Polynomial convolutional neural network with early fan-out
The invention proposes a method of training a convolutional neural network in which, at each convolution layer, weights for one seed convolutional filter per layer are updated during each training iteration. All other convolutional filters are polynomial transformations of the seed filter, or, alternatively, all response maps are polynomial transformations of the response map generated by the seed filter.
1. A method for training a neural network comprising, for each convolution layer in the neural network:
receiving a gradient function;
adjusting a seed convolutional filter based on the gradient function;
generating a plurality of augmented convolutional filters, wherein each weight of each augmented convolutional filter is generated by applying a polynomial to one or more weights of the seed convolutional filter;
receiving an input;
generating a plurality of response maps based on convolutions of the input with the seed convolutional filter and each of the plurality of augmented convolutional filters; and
generating a feature map based on the plurality of response maps.
2. The method of claim 1 wherein in response maps are generated based on m−1 augmented convolutional filters and the seed convolutional filter.
3. The method of claim 2 wherein generating a feature map further comprises:
applying a non-linear function to each of the plurality of response maps to generate a plurality of feature maps; and
applying a vector of learnable coefficients to the plurality of feature maps to generate a single feature map.
4. The method of claim 3 wherein:
m feature maps are generated from the m response maps; and
the vector contains m learnable coefficients.
5. The method of claim 4 further comprising:
adjusting the m learnable coefficients based on the gradient function.
6. The method of claim 4 wherein the single feature map is generated at layer l of the neural network, further comprising:
using the single feature map as the input for layer l+1 of the neural network.
7. The method of claim 1 wherein generating a plurality of augmented convolutional filters comprises raising each element of the seed convolutional filter to a different exponent.
8. The method of claim 7 wherein the different exponents are integer exponents or fractional exponents randomly sampled from a distribution.
9. The method of claim 1 wherein generating a plurality of augmented convolutional comprises applying a polynomial function to each element of the seed convolutional filter.