# Questions tagged [sigmoid-curve]

A sigmoid function is a mathematical function having a characteristic "S"-shaped curve or sigmoid curve. Often, sigmoid function refers to a special case of the logistic function. It is closely related to the logistic regression.

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### Backpropagation With Sigmoid Output Function Question

I am deriving a Weight update for a simple toy network with a Sigmoid Output Layer. I need some help double checking my math to make sure I did it correctly. I am using Cross-Entropy Loss as my Loss ...
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### Strange situation with softmax activation vs sigmoid activation in the last layer of a binary classification problem?

I am building a neural network as a binary classifier with one output neuron at the last output layer. I deliberately balancing out my train label so that the number label corresponding to the binary ...
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### Conceptual explanation of taking derivative of sigmoid function in neural network

In a neural network, we have a bunch of inputs and corresponding weights + a bias which are represented by a multivariable equation. Now we squash this whole equation with a sigmoid function. How ...
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### Why is learning slower for a sigmoid activation function in a neural network?

Andrew Ng in one of his deep learning course videos says that the sigmoid function acts as a slow learner in a neural network. My intuition is that the sigmoid as an activation function contributes ...
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### Has Arcsinh ever been considered as a neural network activation function?

The function $y = arcsinh(x)=ln(x+\sqrt{x^2+1})$ has some nice features that I could imagine being useful as an activation function in a neural network. It has sigmoid behaviour around zero, but far ...
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### Question about Sigmoid Function in Logistic Regression

This is with reference with Andrew Ng's video on Logistic Regression, I just want to confirm a small doubt I have. I get the basic idea of Logistic Regression that $z=\theta^Tx$ Where $\theta$= ...
107 views

### How does Bayes' rule on two exponentials suggest a sigmoid?

In Platt's 1999 paper on turning support vector machine output into a probabilistic score, he says Bayes rule on two exponentials suggests using a parametric form of a sigmoid where he cites this ...
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### Finding the slope at different points in a sigmoid curve

This is my data. x <- c(0.5,3.0,22.2,46.0,77.3,97.0,98.9,100.0) plot(x, pch = 19) I want to fit a curve through these points and then calculate the slope at ...
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### Why do we use the natural exponential in logistic regression?

I would like to intuitively understand the benefit of using the natural exponential in the sigmoid function used in logistic regression. Why should it have to be $e^x$ instead of, for example $2^x$?
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### Why is tanh almost always better than sigmoid as an activation function?

In Andrew Ng's Neural Networks and Deep Learning course on Coursera he says that using $tanh$ is almost always preferable to using $sigmoid$. The reason he gives is that the outputs using $tanh$ ...
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### logistic regression - why we forget assumption on data?

I read logistic regression formula i.e. $\log\frac{P(C_1|X)}{P(C_2|X)}=w^Tx+w_o$ but this equation is true if we have $P(X|C_1)$ and $P(X|C_2)$ sampled from two Gaussian with the same covariance ...
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### Difference between logistic regression models for classification problems

In various papers, I had often seen the logistic regression model for classification problems written in two forms. p(y =\pm1|\mathbf{x},\mathbf{w}) = \sigma(y\mathbf{w}^{T}\mathbf{x}) = \frac{1}{1+...
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### Expected value of softmax transformation of Gaussian random vector

Let $\mathbf w_1,\mathbf w_2,\ldots,\mathbf w_n \in \mathbb R^p$ and $\mathbf v \in \mathbb R^n$ be fixed vectors, and $\mathbf x \sim \mathcal N_p(\boldsymbol{\mu}, \mathbf{\Sigma})$ be an $p$-...
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### Finding the center of a logistic curve

Given a sigmoidal/logistic curve p what's the general procedure to finding at what value of x is the curve centered?