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3

I know that gradient descent allows you to find the local minimum of a function. What I don't know is what exactly that function IS. It's usually called the loss function (and, in general, objective function) and often denoted as $\mathcal{L}$ or $L$ (or something like that, i.e. it is not really important how you denote it). The specific function used as a ...

3

Welcome to AI Stack exchange! You're right, as the network is initialised randomly, the resultant function is essentially impossible to get your head around. This is because most of the time the network has >4 dimensions (4 can be graphed with some effort and a lot of color), and as such is literally beyond human comprehension via graphing. So what do we ...

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I'm going to use slightly different notation, $\leftarrow$ for an assignment, $\alpha$ for learning rate, $\nabla_w J$ in place of $g$* and implied multiplication as these are slightly more common. Also, using bold letters to represent vectors. In that notation, the update rule for basic gradient descent would be written as: \mathbf{w} \leftarrow \mathbf{...

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I am watching the same course too, and I think that in the example graph, the cost function is not a sum of MSE (Mean squarred errors), but it could be a cubic one, so a sum of cubical errors, and thus the cost function could be negative: as there are a variety of cost functions, the MSE ones are not adapted for every problems, and other formulations could ...

2

In your case, $L$ is the loss (or cost) function, which can be, for example, the mean squared error (MSE) or the cross-entropy, depending on the problem you want to solve. Given one training example $(\mathbf{x}_i, y_i) \in D$, where $\mathbf{x}_i \in \mathbb{R}^d$ is the input (for example, an image) and $y_i \in \mathbb{R}$ can either be a label (aka class)...

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Neural networks can have a lot of different structures. CNNs can have a number of parameters that ranges from a few thousands to several millions. In general you aim to increase the number of filters and reduce the first 2 dimensions, as you go deeper in the network. So if you had Conv -> pool -> Conv -> pool -> ... , you could do for example ...

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