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 - [email protected])

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

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

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)

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 } }