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I haven't seen an answer from a trusted source, but I'll try to answer this myself, with a simple example (with my current knowledge). In general, note that training a MLP using back-propagation is usually implemented with matrices. Time complexity of matrix multiplication The time complexity of matrix multiplication for $M_{ij} * M_{jk}$ is simply $\... 13 "Backprop" is the same as "backpropagation": it's just a shorter way to say it. It is sometimes abbreviated as "BP". 8 Gradient descent and back-propagation In deep learning, gradient descent (GD) and back-propagation (BP) are used to update the weights of the neural network. In reinforcement learning, one could map (state, action)-pairs to Q-values with a neural network. Then GD and BP can be used to update the weights of this neural network. How to design the neural ... 8 In reverse order to how you asked: all units in a layer become equal since initially the errors due to all of them are the same and thus we train them to be equal This actually happens if you initialise the weights equally (e.g. all zero). Gradients in that case are the same to each neuron in the same layer, and everything changes in lockstep. A neural ... 7 'Backprop' is short for 'backpropagation of error' in order to avoid confusion when using backpropagation term. Basically backpropagation refers to the method for computing the gradient of the case-wise error function with respect to the weights for a feedforward networkWerbos. And backprop refers to a training method that uses backpropagation to compute ... 7 There are several elementary techniques to try and move a search out of the basin of attraction of local optima. They include: Probabalistically accepting worse solutions in the hope that this will jump out of the current basin (like Metropolis-Hastings acceptance in Simulated Annealing). Maintaining a list of recently-encountered states (or attributes ... 7 Yes this is done routinely. For example this is how the YOLO object detection and classifier system works, to give a real-world for example. In YOLO, the "non-object" classification is "background" i.e. any image segment that doesn't contain one of the types of object we are interested in. In general, you can add an "other" class to any classifier, provided ... 7 You can run gradient descent without back propagation, in some cases: Simple structures such as linear or logistic regression, where the gradients can be calculated directly from the inputs and cost function value. In "black box" gradient-based learning algorithms where you don't know how (or don't want to) calculate gradient analytically, so you choose to ... 6 Unlike backpropagation, evolutionary algorithms do not require the objective function to be differential with respect to the parameters you aim to optimize. As a result, you can optimize "more things" in the network, such as activation functions or number of layers, which wouldn't be possible in the standard backpropagation. Another advantage is that by ... 6 The two examples present essentially the same operation: In both cases, the network is trained with gradient descent using the backpropagated squared error computed at the output. Both examples use the logistic function for node activation (the derivative of the logistic function$s$is$s(1 - s)$. This derivative is obviously very easy to compute, and this ... 6 Backpropagation is a subroutine often used when training Artificial Neural Networks with a Gradient Descent learning algorithm. Gradient Descent requires computation of the error gradient, i.e. derivatives, of a cost function with respect to the network parameters. BP allows you to find this gradient a lot faster than using naive methods. Reinforcement ... 5 When you are training a neural network, you use an algorithm called back propagation. This algorithm uses partial derivatives to determine the optimal values for weights. Partial derivatives are a calculus based method which tell you how far you need to adjust the weights in order to get to an optimum value. However, when you have neural networks with many ... 5 Further to Franck's answer, there may be better optima (even global optima) that exist in the opposite direction to the gradient (which may be in the direction of some local optima). Evolutionary algorithms have scope to search the surrounding area, while backpropagation will always move in the direction of the gradient. With no guarantee (due to their ... 5 For the evaluation of a single pattern, you need to process all weights and all neurons. Given that every neuron has at least one weight, we can ignore them, and have$\mathcal{O}(w)$where$w$is the number of weights, i.e.,$n * n_i$, assuming full connectivity between your layers. The back-propagation has the same complexity as the forward evaluation (... 5 tl;dr: A batch size is the number of samples a network sees before updating its gradients. This number can range from a single sample to the whole training set. Empirically, there is a sweet spot in the range 1 to a few hundreds, where people experience the fastest training speeds. Check this article for more details. A more detailed explanation... If you ... 5 You wouldn't, normally. A HMM is used to model sequences of observations, and it would not make sense to use it for image recognition. Unless they are sequential, such as strokes in handwriting. HMMs are typically used in fields such as speech recognition and part-of-speech tagging. Here you observe a sequence of events that you want to fit to a model in ... 4 Actually the implementation was correct, The source of the problem that causes a big error and really slow learning was the architecture of the neural network it self, the ANN has 7 hidden layers which causes the vanishing gradient problem. When I have decreased the ANN layers to 3 the cost of error was widely reduced besides of that the learning process ... 4 For future reference, I will merely point you to a technique you can implement to test the correctness or lack thereof, of your backpropagation implementation. Ps: don't feel too bad for having gotten it slightly wrong, "backpropagation is notoriously difficult to implement" - source :). In fact, there is a technique called "Gradient checking" meant ... 4 Gradient descent (GD) is an optimisation algorithm, that is, it is used to find a (local) minimum of a multi-variable and differentiable function$f$. GD is an iterative and numerical optimisation algorithm. It is iterative because it proceeds in iterations. It is numerical because it is not an algorithm which produces an exact solution, due to numerical ... 4 What are filters in image processing? In the context of image processing (and, in general, signal processing), the kernels (also known as filters) are used to perform some specific operation on the image. For example, you can use a Gaussian filter to smooth the image (including its edges). What are filters in CNNs? In the context of convolutional neural ... 4 I think what you mean to ask is how can differentiation occur when there's no obvious neural network function to differentiate? Don't worry - lots of people get confused about this, because it seems like an obvious hole in the puzzle. As mentioned by @AtillaOzgur, neural networks use partial differentiation through backpropagation. First, take the output ... 4 Even the first artificial neural network - Rosenblatt's perceptron [1] had a discontinuous activation function. That network is in introductory chapters of many textbooks about AI. For example, Michael Negnevitsky. Artificial intelligence: a guide to intelligent systems. Second Edition shows how to train such networks on pages 170-174. Error backpropagation ... 4 Why is it called back-propagation? I don't think there is anything special here! It's called back-propagation (BP) because, after the forward pass, you compute the partial derivative of the loss function with respect to the parameters of the network, which, in the usual diagrams of a neural network, are placed before the output of the network (i.e. to the ... 4 Introduction First of all, it's completely normal that you are confused because nobody really explains this well and accurately enough. Here's my partial attempt to do that. So, this answer doesn't completely answer the original question. In fact, I leave some unanswered questions at the end (that I will eventually answer). The gradient is a linear ... 3 You should read up on these papers: Deep Q-Networks Asynchronous Deep Reinforcement Learning Both by DeepMind. They achieved super-human results on video-games and other tasks. They describe the algorithms quite well. It is not as simple as the previous answer, which won't converge to a policy in complex environments. 3 I believe the best way to do this is using numerical gradient. To understand the concept, we need to look the definition of derivatives using limits: It means that, when you don't know how to derive some formula (or you just don't want to), you can approximate it by computing the output for a small change in input, subtract from the original result (no ... 3 Multilayer Perceptron (MLP) can theoretically approximate any bounded, continuous function. There's no guarantee for a discontinuous function. There are plenty of important discontinuous functions, like, say, the prime counting function. The prime counting function$\pi(n)$is simply equal to the number of primes less than or equal to$n\$. It has a ...

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There is not single answer to the vanishing gradient problem. However, there a few things that can help. As mentioned in the comments, use of Rectified Linear Units (ReLU) as your activation function can help, since the it does not get saturated for large neuron inputs. Next, careful choice of weight initialization can help avoid saturation, as well. See ...

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The main doubt here is about the intuition behind the derivative part of back-propagation learning. First, I would like to point out 2 links about the intuition about how partial derivatives work Chain Rule Intuition and Intuitive reasoning behind the Chain Rule in multiple variables?. Now that we know how the chain rule works, let's see how we can use it ...

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Backpropagation with stride > 1 involves dilation of the gradient tensor with stride-1 zeroes. I created a blog post that describes this in greater detail.

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