Coding mechanisms & principles

Receptive field

= the field in space and time of the "sensory surface"

Tuning

= the dependency of neuron's response to stimulus features

e.g. Hubel and Wiesel (1962): simple cells

Population coding

Sparse coding

= how many neurons are involved in coding one variable
e.g. grandmother cell (Gross, 2002). = only one neuron ~ complex features => super sparse

Population coding

= more than one neuron are involved in coding one variable

• each cell has a preferred value (e.g. direction)
• overlapping cosine tuning curves (i.e. population vector)
• robust = removal of a few cells does not harm
  => The population code is the vector sum of the preferred direction $p_i$ weighted by response $f_i$ (Georgopoulos, Schwartz, & Kettner, 1986):

Efficient coding

= neural information processing (especially in sensory systems) should be adapted to the environment and input statistics

information theory (Shannon, 1948)

(also check Information theory and Entropy in Neuroscience)
- entropy = sum of information from each message $m$ within an ensemble $M$
- $$ H(M) = - \sum{p(m)\ log_2\ p(m)} $$
- most efficient = maximal entropy = all messages are equally likely = M is an uniform distribution
- mutual information = redundancy between A and B
- conditional entropy
- $$ H(A|B) = H(A, B) \ - H(B)$$
- $$I(A; B) = H(A) \ - H(A|B)$$ which represents the reduction in the uncertainty about one when we know the other.

simplest case: single neuron

• input distribution => transfer function => output distribution
• most efficient = the distribution of firing rates is uniform = the slope of the tranfer function is proportional to input probability

mutiple neurons: redundancy reduction

• PCA
• Zero-phase component analysis
• Independent component analysis