Hi,
I’m a pharmacist, and the statement that the learning rate α is always positive made me think about an analogy from clinical practice.
Sometimes something that would normally be considered an unwanted effect can become useful because our objective has changed.
That made me wonder about gradient descent. I understand why α is normally positive: we want to move down the cost function and minimize the error.
But suppose a model has learned a misleading pattern from the training data…for example, it has learned that “balls are red” because almost all the balls in its training data happened to be red. Later we realize that this was a spurious association and we want the model to reduce or reverse what it learned from that feature.
Could there ever be a reason to use a negative α to “reverse” previously learned information? Or is α kept positive and this kind of correction always handled by changing the data… or another part of the training process?
Is the reason for keeping α positive fundamentally mathematical, or is it a consequence of how we define gradient descent?
Hi, welcome to the community. I’m a pharmacist too, so it’s great to see our little pharmacist community growing here.
Regarding your question, I think the key distinction is between the direction of the update and its magnitude. The gradient determines the direction in which the parameters should move to reduce the cost, while α (the learning rate) controls how large a step we take in that direction.
So, keeping α positive makes sense because we want it to represent a step size, a magnitude rather than a direction. The direction is already accounted for by the gradient (and the minus sign in the gradient descent update). Using a negative α would effectively reverse that direction, turning gradient descent into gradient ascent, rather than specifically “unlearning” a previously learned association.
For something like the spurious “balls are red” association, we would generally address it through the data, objective/loss function, model design, or training procedure rather than by making the learning rate negative.
Hi, thank you so much for the clear explanation, and great to meet another pharmacist here.
The distinction between direction and magnitude really helped. I understand now why a negative α would reverse the whole optimization direction rather than selectively “unlearn” a particular association.
Thanks again for taking the time to explain it