How to Use Custom Losses with Custom Gradients in TensorFlow with Keras

Keras does a great job of abstracting low-level details of neural network creation so you can focus on getting the job done. But, if you're reading this, you've probably discovered that Keras' off-the-shelf methods cannot always be used to learn your model's parameters. Perhaps your model has a gradient that cannot be calculated through the magic of autodiff, or your loss function does not conform to the signature my_loss_fn(y_true, y_pred) mentioned in Keras' documentation. If you found the online documentation wholly unhelpful, read on! I [hopefully] have all the answers you couldn't find anywhere else.