README.md

CNN with Kolmogorov-Arnold Networks

In our investigation of CNN architectures, we integrated Kolmogorov-Arnold Networks (KANs) to compare against traditional fully connected (FC) layers. We found that KANs, with their non-linear spline-based transformations, can capture complex patterns more efficiently than FC layers, potentially reducing the need for deeper or more complex network structures. Despite KANs typically having a larger parameter count due to their intricate spline functions, they offer a significant advantage in modeling capabilities. This study highlighted the potential of KANs to outperform standard FC layers in tasks requiring high levels of data interpretation and complexity.

Benchmark on MNIST Dataset

Model	Epochs	Test Set: Average Loss	Accuracy
CNN with KAN	5	0.0033	7297/10000 (73%)
CNN with MLP	5	0.0037	6813/10000 (68%)

Network Architecture

CNNKAN(
  (conv1): Conv2d(3, 32, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))
  (pool1): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False)
  (conv2): Conv2d(32, 64, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))
  (pool2): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False)
  (kan1): KANLinear(
    (base_activation): SiLU()
  )
  (kan2): KANLinear(
    (base_activation): SiLU()
  )
)

Parameter Count

conv1.weight: 864
conv1.bias: 32
conv2.weight: 18432
conv2.bias: 64
kan1.base_weight: 1048576
kan1.spline_weight: 8388608
kan1.spline_scaler: 1048576
kan2.base_weight: 2560
kan2.spline_weight: 20480
kan2.spline_scaler: 2560
Total trainable parameters: 10530752