Paper:
Neurons Equipped with Intrinsic Plasticity Learn Stimulus Intensity Statistics
Experience constantly shapes neural circuits through a variety of plasticity mechanisms. While the functional roles of some plasticity mechanisms are wellunderstood, it remains unclear how changes in neural excitability contribute to learning. Here, we develop a normative interpretation of intrinsic plasticity (IP) as a key component of unsupervised learning. We introduce a novel generative mixture model that accounts for the class-specific statistics of stimulus intensities, and we derive a neural circuit that learns the input classes and their intensities. We will analytically show that inference and learning for our generative model can be achieved by a neural circuit with intensity-sensitive neurons equipped with a specific form of IP. Numerical experiments verify our analytical derivations and show robust behavior for artificial and natural stimuli. Our results link IP to nontrivial input statistics, in particular the statistics of stimulus intensities for classes to which a neuron is sensitive. More generally, our work paves the way toward new classification algorithms that are robust to intensity variations.

Review:
Neurons with Intrinsic Plasticity Learn Stimulus Statistics  In the paper, the author(s) build a generative product-poisson-gamma model to recognize images with wide dynamic range, by extending a previously used Poisson mixture model. An equivalent neural circuit model with unsupervised learning was also proposed to implement EM-like algorithms to find the model parameters in generative model. In the learning  rule, the synaptic weights are changed according to a Hebb like rule with synaptic scaling, and intrinsic parameters lambda (Eq.7 in the paper) are updated depending on  the net input. It is very interesting that the fixed points of the network updating parameters can have the same form with EM algorithm. However, I have the following  questions about this paper:       1. In the paper, the author claims that the parameter lambda corresponds to a neuron's intrinsic parameter, and updating of lambda implies to plasticity of intrinsic parameters. For me, I think here lambda is like a input gain control parameter in the neuron model, as it controls the input current that leads to saturation of the neuron.   This is a very abstract intrinsic parameter, is it suitable to name it as intrinsic plasticity?  2. The number of neurons configured in the hidden layer. For me, I think in the model, if the number of hidden neuron equals to the classes in input data, then the  network may have a good classification ability. While this is not always the case in reality, what would happen to a network if the number of hidden neuron does not  equal to the number of classes in input data? Will the classification performance would degrade?  3. Time scale. It can be seen that, the synaptic weights and intrinsic parameters are updated at the same time, that is, the updating time  constant would be the same. However, contrast of natural images and input pattern would not likely change with a same time constant in reality.  So, what would happen in your model if synaptic weights and intrinsic parameter are updated with different time scale? 
This is a theoretical beautiful work. It builds a neural circuit model with unsupervised learning to get an theoretical optimal fixed point, which is highly corresponded to EM learning algorithm result. This work considers the effect of contrast variation by extending a previously Poisson mixture model. The main concern is, what would happen when the hidden neuron number does not  equals to the pattern class number, e.g., the number of hidden neuron is larger than the pattern classes.