[...] = in progress
- Xavier initialization (general-purpose activation)
- He et. al initialization (ReLU activation)
- Orthogonal initialization
- SELU initialization (SELU activation)
[...]
[...]
[...]
# Xavier init
for m in model:
if isinstance(m, (nn.Conv2d, nn.Linear)):
nn.init.xavier_normal(m.weight)
# He et. al init
for m in model:
if isinstance(m, (nn.Conv2d, nn.Linear)):
nn.init.kaiming_normal(m.weight)
# orthogonal init
for m in model:
if isinstance(m, (nn.Conv2d, nn.Linear)):
nn.init.orthogonal(m.weight)
# SELU init
for m in model:
if isinstance(m, nn.Conv2d):
n = m.kernel_size[0] * m.kernel_size[1] * m.out_channels
nn.init.normal(m.weight, 0, sqrt(1. / n))
elif isinstance(m, nn.Linear):
n = m.out_features
nn.init.normal(m.weight, 0, sqrt(1. / n))For BatchNorm we initialize the weights to 1 and the biases to 0.
for m in model:
if isinstance(m, nn.BatchNorm2d):
nn.init.constant(m.weight, 1)
nn.init.constant(m.bias, 0)- L2 Regularization: add L2 norm weight penalty to loss function.
- L1 Regularization: add L1 norm weight penalty to loss function.
- Orthogonal Regularization: apply a weight penalty of
|W*W.T - I|to loss function. - Max Norm Constraint: clamp weight norm to less than a constant
W.norm(2) < c.
Heavily penalizes peaky weight vectors and encourages diffuse weight vectors. Has the appealing property of encouraging the network to use all of its inputs a little rather that some of its inputs a lot.
Encourages sparsity, meaning we encourage the network to select the most useful inputs/features rather than use all.
Improves gradient flow by keeping the matrix norm close to 1. This is because orthogonal matrices represent an isometry of R^n, i.e. they preserve lengths and angles. They rotate vectors, but cannot scale or shear them.
If a hidden unit's weight vector's L2 norm L ever gets bigger than a certain max value c, multiply the weight vector by c/L. Enforce it immediately after each weight vector update or after every X gradient update.
This constraint is another form of regularization. While L2 penalizes high weights using the loss function, "max norm" acts directly on the weights. L2 exerts a constant pressure to move the weights near zero which could throw a"way useful information when the loss function doesn't provide incentive for the weights to remain far from zero. On the other hand, "max norm" never drives the weights to near zero. As long as the norm is less than the constraint value, the constraint has no effect.
# l2 reg
l2_loss = Variable(torch.FloatTensor(1), requires_grad=True)
for W in model.parameters():
l2_loss = l2_loss + (0.5 * W.norm(2) ** 2)
# l1 reg
l1_loss = Variable(torch.FloatTensor(1), requires_grad=True)
for W in model.parameters():
l1_loss = l1_loss + W.norm(1)
# orthogonal reg
orth_loss = Variable(torch.FloatTensor(1), requires_grad=True)
for W in model.parameters():
W_reshaped = W.view(W.shape[0], -1)
sym = torch.mm(W_reshaped, torch.t(W_reshaped))
sym -= Variable(torch.eye(W_reshaped.shape[0]))
orth_loss = orth_loss + sym.sum()
# max norm constraint
def max_norm(model, max_val=3, eps=1e-8):
for name, param in model.named_parameters():
if 'bias' not in name:
# l2 norm per row (batch)
norm = param.norm(2, dim=0, keepdim=True)
desired = torch.clamp(norm, 0, max_val)
param = param * (desired / (eps + norm))[...]
[...]
- Learning Rate
- Batch Size
- Effect on Generalization
References
- Cyclical Learning Rates for Training Neural Networks
- SGDR: Stochastic Gradient Descent with Warm Restarts
- On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima
- Don't Decay the Learning Rate, Increase the Batch Size
- https://www.reddit.com/r/MachineLearning/comments/77dn96/r_171006451_understanding_generalization_and/dol2u23/
[...]