This repository contains a TensorFlow implementation of Kolmogorov-Arnold Network.

The modules in layers are similar to those in tf.keras.layers, so you can use these layers as independent modules to assemble the model (in a TensorFlow style):

from tfkan.layers import DenseKAN
# create model using KAN
model = tf.keras.models.Sequential([
    DenseKAN(4),
    DenseKAN(1)
])
model.build(input_shape=(None, 10))

When calling model.summary() you can see the model structure and its trainable parameters:

Model: "sequential"
_________________________________________________________________
 Layer (type)                Output Shape              Param #   
=================================================================
 dense_kan (DenseKAN)        (None, 4)                 484       
                                                                 
 dense_kan_1 (DenseKAN)      (None, 1)                 85        
                                                                 
=================================================================
Total params: 569 (2.22 KB)
Trainable params: 401 (1.57 KB)
Non-trainable params: 168 (672.00 Byte)
_________________________________________________________________

When getting started quickly, we can define the optimizer and loss function used for training through model.compile() and model.fit(), or you can use tf.GradientTape() to more finely control the model training behavior and parameter update logic. All model behaviors are the same in Tensorflow2, and you can truly use KAN as an independent module:

model.compile(
    optimizer=tf.keras.optimizers.Adam(learning_rate=1e-3), 
    loss='mse', metrics=['mae'])
history = model.fit(x_train, y_train, epochs=100, batch_size=64)

The layers currently implemented include:

• DenseKAN

  • The basic dense layer, corresponding to tf.keras.layers.Dense() (or nn.Linear() in torch) in MLP
  • Implement the computational logic described in the KANs paper
  • grid update method is available but it will not be automatically used

• ConvolutionKAN

  • The basic convolution layer, provide Conv1DKAN, Conv2DKAN and Conv3DKAN for classical 1D, 2D and 3D convolution operations
  • The implementation logic is similar to Conv in Tensorflow, expanding convolution operations into matrix multiplication, and then replacing MLP dense kernel with DenseKAN kernel

The grid adaptive update is an important feature mentioned in KANs paper. In this tensorflow implementation of KANs, each KAN layer has two method used to implement this feature:

• self.update_grid_from_samples(...)
  • adaptively update the spline grid points using input samples given
  • this can help the spline grid adapt to the numerical range of the input, avoiding the occurrence of input features outside the support set of the grid (resulting in outputs that are equal to 0, as spline functions outside the support set are not defined)
• self.extend_grid_from_samples(...)
  • extend the spline grid for given gird_size
  • this can help to make the spline activation output more smooth, thereby enhancing the model approximation ability

You can call it in custom training logic or use Tensorflow Callbacks;

• In custom training logic:

def train_model(...):
    # training logic
    ...

    # call update_grid_from_samples
    for layer in model.layers:
        if hasattr(layer, 'update_grid_from_samples'):
            layer.update_grid_from_samples(x)
        x = layer(x)

• or use Tensorflow Callbacks:

# define update grid callback
class UpdateGridCallback(tf.keras.callbacks.Callback):
    def __init__(self, training_data, batch_size: int = 128):
        super(UpdateGridCallback, self).__init__()
        self.training_data = tf.constant(training_data[:batch_size], tf.float32)
        
    def on_epoch_begin(self, epoch, logs=None):
        """
        update grid before new epoch begins
        """
        x_batch = self.training_data
        if epoch > 0:
            for layer in self.model.layers:
                if hasattr(layer, 'update_grid_from_samples'):
                    layer.update_grid_from_samples(x_batch)
                x_batch = layer(x_batch)

then add it into model.fit().

Installation & usage

1. Clone and navigate to the repository folder:

   git clone git@github.com:avrtt/kolmogorov-arnold-network.git
   cd kolmogorov-arnold-network

2. Run:

   pip install .

3. Use as packages:

   from kolmogorov-arnold-network import layers
   from kolmogorov-arnold-network.layers import DenseKAN, Conv2DKAN

License

This project is licensed under the MIT License - see the LICENSE file for details.