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What are the filters? A filter/kernel is a set of learnable weights which are learned using the backpropagation algorithm. You can think of each filter as storing a single template/pattern. When you convolve this filter across the corresponding input, you are basically trying to find out the similarity between the stored template and different locations in ...


5

Note that a CNN is a feed-forward neural network. Thus, if you understand how to perform backpropagation in feed-forward neural networks, you have it for CNNs. A convolution layer can be understood as a fully connected layer, with the constraints that several edge weights are identical and many edge weights are set to 0. You can also build a pooling layer in ...


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Batch Normalization (BN) does not prevent the vanishing or exploding gradient problem in a sense that these are impossible. Rather it reduces the probability for these to occur. Accordingly, the original paper states: In traditional deep networks, too-high learning rate may result in the gradients that explode or vanish, as well as getting stuck in poor ...


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As per Efficient Backprop from Lecun (§4.6) weight should be initialized in the linear region of the activation function. If they are too big, activation function will saturate and provide small gradient step to change those weigth. If they are too small they won't really impact the gradient and make the learning too slow. Yes, if you choose the same weights ...


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Of course that all weights are the same, but the update applied to the weights has a contribution from each of the timesteps, and the contribution associated with the first timesteps is what is more affected by the vanishing gradient problem.


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what issue arises, when trying to train this network with gradient descent? The activation function is sign function or signum function (A little modified). So, its Derivative will be 0 at all the points Hence, the Gradient descent won’t be able to make progress in updating the weights and backpropagation will fail.


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Let's suppose this picture in which we have three layers $$ \nabla_{z_{2}^{2}}C$$ $$ \frac{\partial C}{\partial Z_{2}^{2}} = \frac{\partial C}{\partial Z_{1}^{3}} * \frac{\partial Z_{1}^{3}}{\partial Z_{2}^{2}} + \frac{\partial C}{\partial Z_{2}^{3}} * \frac{\partial Z_{2}^{3}}{\partial Z_{2}^{2}} $$ $$ \delta_{2}^{2} = \sum_{k} \frac{\partial Z_{k}^{l+1}}...


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CNN learns the same way a Dense Neural network learns i.e. Forwardpass and Backpropagation. What we learn here are the weights of the filters. So, answers to your individual questions - But how are they getting initialized? - Standard init. e.g. glorot_uniform then the values should get changed on the training process of the network. Yes How does someone ...


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First, try to understand a few points - Output Neuron value and the prediction both are the same things. In the case of Classification, we convert the output probability to Class based on a Threshold. MSE is used in Regression and In a regression problem, you mostly have one output Neuron e.g. Price. You may have more if you want to club multiple targets e....


1

The idea of mean squared error is find the mean value of the squared errors. Therefore, you divide by the number of squared errors you add up, which is the number of samples. In more inference-oriented applications (e.g. linear regression and ordinary least squares), you may see the denominator given as $n-k$ or $n-p$, where $k$ and $p$ and the number of ...


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If you know that $f(x) = wx + b$, then you also know that $\frac{\partial f}{\partial b} = 1$. The function LossGradient does not use that information, and would estimate it by evaluating the function $f$. Then it computes the loss. In general, it computes $f$ and $Loss$ once for every learnable parameter. Backpropagation uses knowledge about the function ...


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$h_{\theta}$ is an hypothesis function which is parameterized by $\theta$. i.e for differetn value of $\theta$ you get a different hypothesis function. $h_{\theta}(x^{i})$ Calucates the value of the hypothesis function pararameterzied by a certain value $\theta$ on the input $x^i$. This is also called predicted output. $\sum_{i=1}^{n}(h_{\theta}(x^{i}) - y^...


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Using backpropagation is nothing else than performing (stochastic) gradient descent. It computes the gradient, but it is not the "optimal" weight. The gradient is used to update the current weight (according to the gradient descent algorithm). The gradient descent algorithm needs a step size (which is called learning rate in the context of machine ...


1

This is because the derivative wrt $b$ is $1$: $\frac{\partial E}{\partial b} = 1$ dout is the derivative of loss function wrt prediction. Using chain rule, $$ \frac{dE}{dw} = \frac{dE}{dy}\frac{dy}{ds}\frac{ds}{dw} $$ The last term is the vector of input features $x$. In your case dout is the combination of the first two terms. For example, for MSE loss and ...


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In some ways, convolutions do not introduce a radical departure from the standard architecture. Because the operations which are applied to the filtered input (max,min,mean,etc) are continuous, these filters amount to a lossy "layer" of the network. You are right to intuit that the filter parameters can be trained — so a filter which transforms a ...


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As to what I understand from your question, yes you can have multiple features (variables/input) and use gradient descent to minimize the loss function which has the input variables. Here is an article that gives you a basic vector calculus idea as to what exactly does a gradient is and what it does in the algorithm! https://towardsdatascience.com/wondering-...


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This is the Neural Network - $\hspace{5cm}$ This is the equation - $\hspace{5cm}$$\frac{\partial J}{\partial w_{12}^{(2)}} = \frac{\partial J}{\partial h_{1}^{(3)}} \frac{\partial h_{1}^{(3)}}{\partial z_{1}^{(2)}} \frac{\partial z_{1}^{(2)}}{\partial w_{12}^{(2)}}$ $J$ = The calculated Loss $w_{12}^{(2)}$ - Weight for which the rate of Loss is to be ...


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In this layered graph structure, the relevance conservation property can be formulated as follows: Let j and k be indices for neurons of two successive layers. Let Rk be the relevance of neuron k for the prediction f (x). We define R j←k as the share of Rk that is redistributed to neuron j in the lower layer. The conservation property for this neuron imposes ...


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In neural networks, activation functions such as the logistic (sigmoid) and the hyperbolic tangent functions map any real values to a compact range of values. For example, the sigmoid function, S(x)= 1/(1+ e^(-x) ) maps a set of real values x to between 0 and 1. To attain these boundaries of either 0 or 1, large magnitude negative or positive values of x ...


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Since in CNN, we are taking one filter to indicate one feature. We introduce a variable(b) to incorporate the bias from that particular filter. Hence, each filter takes into account the bias that it can cause. The bias is not due to individual filter weights but the whole filter itself. I hope that answers your question.


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According to Kingma and Ba (2014) Adam has been developed for "large datasets and/or high-dimensional parameter spaces". The authors claim that: "[Adam] combines the advantages of [...] AdaGrad to deal with sparse gradients, and the ability of RMSProp to deal with non-stationary objectives" (page 9). In the paper, there are some ...


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