Learning Unions of Rectangles with Queries

We investigate the efficient learnability of unions of k rectangles in the discrete plane (1,...,n)[2] with equivalence and membership queries. We exhibit a learning algorithm that learns any union of k rectangles with O(k^3log n) queries, while the time complexity of this algorithm is bounded by O(k^5log n). We design our learning algorithm by finding "corners" and "edges" for rectangles contained in the target concept and then constructing the target concept from those "corners" and "edges". Our result provides a first approach to on-line learning of nontrivial subclasses of unions of intersections of halfspaces with equivalence and membership queries.

Linking Attention to Learning, Expectation, Competition, and Consciousness

The concept of attention has been used in many senses, often without clarifying how or why attention works as it does. Attention, like consciousness, is often described in a disembodied way. The present article summarizes neural models and supportive data and how attention is linked to processes of learning, expectation, competition, and consciousness. A key them is that attention modulates cortical self-organization and stability. Perceptual and cognitive neocortex is organized into six main cell layers, with characteristic sub-lamina. Attention is part of unified design of bottom-up, horizontal, and top-down interactions among indentified cells in laminar cortical circuits. Neural models clarify how attention may be allocated during processes of visual perception, learning and search; auditory streaming and speech perception; movement target selection during sensory-motor control; mental imagery and fantasy; and hallucination during mental disorders, among other processes.

Cerebellar Learning in an Opponent Motor Controller for Adaptive Load Compensation and Synergy Formation

This paper shows how a minimal neural network model of the cerebellum may be embedded within a sensory-neuro-muscular control system that mimics known anatomy and physiology. With this embedding, cerebellar learning promotes load compensation while also allowing both coactivation and reciprocal inhibition of sets of antagonist muscles. In particular, we show how synaptic long term depression guided by feedback from muscle stretch receptors can lead to trans-cerebellar gain changes that are load-compensating. It is argued that the same processes help to adaptively discover multi-joint synergies. Simulations of rapid single joint rotations under load illustrates design feasibility and stability.

A Neural Network Architecture for Autonomous Learning, Recognition, and Prediction in a Nonstationary World

In a constantly changing world, humans are adapted to alternate routinely between attending to familiar objects and testing hypotheses about novel ones. We can rapidly learn to recognize and narne novel objects without unselectively disrupting our memories of familiar ones. We can notice fine details that differentiate nearly identical objects and generalize across broad classes of dissimilar objects. This chapter describes a class of self-organizing neural network architectures--called ARTMAP-- that are capable of fast, yet stable, on-line recognition learning, hypothesis testing, and naming in response to an arbitrary stream of input patterns (Carpenter, Grossberg, Markuzon, Reynolds, and Rosen, 1992; Carpenter, Grossberg, and Reynolds, 1991). The intrinsic stability of ARTMAP allows the system to learn incrementally for an unlimited period of time. System stability properties can be traced to the structure of its learned memories, which encode clusters of attended features into its recognition categories, rather than slow averages of category inputs. The level of detail in the learned attentional focus is determined moment-by-moment, depending on predictive success: an error due to over-generalization automatically focuses attention on additional input details enough of which are learned in a new recognition category so that the predictive error will not be repeated. An ARTMAP system creates an evolving map between a variable number of learned categories that compress one feature space (e.g., visual features) to learned categories of another feature space (e.g., auditory features). Input vectors can be either binary or analog. Computational properties of the networks enable them to perform significantly better in benchmark studies than alternative machine learning, genetic algorithm, or neural network models. Some of the critical problems that challenge and constrain any such autonomous learning system will next be illustrated. Design principles that work together to solve these problems are then outlined. These principles are realized in the ARTMAP architecture, which is specified as an algorithm. Finally, ARTMAP dynamics are illustrated by means of a series of benchmark simulations.

Space, Time and Learning in the Hippocampus: How Fine Spatial and Temporal Scales Are Expanded into Population Codes for Behavioral Control

The hippocampus participates in multiple functions, including spatial navigation, adaptive timing, and declarative (notably, episodic) memory. How does it carry out these particular functions? The present article proposes that hippocampal spatial and temporal processing are carried out by parallel circuits within entorhinal cortex, dentate gyrus, and CA3 that are variations of the same circuit design. In particular, interactions between these brain regions transform fine spatial and temporal scales into population codes that are capable of representing the much larger spatial and temporal scales that are needed to control adaptive behaviors. Previous models of adaptively timed learning propose how a spectrum of cells tuned to brief but different delays are combined and modulated by learning to create a population code for controlling goal-oriented behaviors that span hundreds of milliseconds or even seconds. Here it is proposed how projections from entorhinal grid cells can undergo a similar learning process to create hippocampal place cells that can cover a space of many meters that are needed to control navigational behaviors. The suggested homology between spatial and temporal processing may clarify how spatial and temporal information may be integrated into an episodic memory.