The Art of Seeing and Painting

The human urge to represent the three-dimensional world using two-dimensional pictorial representations dates back at least to Paleolithic times. Artists from ancient to modern times have struggled to understand how a few contours or color patches on a flat surface can induce mental representations of a three-dimensional scene. This article summarizes some of the recent breakthroughs in scientifically understanding how the brain sees that shed light on these struggles. These breakthroughs illustrate how various artists have intuitively understand paradoxical properties about how the brain sees, and have used that understanding to create great art. These paradoxical properties arise from how the brain forms the units of conscious visual perception; namely, representations of three-dimensional boundaries and surfaces. Boundaries and surfaces are computed in parallel cortical processing streams that obey computationally complementary properties. These streams interact at multiple levels to overcome their complementary weaknesses and to transform their complementary properties into consistent percepts. The article describes how properties of complementary consistency have guided the creation of many great works of art.

ART-EMAP: A Neural Network Architecture for Object Recognition by Evidence Accumulation

A new neural network architecture is introduced for the recognition of pattern classes after supervised and unsupervised learning. Applications include spatio-temporal image understanding and prediction and 3-D object recognition from a series of ambiguous 2-D views. The architecture, called ART-EMAP, achieves a synthesis of adaptive resonance theory (ART) and spatial and temporal evidence integration for dynamic predictive mapping (EMAP). ART-EMAP extends the capabilities of fuzzy ARTMAP in four incremental stages. Stage 1 introduces distributed pattern representation at a view category field. Stage 2 adds a decision criterion to the mapping between view and object categories, delaying identification of ambiguous objects when faced with a low confidence prediction. Stage 3 augments the system with a field where evidence accumulates in medium-term memory (MTM). Stage 4 adds an unsupervised learning process to fine-tune performance after the limited initial period of supervised network training. Each ART-EMAP stage is illustrated with a benchmark simulation example, using both noisy and noise-free data. A concluding set of simulations demonstrate ART-EMAP performance on a difficult 3-D object recognition problem.

Fuzzy ART

Adaptive Resonance Theory (ART) models are real-time neural networks for category learning, pattern recognition, and prediction. Unsupervised fuzzy ART and supervised fuzzy ARTMAP synthesize fuzzy logic and ART networks by exploiting the formal similarity between the computations of fuzzy subsethood and the dynamics of ART category choice, search, and learning. Fuzzy ART self-organizes stable recognition categories in response to arbitrary sequences of analog or binary input patterns. It generalizes the binary ART 1 model, replacing the set-theoretic: intersection (∩) with the fuzzy intersection (∧), or component-wise minimum. A normalization procedure called complement coding leads to a symmetric: theory in which the fuzzy inter:>ec:tion and the fuzzy union (∨), or component-wise maximum, play complementary roles. Complement coding preserves individual feature amplitudes while normalizing the input vector, and prevents a potential category proliferation problem. Adaptive weights :otart equal to one and can only decrease in time. A geometric interpretation of fuzzy AHT represents each category as a box that increases in size as weights decrease. A matching criterion controls search, determining how close an input and a learned representation must be for a category to accept the input as a new exemplar. A vigilance parameter (p) sets the matching criterion and determines how finely or coarsely an ART system will partition inputs. High vigilance creates fine categories, represented by small boxes. Learning stops when boxes cover the input space. With fast learning, fixed vigilance, and an arbitrary input set, learning stabilizes after just one presentation of each input. A fast-commit slow-recode option allows rapid learning of rare events yet buffers memories against recoding by noisy inputs. Fuzzy ARTMAP unites two fuzzy ART networks to solve supervised learning and prediction problems. A Minimax Learning Rule controls ARTMAP category structure, conjointly minimizing predictive error and maximizing code compression. Low vigilance maximizes compression but may therefore cause very different inputs to make the same prediction. When this coarse grouping strategy causes a predictive error, an internal match tracking control process increases vigilance just enough to correct the error. ARTMAP automatically constructs a minimal number of recognition categories, or "hidden units," to meet accuracy criteria. An ARTMAP voting strategy improves prediction by training the system several times using different orderings of the input set. Voting assigns confidence estimates to competing predictions given small, noisy, or incomplete training sets. ARPA benchmark simulations illustrate fuzzy ARTMAP dynamics. The chapter also compares fuzzy ARTMAP to Salzberg's Nested Generalized Exemplar (NGE) and to Simpson's Fuzzy Min-Max Classifier (FMMC); and concludes with a summary of ART and ARTMAP applications.

Fuzzy ART Choice Functions

Adaptive Resonance Theory (ART) models are real-time neural networks for category learning, pattern recognition, and prediction. Unsupervised fuzzy ART and supervised fuzzy ARTMAP networks synthesize fuzzy logic and ART by exploiting the formal similarity between tile computations of fuzzy subsethood and the dynamics of ART category choice, search, and learning. Fuzzy ART self-organizes stable recognition categories in response to arbitrary sequences of analog or binary input patterns. It generalizes the binary ART 1 model, replacing the set-theoretic intersection (∩) with the fuzzy intersection(∧), or component-wise minimum. A normalization procedure called complement coding leads to a symmetric theory in which the fuzzy intersection and the fuzzy union (∨), or component-wise maximum, play complementary roles. A geometric interpretation of fuzzy ART represents each category as a box that increases in size as weights decrease. This paper analyzes fuzzy ART models that employ various choice functions for category selection. One such function minimizes total weight change during learning. Benchmark simulations compare peformance of fuzzy ARTMAP systems that use different choice functions.

Normal and Amnesis Learning, Recognition, and Memory by a Neural Model of Cortico-Hippocampal Interactions

The processes by which humans and other primates learn to recognize objects have been the subject of many models. Processes such as learning, categorization, attention, memory search, expectation, and novelty detection work together at different stages to realize object recognition. In this article, Gail Carpenter and Stephen Grossberg describe one such model class (Adaptive Resonance Theory, ART) and discuss how its structure and function might relate to known neurological learning and memory processes, such as how inferotemporal cortex can recognize both specialized and abstract information, and how medial temporal amnesia may be caused by lesions in the hippocampal formation. The model also suggests how hippocampal and inferotemporal processing may be linked during recognition learning.