Pytorch RBF Layer - Radial Basis Function Layer

Pytorch RBF Layer implements a radial basis function layer in Pytorch.

Radial Basis networks can be used to approximate functions, and can be combined together with other PyTorch layers.

An RBF is defined by 5 elements:

1. A radial kernel

2. The number of kernels , and relative centers

3. Positive shape parameters , which are scaling factors

4. A norm

5. A set of weights

The output of an RBF is given by , where is the input data.

The RBFLayer class takes as input: (1) the dimensionality of ; (2) the number of desired kernels; (3) the output dimensionality; (4) the radial function; (5) the norm to use.

The parameters can be either learnt, or set to a default parameter.

For more information check

• [1] https://en.wikipedia.org/wiki/Radial_basis_function
• [2] https://en.wikipedia.org/wiki/Radial_basis_function_network

An example of input/output mapping learnt by RBF	Multiclass classification example

Author: Alessio Russo (PhD Student at KTH - alessior@kth.se)

License

Our code is released under the MIT license (refer to the LICENSE file for details).

Requirements

To run the library you need atleast Python 3.5 and PyTorch.

Usage/Examples

You can start using the layer by typing python from rbf_layer import RBFLayer in your code.

To learn how to use the RBFLayer, check the examples located in the examples/ folder:

• Multiclass classification example

In general the code has the following structure

import torch
from rbf_layer import RBFLayer

# Define an RBF layer where the dimensionality of the input feature is 20,
# the number of kernels is 5, and 2 output features


# \ell norm
def l_norm(x, p=2):
    return torch.norm(x, p=p, dim=-1)


# Gaussian RBF
def rbf_gaussian(x):
    return (-x.pow(2)).exp()


# Use a radial basis function with euclidean norm
rbf = RBFLayer(in_features_dim=20,            # input features dimensionality
               num_kernels=5,                 # number of kernels
               out_features_dim=2,            # output features dimensionality
               radial_function=rbf_gaussian,  # radial basis function used
               norm_function=l_norm)          # l_norm defines the \ell norm


# Uniformly sample 100 points with 20 features
x = torch.rand((100, 20))

# Compute the output of the RBF layer
# y has shape(100, 2)
y = rbf(x)

Citations

If you find this code useful in your research, please, consider citing it:

@misc{pythonvrft, author = {Alessio Russo}, title = {Pytorch RBF Layer}, year = 2021, doi = {}, url = { https://github.com/rssalessio/PytorchRBFLayer } }