Chapter 4 of the fastai book covers how to build a Neural Network for distinguishing 3s and 7s on MNIST from scratch. We’re going to do a similar thing but instead of building the neural network from the ground up we’re going to use fastai’s layered API to build it top down. We’ll start with the high level API to train a dense neural network in a few lines. Then we’ll redo the problem going deeper and deeper into the API. At the very core it’s mainly PyTorch, and we’ll have a pure PyTorch implementation like in the book. Then we’ll start rebuilding the abstractions from scratch to get a high level API like we started with.
Instead of using the MNIST digits we’ll use Fashion MNIST, which contains little black and white images of different types of clothing. This is a bit harder and a convolutional neural network would perform better here (as demonstrated in v3 of fastai course). But to keep things simple we’ll use a dense neural network.
image.png
We train a model to recognise these items of clothing from scratch in just 6 lines using fastai’s high level API. It should take a minute or two to run on a CPU (for such a small model and data there is marginal benefit running on a GPU).
We can then test the perormance on the test set; note that it’s very close to the accuracy from the last line of the training above.
df_test = pd.read_csv('../input/fashionmnist/fashion-mnist_test.csv', dtype={'label': df.label.dtype})probs, actuals = learn.get_preds(dl=dls.test_dl(df_test))print(f'Accuracy on test set {float(accuracy(probs, actuals)): 0.2%}')
Accuracy on test set 85.88%
Looking at the sklearn benchmarks on this dataset it’s outperformed by some other models such as Support Vector Machines (SV) with 89.7% accuracy, and Gradient Boosted Trees with 88.8% accuracy. In fact our model is almost the same as the MLPClassifier (87.7%). See if you can beat this baseline by changing the layers, learning rate, and number of epochs.
The best results on this dataset, around 92-96%, come from Convolutional Neural Networks (CNN). The kind of approach we use here can be extended to a CNN; the other kinds of models are quite different.
What did we just do?
Let’s go back through those 5 lines slowly to see what was going on.
1. Import
The first line imports all the libraries we need for tabular analysis.
This includes specific fastai libraries, as well as general utilities such as Pandas, numpy and PyTorch, and much more
from fastai.tabular.allimport*
If you want to see exactly what was imported you can look into the module or the source code.
Now we have our raw data we need a way to pass that into the model in a way it understands. We do this with a DataLoader reading from the dataframe. We need to tell it:
df: the dataframe to read from
y_names: the name of the column containing the outcome variable, here label
bs: the batch size, how many rows to feed to the model each time. We use 4096 because the data and models are small
procs: any preprocessing steps to do, here we use Normalize to map them from 0-255 to a more reasonable range.
cont_names: The name of the continuous columns
Note that before we didn’t pass cont_names and it automatically detected them; however it can reorder the columns so we specify it here for clarity.
This data loader can then produce the pixel arrays for a subset of rows, and the outcome labels on demand. Note these are the values before using procs.
dls.show_batch()
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4
Behind the scenes this also splits our data into a training dataset that we use to update the model parameters, and a validation dataset that we use to evaluate the model. This is really important because neural networks are incredibly flexible and can often memorise the training data; the validation dataset is an exam with questions the model has never seen before.
We can access the individual dataloaders with .train and .valid respectively.
dls.train, dls.valid
(<fastai.tabular.core.TabDataLoader at 0x7f4c0e502d10>,
<fastai.tabular.core.TabDataLoader at 0x7f4c0e502e90>)
These can be iterated on to get batches of examples to train or evaluate the model on.
This particular dataloader returns a tuple containing 3 items
The first is an empty array. This would contain any categorical variables in our model, but since we are only using the continuous pixel values it’s empty.
batch[0]
tensor([], size=(4096, 0), dtype=torch.int64)
The second is a 4096x784 array of numbers. These correspond to 4096 of the rows from the initial training data.
We can see the image has been slightly whitened by the normalization. This is because we normalized each pixel column independently; we may get better results if the normalize them all together. But you can still tell it’s some kind of top.
Apparently the image above is a shirt (and not a pullover or t-shirt/top).
labels[str(batch[2][0][0].item())]
'Pullover'
We can iterate through the batches to see we have about 4500 labels from each category in the training dataloader
from collections import Countertrain_label_count = Counter()for batch in dls.train: train_label_count.update(batch[2].squeeze().numpy())train_label_count
The reason for this is fastai has made all the batches equal length by dropping the extra examples.
n_train /4096
11.0
5. Learner
Now we have our dataloaders to load the data for training and validation we need a way to learn from the data. The fastai learner contains all the things we need to do that:
the dataloaders
a model consisting of an architecture and parameters, which can make output predictions from inputs
any metrics for quantitatively evaluating the system
a loss function for automatically evaluating the quality of output predictions against labels
an optimiser for updating the parameters to minimise the loss function
layers: The hidden layers that define the architecutre of the model, we use a single layer of dimension 100
opt_fun: The optimiser to use for updating parameters, here Stochastic Gradient Descent
metrics: human interpretable metrics; accuracy is the proportion of labels the model correctly guesses
config: model configuration; here we are turning off BatchNorm which is a technique to help train Deep Neural Networks. As we’re trying to keep the model simple we leave them off.
The metrics are the human interpretable quantitative measures of the model; in this case we just used the accuracy.
We can get the loss and any metrics we passed in by calling learn.validate().
The accuracy should be close to 10% because we have a randomly initialised model with 10 equally likely categories.
learn.validate()
(#2) [2.344938278198242,0.08091666549444199]
We can list out all the metrics
learn.metrics
(#1) [<fastai.learner.AvgMetric object at 0x7f4c0e492490>]
We can get the name of each metric
learn.metrics[0].name
'accuracy'
and call it on our predictions to get the accuracy
learn.metrics[0].func(probs, actual)
TensorBase(0.0809)
Our actual predictions are the categories with the highest probability
preds = probs.argmax(axis=1)preds
tensor([4, 2, 0, ..., 5, 8, 2])
Then the accuracy is just the proportion of predictions that are the same as the actuals
sum(preds == actual.flatten()) /len(preds)
tensor(0.0809)
5.4 Loss
Accuracy is a good easy to understand metric, but it’s hard to optimise. The accuracy only changes when the order of the probabilities change. A small change in probabilities won’t change accuracy most of the time so it’s hard to tell which direction to move the parameters to make it better.
Instead for multicategory classification we use something called CrossEntropyLoss
learn.loss_func
FlattenedLoss of CrossEntropyLoss()
We can evaluate it on a single batch by passing the model predictions (not the probabilities) and the labels
learn.loss_func(batch_pred, batch[2])
TensorBase(2.3452, grad_fn=<AliasBackward0>)
What is CrossEntropyLoss?
Find the probability of each actual category
Take the negative logarithm of each
Average over all entries
Since the logarithm is bigger the bigger the input (in mathematical jargon it’s strictly monotonic) the higher the probability for the correct class the lower the CrossEntropyLoss. If we bump up the probability for the correct class by x for all predictions, then the loss decreases by -log(x).
actual_probs = torch.tensor([prob[idx] for prob, idx inzip(batch_probs, batch[2].flatten())])-actual_probs.log().mean()
tensor(2.3452)
Here’s a way to do this with just indexing:
pass torch.arange(len(batch_probs)), this generates the list [0, 1, 2, ..., N]
pass the label index as a long [0, 0, ... 9]
This will extract the pairs of row 0 to N, and the corresponding label column.
This is faster and PyTorch knows how to differentiate it.
Let’s create a copy of the old parameters for reference
old_params = [p.detach().numpy().copy() for p in learn.parameters()]
We want to move the parameters in the direction that decreases the loss. To do this we call backward to fill in all the derivatives with respect to the parameters
*x, y =next(iter(dls.valid))preds = learn.model(*x)loss = learn.loss_func(preds, y)
loss
TensorBase(2.3452, grad_fn=<AliasBackward0>)
with torch.no_grad(): loss.backward() learn.opt.step() learn.zero_grad()
new_params = [p.detach().numpy() for p in learn.parameters()]
We can create Datasets containing the pairs of (image, label) for each of the train, validation and test splits.
We normalize the pixels to be between 0 and 1. (This is slightly different to Normalize which performs a linear transform on each column so that it has mean 0 and standard deviation 1).
ds_train = [(np.array(img, dtype=np.float32) /255., label) for _idx, (label, *img) in df[~valid_mask].iterrows()]ds_valid = [(np.array(img, dtype=np.float32) /255., label) for _idx, (label, *img) in df[ valid_mask].iterrows()]ds_test = [(np.array(img, dtype=np.float32) /255., label) for _idx, (label, *img) in df_test.iterrows()]
We can pick out an example
x, y = ds_train[0]plt.imshow(x.reshape(28,28), cmap='Greys')y
2
We then put these into a PyTorch DataLoaders to shuffle them and collate them into batches
We can calculate accuracy as the number of predictions that are the same as the labels. Since we have 10 equally likely classes for our randomly initialised model it should be about 10%.
The appropriate loss function for multiclass classification is CrossEntropy loss.
loss_function = nn.CrossEntropyLoss()
loss_function(pred, y)
tensor(2.3009, grad_fn=<NllLossBackward0>)
Optimizer
PyTorch provides torch.optim.SGD optimizer but we can’t use it directly with a Learner; from the docs
The most important is opt_func. If you are not using a fastai optimizer, you will need to write a function that wraps your PyTorch optimizer in an OptimWrapper. See the optimizer module for more details. This is to ensure the library’s schedulers/freeze API work with your code.
Note that this performs slightly worse than our original model which got to 82% accuracy and 0.5 validation loss in 5 epochs. It would be interesting to know what’s changed!
With this kind of machine learning code a small change can make a big difference in how fast a model trains and how accurate it gets; this is why it’s good to be able to dig into the detail!
learn.fit(5, lr=0.2)
epoch
train_loss
valid_loss
accuracy
time
0
1.773703
1.286911
0.647599
00:00
1
1.426255
1.041697
0.638919
00:00
2
1.228973
0.891194
0.687113
00:00
3
1.102247
0.816285
0.696784
00:01
4
1.006129
0.768820
0.736877
00:00
Training with base PyTorch
Now we’re going to train the model again, but this time just using the basic utilities from Pytorch. We’ll also use no classes and keep everything as simple low level functions so we can see the underlying mechanics.
First we clear our namespace to prevent cheating.
for name indir():ifnot name.startswith('_'):delglobals()[name]
Now, as before, we can set up 2 linear models with a ReLU between them. In torch nn code this looks like:
model = nn.Sequential(
nn.Linear(784, 100),
nn.ReLU(),
nn.Linear(100, 10),
)
The first linear layer consists of 784 * 100 weights plus 100 biases. The ReLU layer has no parameters; it’s just a nonlinear activation. The final layer consists of 100 * 10 weights to 10 biases.
Our loss function is the negative log likelihood; the likelihood is how probable the data is given the model, that is we average the probabilities for the correct label, and then take the negative log.
The first step in calculating this is getting the model probabilities. We normalise th predictions with a softmax; expoentiate to make positive, and then divide by the sum to normalise to 1.
Unfortunately if we do this naively we end up getting infinity because of the limits of floating point arithmetic.
Instead we use the log probabilities, which have a better range in floating point space, and use the log-sum-exp trick to make it stable (PyTorch has a logsumexp function, but it’s easy to write.
def logsumexp(x): c = x.max(axis=1).values x_shift = x - c[:, None]return c + x_shift.exp().sum(axis=1).log()
Our randomly initialised weights should on average give a ~1/10 probability to each class, and so the loss should be around -log(1/10) = 2.3.
loss = loss_func(pred, y)loss
tensor(126.1162, grad_fn=<NegBackward0>)
Optimizer
The SGD optimizer just moves each paramater a small step down the gradient to reduce the overall loss (and then we need to reset the gradients to zero).
We can easily run the whole training loop as follows (though note we get slightly worse accuracy than last time).
batch_size =2048lr =0.2for epoch inrange(5):for _batch inrange(len(X_train) // batch_size):# Data loader idx = np.random.choice(len(X_train), batch_size, replace=False) X, y = X_train[idx], y_train[idx] pred = model(X) loss = loss_func(pred, y) loss.backward()with no_grad():for p in params: p -= lr * p.grad p.grad.zero_()print(epoch, accuracy(model(X_valid), y_valid))
The high level tabular API is convenient for very quickly training a good model. It has good defaults for things like the loss, model architecture and the optimiser, but it highly configurable if we want to change the defaults. However this API is limited to the kinds of applications it’s been built for; if we wanted a very different architecture or to work on a novel kind of input or output we can’t use it.
The midlevel API exposes the Learner which is a very flexible training loop, and lets us use whatever kind of model, data, and optimiser we want. This can be used for any number of tasks, but requires more work to implement the model, and choose the right hyperparameters.
Using the low level PyTorch API with minimal abstraction we can see how everything fits together. There’s no magic, and the training loop itself is rather simple. However if we want to for example switch the optimiser, or the model, or the data type, it involves rewriting the training loop and it’s a lot of work to maintain and debug. The abstractions in the midlevel API often allow switching models, optimisers, data types, or metrics without changing anything else.
The next step would be to rebuild the abstractions to understand what they’re actually doing. Each time we went down a layer our model trained slower; with the right abstractions it’s easy to focus on one piece at a time and work out why this happened (and maybe even discover a better way of training!)