# How is back-propagation useful in neural networks?

I am reading about backpropagation and I wonder why I have to backpropagate.

For example, I would update the network by randomly choosing a weight to change, $$w$$. I would have $$X$$ and $$y$$. Then, I would choose $$dw$$, a random number from $$-0.1$$ to $$0.1$$, for example. Then, I would do two predictions of the neural network and get their losses with the original neural network and one with $$w$$ changed by $$dw$$ to get the respective losses $$L_{\text{original}}$$ and $$L_{\text{updated}}$$. $$L_{\text{updated}} - L_{\text{original}}$$ is $$dL$$. I would update $$w$$ by $$\gamma \frac{d L}{dw}$$, where $$\gamma$$ is the learning rate and $$L$$ is the loss.

This does not need a gradient backpropagation throughout the system, and must have somehow a disadvantage because no one uses it. What is this disadvantage?

• Algorithms like this exist. Perceptrons, RBMs, Swarm and genetic use this kind of logic (at least it appears similar to me), the problem with this approach is it's not a very good optimisation method and might take long to converge, not to mention the complexity associated with larger networks with lots of connections. BP on the other hand gives straightforward cause and action relationship. – user9947 Jan 18 '20 at 16:50
• Since there's already a good answer I'd like to point out that BP only requires one forward pass (per update) whereas this method requires 2. – respectful Jan 18 '20 at 18:23
• You might find this interesting/related: arxiv.org/abs/1707.04585 Reversible residual layers are another approach at optimizing backpropagation. Google recently announced Reformer, a transformer model that somewhat leverages this: ai.googleblog.com/2020/01/reformer-efficient-transformer.html – oeste Feb 24 '20 at 6:42