Based on the lecture, this is the given formula:

We are still training the model based on Is/Isn’t Cat, but the weight factor is just a separate enhancement that helps us rule out inappropriate images.

My problem is: if inappropriate images’ true labels are 1, then they are identified as cats. If their true labels are 0, then they are identified as not cats. Regardless, since if I(y_hat != y) = 0 then w*0 = 0 means that weight is disregarded, we are essentially only applying the punishing weights to misclassified inappropriate images. This feels underwhelming. **Don’t we want to apply punishing weights to all inappropriate images regardless of their accuracy stats?**

With the current formula, if inappropriate images have true label 0, then a model (A) that accidentally misclassifies a few of them would have more error than a model (B) that doesn’t make any mistakes with them if inappropriate images were to have true label 1. But in this case we prefer A more since it mostly thinks inappropriate images are not cats, but metric would select B, which thinks inappropriate images are cats (i.e. cat = pusy). I guess we are putting full faith in that inappropriate images have true label 0 so the formula works as intended?

**Functional logic:**

**Assume inappropriate images are not cats (y=0). If classification is correct, then no punishment needed (w*0) since the algorithm correctly identifies that it is / isn’t a cat. If classification is misclassified, then there will be two cases. 1) the image is inappropriate: this means the algorithm thinks the image is a cat but it isn’t and it is inappropriate (severe misclassification), so we punish it with heavy weight w=10*1. 2) the image isn’t inappropriate: this is just a general misclassification, and the image is perfectly fine so we don’t need to punish it or whatsoever, so we proceed with w=1*1.**

Actually I kinda see why this logic makes sense.

Sorry about the train of thought. A quick confirmation on the functional logic would help. Thank you so much for your time and help!