Unbiased credit assignment alone isn't sufficient for stable learning; you also need sufficiently frequent and informative feedback, which creates additional constraints for biologically plausible learning algorithms.
This paper analyzes when learning algorithms remain stable when gradient information is sparse, noisy, and intermittently available—conditions common in biological neural networks. The authors show that even if learning converges on average, variance can grow infinitely, and derive explicit stability conditions for linear networks that go beyond standard stochastic gradient descent analysis.