Bio-Inspired NMF Object Perception

The paper describes Neural Modeling Fields (NMF) for object perception, a bio-inspired paradigm. I discuss previous difficulties in object detection and recognition, and describe how NMF overcomes this difficulties. Neural and mathematical mechanisms are described and future research directions outlined. I. PAST DIFFICULTIES, COMPLEXITY AND LOGIC Biological object perception involves signals from sensory organs and internal mind’s representations (memories) of objects. During perception, the mind associates subsets of signals corresponding to objects with representations of object. This produces object recognition. Mathematical descriptions of the very first recognition step in this seemingly simple association-recognitionunderstanding process met a number of difficulties during the past fifty years. These difficulties were summarized under the notion of combinatorial complexity (CC). CC refers to multiple combinations of various elements in a complex system; for example, recognition of a scene often requires concurrent recognition of its multiple elements that could be encountered in various combinations. CC is prohibitive because the number of combinations is very large: for example, consider 100 elements (not too large a number); the number of combinations of 100 elements is 100, exceeding the number of all elementary particle events in life of the Universe; no computer would ever be able to compute that many combinations. Algorithmic complexity was first identified in pattern recognition and classification research in the 1960s and was named “the curse of dimensionality”. It seemed that adaptive self-learning algorithms and neural networks could learn solutions to any problem ‘on their own’, if provided with a sufficient number of training examples. The following thirty years of developing adaptive statistical pattern recognition and neural network algorithms led to a conclusion that the required number of training examples often was combinatorially large. Thus, self-learning approaches encountered CC of learning requirements. Rule-based systems were proposed in the 1970’s to solve the problem of learning complexity [ ]. An initial idea was that rules would capture the required knowledge and eliminate a need for learning. However in presence of variability, the number of rules grew; rules became contingent on other rules; combinations of rules had to be considered; rule systems encountered CC of rules. Model-based systems were proposed in the 1980s. They used models, which depended on adaptive parameters. The idea was to combine advantages of rules with learning⋅ Harvard University, Cambridge, MA; and the US Air Force Research Laboratory, Sensors Directorate, Hanscom, MA; [email protected] adaptivity by using adaptive models. The knowledge was encapsulated in models, whereas unknown aspects of particular situations were to be learned by fitting model parameters. Fitting models to data required selecting data subsets corresponding to various models. The number of subsets, however, is combinatorially large. A general popular algorithm for fitting models to the data, multiple hypothesis testing, is known to face CC of computations. Model-based approaches encountered computational CC (N and NP complete algorithms). Later research related CC the type of logic, underlying various algorithms and neural networks. Combinatorial complexity of algorithms based on logic is related to Gödel theory: it is a manifestation of the inconsistency of logic in finite systems. Various manifestations of CC are all related to formal logic and Gödel theory. Rule systems rely on formal logic in a most direct way. Self-learning algorithms and neural networks rely on logic in their training or learning procedures: every training example is treated as a separate logical statement. Fuzzy logic systems rely on logic for setting degrees of fuzziness. CC of mathematical approaches to the mind is related to the fundamental inconsistency of logic. II. MATHEMATICAL FORMULATION Biological object perception is modeled by Neural Modeling Fields (NMF) as follows. NMF is a multi-level, hetero-hierarchical system. It mathematically implements several mechanisms of the mind, and this paper describes the mechanisms of perception. This section describes a basic mechanism of interaction between two adjacent hierarchical levels of bottom-up and top-down signals (fields of neural activation). At each hierarchical level, we enumerate neurons by index n = 1,... N. These neurons receive bottom-up input signals, X(n), from lower levels in the processing hierarchy. X(n) is a field of bottom-up neuronal synapse 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) = {Xd(n), d = 1,... D}. Top-down, or priming signals to these neurons are sent by conceptmodels, Mm(Sm,n); we enumerate models by index m = 1,... M. Each model is characterized by its parameters, Sm; in the neuron structure of the brain they are encoded by strength of synaptic connections, mathematically, we describe them as a set of numbers, Sm = {Sa m, 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 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. A neuron n is activated if both bottom-up signal from lower-level-input and 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 models and learning. In perception, models correspond to objects; in cognition models correspond to relationships and situations. In NMF, bottom-up signals are unstructured data {X(n)} and output signals are recognized or formed concepts {m}. Top-down, “priming” signals are models, Mm(Sm,n), which upon recognition become bottom-up signals for the hext, higher level. Learning is an essential part of perception and cognition. NMF learns driven by the knowledge instinct, an internal “desire” to improve correspondence between top-down and bottom-up signals. It increases a similarity measure between the sets of models and signals, L({X},{M})Error! Bookmark not defined. L({X},{M}) = l(X(n)). (1) (1) ∏