Question about the value that decides if an image is a 3 or a 7

[ForBo7 (Salman Naqvi)]

Forgot to click “Reply” on the response I meant to send yesterday (－‸ლ)

That forum post definitely is helpful, and now I think I understand why 0 is chosen.

• Firstly, it’s because the way that the weights that have been chosen means the model ends up producing predictions that are either 0 or 1.

Lesson 3 official topic

Let us start from the beginning. Randomly initializing weights gives values like so [image] We know that train_x has values between 0 and 1. So, train_x@weights (with weights initialized randomly) gives outputs like so [image] This confirms that our linear model outputs both negative and positive values around 0. Convincing yourself of this and then reading @ benkarr 's comment should help you understand why > 0.0 equals a good prediction.

• Secondly, it’s because of the sigmoid loss function we use later on. This function maps any input number to a value between 0 and 1, with negative numbers resulting in an output closer to 0, positive numbers resulting in an output closer to 1, and a 0 resulting in an output of 0.5 — the middle point of the sigmoid. Later on in the notebook, we use the sigmoid function in such a way that any output larger than 0.5 is one class, and any output less than 0.5 is another class.

Lesson 3: deciding MNIST prediction accuracy

I think traditionally it comes from ‘logistic regression’ and the use of the ‘sigmoid function’ (if you want to dig a bit deeper you can have a look at those terms). Most of the time you would not predict ‘high’ and ‘low’ values but (something that we interpret as) probabilities, so values between 0 and 1. The question the model then tries to answer is 'Is the given image a 3?" and the prediction 0.8 would mean that the model is 80% sure that the image is a 3. A way to get from arbitrary valu…

That post definitely helped clear this confuzzlement.