|
==The Knowledge Instinct==
At a particular hierarchical level, we enumerate neurons by index n=1,2..N. These neurons receive input, bottom-up signals, '''X(n)''', from lower levels in the processing hierarchy. '''X'''(n) is a field of bottom-up neuronal [[synapse | synaptic ]] activations, coming from [[neurons ]] at a lower level. Each [[neuron ]] has a number of [[synapses ]]; for generality, we describe each neuron activation as a set of numbers, '''X'''(n) = {X<sub>d</sub>(n), d = 1,... D}. Top-down, or priming signals to these [[neurons ]] are sent by [[concept-models ]], M<sub>m</sub>(S<sub>m</sub>,n); we enumerate [[concept-models ]] by index m=1,2..M. Each model is characterized by its parameters, '''S<sub>m</sub>'''; in the [[neuron ]] structure of the [[brain ]] they are encoded by strength of synaptic connections, mathematically, we describe them as a set of numbers, '''S<sub>m</sub>''' = {S<sub>m</sub><sup>a</sup>, a = 1,... A}. ▼
At a particular hierarchical level, we enumerate [[neurons]] by index n=1,2..N. These [[neurons]] receive input, [[bottom-up signals (bottom-up neural signals)|bottom-up signals]],
▲'''X(n)''', from lower levels in the processing hierarchy. '''X'''(n) is a field of bottom-up neuronal [[synapse | synaptic]] activations, coming from [[neurons]] at a lower level. Each [[neuron]] has a number of [[synapses]]; for generality, we describe each neuron activation as a set of numbers, '''X'''(n) = {X<sub>d</sub>(n), d = 1,... D}. Top-down, or priming signals to these [[neurons]] are sent by [[concept-models]], M<sub>m</sub>(S<sub>m</sub>,n); we enumerate [[concept-models]] by index m=1,2..M. Each model is characterized by its parameters, '''S<sub>m</sub>'''; in the [[neuron]] structure of the [[brain]] they are encoded by strength of synaptic connections, mathematically, we describe them as a set of numbers, '''S<sub>m</sub>''' = {S<sub>m</sub><sup>a</sup>, a = 1,... A}.
Models represent signals in the following way. Say, signal '''X(n)''', is coming from sensory [[neurons]] activated by object m, characterized by parameters '''S<sub>m</sub>'''. These parameters may include position, orientation, or lighting of an object m. [[Model (concept-models)|Model]] '''M<sub>m</sub>'''('''S<sub>m</sub>''',n) predicts a value '''X'''(n) of a signal at [[neuron]] n. For example, during visual perception, a [[neuron]] n in the visual cortex receives a signal '''X'''(n) from retina and a [[priming signal]] '''M<sub>m</sub>'''('''S<sub>m</sub>''',n) from an object-[[concept-model]] m. Neuron n is activated if both the bottom-up signal from lower-level-input and the top-down priming signal are strong. Various [[models (concept-models)|models]] compete for evidence in the [[bottom-up signals (bottom-up neural signals)|bottom-up signals]], while adapting their parameters for better match as described below. This is a simplified description of perception. The most benign everyday visual perception uses many levels from retina to object perception. The NMF premise is that the same laws describe the basic interaction dynamics at each level. Perception of minute features, or everyday objects, or cognition of complex abstract concepts is due to the same mechanism described below. Perception and cognition involve [[concept-models]] and learning. In perception, [[concept-models]] correspond to objects; in cognition [[models (concept-models)|models]] correspond to relationships and situations.
Learning is an essential part of perception and cognition, and it is driven by the knowledge instinct. It increases a similarity measure between the sets of [[models (concept-models)|models]] and signals, L({'''X'''},{'''M'''}). The similarity measure is a function of model parameters and associations between the input [[bottom-up signals (bottom-up neural signals)|bottom-up signals]] and top-down, concept-model signals. For concreteness the following text refers to an object perception using simplified terminology, as if perception of objects in retinal signals occurs in a single level.
In constructing a mathematical description of the similarity measure, it is important to acknowledge two principles (which are almost obvious). ''First'', the visual field content is unknown before perception occurred and ''second'', it may contain any of a number of objects. Important information could be contained in any bottom-up signal; therefore, the similarity measure is constructed so that it accounts for all [[bottom-up signals (bottom-up neural signals)|bottom-up signals]], X(n),
This expression contains a product of partial similarities, l('''X'''(n)), over all [[bottom-up signals (bottom-up neural signals)|bottom-up signals]] ; therefore it forces the mind to account for every signal (even if one term in the product is zero, the product is zero, the similarity is low and the [[knowledge instinct]] is not satisfied); this is a reflection of the first principle. Second, before perception occurs, the [[mind]] does not know which object gave rise to a signal from a particular retinal neuron. Therefore a partial similarity measure is constructed so that it treats each model as an alternative (a sum over [[concept-models]]) for each input neuron signal. Its constituent elements are conditional partial similarities between signal '''X'''(n) and model '''M<sub>m</sub>''', l('''X'''(n)|m). This measure is “conditional” on object m being present (Perlovsky 2001), therefore, when combining these quantities into the overall similarity measure, L, they are multiplied by r(m), which represent a probabilistic measure of object m actually being present. Combining these elements with the two principles noted above, a similarity measure is constructed as follows:
The structure of the expression above follows standard principles of the probability theory: a summation is taken over alternatives, m, and various pieces of evidence, n, are multiplied. This expression is not necessarily a probability, but it has a probabilistic structure. If learning is successful, it approximates probabilistic description and leads to near-optimal Bayesian decisions. The name “conditional partial similarity” for l('''X'''(n)|m) (or simply l(n|m)) follows the probabilistic terminology. If learning is successful, l(n|m) becomes a conditional probability density function, a probabilistic measure that signal in neuron n originated from object m. Then L is a total likelihood of observing signals {'''X'''(n)} coming from objects described by concept-model {'''M<sub>m</sub>'''}. Coefficients r(m), called priors in probability theory, contain preliminary biases or expectations, expected objects m have relatively high r(m) values; their true values are usually unknown and should be learned, like other parameters '''S<sub>m</sub>'''.
We note that in probability theory, a product of probabilities usually assumes that evidence is independent. Expression for L contains a product over n, but it does not assume independence among various signals '''X'''(n). There is a dependence among signals due to [[(concept-models)]]: each model '''M<sub>m</sub>'''('''S<sub>m</sub>''',n) predicts expected signal values in many neurons n.
During the learning process, [[concept-models]] are constantly modified. In this review we consider a case when functional forms of [[models (concept-models)|models]] , '''M<sub>m</sub>'''('''S<sub>m</sub>''',n), are all fixed and learning-adaptation involves only model parameters, '''S<sub>m</sub>'''. From time to time a system forms a new concept, while retaining an old one as well; alternatively, old concepts are sometimes merged or eliminated. This requires a modification of the similarity measure L;
==References==
|
