Week 3.10 - Neural Decoding: Signal Reconstruction

Question 1

What is the definition of a feature?

Answer 1

Features are attributes of patterns (e.g., from the sensory system). Features are essential elements of the input.

Question 2

Name a few examples of features

Answer 2

Features are specific aspects of an input that help distinguish it.

For instance: shapes (e.g.’ovalness’), orientations (e.g.’slantedness’), colour, smell (‘sweetness’), distance (‘far-ness’), rhythm, brightness , texture (‘roughness’), temperature (‘warmness’), frequency (‘shriek’), loudness, …

Question 3

What is a feature space?

Answer 3

A feature space is a space formed by the dimensions that measure the characteristics of an object.

The number of dimensions is often equal to the number of measurable variables of the object.

Note that complex features can be combinations of lower-level features, and so the feature space is ‘combinatorial’ in nature.

Question 4

What is neural decoding?

Answer 4

To decode something is to retrieve/obtain information from neuronal activity.

The general assumption is that neurons do not fire at random, there is structure in their activity, relating the functional processes that the brain engages in.

That is, the brain represents information about thought and behavior with neuronal activity.

Using specific decoding algorithms (such as linear decoding), we can take spiking activity and output the predicted response. For example, when a person thinks about moving her arm, the decoding algorithm can retrieve the direction of the motion from which neurons are spiking

In short, neural decoding attempts to understand how spikes elicit activity and responses in the brain; reading out the brain.

Question 5

What is neural encoding?

Answer 5

A map from a stimulus to a neural response.

Transduction that appears in cells that are transforming the physical perturbation to the body in some systematic way.

Question 6

What are the advantages of population coding?

Answer 6

1. Reduction of uncertainty due to neuronal variability.
2. Ability to represent a number of stimulus attributes simultaneously.
3. Driving a large population of downstream neurons.

Question 7

This equation shows how a neuron encodes wind direction.

• f(s) is the firing frequency of neuron ‘a’ in response to a certain stimulus ‘s’
• r_max is the maximum firing rate of the neuron
• v is the wind direction
• c_a is the preferred direction of a neuron’s tuning curve

When is the activity of the neuron maximal?

Answer 7

When the velocity of the wind is aligned with the neuron’s preferred direction.

Question 8

How can we estimate wind direction using the activity of four neurons of a cricket?

Answer 8

Through population decoding. We take the activity of the neurons to indicate their alignment according to their preferred directions. We obtain the population vector by summing the activations of four individual vectors.

In this equation, r/r_max denotes the spike count rate of a given neuron over its maximum firing rate (modulation).

Unit vector C_a denotes the preferred direction of the wind for a given neuron.

Question 9

The graph below shows behavioral and electrophysiological data from a random dot motion discrimination task performed by a monkey.

What does the graph tell you about neuronal decoding accuracy?

Answer 9

The discriminations made by a monkey as a function of coherence of random dot movement is similar to the discriminations that an ideal observer could make given the neuronal responses.

Question 10

What is an overcomplete basis?

How does this concept relate to decoding?

Answer 10

To encode a point in 2 dimensions, one needs two (linearly independent) coordinate axes (such as the Descartes plane x,y).

An overcomplete basis is when we use more axes than there are dimensions to encode.

When multiple neurons encode a lower-dimensional stimulus we have an overcomplete basis. An overcomplete basis leads to better decoding accuracy.

Question 11

What are the assumptions of the McCullogh-Pitts neuron?

Answer 11

1. The activity of a neuron is all or none.
2. A certain fixed number of synapses must be excited within the period of latent addition in order to excite a neuron at any time, and this number is independent of the previous activity of the neuron.
3. The only significant delay within the nervous system is a synaptic delay.
4. The activity of any inhibitory synapse absolutely prevents the excitation of the neuron at any time.
5. The structure of the net does not change with time.

Question 12

How do we linearly decode information from a neuronal population?

Answer 12

1. Find neuronal tuning curves of all neurons
2. Record activity of these neurons during stimulus presentation
3. Use least squares regression to solve for output weights according to a desired function

for review: https://www.nengo.ai/nengo/v2.8.0/examples/advanced/nef_algorithm.html