neurodudes

Neuroimaging data of different brain areas fit to a Rescorla-Wagner model show that different cortical areas integrate stimulus changes over different time intervals. The result itself probably isn’t that shocking but I liked the nice combination of theory and experiment.

From the July 21 Neuron:

Formal Learning Theory Dissociates Brain Regions with Different Temporal Integration

Jan Gläscher and Christian Büchel

Learning can be characterized as the extraction of reliable predictions about stimulus occurrences from past experience. In two experiments, we investigated the interval of temporal integration of previous learning trials in different brain regions using implicit and explicit Pavlovian fear conditioning with a dynamically changing reinforcement regime in an experimental setting. With formal learning theory (the Rescorla-Wagner model), temporal integration is characterized by the learning rate. Using fMRI and this theoretical framework, we are able to distinguish between learning-related brain regions that show long temporal integration (e.g., amygdala) and higher perceptual regions that integrate only over a short period of time (e.g., fusiform face area, parahippocampal place area). This approach allows for the investigation of learning-related changes in brain activation, as it can dissociate brain areas that differ with respect to their integration of past learning experiences by either computing long-term outcome predictions or instantaneous reinforcement expectancies.

How does this relate to Hawkins’s idea that all cortex implements the same underlying “algorithm”? Is the integration time constant (or, in RW terms, the learning rate) tuned differently by different inputs?

I wrote up a little primer on differential equations for neuroscientists. It can be found here: http://science.ethomson.net/Diff_Eq.pdf. Any comments or suggestions appreciated, especially at this early stage!

Here is the first paragraph:

Ordinary first-order differential equations come up frequently in neuroscience. They are used to model many fundamental processes such as passive membrane dynamics and gating kinetics in individual ion channels. When the equations come up, most electrophysiology texts provide the solution, but do not provide any explanation. This manuscript tries to fill the gap, providing an introduction to many of the mathematical facets of the first-order differential equation. Section One provides a brief statement of the problem and its solution. Section Two works through the solution for a special case that often comes up in practice. I also work through a concrete example chosen for its near-ubiquity in neuroscience, the equivalent circuit model of a patch of neuronal membrane. Section Three contains a simple derivation of the general solution given in Section One. The manuscript presupposes a little knowledge of first-year calculus, much of which is reviewed when needed.

Best,
Eric (Thomson)

Interesting article in the NYT about a new biography of Norbert Wiener, the father of the field of cybernetics. The surprising revelation is that Wiener (who received a PhD from Harvard in mathematical psychology at the age of 18) was “tricked” by his wife into stopping his collaboration with McCulloch, shortly before McCulloch went on to propose the perceptron with Walter Pitts.

The relevant portion is cited below…
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Neural Network Resources: www.neoxi.com

This website has short, free, open-source C implementations of 8 kinds of neural networks: