Perceptron | purpose Perceptron that can solve a linear equation

I have a Perceptron written in Javascript that works fine, code below. My question is about the threshold in the activation function. Other code I have seen has something like if (sum > 0) {return 1} else {return 0}. My perceptron only works with if (sum > 1) {return 1} else {return 0}. Why is that? Full code below.

Are there tasks a sigle layer perceptron can do better than a multilayer perceptron? If yes, do you have an example?

i am using du functional api from keras and would like to add a dropout to my multi layer perceptron.

do i have to put the dropout before or after the layer and do i have to connect the next layer to the dropout or to the previous layer?

I would like to know how does the algorithm update the biais in this situation?

Is it

or

?

both give me different results. Or is the way i put the bias above wrong? I think it should differents bias per perceptron.

Why is tensor flow throwing me this exception " module 'tensorboard.summary._tf.summary' has no attribute 'FileWriter'" each time i try to run my MCP Neuron, How can i go about solving the issue at hand ? I have search on stack but couldn't find any solution that fit my problem. can anyone help me out.

I have a general question about Keras. When training a Artificial Neural Network (e.g. a Multi-Layer-Perceptron or a LSTM) with a split of training, validation and test data (e.g. 70 %, 20 %, 10 %), I would like to know which parameter configuration the trained model is eventually using for predictions?

Here I have an exmaple from a training process with 11 epoch:

I could think about 3 possible parameter configurations (surely there are also others):

1. The configuration that led to the lowest error in the training dataset (which would be after the 11th epoch)
2. The configuration after the last epoch (which would the after the 11th epoch, as in 1.)
3. The configuration that led to the lowest error in the validation dataset (which would be after the 3rd epoch)

If you just build the model without for example like this:

Suppose I have my custom loss function and I want to fit the solution of some differential equation with help of my neural network. So in each forward pass, I am calculating the output of my neural net and then calculating the loss by taking the MSE with the expected equation to which I want to fit my perceptron.

Now my doubt is: should I use grad(loss) or should I do loss.backward() for backpropagation to calculate and update my gradients?

I understand that while using loss.backward() I have to wrap my tensors with Variable and have to set the requires_grad = True for the variables w.r.t which I want to take the gradient of my loss.

So my questions are :

• Does grad(loss) also requires any such explicit parameter to identify the variables for gradient computation?
• How does it actually compute the gradients?
• Which approach is better?
• what is the main difference between the two in a practical scenario.

It would be better if you could explain the practical implications of both approaches because whenever I try to find it online I am just bombarded with a lot of stuff that isn't much relevant to my project.

I have this neural network model to create anomaly detection model. I copy this model from one of a tutorial website

Let N be a (linear) single-layer perceptron with weight matrix w of dimension nxn.

I want to train N under the Boolean constraint that the condition number k(w) of the weights w remain below a given threshold k_0 at each step of the optimisation.

Is there a standard way to implement this constraint (in pytorch, say)?