Unified Neural Network Training¶

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ΦML provides basic tools to set up and train neural networks. Users can choose one of several standard network architectures and configure them in one line of code. After defining a loss function, they can then be trained in a unified way or using library-specific functions.

In [1]:
%%capture
!pip install phiml

from matplotlib import pyplot as plt

Network Architectures¶

The neural network API includes multiple common network architectures, such as multi-layer perceptrons, U-Nets, convolutional networks, ResNets, invertible networks, and VGG-like networks. All networks operating on grids are supported in 1D, 2D and 3D for periodic and non-periodic domains.

In [2]:
from phiml import math, nn
math.use('torch')
Out[2]:
torch

Training an MLP¶

Let's create an MLP and train it to learn a 1D sine function. First, we set up the network with two hidden layers of 64 neurons each.

In [3]:
mlp = nn.mlp(in_channels=1, out_channels=1, layers=[64, 64], activation='ReLU')
mlp
Out[3]:
DenseNet(
  (linear0): Linear(in_features=1, out_features=64, bias=True)
  (linear1): Linear(in_features=64, out_features=64, bias=True)
  (linear_out): Linear(in_features=64, out_features=1, bias=True)
)

Note that this is a standard neural network of the chosen library (a PyTorch Module in this case). This allows you to quickly try many network designs without writing much code, even if you don't use ΦML for anything else.

Next, let's generate some training data.

In [4]:
DATASET = math.batch(examples=100)
x = math.random_uniform(DATASET, low=-math.PI, high=math.PI)
y = math.sin(x) + math.random_normal(DATASET) * .1
plt.scatter(x.numpy(), y.numpy())
Out[4]:
<matplotlib.collections.PathCollection at 0x7efec3d562e0>

For the loss function, we will use the $L^2$ comparing prediction to labels. We use math.native_call() to call the network with native tensors reshaped to the preferences of the current backend library. This will pass tensors of shape BCS to PyTorch and BSC to TensorFlow and Jax, where B denotes the packed batch dimensions, C the packed channel dimensions and S all spatial dimensions.

In [5]:
def loss_function(network_input, label):
    prediction = math.native_call(mlp, network_input)
    return math.l2_loss(prediction - label), prediction

Next, we create an optimizer, such as SGD, Adam, AdaGrad, or RMSprop. The returned optimizer is again a library-specific type (in this case a PyTorch optimizer).

In [6]:
optimizer = nn.adam(mlp, learning_rate=5e-3)
optimizer
Out[6]:
Adam (
Parameter Group 0
    amsgrad: False
    betas: (0.9, 0.999)
    capturable: False
    differentiable: False
    eps: 1e-07
    foreach: None
    fused: None
    lr: 0.005
    maximize: False
    weight_decay: 0
)

Finally, we repeatedly update the weights using backprop. Here, we use update_weights(), passing in the network, optimizer, loss function, and loss function arguments. If you want more control over the training loop, you can use library-specific functions as well, since the network and optimizer do not depend on ΦML.

In [7]:
for i in range(200):
    loss, pred = nn.update_weights(mlp, optimizer, loss_function, x, y)
plt.scatter(x.numpy(), pred.numpy())
Out[7]:
<matplotlib.collections.PathCollection at 0x7efec020dd30>

Training a U-Net¶

Following the principles of ΦML, U-Nets, as well as many other network architectures, can operate on 1D, 2D or 3D grids. The number of spatial dimensions, in_spatial, must be specified when creating the network.

In [8]:
u_net = nn.u_net(in_channels=1, out_channels=1, levels=4, periodic=False, in_spatial=2)
optimizer = nn.adam(u_net, 1e-3)

Let's train the network to turn a 2D grid of random noise into a Gaussian distribution.

In [9]:
SPATIAL = math.spatial(x=64, y=64)
x = math.random_normal(SPATIAL)
y = math.exp(-.5 * math.vec_squared((math.meshgrid(SPATIAL) / SPATIAL) - .5))

fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(8, 4))
ax1.imshow(x.numpy('y,x'))
ax2.imshow(y.numpy('y,x'))

/tmp/ipykernel_2943/1475163513.py:3: DeprecationWarning: phiml.math.vec_squared is deprecated in favor of phiml.math.squared_norm
  y = math.exp(-.5 * math.vec_squared((math.meshgrid(SPATIAL) / SPATIAL) - .5))
Out[9]:
<matplotlib.image.AxesImage at 0x7efec0135fd0>

Let's train the network!

In [10]:
def loss_function():
    prediction = math.native_call(u_net, x)
    return math.l2_loss(prediction - y), prediction

for i in range(200):
    loss, pred = nn.update_weights(u_net, optimizer, loss_function)

plt.imshow(pred.numpy('y,x'))
Out[10]:
<matplotlib.image.AxesImage at 0x7efec00ae310>

Further Reading¶

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