18
votes
Accepted
What activation function does the human brain use?
The thing you were reading about is known as the action potential. It is a mechanism that governs how information flows within a neuron.
It works like this: Neurons have an electrical potential, ...
- 2,051
16
votes
Accepted
How to choose an activation function for the hidden layers?
It seems to me that you already understand the shortcomings of ReLUs and sigmoids (like dead neurons in the case of plain ReLU).
You may want to look at ELU (exponential linear units) and SELU (self-...
- 943
13
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 ...
- 7,393
13
votes
Accepted
Are softmax outputs of classifiers true probabilities?
The answer is both yes, and no. Or, to put it another way, the answer depends on what exactly you mean by "represent probabilities", and there is a valid sense in which the answer is yes, ...
- 278
12
votes
Accepted
What does it mean for a neuron in a neural network to be activated?
A neuron is said activated when its output is more than a threshold, generally 0.
For examples :
\begin{equation}
y = Relu(a) > 0
\end{equation}
when
\begin{equation}
a = w^Tx+b > 0
\end{...
- 515
11
votes
What is the purpose of an activation function in neural networks?
If you only had linear layers in a neural network, all the layers would essentially collapse to one linear layer, and, therefore, a "deep" neural network architecture effectively wouldn't be deep ...
11
votes
Are softmax outputs of classifiers true probabilities?
Excellent question.
The simple answer is no. Softmax actually produces uncalibrated probabilities. That is, they do not really represent the probability of a prediction being correct.
What usually ...
- 1,122
10
votes
Why is the derivative of the activation functions in neural networks important?
Consider a dataset $\mathcal{D}=\{x^{(i)},y^{(i)}:i=1,2,\ldots,N\}$ where $x^{(i)}\in\mathbb{R}^3$ and $y^{(i)}\in\mathbb{R}$ $\forall i$
The goal is to fit a function that best explains our dataset....
- 131
10
votes
Accepted
Do neurons of a neural network model a linear relationship?
In a neural network (NN), a neuron can act as a linear operator, but it usually acts as a non-linear one. The usual equation of a neuron $i$ in layer $l$ of an NN is
$$o_i^l = \sigma(\mathbf{x}_i^l \...
- 38.2k
7
votes
Why is no activation function used at the final layer of super-resolution models?
I am not into the field of super-resolution, but I think this question applies to general neural network construction.
Usually, you try to solve a classification problem or a regression problem with ...
7
votes
Why is the derivative of the activation functions in neural networks important?
If what you are asking is what is the intuition for using the derivative in backpropagation learning, instead of an in-depth mathematical explanation:
Recall that the derivative tells you a function'...
- 181
7
votes
Accepted
Why do ResNets avoid the vanishing gradient problem?
Before proceeding, it's important to note that ResNets, as pointed out here, were not introduced to specifically solve the VGP, but to improve learning in general. In fact, the authors of ResNet, in ...
- 38.2k
6
votes
What activation function does the human brain use?
The brains of mammals do not use an activation function. Only machine learning designs based on the perceptron multiply the vector of outputs from a prior layer by a parameter matrix and pass the ...
- 7,393
6
votes
Why do activation functions need to be differentiable in the context of neural networks?
No, it is not necessary that an activation function is differentiable. In fact, one of the most popular activation functions, the rectifier, is non-differentiable at zero!
This can create problems ...
- 161
6
votes
What is the purpose of an activation function in neural networks?
Let's first talk about linearity. Linearity means the map (a function), $f: V \rightarrow W$, used is a linear map, that is, it satisfies the following two conditions
$f(x + y) = f(x) + f(y), \; x, ...
- 825
6
votes
Accepted
Why isn't the ElliotSig activation function widely used?
I can't speak for individual researchers, but I can guess why the community as a whole hasn't adopted this activation function.
ReLU is just so incredibly cheap. This benefit continues to grow as ...
- 2,018
6
votes
Accepted
Smallest possible network to approximate the $sin$ function
Before anything, the function you have wrote for the network lacks the bias variables (I'm sure you used bias to get those beautiful images, otherwise your tanh ...
- 420
6
votes
Accepted
What does "linear unit" mean in the names of activation functions?
Have a look at these graphics showing popular linear units (image taken from Clevert et al. 2016):
You can see that these functions are linear functions for $x > 0$, that's why they are called ...
- 186
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 ...
- 212
5
votes
Accepted
What makes multi-layer neural networks able to perform nonlinear operations?
Nonlinear relations between input and output can be achieved by using a nonlinear activation function on the value of each neuron, before it's passed on to the neurons in the next layer.
- 558
5
votes
Accepted
What is a "logit probability"?
Indeed I haven't seen the term "logit probability" used in many places other than that specific paper. So, I cannot really comment on why they're using that term / where it comes from / if anyone else ...
- 9,824
5
votes
Do neurons of a neural network model a linear relationship?
Almost never. The sum of linear functions is another linear function, so if neurons were only linear transformations there would be basically no point to having more than one neuron per layer. Instead,...
- 151
5
votes
Accepted
Why is there a sigmoid function in the hidden layer of a neural network?
Let us suppose we have a network without any functions in between. Each layer consists of a linear function. i.e
layer_output = Weights.layer_input + bias
...
5
votes
What is the mathematical definition of an activation function?
There is no strict definition of suitability of an activation function for neural networks. Instead there are a number of desirable traits, and functions that don't meet them or come close enough may ...
- 27k
5
votes
Accepted
Is a non-linear activation function needed if we perform max-pooling after the convolution layer?
Let's first recapitulate why the function that calculates the maximum between two or more numbers, $z=\operatorname{max}(x_1, x_2)$, is not a linear function.
A linear function is defined as $y=f(x) =...
- 38.2k
5
votes
Can LSTM model use ReLU or LeakyReLU as the activation funtion?
Yes an LSTM can use any of these.
There are no hard rules of which to use. That is why they all exist.
Some rules of thumb are:
Relu is the cheapest computationally. Almost always worth trying first.
...
- 2,155
5
votes
Accepted
Can LSTM model use ReLU or LeakyReLU as the activation funtion?
Yes, you can use ReLU or LeakyReLU in an LSTM model.
There aren't hard rules for choosing activation functions. Run your model with each activation function and pick the best performing one.
See the ...
- 1,728
4
votes
What does it mean for a neuron in a neural network to be activated?
The term "activated" is mostly used when talking about activation functions which only outputs a value (except 0) when the input to the activation function is greater than a certain treshold.
...
- 558
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