Neural Networks from Scratch in Python by Harrison Kinsley, Daniel Kukie a

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Chapter 2 - Coding Our First Neurons - Neural Networks from Scratch in PythonWith 3-dimensional arrays, like in lolol below, we’ll have a 3rd level of brackets:17lolol = [[[1,5,6,2],[3,2,1,3]],[[5,2,1,2],[6,4,8,4]],[[2,8,5,3],[1,1,9,4]]]The first level of this array contains 3 matrices:And[[1,5,6,2],[3,2,1,3]][[5,2,1,2],[6,4,8,4]][[2,8,5,3],[1,1,9,4]]That’s what’s inside the most outer brackets and the size of this dimension is then 3. If we look atthe first matrix, we can see that it contains 2 lists — [1,5,6,2] and [3,2,1,3] so the size ofthis dimension is 2 — while each list of this inner matrix includes 4 elements. These 4 elementsmake up the 3rd and last dimension of this matrix since there are no more inner brackets.Therefore, the shape of this array is (3, 2, 4) and it’s a 3-dimensional array, since the shapecontains 3 dimensions.Fig 2.05: Example of a 3-dimensional array.Anim 2.05: https://nnfs.io/jps
Chapter 2 - Coding Our First Neurons - Neural Networks from Scratch in Python18Finally, what’s a tensor? When it comes to the discussion of tensors versus arrays in the contextof computer science, pages and pages of debate have ensued. This intense debate appears to becaused by the fact that people are arguing from entirely different places. There’s no question thata tensor is not just an array, but the real question is: “What is a tensor, to a computer scientist, inthe context of deep learning?” We believe that we can solve the debate in one line:A tensor object is an object that can be represented as an array.What this means is, as programmers, we can (and will) treat tensors as arrays in the context ofdeep learning, and that’s really all the thought we have to put into it. Are all tensors just arrays?No, but they are represented as arrays in our code, so, to us, they’re only arrays, and this is whythere’s so much argument and confusion.Now, what is an array? In this book, we define an array as an ordered homologous container fornumbers, and mostly use this term when working with the NumPy package since that’s what themain data structure is called within it. A linear array, also called a 1-dimensional array, is thesimplest example of an array, and in plain Python, this would be a list. Arrays can also consistof multi-dimensional data, and one of the best-known examples is what we call a matrix inmathematics, which we’ll represent as a 2-dimensional array. Each element of the array can beaccessed using a tuple of indices as a key, which means that we can retrieve any array element.We need to learn one more notion — a vector. Put simply, a vector in math is what we call a listin Python or a 1-dimensional array in NumPy. Of course, lists and NumPy arrays do not havethe same properties as a vector, but, just as we can write a matrix as a list of lists in Python, wecan also write a vector as a list or an array! Additionally, we’ll look at the vector algebraically(mathematically) as a set of numbers in brackets. This is in contrast to the physics perspective,where the vector’s representation is usually seen as an arrow, characterized by a magnitude anda direction.
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Neural Networks from Scratch in Python by Harrison Kinsley, Daniel Kukie a

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