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### Algorithms for curve construction

I am interested in algorithms that construct continuous curves between two points in such a way that minimizes an energy functional of the curve. What sort of algorithms are most used for such tasks? ...
1k views

### Why update weights and biases after training a Neural Network on whole set of training samples

I am reading the book Neural Networks and Deep Learning by Micheal Nielsen. In the second chapter of his book, he describes the following algorithm for updating weights and biases for a neural ...
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### How to optimize a function by maximizing 1 variable and minimizing another?

Problem I want to implement an optimization algorithm for my file transfer program. The program buffers data in a local file before uploading to central server periodically and it compresses the ...
83 views

### Is there a universal learning rate for NeuralNetworks?

I'm currently creating a NeuralNetwork with backpropagation/gradient descent. There is this hyperparameter introduced called "learning rate" (η). Which has to be chosen to guarantee not overshooting ...
761 views

### Calculating gradient in a neural net using batches

I am a CS student learning about neural nets. Currently I am confused about how to train a neural net in batches. If I calculate error in a batch, I will get a vector of errors e.g. real1 - predicted1,...
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### Is it possible to solve the Mountain Car reinforcement learning task with linear Q-Learning using the state as direct input?

I'm trying to solve the Mountain Car task on OpenAI Gym (reach the top in 110 steps or less, having a maximum of 200 steps per episode) using linear Q-learning (the algorithm in figure 11.16, except ...
35 views

### How is momentum an approximation of Hessian based optimization?

In the answer to "what is the Hessian" at this site: https://stackoverflow.com/questions/23297090/how-calculating-hessian-works-for-neural-network-learning the person answering the question ...
25 views

### Inverse kinematics step

I am working on an implementation of inverse kinematics using the jacobian transpose method. The implementation seems to be working as it does find the "theta" vector, although sometimes it might take ...
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### Line-search does not guarantee convergence so how to use it?

Line-search/backtracking in gradient descent methods essentially boils down to picking the current estimate $\theta_n$ (which depends on the stepsize $\gamma$ and the prior estimate $\theta_{n-1}$) by ...
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### Solving analytic gradient of loss function for neural networks [closed]

Please note that I am talking in about theory rather than ''what someone would do in a real, practical situation''. Given a multi-layer Perceptron with at least 1 hidden layer, and sigmoid (or other ...
69 views

### Why don't Artificial Neural Networks Commonly Diverge?

Introduction: I'm using divergence here as to mean that the gradient is getting further and further from zero in stochastic gradient descent. I've written my own feed-forward neural network and tried ...
2k views

### Gradient descent overshoot - why does it diverge?

I'm thinking about gradient descent, but I don't get it. I understand that it can overshoot the minimum when the learning rate is too large. But I can't understand why it would diverge. Let's say we ...
1k views

### What are the challenges of using gradient descent on hyper parameters λ and η to find out their optimum values?

A question from chapter 3 of Michael Nielsen's [Neural Networks and Deep Learning]: It's tempting to use gradient descent to try to learn good values for hyper-parameters such as the regularization ...
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### Is SGD used in machine learning libraries?

SGD (Stochastic Gradient Descent) is used in most libraries of different programming languages. Is it also used in machine learning libraries?
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### What is the difference between derivative free optimization and derivative optimization in terms of advantages/disadvantages?

I understand the basic operation of the algorithms however i'm unclear as to when to use one over the other and what advantages/disadvantages they offer over each other. Also as an aside, if anyone ...
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### Stochastic Gradient Descent for Multi-Class SVM

I'm trying to compute the optimization problem for a multi-class SVM loss function with $L2$ regularization. \$\displaystyle f(W) = \frac{1}{n}\sum_{i=1}^n\sum_{c\neq y_i} \max\{0,1-w_{y_i}^Tx_i+w_c^...
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### Gradient Descent in MLPs using Computational Graphs

I'm working through Deep Learning by Goodfellow et al. The textbook introduces backpropagation for MLPs in page 203 (http://www.deeplearningbook.org/contents/mlp.html). However, it does not expand ...
63 views

I'm playing around with some historical stock data and attempting to optimize a portfolio. I essentially have created a function that generates certain statistics about a portfolio (right now it's ...