XOR Logic Gate – Neural Networks (3/3)

(Part 3 of a series on logic gates) We have previously discussed OR logic gates and the importance of bias units in AND gates. Here, we will introduce the XOR gate and show why logistic regression can't model the non-linearity required for this particular problem. As always, the full code for these examples can be found in my GitHub repository here. XOR gates output True if either of the inputs are True, but not both. It acts like a more specific version of the OR gate: Input 1 Input 2 Output 0 0 0 0 1 1 1 0 1…

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AND Logic Gate – Importance of bias units (2/3)

(Part 2 of a series on logic gates) Previously, we talked about simple OR gates and now we'll continue that discussion with AND gates, and specifically the role of bias units. We often neglect to consider the role bias plays in our models. We know that we should include bias units, but why? Here, I'll walk through a short example using an AND gate to highlight the importance of the bias unit. Bias units allow us to offset the model in the same way that an intercept allows us to offset a regression line. Imagine a simple AND gate. It…

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OR Logic Gate using Theano (1/3)

(Part 1 of a series on logic gates) Theano is a powerful Python library that provides some useful tools for machine learning, such as GPU training and symbolic differentiation of the cost function during gradient descent. It can be a bit challenging to understand how Theano works, so before jumping into more complex non-linear models, we can get to grips with Theano by implementing something simple like an OR gate. An OR gate receives 2 inputs and will output true if either of the inputs are true. So, there are 3 cases where an OR gate will output a true…

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