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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20
votes
3answers
25k views

How can we process the data from both the true distribution and the generator?

I'm struggling to understand the GAN loss function as provided in Understanding Generative Adversarial Networks (a blog post written by Daniel Seita). In the standard cross-entropy loss, we have an ...
11
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1answer
4k views

Loss jumps abruptly when I decay the learning rate with Adam optimizer in PyTorch

I'm training an auto-encoder network with Adam optimizer (with amsgrad=True) and ...
7
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1answer
607 views

What loss function to use when labels are probabilities?

What loss function is most appropriate when training a model with target values that are probabilities? For example, I have a 3-output model. I want to train it with a feature vector $x=[x_1, x_2, \...
6
votes
3answers
4k views

Can the mean squared error be negative?

I'm new to machine learning. I was watching a Prof. Andrew Ng's video about gradient descent from the machine learning online course. It said that we want our cost function (in this case, the mean ...
6
votes
1answer
206 views

What is the formula used to calculate the loss in the FaceNet model?

The FaceNet model returns the loss of the predictions and ground-truth classes. How is this loss calculated?
6
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1answer
165 views

How is the DQN loss derived from (or theoretically motivated by) the Bellman equation, and how is it related to the Q-learning update?

I'm doing a project on Reinforcement Learning. I programmed an agent that uses DDQN. There are a lot of tutorials on that, so the code implementation was not that hard. However, I have problems ...
6
votes
1answer
1k views

What's the advantage of log_softmax over softmax?

Previously I have learned that the softmax as the output layer coupled with the log-likelihood cost function (the same as the ...
6
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2answers
1k views

How do we design a neural network such that the $L_1$ norm of the outputs is less than or equal to 1?

What are some ways to design a neural network with the restriction that the $L_1$ norm of the output values must be less than or equal to 1? In particular, how would I go about performing back-...
5
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3answers
204 views

Which function $(\hat{y} - y)^2$ or $(y - \hat{y})^2$ should I use to compute the gradient?

The MSE can be defined as $(\hat{y} - y)^2$, which should be equal to $(y - \hat{y})^2$, but I think their derivative is different, so I am confused of what derivative will I use for computing my ...
5
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1answer
64 views

Why is the mean used to compute the expectation in the GAN loss?

From Goodfellow et al. (2014), we have the adversarial loss: $$ \min_G \, \max_D V (D, G) = \mathbb{E}_{x∼p_{data}(x)} \, [\log \, D(x)] \\ \quad\quad\quad\quad\quad\quad\quad + \, \mathbb{E}_{z∼p_z(...
5
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1answer
131 views

Loss function for choosing a subset of objects

I'm trying to train a neural net to choose a subset from some list of objects. The input is a list of objects $(a,b,c,d,e,f)$ and for each list of objects the label is a list composed of 0/1 - 1 for ...
5
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2answers
288 views

How to calculate the advantage in policy gradient functions?

From my understanding of the REINFORCE policy gradient method, we gently nudge the probabilities of actions based on the advantages. More specifically, the positive advantages increase the ...
5
votes
1answer
359 views

Why is Jensen-Shannon divergence preferred over Kullback-Leibler divergence in measuring the performance of a generative network?

I have read articles on how Jensen-Shannon divergence is preferred over Kullback-Leibler in measuring how good a distribution mapping is learned in a generative network because of the fact that JS-...
5
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4answers
775 views

How to stop DQN Q function from increasing during learning?

Following the DQN algorithm with experience replay: Store transition $\left(\phi_{t}, a_{t}, r_{t}, \phi_{t+1}\right)$ in $D$ Sample random minibatch of transitions $\left(\phi_{j}, a_{j}, r_{j}, \...
5
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1answer
96 views

How to define a loss function for a classifier where the confusion between some classes is more important than the confusion between others?

I have a dataset of images belonging to $N$ classes, $A_1, A_2...A_n,B_1,B_2...B_m$ and I want to train a CNN to classify them. The classes can be considered as subclasses of two broader classes $A$ ...
5
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1answer
304 views

How should we interpret this figure that relates the perceptron criterion and the hinge loss?

I am currently studying the textbook Neural Networks and Deep Learning by Charu C. Aggarwal. Chapter 1.2.1.2 Relationship with Support Vector Machines says the following: The perceptron criterion is ...
4
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2answers
70 views

Could error surface shape be useful to detect which local minima is better for generalization?

The following plot shows error function output based on system weights. Two equal local minima are shown in green pointers. Note that the red dots are not related to the question. Does the right one ...
4
votes
1answer
266 views

Why is the evidence equal to the KL divergence plus the loss?

Why is the equation $$\log p_{\theta}(x^1,...,x^N)=D_{KL}(q_{\theta}(z|x^i)||p_{\phi}(z|x^i))+\mathbb{L}(\phi,\theta;x^i)$$ true, where $x^i$ are data points and $z$ are latent variables? I was ...
4
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1answer
134 views

Is there a reason to choose regular momentum over Nesterov momentum for neural networks?

I've been reading about Nesterov momentum from here and it seems like a nice improvement over regular momentum with no extra cost whatsoever. However, is this really the case? Are there instances ...
4
votes
1answer
96 views

What is the cost function of a transformer?

The paper Attention Is All You Need describes the transformer architecture that has an encoder and a decoder. However, I wasn't clear on what the cost function to minimize is for such an architecture. ...
4
votes
1answer
1k views

What's the difference between RMSE and Euclidean distance, and when to use a custom loss? [closed]

I'm searching for a loss function that fits my project. Actually, I have two questions, but they are in the same direction. I take a look at the definition of the root mean squared error (RMSE) and ...
4
votes
1answer
53 views

How to add weights to one specific input feature to ensure fair training in the network?

I am trying to create a multiclass product-rating network based on product reviews and other input features. Two of the other input features are "product category" and "gender". However, I want to ...
4
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2answers
578 views

Why does TensorFlow docs discourage using softmax as activation for the last layer?

The beginner colab example for tensorflow states: Note: It is possible to bake this tf.nn.softmax in as the activation function for the last layer of the network....
4
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1answer
306 views

Why does the binary cross-entropy work better than categorical cross-entropy in a multi-class single label problem?

I was just doing a simple NN example with the fashion MNIST dataset, where I was getting 97% accuracy, when I noticed that I was using Binary cross-entropy instead of categorical cross-entropy by ...
4
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0answers
28 views

How do weights changes handles during back-propagation when there are unknown labels

I have a question about how weights are updated during back-propagation for some of my samples that have unknown labels (please note, unknown, not missing). The reason they are unknown is because this ...
3
votes
3answers
2k views

In which cases is the categorical cross-entropy better than the mean squared error?

In my code, I usually use the mean squared error (MSE), but the TensorFlow tutorials always use the categorical cross-entropy (CCE). Is the CCE loss function better than MSE? Or is it better only in ...
3
votes
3answers
762 views

What's the function that SGD takes to calculate the gradient?

I'm struggling to fully understand the stochastic gradient descent algorithm. I know that gradient descent allows you to find the local minimum of a function. What I don't know is what exactly that ...
3
votes
2answers
147 views

How to obtain a formula for loss, when given an iterative update rule in gradient descent?

From the reinforcement learning book section 13.3: Using pytorch, I need to calculate a loss, and then the gradient is calculated internally. How to obtain the loss from equations which are stated ...
3
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1answer
8k views

What is an objective function?

Local search algorithms are useful for solving pure optimization problems, in which the aim is to find the best state according to an objective function. My question is what is the objective function?
3
votes
1answer
74 views

How to incorporate a symmetry constraint in the loss function to train a CNN?

I have a task of extremely sparse binary segmentation, i.e. the segmentation mask contains either 0 or 1, and there are ~95% zeros and only ~5% ones. I use the focal loss to address the sparseness (...
3
votes
1answer
1k views

Are the training loss and validation loss plotted per sample or per batch?

I am using a CNN to train on some data, where training size = 21700 samples, and test size is 653 samples, and say I am using a batch_size of 500 (I am accounting for samples out of batch size as well)...
3
votes
2answers
65 views

If loss reduction means model improvement, why doesn't accuracy increase?

Problem Statement I've built a classifier to classify a dataset consisting of n samples and four classes of data. To this end, I've used pre-trained VGG-19, pre-trained Alexnet and even LeNet (with ...
3
votes
1answer
440 views

Alphazero policy head loss not decreasing

I am now working on training an alphazero player for a board game. The implementation of board game is mine, MCTS for alphazero was taken elsewhere. Due to complexity of the game, it takes a much ...
3
votes
1answer
158 views

How is equation 8 derived in the paper “Self-critical sequence training for image captioning”?

In the paper "Self-critical sequence training for image captioning", on page 3, they define the loss function (of the parameters $\theta$) of an image captioning system as the negative expected reward ...
3
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1answer
1k views

Dice loss gives binary output whereas binary crossentropy produces probability output map

On recommendation of Kanak on stackoverflow I am posting this question here: Currently I am experimenting with various loss functions and optimizers for my binary image segmentation problem. The loss ...
3
votes
1answer
569 views

Chess policy network

I am interested in making a simple chess engine using neural networks. I already have a fairly good value network but I can't figure out how to train a policy network. I know that Leela chess zero ...
3
votes
1answer
2k views

Why is the hyperbolic tangent with MSE better than the sigmoid with cross-entropy?

Usually, in binary classification problems, we use sigmoid as the activation function of the last layer plus the binary cross-entropy as cost function. However, I have already experienced (more than ...
3
votes
1answer
48 views

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 ...
3
votes
1answer
1k views

Advantages of Kullback-Leibler over L1/L2?

I've recently encounter different articles that are recommending to use KL instead of L1/L2 norm when trying to minimize a probability distribution. But none of the articles are giving a clear ...
3
votes
1answer
582 views

Which loss function should I use for binary classification?

I plan to create a neural network using Python, Keras and TensorFlow. All the tutorials I have seen so far are concerned with image recognition. However, the goal of my program would be to take in 10+ ...
3
votes
1answer
3k views

How do I calculate the gradient of the hinge loss function?

With reference to the research paper entitled Sentiment Embeddings with Applications to Sentiment Analysis, I am trying to implement its sentiment ranking model in Python, for which I am required to ...
3
votes
1answer
236 views

Should the input to the negative log likelihood loss function be probabilities?

I am trying to train a supervised model where the output from the model is output of a linear function $WX + b$. Kindly note that I'm not using any softmax or $\log$ softmax on the result of the ...
3
votes
1answer
43 views

How to define loss function for Discriminator in GANs?

To train the discriminator network in GANs we set the label for the true samples as $1$ and $0$ for fake ones. Then we use binary cross-entropy loss for training. Since we set the label $1$ for true ...
3
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0answers
37 views

Enforcing sparsity constraints that make use of spatial contiguity

I have a deep learning network that outputs grayscale image reconstructions. In addition to good reconstruction performance (measured through mean squared error or some other measure like psnr), I ...
3
votes
1answer
124 views

When should I create a custom loss function?

I'm using a neural network to solve a multi regression problem because I'm trying to predict continuous values. To be more specific, I'm making a tracking algorithm to track the position of an object, ...
3
votes
1answer
77 views

When to use RMSE as opposed to MSE and vice versa?

I understand that RMSE is just the square root of MSE. Generally, as far as I have seen, people seem to use MSE as a loss function and RMSE for evaluation purposes, since it exactly gives you the ...
3
votes
0answers
227 views

Understanding log probabilities of actions in the PPO objective

I'm trying to implement the Proximal Policy Optimization (PPO) algorithm (code here), but I am confused about certain concepts. What is the correct way to implement log probability of a policy (...
2
votes
3answers
156 views

How do you interpret this learning curve?

Loss is MSE; orange is validation loss, blue training loss. The task is NN regression (18 inputs, 2 outputs), one layer 300 hidden units. Tuning the lr, mom, l2 regularization parameters this is the ...
2
votes
1answer
122 views

Why L2 loss is more commonly used in Neural Networks than other loss functions?

Why L2 loss is more commonly used in Neural Networks than other loss functions? What is the reason to L2 being a default choice in Neural Networks?
2
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3answers
234 views

Where does the so-called 'loss' / 'loss function' fit into the idea of a perceptron / artificial neuron (as presented in the figure)?

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 presents the following figure: $\overline{X}$ is ...

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