Questions tagged [gradient-descent]

For questions surrounding gradient descent, a method for finding the optimum state of a parameterized function based on another function often called the loss or error function. It iteratively descends the loss surface to the minimum loss by adjusting parameters based on the product of the partial derivatives comprising the gradient and a learning rate.

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901 views

Is neural networks training done one-by-one? [duplicate]

I'm trying to learn neural networks by watching this series of videos and implementing a simple neural network in Python. Here's one of the things I'm wondering about: I'm training the neural network ...
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2answers
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Is the mean-squared error always convex in the context of neural networks?

Multiple resources I referred to mention that MSE is great because it's convex. But I don't get how, especially in the context of neural networks. Let's say we have the following: $X$: training ...
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1answer
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Can non-differentiable layer be used in a neural network, if it's not learned?

For example, AFAIK pooling layer in CNN is not differentiable, but it can be used because it's not learning. Is it always true?
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1answer
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What are the best known gradient-free training methods for deep learning?

As I know, the current state of the art methods for training deep learning networks are variants of gradient descent or stochastic gradient descent. What are the best known gradient-free training ...
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Why is the perceptron criterion function differentiable?

I'm reading chapter one of the book called Neural Networks and Deep Learning from Aggarwal. In section 1.2.1.1 of the book, I'm learning about the perceptron. One thing that book says is, if we use ...
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2answers
325 views

Is there an ideal range of learning rate which always gives a good result almost in all problems?

I once read somewhere that there is a range of learning rate within which learning is optimal in almost all the cases, but I can't find any literature about it. All I could get is the following graph ...
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1answer
749 views

What is the formula for the momentum and Adam optimisers?

In the gradient descent algorithm, the formula to update the weight $w$, which has $g$ as the partial gradient of the loss function with respect to it, is: $$w\ -= r \times g$$ where $r$ is the ...
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1answer
2k views

What is the relationship between gradient accumulation and batch size?

I am currently training some models using gradient accumulation since the model batches do not fit in GPU memory. Since I am using gradient accumulation, I had to tweak the training configuration a ...
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3answers
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CNN backpropagation with stride>1

I read that to compute the derivative of the error with respect to the input of a convolution layer is the same to make of a convolution between deltas of the next layer and the weight matrix rotated ...
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1answer
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How is the gradient calculated for the middle layer's weights?

I am trying to understand backpropagation. I used a simple neural network with one input $x$, one hidden layer $h$ and one output layer $y$, with weight $w_1$ connecting $x$ to $h$, and $w_2$ ...
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1answer
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How to avoid falling into the “local minima” trap?

How do I avoid my gradient descent algorithm into falling into the "local minima" trap while backpropogating on my neural network? Are there any methods which help me avoid it?
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How is local minima possible in gradient descent?

Gradient descent works on the equation of mean squared error, which is an equation of a parabola $y=x^2$. We often say that weight adjustment in a neural network by gradient descent algorithm can hit ...
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2answers
505 views

Can neuroevolution be combined with gradient descent?

Is there any precedent for using a neuroevolution algorithm, like NEAT, as a way of getting to an initialization of weights for a network that can then be fine-tuned with gradient descent and back-...
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3answers
407 views

How can a neural network learn when the derivative of the activation function is 0?

Imagine that I have an artificial neural network with a single hidden layer and that I am using ReLU as my activating function. If by change I initialize my bias and my weights in such a form that: $$ ...
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1answer
108 views

During neural network training, can gradients leak sensitive information in case training data fed is encrypted (homomorphic)?

Some algorithms in the literature allow recovering the input data used to train a neural network. This is done using the gradients (updates) of weights, such as in Deep Leakage from Gradients (2019) ...
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202 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 ...
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3answers
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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 ...
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1answer
137 views

Why evolutionary training of neural networks is not popular?

Evolutionary algorithms are mentioned in some sources as a method to train a neural network (finding weights, not hyperparameters). However, I have not heard about one practical application of such an ...
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1answer
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What, exactly, does the REINFORCE update equation mean?

I understand that this is the update for the parameters of a policy in REINFORCE: $$ \Delta \theta_{t}=\alpha \nabla_{\theta} \log \pi_{\theta}\left(a_{t} \mid s_{t}\right) v_{t} $$ Where 𝑣𝑡 is ...
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2answers
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Is the gradient at a layer independent of the activations of the previous layers?

Is the gradient at a layer (of a feed-forward neural network) independent of the activations of the previous layers? I read this in a paper titled Mean Field Residual Networks: On the Edge of Chaos (...
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2answers
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Are on-line backpropagation iterations perpendicular to the constraint?

Raul Rojas' Neural Networks A Systematic Introduction, section 8.1.2 relates off-line backpropagation and on-line backpropagation with Gauss-Jacobi and Gauss-Seidel methods for finding the ...
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1answer
248 views

For each epoch, can I use only on a subset of the full training dataset to train the neural network?

If one has a dataset large enough to learn a highly complex function, say learning chess game-play, and the processing time to run mini-batch gradient descent on this entire dataset is too high, can I ...
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3answers
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Does gradient descent in deep learning assume a smooth fitness landscape?

I've come across the concept of fitness landscape before and, in my understanding, a smooth fitness landscape is one where the algorithm can converge on the global optimum through incremental ...
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1answer
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An intuitive explanation of Adagrad, its purpose and its formula

It (Adagrad) adapts the learning rate to the parameters, performing smaller updates (i.e. low learning rates) for parameters associated with frequently occurring features, and larger updates (i.e. ...
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2answers
505 views

What exactly is averaged when doing batch gradient descent?

I have a question about how the averaging works when doing mini-batch gradient descent. I think I now understood the general gradient descent algorithm, but only for online learning. When doing mini-...
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2answers
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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 ...
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1answer
398 views

Eligibility vector for softmax policy with policy gradients

There is this nice result for policy gradients that the gradient of some performance measure, $\nabla v_{\pi_{\theta}}(s_0)$ (here, in the episodic case for the starting state $s_0$ and policy $\pi$, ...
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1answer
1k views

Is back-propagation applied for each data point or for a batch of data points?

I am new to deep learning and trying to understand the concept of back-propagation. I have a doubt about when the back-propagation is applied. Assume that I have a training data set of 1000 images ...
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1answer
1k views

Deep Q-Learning: why don't we use mini-batches during experience reply?

In examples and tutorial about DQN, I've often noticed that during the experience replay (training) phase people tend to use stochastic gradient descent / online learning. (e.g. link1, link2) ...
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1answer
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Do good approximations produce good gradients?

Let’s say I have a neural net doing classification and I’m doing stochastic gradient descent to train it. If I know that my current approximation is a decent approximation, can I conclude that my ...
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1answer
126 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 ...
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2answers
117 views

What is the goal of weight initialization in neural networks?

This is a simple question. I know the weights in a neural network can be initialized in many different ways like: random uniform distribution, normal distribution, and Xavier initialization. But what ...
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1answer
121 views

What are some concrete steps to deal with the vanishing gradient problem?

I am training an ANN for classification between 3 classes. The ANN has an input layer, one hidden layer and a 3 node output layer. The problem I am facing is that the output being produced by the 3 ...
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1answer
123 views

Is running more epochs really a direct cause of overfitting?

I've seen some comments in online articles/tutorials or Stack Overflow questions which suggest that increasing number of epochs can result in overfitting. But my intuition tells me that there should ...
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1answer
95 views

Why is batch gradient descent performing worse than stochastic and minibatch gradient descent?

I have implemented a neural network from scratch (only using numpy) and I am having problems understanding why the results are so different between stochastic/minibatch gradient descent and batch ...
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1answer
157 views

Can a neural network learn to avoid wrong decisions using backpropagation?

I studied the articles on Neural Networks and Deep Learning from Michael Nielsen and developed a simple neural network based on his examples. I understand how backpropagation works and I already ...
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1answer
95 views

How is the Jacobian a generalisation of the gradient?

I came across these slides Natural Language Processing with Deep Learning CS224N/Ling284, in the context of natural language processing, which talk about the Jacobian as a generalization of the ...
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1answer
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How is the gradient of the loss function in DQN derived?

In the original DQN paper, page 1, the loss function of the DQN is $$ L_{i}(\theta_{i}) = \mathbb{E}_{(s,a,r,s') \sim U(D)} [(r+\gamma \max_{a'} Q(s',a',\theta_{i}^{-}) - Q(s,a;\theta_{i}))^2] $$ ...
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0answers
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Why are most commonly used activation functions continuous?

I have come to notice that the most commonly used activation functions are continuous. Is there any specific reason behind this? Results such as this paper have worked on training networks with ...
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2answers
461 views

What is the advantage of using cross entropy loss & softmax?

I am trying to do the standard MNIST dataset image recognition test with a standard feed forward NN, but my network failed pretty badly. Now I have debugged it quite a lot and found & fixed some ...
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3answers
735 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
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1answer
73 views

Why is the learning rate generally beneath 1?

In all examples I've ever seen, the learning rate of an optimisation method is always less than $1$. However, I've never found an explanation as to why this is. In addition to that, there are some ...
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2answers
121 views

Are filters fixed or learned?

No matter what I google or what paper I read, I can't find an answer to my question. In a deep convolutional neural network, let's say AlexNet (Krizhevsky, 2012), filters' weights are learned by means ...
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1answer
350 views

Does Musk know what gradient descent is?

From Futurism.com: Musk indicates that internet infrastructure is "particularly susceptible" to a method called gradient descent algorithm, a mathematical problem-solving process. Bad news is, AI ...
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2answers
142 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 ...
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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 ...
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1answer
542 views

Why Feature Scaling for skewed contour?

Why is it that the skewed contour (unscaled features) will result in slow performance of gradient descent? In other words, how (or why) will the gradients end up taking a long time before finding the ...
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2answers
829 views

Why use semi-gradient instead of full gradient in RL problems, when using function approximation?

Semi-gradient methods work well in reinforcement learning, but what is there a reason of not using the true gradient if it can be computed? I tried it on the cart pole problem with a deep Q-network ...
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0answers
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What is the time complexity for training a gated recurrent unit (GRU) neural network using back-propagation through time?

Let us assume we have a GRU network containing $H$ layers to process a training dataset with $K$ tuples, $I$ features, and $H_i$ nodes in each layer. I have a pretty basic idea how the complexity of ...
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109 views

How does SGD escape local minima?

SGD is able to jump out of local minima that would otherwise trap BGD I don't really understand the above statement. Could someone please provide a mathematical explanation for why SGD (Stochastic ...