Hey; I construct a very simple classification model to classify mixture of gaussian.
In this case, bivariate Gaussian. The data close to mode one has label 0 and data close to mode two has label 1.
Here is how I generate train samples
from torch.distributions.multivariate_normal import MultivariateNormal
m1 = MultivariateNormal(torch.zeros(2) + 300,torch.eye(2) * .01)
m2 = MultivariateNormal(torch.zeros(2) + 200.,torch.eye(2) * .01)

x1 = m1.sample((1000,)) # mode 1 
x2 = m2.sample((1000,)) # mode 2

c1 = torch.zeros(1000) # labels for mode 1
c2 = torch.ones(1000) # labels for mode 2


x = torch.cat([x1,x2],dim=0)
c = torch.cat([c1,c2],dim=0).view(-1,1)

The train sample look like this

Now I construct a simple classifier
class Classifier(nn.Module):
    def __init__(self,num_in_dim=2,num_hidden=100):
        super(Classifier, self).__init__()

        self.fc1 = nn.Sequential(
        nn.Linear(num_in_dim, num_hidden),
        nn.ReLU(inplace=True),
        nn.Linear(num_hidden, 1),
       nn.Sigmoid())


    def forward(self,x):
        return self.fc1(x)

Now I set up my training as
net = Classifier()
optimizer = optim.Adam(net.parameters(), lr=1e-3)
criterion = nn.BCELoss()
for i in range(100):
    optimizer.zero_grad()
    a = net(x)
    loss = criterion(a, c)
    loss.backward()
    optimizer.step()
    if i % 100 == 0:
        print(loss.item())

The weird behaviour I observe is that. Here are the train loss. I use the same set of batch samples train the same network with only initial parameters different. Each line is a one initialization of network. We see that sometimes the network doesn’t learn at all but some times it works really well. Though, there are many theory on optimization about local minimal etc. But I think example like this is too trivia and same thing happens even I use linear neural network.