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In the model due to Anastasio and Patton, deep SC neurons combine cortical input multiplicatively with primary input.

Anastasio and Patton's model is trained in two steps:

First, connections from primary input to deep SC neurons are adapted in a SOM-like fashion.

Then, connections from uni-sensory, parietal inputs are trained, following an anti-Hebbian regime.

The latter phase ensures the principles of modality-matching and cross-modality.

Verschure says neurons don't seem to multiply. Gabbiani et al. say they might.

Patton and Anastasio present a model of "enhancement and modality-specific suppression in multi-sensory neurons" that requires no multiplicative interaction. It is a follow-up of their earlier functional model of these neurons which requires complex computation.

Anastasio et al. present a model of the response properties of multi-sensory SC neurons which explains enhancement, depression, and super-addititvity using Bayes' rule: If one assumes that a neuron integrates its input to infer the posterior probability of a stimulus source being present in its receptive field, then these effects arise naturally.

Anastasio et al.'s model of SC neurons assumes that these neurons receive multiple inputs with Poisson noise and apply Bayes' rule to calculate the posterior probability of a stimulus being in their receptive fields.

Jazayeri and Movshon present an ANN model for computing likelihood functions ($\approx$ probability density functions with uniform priors) from input population responses with arbitrary tuning functions.

Their assumptions are

  • restricted types of noise characteristics (eg. Poisson noise)
  • statistically independent noise

Since they work with log likelihoods, they can circumvent the problem of requiring neural multiplication.

Multiplying probabilities is equivalent to adding their logs. Thus, working with log likelihoods, one can circumvent the necessity of neural multiplication when combining probabilities.

Multisensory integration, however, has been viewed as integration of information in exactly that sense, and it is well known that multisensory neurons respond super-additively to stimuli from different modalities.

In Jazayeri and Movshon's model decoding (or output) neurons calculate the logarithm of the input neurons' tuning functions.

This is not biologically plausible because that would give them transfer functions which are non-linear and non-sigmoid (and typically biologically plausible transfer functions said to be sigmoid).

We do not know the types of functions computable by neurons.