReLU a non-linear activation function?

Short Answer: Yes Visually: if you see the image from wikipedia, it shown that ReLU (the blue line) is non-Linear (the line is not straight, it turns in 0). You can also check "visual" definition of ...
malioboro's user avatar
  • 2,819
2 votes
Accepted

How is the performance of a model affected by adding a ReLU to fully connected layers?

ReLU is piecewise linear function that outputs the received input directly if it's positive, or outputs a zero. i.e., $max(0, x)$ How significant is adding relu to full connected layers? ReLU, being ...
mugoh's user avatar
  • 531
2 votes

Is it possible to have a negative output using only ReLU activation functions, but not in the final layer?

Yes, if there's no activation function in the last layer, the weights could simply be negative there, so the network would multiply a positive value with a negative weight, therefore outputting a ...
N. Kiefer's user avatar
  • 321
2 votes
Accepted

Can residual neural networks use other activation functions different from ReLU?

The problem with certain activation functions, such as the sigmoid, is that they squash the input to a finite interval (i.e. they are sometimes classified as saturating activation functions). For ...
nbro's user avatar
  • 40.6k
2 votes

Why is tf.abs non-differentiable in Tensorflow?

Creating custom gradient for tf.abs may solve the problem: ...
Dan D.'s user avatar
  • 1,283
2 votes
Accepted

How are exploding numbers in a forward pass of a CNN combated?

The most effective way to prevent both the forward and backward propagation of exploding is keeping the weights in a small range. The main way this is accomplished is through their initialization. ...
Djib2011's user avatar
  • 3,183
2 votes

Why the partial derivative is $0$ when $F_{ij}^l < 0$?. Math behind style transfer

$F_l$ is the activation of the filter. They state in the paper that they base their method on VGG-Network, which uses ReLU as its activation function. In fact, VGG uses it in all of its hidden layers. ...
Avatrin's user avatar
  • 486
2 votes

Why should one ever use ReLU instead of PReLU?

I suppose, the situation is as follows - PReLU increases the expressiveness of a model for a bit at a small cost, but the gain is almost negligible as well (...
spiridon_the_sun_rotator's user avatar
2 votes

Effects of ReLU Activation on Convexity of Loss Functions

You're missing a couple of quite important concepts: Universal approximation theorem: with enough parameters a neural network can approximate any function. Basically every loss function is non convex....
Edoardo Guerriero's user avatar
2 votes
Accepted

Does it make sense to provide a DQN with negative rewards for a network with relu and sigmoid activations?

A network with ReLU activation can predict negative values; we put ReLU between the hidden layers but return the output of the final layer without any activation function, or with a linear activation ...
Lee Reeves's user avatar
2 votes

Why and when do we use ReLU over tanh activation function?

For a discussion about the advantages of ReLU, see the original paper by Glorot (2011) "Deep sparse rectifier neural networks". "Efficient Backprop" is a 1998 paper. At the time ...
Martino's user avatar
  • 215
2 votes

Why does Batch-Normalization before ReLU work?

Batch-normalization (BN) does NOT transform all values by restricting them to a value between zero and one. BN performs two operations: a normalization, and a shifting with scaling. The normalization ...
Luca Anzalone's user avatar
1 vote
Accepted

How to explain that a same DNN model have radically different behaviours with each new initialization and training?

I'm sure the biases are initially initialized to zero but I don't know how the weights are handled. Looking at the Dense layer docs: by default Dense layers biases are initialized with zeros (...
Kostya's user avatar
  • 2,524
1 vote

Does net with ReLU not learn when output < 0?

There is no benefit to using ReLU as the output activation of a neural network. As you said, the network will ignore training labels below zero and it will train on labels above zero as if no output ...
danijar's user avatar
  • 201

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