Each Answer to this Q is separated by one/two green lines.
Is there any way, I can add simple L1/L2 regularization in PyTorch? We can probably compute the regularized loss by simply adding the
data_loss with the
reg_loss but is there any explicit way, any support from PyTorch library to do it more easily without doing it manually?
Following should help for L2 regularization:
optimizer = torch.optim.Adam(model.parameters(), lr=1e-4, weight_decay=1e-5)
This is presented in the documentation for PyTorch. You can add L2 loss using the
weight_decay parameter to the Optimization function.
Previous answers, while technically correct, are inefficient performance wise and are not too modular (hard to apply on a per-layer basis, as provided by, say,
PyTorch L2 implementation
Why PyTorch implemented
Let’s take a look at
torch.optim.SGD source code (currently as functional optimization procedure), especially this part:
for i, param in enumerate(params): d_p = d_p_list[i] # L2 weight decay specified HERE! if weight_decay != 0: d_p = d_p.add(param, alpha=weight_decay)
- One can see, that
d_p(derivative of parameter, gradient) is modified and re-assigned for faster computation (not saving the temporary variables)
- It has
O(N)complexity without any complicated math like
- It does not involve
autogradextending the graph without any need
Compare that to
**2 operations, addition and also taking part in backpropagation.
L2 equation with
alpha regularization factor (same could be done for L1 ofc):
If we take derivative of any loss with
L2 regularization w.r.t. parameters
w (it is independent of loss), we get:
So it is simply an addition of
alpha * weight for gradient of every weight! And this is exactly what PyTorch does above!
L1 Regularization layer
Using this (and some PyTorch magic), we can come up with quite generic L1 regularization layer, but let’s look at first derivative of
L1 first (
sgn is signum function, returning
1 for positive input and
-1 for negative,
Full code with
WeightDecay interface located in torchlayers third party library providing stuff like regularizing only weights/biases/specifically named paramters (disclaimer: I’m the author), but the essence of the idea outlined below (see comments):
class L1(torch.nn.Module): def __init__(self, module, weight_decay): super().__init__() self.module = module self.weight_decay = weight_decay # Backward hook is registered on the specified module self.hook = self.module.register_full_backward_hook(self._weight_decay_hook) # Not dependent on backprop incoming values, placeholder def _weight_decay_hook(self, *_): for param in self.module.parameters(): # If there is no gradient or it was zeroed out # Zeroed out using optimizer.zero_grad() usually # Turn on if needed with grad accumulation/more safer way # if param.grad is None or torch.all(param.grad == 0.0): # Apply regularization on it param.grad = self.regularize(param) def regularize(self, parameter): # L1 regularization formula return self.weight_decay * torch.sign(parameter.data) def forward(self, *args, **kwargs): # Simply forward and args and kwargs to module return self.module(*args, **kwargs)
Read more about hooks in this answer or respective PyTorch docs if needed.
And usage is also pretty simple (should work with gradient accumulation and and PyTorch layers):
layer = L1(torch.nn.Conv2d(in_channels=3, out_channels=32, kernel_size=3))
Also, as a side note,
L1 regularization is not implemented as it does not actually induce sparsity (lost citation, it was some GitHub issue on PyTorch repo I think, if anyone has it, please edit) as understood by weights being equal to zero.
More often, weight values are thresholded (simply assigning zero value to them) if they reach some small predefined magnitude (say
For L2 regularization,
l2_lambda = 0.01 l2_reg = torch.tensor(0.) for param in model.parameters(): l2_reg += torch.norm(param) loss += l2_lambda * l2_reg
for L1 regularization and inclulde
L1_reg = torch.tensor(0., requires_grad=True) for name, param in model.named_parameters(): if 'weight' in name: L1_reg = L1_reg + torch.norm(param, 1) total_loss = total_loss + 10e-4 * L1_reg
L2 regularization out-of-the-box
Yes, pytorch optimizers have a parameter called
weight_decay which corresponds to the L2 regularization factor:
sgd = torch.optim.SGD(model.parameters(), weight_decay=weight_decay)
L1 regularization implementation
There is no analogous argument for L1, however this is straightforward to implement manually:
loss = loss_fn(outputs, labels) l1_lambda = 0.001 l1_norm = sum(torch.linalg.norm(p, 1) for p in model.parameters()) loss = loss + l1_lambda * l1_norm
The equivalent manual implementation of L2 would be:
l2_norm = sum(torch.linalg.norm(p, 2) for p in model.parameters())
Source: Deep Learning with PyTorch (8.5.2)
torch.norm is slower on CPU and faster on GPU vs. direct approach.
import torch x = torch.randn(1024,100) y = torch.randn(1024,100) %timeit torch.sqrt((x - y).pow(2).sum(1)) %timeit torch.norm(x - y, 2, 1)
1000 loops, best of 3: 910 µs per loop 1000 loops, best of 3: 1.76 ms per loop
On the other hand:
import torch x = torch.randn(1024,100).cuda() y = torch.randn(1024,100).cuda() %timeit torch.sqrt((x - y).pow(2).sum(1)) %timeit torch.norm(x - y, 2, 1)
10000 loops, best of 3: 50 µs per loop 10000 loops, best of 3: 26 µs per loop