One of my job responsibilities is to teach engineers and data scientists how to use the PyTorch neural network code library. There are many examples of how convolution works, but they tend to be too generic (not specific to PyTorch), or too specific (a very low-level explanation of the library functions).

Here’s an example that I use. The demo sets up an input of a simple 4×4 grayscale (1 channel) image with dummy pixel values 1 through 16. The demo sets up a convolution layer with a 2×2 kernel/weights of [[0.5, 0.6],[0.7,0.8]] and a bias of 1.0.

The diagram shows how sending the input to the convolution layer results in a 3×3 array of numbers. These values don’t have any direct interpretation — they’re just an abstract representation of the image. This abstract representation would be fed to other parts of a neural network. Training the network would give values of the convolution weights that best represent the image for classification or whatever the neural network is trained to do.

The demo leaves out a ton of optional details. For example, the kernel shifts one column to the right, and then when it hits the end of the rows, it shift one row down. This (1,1) is the stride movement. There are other details, like padding, but the point of my demo is to explain how PyTorch convolution works, not to dive into the details.

The word “convolutional” means “a thing that is complex and difficult to follow”. That definition applies well to convolutional neural networks. I think the description also applies to synthetic biology. Left: The major obstacle for storing information in DNA is synthesis — reading information from DNA is not as big a challenge. Right: A mouse gut that has been colonized with multiple engineered strains of Bacteroides labeled with different colors.

Demo code:

# convolution_demo.py
# PyTorch 1.10.0-CPU Anaconda3-2020.02  Python 3.7.6
# Windows 10 

import numpy as np
import torch as T
device = T.device('cpu')

# -----------------------------------------------------------

class Net(T.nn.Module):
  def __init__(self):
    super(Net, self).__init__()  # pre Python 3.3 syntax
    self.conv1 = T.nn.Conv2d(1, 1, 2)  # chnl-in, out, krnl
    wts = T.tensor([[[[0.5,0.6],[0.7,0.8]]]], dtype=T.float32)
    self.conv1.weight = T.nn.Parameter(wts)
    self.conv1.bias = T.nn.Parameter(T.tensor([1.0],
      dtype=T.float32))
    
  def forward(self, x):
    z = self.conv1(x)
    return z

# -----------------------------------------------------------

print("\nBegin PyTorch convolution demo ")

print("\nCreating net with one conv layer ")
net = Net().to(device)

print("\nConvolution layer wts: ")
print(net.conv1.weight)
print("Convolution layer bias: ")
print(net.conv1.bias)

x = np.array([[1,2,3,4],[5,6,7,8],[9,10,11,12],[13,14,15,16]])
x = x.reshape(1,1,4,4)  # bs, chnls, rows, cols
x = T.tensor(x, dtype=T.float32).to(device)
print("\nInput x is: ")
print(x)

print("\nSending x to net ")
z = net(x)

print("\nOutput is: ")
print(z)

print("\nEnd convolution demo ")