# Questions tagged [objective-functions]

For questions related to the concept of loss (or cost) function in the context of machine learning.

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### Does average loss function in GAN training is just an approximation of value function and does not ensure convergence of generator and discriminator?

The value function on which convergence has been proved by the original paper of GAN is $$\min_G \max_DV(D, G) = \mathbb{E}_{x ∼ P_{data}}[\log D(x)] + \mathbb{E}_{z ∼ p_z}[log (1 - D(G(z)))]$$ and ...
55 views

### How to check whether my loss function is convex or not?

Loss functions are useful in calculating loss and then we can update the weights of a neural network. The loss function is thus useful in training neural networks. Consider the following excerpt from ...
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### What are the necessary mathematical properties to be a loss function in gradient based optimizations?

Loss functions are used in training neural networks. I am interested in knowing the mathematical properties that are necessary for a loss function to participate in gradient descent optimization. I ...
35 views

### Why is the exponential loss used in this case?

I am reading a paper "Tracking-by-Segmentation With Online Gradient Boosting Decision Tree". In Section 2.1, the paper says I cannot understand the exponential loss function. In my opinion, ...
26 views

### Is optimizing weighted sum multi objective tasks considered a multi-task learning?

I have two sequence prediction tasks, finding $\vec{\pi} \in \Pi$ and $\vec{\psi} \in \Psi$. Each sequence has its own objective function, i.e. $f_1(\vec{\pi})$ and $f_2(\vec{\psi})$. The input for ...
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### Can people set loss function of neural network by themselves instead of choosing cross entropy or mean square error?

I found people used deep neural network to get optimal policy by solving a nonconvex optimization problem. Moreover, they didn't use any set of training data and claimed that it's the difference ...
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### An explanation involving the sign activation, its affect on the loss function, and the perceptron and perceptron criterion: what is this saying? (#2)

I recently asked a very similar question here, but the answer only seems to address the first part of the quote, rather than the second part that contains the perceptron criterion example. Therefore, ...
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### Is the formula $\frac {1}{s}\sum _{j=1}^{s}|d_{j}-y_{j}(t)|$ the correct form of 0-1 loss function, in the context of Perceptron?

Per page 7 of this MIT lecture notes, the original single-layer Perceptron uses 0-1 loss function. Wikipedia uses $${\frac {1}{s}}\sum _{j=1}^{s}|d_{j}-y_{j}(t)|} \tag{1$$ to denote ...
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### Loss function to Push response value towards extremes

I have a feature map whose values are in the range of [0,1]. I want to push these values either towards extreme 0 or 1 using some loss function. Since I don't have any target value so it had to be in ...
55 views

### An explanation involving the sign activation, its affect on the loss function, and the perceptron and perceptron criterion: what is this saying?

I am currently studying the textbook Neural Networks and Deep Learning by Charu C. Aggarwal. Chapter 1.2.1.3 Choice of Activation and Loss Functions says the following: The classical activation ...
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### How is it possible that the softmax combined with the MSE in a molecule classification task performs than than the cross-entropy?

I'm working on a GNN project associated with molecule classification. The project is to classify if the atom in the molecule will initiate a certain reaction. For example, a molecule can be ...
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### Training labels: integers or vectors?

I'm trying to implement Deep Q Learning using Tensorflow. The input is a vectorized representation of the state, and the output is a vector whose length is the number of possible actions. I've already ...