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Questions tagged [softmax]

Normalizing exponential function which transforms a numeric vector such that all its entries become between 0 and 1 and together sum to 1. It is often used as the final layer of a neural network performing a classification task.

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Reinforcement Learning partial derivative of loss function w.r.t. input of softmax

In the paper "Self-critical sequence training for image captioning" (link) on page 3 they define the loss function (of the parameters $\theta$) of an image captioning system as the negative expected ...
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Difference between sigmoid and softmax [duplicate]

I know, that usually we use sigmoid in the hidden layer, and softmax as an output but what is the difference between neural network with one output and sigmoid activation layer and network with two ...
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72 views

Softmax layer derivative by hand

I would like to compute the gradient of the loss function with respect to the input to a sigmoid layer. This is a question in some online course I found (see 1:09:22 in https://www.youtube.com/watch?v=...
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25 views

Problem with Softmax decision boundary

While reading this paper: sphere face on page 2, it explains that original softmax boundary is given by: $$(W_1 −W_2)x+b_1 −b_2 = 0$$ While trying to obtain the boundary on a toy generated 2D dataset ...
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33 views

Softmax regression vector features?

I'm working on a difficult classification problem where there are a very large number of known classes (~50k). I have only about 20k labelled points, but these only represent <1% of the possible ...
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85 views

confusion matrix for one hot vectors

Let $\mathbf{Y}$ be a matrix where each row is a one-hot encoding of true labels and $\hat{\mathbf{Y}}$ be a similar matrix for predicted labels that are generated by a softmax function. How is the ...
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372 views

Is a neural network consisting of a single softmax classification layer only a linear classifier?

Since the softmax function is a generalization of the logistic function it is continuous and non-linear. So the output of the softmax layer is: softmax( weight_matrix * input_activation) ...
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319 views

Softmax weights initialization

I am a new to deep learning and neural networks, and I need to know if there is a good weights initialization method to use if the activation function is Softmax like Tanh, ReLU and Sigmoid. Related ...
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99 views

Tensorflow tf.nn.sampled_softmax_loss: Should uniform_candidate_sampler be the default sampler instead of log_uniform_candidate_sampler?

I was reading the documentation for tf.nn.sampled_softmax_loss: https://www.tensorflow.org/api_docs/python/tf/nn/sampled_softmax_loss It says for choosing the negative samples, if we don't put ...
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1answer
28 views

Meaning of different softmax notations in papers

I was wondering if the different notations of the softmax input mean different things especially about the size of the output. For example, in the paper Pointer Networks, it sometimes state the input ...
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1answer
90 views

How to get meaningful results from Softmax activation in Deep Unsupervised Clustering Network

I found this interesting paper regarding deep unsupervised clustering and am looking to mimic some of the things done, however there is one thing that is not clear to me. In the paper, they use a ...
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65 views

multi class logistic regression : $K-1$ regressors or $K$ regressors (softmax)?

I read that, in multiclass logistic regression, we have a pivot class $K$ and $K-1$ set of $\vec{w}$ weights, then, for the pivot class: \begin{eqnarray} P( C_K | \vec{x} ) &= 1- \sum_\limits{t=...
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What does this cross entropy notation $J(o, v_c, U) = CE(y, \hat y)$ mean?

From http://web.stanford.edu/class/cs224n/assignment1/index.html under "complementary written problems" problem $3(a)$: What does $J_{\text{Softmax---CE}}(o, v_c, U) = CE(y, \hat y)$ fully stand for? ...
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298 views

Candidate Sampling for Softmax - Tensorflow; Sampling Probability

I am trying to understand the mathematics behind the sampled softmax in Tensorflow. They have the following document, trying to explain how the sampling process works: https://www.tensorflow.org/...
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89 views

Proof for the efficiency of Softmax in multi-classification

I already search for this question but I can't find any convincing explanation so I want to ask it here. my problem is with softmax activation function and cross-entropy.why they can produce a better ...
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39 views

Softmax derivation - case i==j

I am reading this article: https://eli.thegreenplace.net/2016/the-softmax-function-and-its-derivative about softmax derivation w.r.t. to the input. Please confirm my understanding of the case when j==...
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45 views

Neural Network Layer for Binary Outputs

I'm currently using an LSTM network to make a yes or no decision in a robot. The network has a single output with the values in training data being 0 for one decision and 1 for another. The problem ...
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1answer
292 views

machine learning - Derivative of log-likelihood function in softmax regression

I'm trying to find the derivative of the log-likelihood function in softmax regression. I have (with $\Theta$ being the parameters, and $x^{(i)}$ being the $i$th training example, and $s_j$ ...
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119 views

change hinge loss error function with cross-entropy

I'm trying to implement cross-entropy as an error function in RBF neural networks instead of hinge loss error function. I need to find cross-entropy error for each output neuron, like hinge loss error ...
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1answer
113 views

In multi-class logistic regression, does SGD one training example update all the weights?

In multi-class logistic regression, lets say we use softmax and cross entropy. Does SGD one training example update all the weights or only a portion of the weights which are associated to the label ? ...
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Softmax regression learning curve intersecting

I've implemented softmax regression on python. I've separated the Iris data into training, validation and test data. When I plot the learning curve for training data and validation data I get this: ...
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48 views

Loss function for partial/splitted softmax outputs on binary ground truth

I need to find a loss function for the scenario where each output is a vector instead of a scalar. And each of these vectors in one-hot-encoded. So I would like to use something like softmax loss on ...
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292 views

Definition of softmax function

This question follows up on stats.stackexchange.com/q/233658 The logistic regression model for classes {0, 1} is $$ \mathbb{P} (y = 1 \;|\; x) = \frac{\exp(w^T x)}{1 + \exp(w^T x)} \\ \mathbb{P} (y =...
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How to interpret Gelman's multivariate Gaussian prior for multinomial distribution?

Andrew Gelman suggested the use of a multivariate Normal distribution as prior for hierarchical models that have a multinomial distribution at the lowest level (http://andrewgelman.com/2009/04/29/...
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201 views

Does hierarchical softmax of skip gram and CBOW only update output vectors on the path from the root to the actual output word?

After reading word2vec Parameter Learning Explained by Xin Rong, I understand that in the hierarchical softmax model, there is no output vector representation for words, instead, each of the $V-1$ ...
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1answer
165 views

Optimal neural net weights when using cross entropy loss

I'm trying to understand how cross-entropy works for finding the optimal weights in neural networks. According to Eli Bendersky's website and neural networks and deeplearning tutorial, we can find the ...
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1answer
707 views

Difference between mathematical and Tensorflow implementation of Softmax Crossentropy with logit

Softmax cross entropy with logits is define as follows: $a_i = \frac{e^{z_i}}{\sum_{\forall j} e^{z_j}}$ $l={\sum_{\forall i}}y_ilog(a_i)$ Where $l$ is the actual loss. But when you look deep into ...
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24 views

Cost function to output reliable error probabilities?

I'm using softmax regression but my goal is not to increase the 'accuracy' but instead to create probabilities which are accurate. Using cross entropy or the means squared error (which I'm aware I'm ...
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1answer
247 views

How deep is the connection between the softmax function in ML and the Boltzmann distribution in thermodynamics?

The softmax function, commonly used in neural networks to convert real numbers into probabilities, is the same function as the Boltzmann distribution, the probability distribution over energies for en ...
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271 views

Tensorflow Sampled_Softmax_loss - correct usage [closed]

I am working on a Speaker recognition problem, I have very big number of classes so I need to use, tf.nn.sampled_softmax_loss to speed up training time. The problem is I am using Keras with Tensorflow ...
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168 views

How do I implement softmax forward propagation and backpropagation to replace sigmoid in a neural network?

I'm currently using 3Blue1Brown's tutorial series on neural networks and lack extensive calculus knowledge/experience. I'm using the following equations to calculate the gradients for weights and ...
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question about backpropagation with a softmax

When we have a neural network with a softmax layer, I'm a little confused how the weights get updated which are NOT associated with the correct answer. The issue is that the cost function will ...
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37 views

Neural Nets: Benefits of Mixing Activation Functions? [duplicate]

I'm currently studying and would like to know if there are any actual benefits of using a mixture of activation functions for each layer. For example, if I am trying to predict the probabilities of ...
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1answer
431 views

How does the subtraction of the logit maximum improve learning?

My question comes from another question answered on Stackoverflow; the Keras implemantion of softmax activation function is customized to subtract the maximum value ...
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1answer
87 views

Softmax dealing with non present classes [closed]

Is it okey to assume that, if I have trained my neural network for image classification using k classes using a Softmax output function, whenever I feed an image that does not belong to any of the k ...
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307 views

Are weights 1-D or 2-D in softmax Regression?

I've learned ML and have been learning DL from Andrew Ng's coursera courses, and every time he talks about a linear classifier, the weights are just a 1-D vector. Even during the assignments, when we ...
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258 views

finding the loss derivative w.r.t. weights for a convolutional layer

Take the loss function: $$ \mathrm{loss} ~~=~~ \sum_{i=1}^N \left( -z_{}[y] + \log{\left( \sum_{c=1}^{10} \exp(z_{}[c]) \right)} \right)$$ where $z \in \mathbb{R}^{10}$ is the input to the softmax ...
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243 views

Why does deriving the softmax for a single vector come to 0 for me?

There is a lot of material explaining how to calculate the jacobian for the softmax backwards pass, but I find it confusing how to get to the actual errors from the jacobian. The obvious answer would ...
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1answer
233 views

What is the meaning of fully-convolutional cross entropy loss in the function below (image attached)?

I am trying to understand the loss function given below from this paper. I do not understand $l_{p}(x_{hw}; y_{hw})$ part.
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Expectation of the softmax transform for Gaussian multivariate variables

Prelims In the article Sequential updating of conditional probabilities on directed graphical structures by Spiegelhalter and Lauritzen they give an approximation to the expectation of a logistic ...
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2answers
400 views

How can't the Softmax layer never converge using hard targets

Here's a quote from the deep learning book by Ian Goodfellow (page 236): Maximum likelihood learning with a softmax classifier and hard targets may actually never converge -- the softmax can ...
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1answer
576 views

Is minimizing softmax cross entropy with two labels equivalent to minimizing sigmoid binary cross entropy with 1 label?

Is using a sigmoid at the end of a neural network with 1 label equivalent to using a softmax with 2 labels?
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136 views

Mutual exclusive classes for deciding Softmax Regression vs. k Binary Classifiers

I realise that similar questin is asked here also Softmax regression or $K$ binary logistic regression But my concern is related to last section of this article from stanford http://ufldl.stanford....
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2answers
1k views

What is distribution parameterization?

I encountered this term in the Stanford notes about softmax regression: we will begin by expressing the multinomial as an exponential family distribution. To parameterize a multinomial over k ...
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1answer
784 views

Training in one step vs multiple steps

I'm about 5 minutes in to learning about machine learning (using the Tensorflow MNIST tutorial) and have already managed to confuse myself. No big surprise there. But Google isn't giving me any good ...
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7k views

Why is softmax output not a good uncertainty measure for Deep Learning models?

I've been working with Convolutional Neural Networks (CNNs) for some time now, mostly on image data for semantic segmentation/instance segmentation. I've often visualized the softmax of the network ...
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1k views

Softmax with log-likelihood cost

I am working on my understanding of neural networks using Michael Nielsen's "Neural networks and deep learning." Now in the third chapter, I am trying to develop an intuition of how softmax works ...
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47 views

Why, empirically, does cross entropy composed with softmax have such a simple derivative? [closed]

Was one function chosen to simplify the derivatives based on the other? There has to be some intelligent design relating to their derivatives, right? The derivative is simply ...
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25 views

How can I make a classifier that adapts to increasing number of classes in the dataset. How many nodes should I use as output?

How can I make a classifier that adapts to an increasing number of classes in the dataset. How many nodes should I use as output? If I use a softmax I need to specify the classes but if the classes ...
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1answer
2k views

Softmax overflow [closed]

Waiting the next course of Andrew Ng on Coursera, I'm trying to program on Python a classifier with the softmax function on the last layer to have the different probabilities. However, when I try to ...