Neural Encoding

Finding a stimulus parameter along which the neural response varies

Higher Order Feature Selectivity

There are localized regions in the temporal lobe that are responsive to semantic categories

There is an increasing complexity of stimulus representations in neurons

Starting from geometric to more semantic

Response Models

Methods of finding relevant features

Information theoretic methods using maximisation of mutual information between prior and response

A family of filters derived using PCA

Single filter determined by spike conditional average

Multiple feature response models

We can try reversing from the filter to find the input output function, by maximising the difference between the prior and and prior conditional

Kullback Leiber Divergence


We find f that maximises the difference between the two distributions (that is Dkl) - aka maximising the mutual information between the spike and the prior

DKL(P(s),Q(s))=∫dsP(s)log2P(s)Q(s)

Use Gaussian white noise to sample stimulus to response, and use PCA (covariance) to find low dimensional structure in high dimensional data

3-Figure1-1

Non Linearity

This model can only track one dimensional relationships - one feature per s


\[ P(spike|s1) = \frac{P(s1|spike)P(spike)}{P(s1)} \]


Where P(s1|spike) is the spike conditional distribution, and p(s1) is the prior distribution

We want the P(s1|spike) to be as different as it can be from P(s1) meaning that the filter is encoding some feature of the stimulus

Linear Filter

Determining the linear filter using Gaussian white noise

We project an arbitrary stimulus onto the sta to filter it.

the spike triggered average is the single feature that captures the relevant components of the system - a linear filter

To reduce dimensionality, find the spike triggered average - the vector running along it can give a good idea of structure of data

Sample responses of the system to Gaussian white noise to characterize what it is about the input that triggers a response

The response of the neuron is proportional to the similarity of the stimulus to the linear filter/ receptive field of that neuron

Portions of the signal that resemble the filter

Linear relationship of stimulus with response with a delayed time period

Poission Spiking

Create bins of dt time and calculate firing rate based on the rate of firing in each bin

Intervals between successive spikes has an exponential distribution

The generalised linear model

Stimulus filter

Non Linearity

Stochastic Spiking

Backpropogation

Inputs from other neurons

Post Spike filter (taking into consideration the refactory period of a neuron)

Variance == mean

Low r - heavy e, High r - more and more gaussian

\[p_t[k] = (rT)^k \frac{e^{-rT}}{k!}\]

Time rescaling algorithm

We can use the poisson nature to see if we have captured everything we can in our model

Take intervals between successive spikes and scale them by their predicted firing rates from the model

If we have extracted all features, the new scaled intervals should be purely possion - as a clean exponential

Models still ignore - CONTEXT, PERCEPTION AND MOVEMENT OF ORGANISM