Neural modeling field (NMF) is a mathematical framework for machine learning which combines ideas from neural networks, fuzzy logic, and model based recognition. It has also been referred to as modeling fields, modeling fields theory (MFT), Maximum likelihood artificial neural networks (MLANS).
This framework has been developed by Leonid Perlovsky at the AFRL. NMF is interpreted as a mathematical description of the mind's mechanisms, including concepts, emotions, instincts, imagination, thinking, and understanding. NMF is a multi-level, hetero-hierarchical system. At each level in NMF there are concept-models encapsulating the knowledge; they generate so-called top-down signals, interacting with input, bottom-up signals. These interactions are governed by dynamic equations, which drive concept-model learning, adaptation, and formation of new concept-models for better correspondence to the input, bottom-up signals.
Concept models and similarity measures In the general case, NMF system consists of multiple processing levels. At each level, output signals are the concepts recognized in (or formed from) input, bottom-up signals. Input signals are associated with (or recognized, or grouped into) concepts according to the models and at this level. In the process of learning the concept-models are adapted for better representation of the input signals so that similarity between the concept-models and signals increases. This increase in similarity can be interpreted as satisfaction of an instinct for knowledge, and is felt as aesthetic emotions. Each hierarchical level consists of N "neurons" enumerated 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 synaptic activations, coming from neurons at a lower level. Each neuron has a number of synapses; for generality, each neuron activation is described as a set of numbers,
X → ( n ) = { X d ( n ) } , d = 1.. D . {\displaystyle {\vec {X}}(n)=\{X_{d}(n)\},d=1..D.}
, where D is the number or dimensions necessary to describe individual neuron's activation. Top-down, or priming signals to these neurons are sent by concept-models, Mm(Sm,n)
M → m ( S → m , n ) , m = 1.. M . {\displaystyle {\vec {M}}_{m}({\vec {S}}_{m},n),m=1..M.}
, where M is the number of models. Each model is characterized by its parameters, Sm; in the neuron structure of the brain they are encoded by strength of synaptic connections, mathematically, they are given by a set of numbers,
S → m = { S m a } , a = 1.. A . {\displaystyle {\vec {S}}_{m}=\{S_{m}^{a}\},a=1..A.}
, where A is the number of dimensions necessary to describe individual model. Models represent signals in the following way. Suppose that signal X(n) is coming from sensory neurons n activated by object m, which is characterized by parameters Sm. These parameters may include position, orientation, or lighting of an object m. Model Mm(Sm,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 Mm(Sm,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 compete for evidence in the 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 correspond to relationships and situations. Learning is an essential part of perception and cognition, and in NMF theory it is driven by the dynamics that increase a similarity measure between the sets of models and signals, L({X},{M}). The similarity measure is a function of model parameters and associations between the input bottom-up signals and top-down, concept-model signals. In constructing a mathematical description of the similarity measure, it is important to acknowledge two principles:
First, the visual field content is unknown before perception occurred 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, X(n),
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