Introduction

We should be able to answer the following by the end of this course:

How convolution works
How to create a convolution layer for a neural network
What considerations need to be taken when working with one-dimension data
How to modify a convolution neural network to get good performance

As well as some general questions about NNs

How to use a neural network to perform classification tasks
How a softmax layer works and how to implement it
How a batch normalization layer works and how to implement it
How to create a neural network out of any differentiable function you like

When $a \ne 0$, there are two solutions to $(ax^2 + bx + c = 0)$ and they are $$ x = {-b \pm \sqrt{b^2-4ac} \over 2a} $$

Mathjax block:

\[a \ne 0\]

Inline shortcode $a \ne 0$ with Mathjax.

# convolution in one dimension using numba

import time
from numba import njit
import numpy as np

@njit
def convolve(signal, kernel):
    """Convolve a signal with a kernel using numba"""
    signal_len = len(signal)
    kernel_len = len(kernel)
    output_len = signal_len - kernel_len + 1
    reversed_kernel = kernel[::-1]
    result = np.zeros(output_len)
    for i in range(output_len):
        result[i] = np.dot(signal[i:i+kernel_len], reversed_kernel)
    return result

Introduction#

Introduction