Various Deep Learning algorithms  and neural models  make use of neurogenesis to reduce prediction errors. How much evidence is there that neurogenesis is driven by prediction error or novel inputs?
This question is very difficult to provide a satisfactory answer to because the technical neuroscience definition of prediction error is murky and since your question brings up machine learning then the answer is going to depend on what you're trying to do. I'm going to assume you're referring to neurogenesis in an adult brain and not the process that happens immediately after conception because that process is more analogous to deep learning.
From the neuroscience perspective: I'm not aware of much direct evidence that neurogenesis is a response to prediction errors because we understand very little about the phenomenon. However, it seems bizarre to think that neurogenesis just occurs spontaneously and randomly, so we come to the nature vs. nurture debate. Pure logic would tell me that neurogenesis in adults is something more of a maintenance response to DNA pressures and has little to do with any prediction errors generated by external environmental stimuli. Will explain why in my concluding paragraph.
Keep in mind that even the death of a neuron can be considered prediction error because the machine learning equivalent of "prediction error" in biology is simply a signal that communicates a "deficit" that needs to be filled in some way. In fact, to answer this properly, we must first make it clear that there are potentially dozens, hundreds, or an arbitrarily high number of other "prediction error types" in use by the brain. Here are just a few major ways, hypothetically:
- Lots of different neurotransmitters
- The opening/closing of various ion channel species that regulate the membrane potential
- Synaptic vescicles/receptors
- Neuronal firing rates (as in bursting, a rapid succession of action potentials)
- Temporal coding (relative firing times to the firing of other neurons)
- And I can think of 10 other more-subtle and harder to explain possibilities, but that are just as important, off the top of my head
Keep in mind that each neuron also seems to have its own differentiated mechanisms for, both, interpreting and signaling prediction error. This complicates things further. For instance, one neurotransmitter may communicate prediction error to one particular neuron, but has no effect (or a different effect) on a different neuron. It may even be that neurotransmitter X must be present while temporal code Y happens for the event to be interpreted as a prediction error.
From the machine learning perspective: In machine learning, we tend to oversimplify prediction error but the brain conforms to no such simplicity. I didn't want to mislead you by saying "yes" to your question because prediction error in artificial neural networks is traditionally a singular concept and not multiplexed like it is in neuroscience. So there is no analogy between prediction error in deep learning and prediction error in neuroscience evidence.
You might need to clarify the reason you are asking so that I can provide a more applicable response.
Deep learning is not biologically plausible, and it sounds like you are trying to discover a more accurate biological solution. If that's the case, looking into neurogenesis as a way to reduce prediction error may not be very fruitful because the new neurons created in adulthood only account for an incredibly tiny portion of the neurons that already exist, and humans encounter prediction errors potentially every second of every day. If we simply created new neurons for all prediction errors, then why are we born with pretty much all the neurons we will ever have? The brain overwhelmingly seems to have a way of learning and retaining the important information without having to create new neurons in response to prediction errors.