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First of all, let me add this schema which I think is quite nice to understand the transition and improvement from the initial Rosenblatt's perceptron and the Adaline algorithm: In Adaline, provided that the cost function (your y(t)-s(t)) is differentiable, the weights can be updated and there is no restriction of y and s having the same sign: the objective ...

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The two pictures you show illustrate how to interprete one perceptron and a MLP consisting of 3 layers. Let us discuss the geometry behind one perceptron first, before explaining the image. We consider a perceptron with $n$ inputs. Thus let $\mathbf{x} \in \mathbb{R}^{n}$ be the input vector, $\mathbf{w} \in \mathbb{R}^{n}$ be the weights, and let $b \in \... 2 I think the problem is in your predict method: (self.bias + self.weights * inputs).sum(axis=1) adds the bias to both of the weight*input values before summing (the arrays are broadcast to the same shape). Hence why the 2*intercept makes things match up. 2 what issue arises, when trying to train this network with gradient descent? The activation function is sign function or signum function (A little modified). So, its Derivative will be 0 at all the points Hence, the Gradient descent won’t be able to make progress in updating the weights and backpropagation will fail. 1 1.) Perceptron is a non-linear transformation! 2.) Linear seperable function is only defined for boolean functions, see Wikipedia. Therefore, yes, the statement is meant only for binary classification. 3.) For general functions, see the universal approximation theorem. 1 I will answer your questions one by one: By hidden layer we mean the layer that is inbetween the input and output. If number of layers = 1 with 10 hidden neurons (as shown in second figure) then is it essentially a neural network which is termed as an MLP. Is my understanding correct? The fundamental building block of a Neural Network is the perceptron. It'... 1 The behavior appears to actually depend on the learning rate$\eta$; a smaller$\eta$affects which points are misclassified in the next iteration, which affects the weight update more than just by the simple scaling you alluded to. With appropriately small learning rates though, it seems you are guaranteed convergence to some local minimum, if you avoid ... 1 I think that the "neurons" analogy is not very helpful to understand what is going on with artificial neural networks. Neural networks are not comprised by "neurons", but by differentiable operations. These operations are arbitrary, e.g. convolutions, indexing (in embeddings), pooling, etc. What you proposed is a perfectly valid building ... 1 The example you cited (using x^2 instead of x) is the idea more popular outside deep learning community, called feature engineering. The trend in neural network modeling is instead to, Play with weights (w) and fine tune them. Not change the input vector (x) but feed it to the network directly. If a single layer neural network is not good enough, add more ... 1 In a fully connected setting the bias shifts the weighted sum of the previous node output by a certain amount before applying the activation function. In practice, it's a column vector b (bias [initialized as a constant vector]) added to the vector Wx (the product of weight matrix (W) and input vector (x)) as:$\$\mathrm{Layer2output} = W.\mathrm{Layer1output}...

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No, bias neurons are not connected to any previous neuron. This is visualized like this: (source)

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MP model : 1) inputs are binary values; 2) has not weights Rosenblatt model: 1) inputs can take any real numbers; 2) has weights. Thank you, https://medium.com/@manushaurya/mcculloch-pitts-neuron-vs-perceptron-model-8668ed82c36

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n is the dimension of the vector x and also y, as you can see wT is a transpose of w with dimension (n,n), is the image z is y and a is x. and dont bother about l it indicates the index of layer.

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You are forgetting one element of the MLP which is the activation function. If your activation function is linear - then you can simply flatten out all the neurons into one single linear equation. The advantage of MLP however is its non-linearities so I suspect in your network you do have some activation (sigmoid? tanh? relu? etc..). As for your graph - you ...

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