Examples

The repository ships two runnable demos. Here is exactly what they print today.

1. XOR — a multi-layer perceptron

examples/xor_mlp.py trains a small network on the classic XOR problem:

model = gorch.nn.Sequential(
    gorch.nn.Linear(2, 8),
    gorch.nn.Tanh(),
    gorch.nn.Linear(8, 2),
    gorch.nn.Softmax(),
)
loss_fn = gorch.nn.CrossEntropyLoss()
opt = gorch.optim.Adam(model.parameters(), lr=0.05)

epoch    0  loss 0.4915  accuracy 50%
epoch  100  loss 0.0015  accuracy 100%
epoch  200  loss 0.0006  accuracy 100%
epoch  300  loss 0.0003  accuracy 100%
epoch  400  loss 0.0002  accuracy 100%
epoch  500  loss 0.0001  accuracy 100%
epoch  600  loss 0.0001  accuracy 100%
epoch  700  loss 0.0001  accuracy 100%
final accuracy: 100%
predictions: [0, 1, 1, 0]

It reaches 100% accuracy in about 100 epochs of vanilla Adam.

2. Neural control

examples/neural_control.py demos three control-flavoured tools.

Kalman filter — state estimation

A double-integrator with noisy position measurements, filtered online:

1) Kalman filter: estimating position/velocity of a noisy double integrator
  measurement MSE : 0.0836
  filtered   MSE  : 0.0275   <- filtered is tighter

EKF optimizer — identifying a nonlinear plant

A neural network learns the unknown nonlinear mapping y = tanh(Wx) + 0.2 x₀ x₁ using the extended-Kalman optimizer instead of gradient descent:

2) EKF optimizer: identify a nonlinear plant with a neural network
  mean absolute prediction error: 0.0993 (random init ~ 1.2)

RLS — online system identification

Recursive least squares recovers the weights of a linear plant sample by sample:

3) RLS: online least-squares identification of a linear plant
  true weights : [0.01709638 0.67987377]
  estimated    : [0.01710572 0.67987443]
  max error    : 9.33e-06

Run them yourself

python examples/xor_mlp.py
python examples/neural_control.py