I use torch.nn.Embedding to embed my model’s categorical input features, however, I face problems when I set the max_norm parameter to not None.
There is a note on the pytorch docs page that explains how to use max_norm parameter through the following example:
n, d, m = 3, 5, 7
embedding = nn.Embedding(n, d, max_norm=True)
W = torch.randn((m, d), requires_grad=True)
idx = torch.tensor(\[1, 2\])
a = embedding.weight.clone() # W.t() # weight must be cloned for this to be differentiable
b = embedding(idx) # W.t() # modifies weight in-place
out = (a.unsqueeze(0) + b.unsqueeze(1))
loss = out.sigmoid().prod()
loss.backward()
I can’t easily understand this example from the docs. What is the purpose of having both ‘a’ and ‘b’ and why ‘out’ is defined as, out = (a.unsqueeze(0) + b.unsqueeze(1))?
Do we need to first clone the entire embedding tensor as in ‘a’, and then finding the embeddings for our desired indices as in ‘b’? Then how do ‘a’ and ‘b’ need to be added?
In my code, I don’t have W explicitly, I am assuming that W is representative of the weights applied by the torch.nn.Linear layers. So, I just need to prepare the input (which includes the embeddings for categorical features) that goes into my network.
I greatly appreciate any instructions on this, as understanding this example would help me adapt my code accordingly.
Because W in the line computing a requires gradients, we must save embedding.weight to compute those gradients in the backward pass. However, in the line computing b, executing embedding(idx) will scale embedding.weight by max_norm - in place. So, without cloning it in line a, embedding.weight will be modified when line b is executed - changing what was saved for the backward pass to update W. Hence the requirement to clone embedding.weight - to save it before it gets scaled in line b.
If you don't use embedding.weight outside of the normal forward pass, you don't need to worry about all this.
If you get an error, post it (and your code).
Related
Is there any method to find the root of a polynomial, not in matrix form, in MATLAB?
I know, to find roots of a polynomial (say, p(x) = x^.2 - 4), I should do the following:
p = [1 0 -4];
r = roots(p)
What I wanted to know if there is some way to find the root of a function (say p(x) = x^.2 - 4) already present in polynomial form (not in matrix form) in my matlab code? Like anything similar to r = roots(p(x)) (this doesn't work, of course).
Root is good
First of all the solution using roots is probably the one that will give you the most accurate and fastest results if you are indeed working with polynomials. I will acknowledge that it might be an issue if your function is not a polynomial.
Finding the roots of a function
If you don't want to use roots that means you will probably have to represent your polynomial as an anonymous function. Then you can use any root-finding algorithm on that function. Wikipedia has a few of them listed. What is tricky is that in general they don't guarantee that they will find one root, let alone all of them. So you might need as much prior information on your function as you can.
In matlab you can use fzero. The issue with it is that it only finds one zero and that it will only find zeros where the function changes sign (it wouldn't work on p(x) = x² for example). This is how you would implement it:
p = #(x) x.^2 - 4; % Define your polynomial as an anonymous function
x0 = 12; % Initial guess for the zero
% Find a root
fzero(p, x0)
>>> ans = 2
% Now with a different initial guess for a different solution
x0 = -12;
fzero(p, x0)
>>> ans = -2
As you can see this works only if you want to find a root and don't care which one it is.
Problem
The issue is that you polynomials with integer or rational coefficients have a way of finding the roots by using square-free factorization. Yet you can only apply that if you have some way of storing and accessing those coefficients in matlab. The anonymous functions don't allow you to do that. That's why roots works with a matrix and not an anonymous function.
I have a model M and I am cloning it M.clone()
Now, I want to freeze certain layers of M.clone(). When I set requires_grad=False, it results in this error:
RuntimeError: you can only change requires_grad flags of leaf variables. If you want to use a computed variable in a subgraph that doesn't require differentiation use var_no_grad = var.detach().
How to freeze the layers of M.clone() in that case? I want to ensure that when I backpropagate using the loss computed on a batch using M.clone(), I compute the gradients of M
A small script:
model = ResNet()
optimizer = Adam(model.parameters())
cloned_model = model.clone()
for p in cloned_model.features.parameters():
p.require_grad = False
error = loss(cloned_model(data), labels)
error.backward()
optimizer.step()
P.S. I am not sure if I can use .detach() as I don't want to break the graph. Do correct me if I am wrong.
Thank you!
You can use the in-place requires_grad_ function either on a nn.Module or on a torch.Tensor directly. Here you could do:
cloned_model = copy.deepcopy(model)
cloned_model.requires_grad_(False)
Where deepcopy is from copy.
You should copy your optimizer as well otherwise optimizer will be updating model, not cloned_model... resulting in no changes at all since you are not back-propagating on model.
I am a beginner python user who is trying to get a feel for computer science, I've been learning how to use it by studying concepts/subjects I'm already familiar with, such as Computation Fluid Mechanics & Finite Element Analysis. I got my degree in mechanical engineering, so not much CS background.
I'm studying a series by Lorena Barba on jupyter notebook viewer, Practical Numerical Methods, and i'm looking for some help, hopefully someone familiar with the subjects of CFD & FEA in general.
if you click on the link below and go to the following output line, you'll find what i have below. Really confused on this block of code operated within the function that is defined.
Anyway. If there is anyone out there, with any suggestions on how to tackle learning python, HELP
In[9]
rho_hist = [rho0.copy()]
rho = rho0.copy() **# im confused by the role of this variable here**
for n in range(nt):
# Compute the flux.
F = flux(rho, *args)
# Advance in time using Lax-Friedrichs scheme.
rho[1:-1] = (0.5 * (rho[:-2] + rho[2:]) -
dt / (2.0 * dx) * (F[2:] - F[:-2]))
# Set the value at the first location.
rho[0] = bc_values[0]
# Set the value at the last location.
rho[-1] = bc_values[1]
# Record the time-step solution.
rho_hist.append(rho.copy())
return rho_hist
http://nbviewer.jupyter.org/github/numerical-mooc/numerical-mooc/blob/master/lessons/03_wave/03_02_convectionSchemes.ipynb
The intent of the first two lines is to preserve rho0 and provide copies of it for the history (copy so that later changes in rho0 do not reflect back here) and as the initial value for the "working" variable rho that is used and modified during the computation.
The background is that python list and array variables are always references to the object in question. By assigning the variable you produce a copy of the reference, the address of the object, but not the object itself. Both variables refer to the same memory area. Thus not using .copy() will change rho0.
a = [1,2,3]
b = a
b[2] = 5
print a
#>>> [1, 2, 5]
Composite objects that themselves contain structured data objects will need a deepcopy to copy the data on all levels.
Numpy array values changed without being aksed?
how to pass a list as value and not as reference?
i have been following cs231n lectures of Stanford and trying to complete assignments on my own and sharing these solutions both on github and my blog. But i'm having a hard time on understanding how to modelize backpropagation. I mean i can code modular forward and backward passes but what bothers me is that if i have the model below : Two Layered Neural Network
Lets assume that our loss function here is a softmax loss function. In my modular softmax_loss() function i am calculating loss and gradient with respect to scores (dSoft = dL/dY). After that, when i'am following backwards lets say for b2, db2 would be equal to dSoft*1 or dW2 would be equal to dSoft*dX2(outputs of relu gate). What's the chain rule here ? Why isnt dSoft equal to 1 ? Because dL/dL would be 1 ?
The softmax function is outputs a number given an input x.
What dSoft means is that you're computing the derivative of the function softmax(x) with respect to the input x. Then to calculate the derivative with respect to W of the last layer you use the chain rule i.e. dL/dW = dsoftmax/dx * dx/dW. Note that x = W*x_prev + b where x_prev is the input to the last node. Therefore dx/dW is just x and dx/db is just 1, which means that dL/dW or simply dW is dsoftmax/dx * x_prev and dL/db or simply db is dsoftmax/dx * 1. Note that here dsoftmax/dx is dSoft we defined earlier.
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I'm going through this tutorial on RNNs/LSTMs and I'm having quite a hard time understanding stateful LSTMs. My questions are as follows :
1. Training batching size
In the Keras docs on RNNs, I found out that the hidden state of the sample in i-th position within the batch will be fed as input hidden state for the sample in i-th position in the next batch. Does that mean that if we want to pass the hidden state from sample to sample we have to use batches of size 1 and therefore perform online gradient descent? Is there a way to pass the hidden state within a batch of size >1 and perform gradient descent on that batch ?
2. One-Char Mapping Problems
In the tutorial's paragraph 'Stateful LSTM for a One-Char to One-Char Mapping' were given a code that uses batch_size = 1 and stateful = True to learn to predict the next letter of the alphabet given a letter of the alphabet. In the last part of the code (line 53 to the end of the complete code), the model is tested starting with a random letter ('K') and predicts 'B' then given 'B' it predicts 'C', etc. It seems to work well except for 'K'. However, I tried the following tweak to the code (last part too, I kept lines 52 and above):
# demonstrate a random starting point
letter1 = "M"
seed1 = [char_to_int[letter1]]
x = numpy.reshape(seed, (1, len(seed), 1))
x = x / float(len(alphabet))
prediction = model.predict(x, verbose=0)
index = numpy.argmax(prediction)
print(int_to_char[seed1[0]], "->", int_to_char[index])
letter2 = "E"
seed2 = [char_to_int[letter2]]
seed = seed2
print("New start: ", letter1, letter2)
for i in range(0, 5):
x = numpy.reshape(seed, (1, len(seed), 1))
x = x / float(len(alphabet))
prediction = model.predict(x, verbose=0)
index = numpy.argmax(prediction)
print(int_to_char[seed[0]], "->", int_to_char[index])
seed = [index]
model.reset_states()
and these outputs:
M -> B
New start: M E
E -> C
C -> D
D -> E
E -> F
It looks like the LSTM did not learn the alphabet but just the positions of the letters, and that regardless of the first letter we feed in, the LSTM will always predict B since it's the second letter, then C and so on.
Therefore, how does keeping the previous hidden state as initial hidden state for the current hidden state help us with the learning given that during test if we start with the letter 'K' for example, letters A to J will not have been fed in before and the initial hidden state won't be the same as during training ?
3. Training an LSTM on a book for sentence generation
I want to train my LSTM on a whole book to learn how to generate sentences and perhaps learn the authors style too, how can I naturally train my LSTM on that text (input the whole text and let the LSTM figure out the dependencies between the words) instead of having to 'artificially' create batches of sentences from that book myself to train my LSTM on? I believe I should use stateful LSTMs could help but I'm not sure how.
Having a stateful LSTM in Keras means that a Keras variable will be used to store and update the state, and in fact you could check the value of the state vector(s) at any time (that is, until you call reset_states()). A non-stateful model, on the other hand, will use an initial zero state every time it processes a batch, so it is as if you always called reset_states() after train_on_batch, test_on_batch and predict_on_batch. The explanation about the state being reused for the next batch on stateful models is just about that difference with non-stateful; of course the state will always flow within each sequence in the batch and you do not need to have batches of size 1 for that to happen. I see two scenarios where stateful models are useful:
You want to train on split sequences of data because these are very long and it would not be practical to train on their whole length.
On prediction time, you want to retrieve the output for each time point in the sequence, not just at the end (either because you want to feed it back into the network or because your application needs it). I personally do that in the models that I export for later integration (which are "copies" of the training model with batch size of 1).
I agree that the example of an RNN for the alphabet does not really seem very useful in practice; it will only work when you start with the letter A. If you want to learn to reproduce the alphabet starting at any letter, you would need to train the network with that kind of examples (subsequences or rotations of the alphabet). But I think a regular feed-forward network could learn to predict the next letter of the alphabet training on pairs like (A, B), (B, C), etc. I think the example is meant for demonstrative purposes more than anything else.
You may have probably already read it, but the popular post The Unreasonable Effectiveness of Recurrent Neural Networks shows some interesting results along the lines of what you want to do (although it does not really dive into implementation specifics). I don't have personal experience training RNN with textual data, but there is a number of approaches you can research. You can build character-based models (like the ones in the post), where your input and receive one character at a time. A more advanced approach is to do some preprocessing on the texts and transform them into sequences of numbers; Keras includes some text preprocessing functions to do that. Having one single number as feature space is probably not going to work all that well, so you could simply turn each word into a vector with one-hot encoding or, more interestingly, have the network learn the best vector representation for each for, which is what they call en embedding. You can go even further with the preprocessing and look into something like NLTK, specially if you want to remove stop words, punctuation and things like that. Finally, if you have sequences of different sizes (e.g. you are using full texts instead of excerpts of a fixed size, which may or may not be important for you) you will need to be a bit more careful and use masking and/or sample weighting. Depending on the exact problem, you can set up the training accordingly. If you want to learn to generate similar text, the "Y" would be the similar to the "X" (one-hot encoded), only shifted by one (or more) positions (in this case you may need to use return_sequences=True and TimeDistributed layers). If you want to determine the autor, your output could be a softmax Dense layer.
Hope that helps.