Paper:
Synaptic Sampling: A Bayesian Approach to Neural Network Plasticity and Rewiring
We reexamine in this article the conceptual and mathematical framework for understanding the organization of plasticity in spiking neural networks. We propose that inherent stochasticity enables synaptic plasticity to carry out probabilistic inference by sampling from a posterior distribution of synaptic parameters. This view provides a viable alternative to existing models that propose convergence of synaptic weights to maximum likelihood parameters. It explains how priors on weight distributions and connection probabilities can be merged optimally with learned experience. In simulations we show that our model for synaptic plasticity allows spiking neural networks to compensate continuously for unforeseen disturbances. Furthermore it provides a normative mathematical framework to better understand the permanent variability and rewiring observed in brain networks.

Review:
The paper proposes a mechanism for explaining Bayesian inferenceand network plasticity in the brain using an algorithm very similar to Stochastic Gradient Langevin Dynamics. Clarity: The paper is well written. Even though my background is machine learning and not neuroscience, I was able to follow most of the paper. Originality: The mechanism itself is well studied in the machine learning literature where it is called Stochastic Gradient Langevin Dynamics (SGLD) (see Ref[1] and analysis in Ref[2]). This is also well known in physics where it is usually called the Langevin equation with noisy force (see e.g. section 5.3.'Noisy inexact algorithms' of Ref[3]and references therein). The difference seems to be that the step size (b(\theta) in Eqn. 2) is usually constant in existing work. Also, SGLD has been used only for posterior inference over weights, not for learning the network structure and rewiring.Significance: Although the proposed mechanism is well known in ML and physics, the paper could be very interesting to the neuroscience community. Both network plasticity and whether the brain does Bayesian inference are important questions, and this seems like a plausible explanation worth investigating more. I would suggest to rewrite the paper so that the mechanism itself is presented as existing work in ML, and focus more on how this is realized in biological neural networks.Quality: The paper is convincing and shows experimentally how Bayesian inference using the proposed mechanism can help plasticity. Not having much of a neuroscience background, I wasn't able to tell whether this is actually biologically plausible or not, e.g. a) how are priors represented in biological neural networks? b) Also a problem with SGLD is that it is difficult to mix between modes of the posterior distribution. Is this not a problem in biological neural nets?The paper should cite these (and/or related) references:[1] Bayesian Learning via Stochastic Gradient Langevin Dynamics, Welling and Teh, ICML 2011[2] Approximation Analysis of Stochastic Gradient Langevin Dynamics by using Fokker-Planck Equation and Ito Process, Sato and Nakagawa, ICML 2014[3]The Hybrid Monte Carlo algorithm on parallel computers, A.D. Kennedy, Parallel Computing 1999