gradients | CSS module for quickly setting gradients | Data Visualization library

It is indeed true that sampling is not a differentiable operation per se. However, there exist two (broad) ways to mitigate this - [1] The REINFORCE way and [2] The reparameterization way. Since your example is related to [1], I will stick my answer to REINFORCE.

What REINFORCE does is it entirely gets rid of sampling operation in the computation graph. However, the sampling operation remains outside the graph. So, your statement

.. how does the gradient passes through a random operation ..

isn't correct. It does not pass through any random operation. Let's see your example

TLDR; Both are two different interfaces to perform gradient computation: torch.autograd.grad is non-mutable while torch.autograd.backward is.

Descriptions

The torch.autograd module is the automatic differentiation package for PyTorch. As described in the documentation it only requires minimal change to code base in order to be used:

you only need to declare Tensors for which gradients should be computed with the requires_grad=True keyword.

The two main functions torch.autograd provides for gradient computation are torch.autograd.backward and torch.autograd.grad:

torch.autograd.backward (source) torch.autograd.grad (source) Description Computes the sum of gradients of given tensors with respect to graph leaves. Computes and returns the sum of gradients of outputs with respect to the inputs. Header torch.autograd.backward(
tensors,
grad_tensors=None,
retain_graph=None,
create_graph=False,
grad_variables=None,
inputs=None) torch.autograd.grad(
outputs,
inputs,
grad_outputs=None,
retain_graph=None,
create_graph=False,
only_inputs=True,
allow_unused=False) Parameters - tensors – Tensors of which the derivative will be computed.
- grad_tensors – The "vector" in the Jacobian-vector product, usually gradients w.r.t. each element of corresponding tensors.
- retain_graph – If False, the graph used to compute the grad will be freed. [...]
- inputs – Inputs w.r.t. which the gradient be will be accumulated into .grad. All other Tensors will be ignored. If not provided, the gradient is accumulated into all the leaf Tensors that were used [...]. - outputs – outputs of the differentiated function.
- inputs – Inputs w.r.t. which the gradient will be returned (and not accumulated into .grad).
- grad_tensors – The "vector" in the Jacobian-vector product, usually gradients w.r.t. each element of corresponding tensors.
- retain_graph – If False, the graph used to compute the grad will be freed. [...]. Usage examples

In terms of high-level usage, you can look at torch.autograd.grad as a non-mutable function. As mentioned in the documentation table above, it will not accumulate the gradients on the grad attribute but instead return the computed partial derivatives. In contrast torch.autograd.backward will be able to mutate the tensors by updating the grad attribute of leaf nodes, the function won't return any value. In other words, the latter is more suitable when computing gradients for a large number of parameters.

In the following, we will take two inputs (x1 and, x2), calculate a tensor y with them, and then compute the partial derivatives of the result w.r.t both inputs, i.e. dL/dx1 and dL/dx2:

I'm afraid you just have to put up with the vulnerabilities. Angular has a very strict set of dependencies, and in changing the versions of those dependencies you've broken your app.

Make sure you keep updating your Angular project as often as is feasible, as the Angular team regularly update Angular's dependencies to mitigate these issues.

You did not move your model to device, only the data. You need to call model.to(device) before using it with data located on device.

Maybe with repeating gradient:

Looks great, as you have already followed most of the solutions to resolve gradient exploding problem. Below is the list of all solutions you can try

Solutions to avoid Gradient Exploding problem

1. Appropriate Weight initialization: utilise appropriate weight Initialization based on the activation function used.

   Initialization Activation Function He ReLU & variants LeCun SELU Glorot Softmax, Logistic, None, Tanh

2. Redesigning your Neural network: use fewer layers in neural network and/or use smaller batch size

3. Choosing Non Saturation activation function: choose the right activation function with reduced learning rates

   • ReLU
   • Leaky ReLU
   • randomized leaky ReLU (RReLU)
   • parametric leaky ReLU (PReLU)
   • exponential linear unit (ELU)

4. Batch Normalisation: Ideally using batch normalisation before/after each layer, based on what works best for your dataset.

   • after each layer Paper reference

These are different concepts and are used like this:

• train_step is called by fit. Basically, fit loops over the dataset and provide each batch to train_step (and then handles metrics, bookkeeping, etc., of course).
• call is used when you, well, call the model. To be precise, writing model(inputs) or in your case self(inputs) will use the function __call__, but the Model class has that function defined such that it will in turn use call.

Those are the technical aspects. Intuitively:

• call should define the forward-pass of your model. i.e. how is the input transformed to the output.
• train_step defines the logic of a training step, usually with gradient descent. It will often make use of call since the training step tends to include a forward pass of the model to compute gradients.

As for the GAN tutorial you linked, I would say that can actually be considered incomplete. It works without defining call because the custom train_step explicitly calls the generator/discriminator fields (as these are predefined models, they can be called as usual). If you tried to call the GAN model like gan(inputs), I would assume you get an error message (I did not test this). So you would always have to call gan.generator(inputs) to generate, for example.

Finally (this part may be a bit confusing), note that you can subclass a Model to define a custom training step, but then initialize it via the functional API (like model = Model(inputs, outputs)), in which case you can make use of call in the training step without ever defining it yourself because the functional API takes care of that.

Add the smallest value (in this case is negative) so that everything is >= 0. Then use Poisson.

If we take your example we have function f which takes as input x shaped (n,) and outputs y = f(x) shaped (n, n). The input is described as column vector [x_i]_i for i ∈ [1, n], and f(x) is defined as matrix [y_jk]_jk = [x_j*x_k]_jk for j, k ∈ [1, n]².

It is often useful to compute the gradient of the output with respect to the input (or sometimes w.r.t the parameters of f, there are none here). In the more general case though, we are looking to compute dL/dx and not just dy/dx, where dL/dx is the partial derivative of L, computed from y, w.r.t. x.

The computation graph looks like: