Abstracting Spatial Relations Among Goal Locations


Michael Brown
Villanova University

      

Introduction

Learning can be defined and understood as the processes that allow animals to detect systematic relations among events in their world.   For example, events are often correlated because of the causal relations among them.  Thunder consistently follows lightning and the expectation of hearing thunder that occurs when one sees a flash of lightning is an example of classical conditioning - the well-studied and ubiquitous learning process that allows animals to detect systematic relations among the occurrence of  two (or more) kinds of events.  Another very well-studied kind of systematic relation among events is the fact that particular behaviors are reliably followed by particular events, usually because the behavior is the cause of the event.  For example, a rat for whom food is programmed to reliably follow the pressing of a lever in a Skinner Box soon learns to press the lever.  This learning about the systematic relation between one's own behavior and its outcomes, of course, is instrumental conditioning.  These forms of associative learning have been described as the means by which the nervous system detects systematic patterns in the relations among event occurrences (e.g., Dickinson, 1980).

But relations among the occurrence of events is not the only sort of relations among events that exist.  At least three other kinds of relations among events have been shown to support learning.

If there is a sequential relationship among events presented in a series, animals come to be controlled by that relationship.  For example, if a rat is presented with a series of trials in which the number of pellets provided as reinforcement systematically increases (or decreases) over the trial series, running speed systematically increases (or decreases) over the trial series (e.g., Capaldi, Blitzer, & Molina, 1979; Hulse & Dorsky, 1980).  It has been argued that this control is produced by a learning process that represents the sequential relationship among the events, in this case by representing the systematic increase (or decrease) in reward magnitude (Hulse, 1978).

Learning processes that are sensitive to temporal relations among events have received a great deal of experimental and theoretical attention.  The study of animals exposed to events that are systematically separated in time by intervals on the order of seconds to minutes has led to well developed theories of learning systems specialized for learning about the temporal relations among events (see Church, 2002 for a review).

 

Table A-1: Proposed Relational Learning Processes

Learning Process

Type of Relation

Example

     

Classical Conditioning

Correlation Among Event Occurrences

One event (e.g., bell) consistently followed by a second event (e.g., food)

Instrumental Conditioning

Correlation Between Behavior and Event

Behavior (e.g., lever press) consistently followed by event (e.g., food pellet)

Serial Learning

Ordered Change in Event Property

Increase in Reinforcement Magnitude Over Trials

Interval Timing

Systematic Temporal Interval Between Events

Reinforcement Available on a Fixed Interval Schedule

Spatial Pattern Learning

Systematic Spatial Relations Among Events

Reinforcement Arranged in a Consistent Spatial Pattern

 

This cyberchapter is about the means and mechanisms by which spatial relations are learned.  The focus is on a series of experiments that attempt to isolate spatial relations the target of learning.  

Two illustrations of Pole Box apparatus used in our spatial pattern learning experiments are shown below.  Poles are equally spaced, with separations in different versions of the apparatus ranging from 12 cm to 21 cm.  The poles are arranged in a matrix - we have used apparatus with 4 X 4, 5 X 5, and 4 X 5 matrixes of poles.   There is a well on top of each pole, in which a pellet (or other small food item) can be hidden.  In the critical conditions of our experiments, the location of the baited poles varies unpredictable from trial to trial.  However, the baited poles form a consistent spatial pattern over trials.  

Figure A-1:
Drawing of 5 X 5 Pole Box apparatus (front wall cutaway for illustration purposes (Drawing by Morgan Terrinoni) 

 

Figure A-2:
Photograph of 5 X Pole box apparatus

Figure A-3 shows one exemplar of each of three spatial patterns for which we have evidence of behavioral control and, by inference, of spatial pattern learning.   Spatial pattern learning can be contrasted with other forms of spatial learning that have been described, as outlined in Part II of this cyberchapter.  The evidence for control by the square (top panel), line (middle panel), and checkerboard (bottom panel) patterns is reviewed in Part III.

Figure A-3:
Exemplars of three spatial patterns used in experiments with the poles box (Top: one of 16 possible exemplars of the square pattern; Middle: one of eight possible exemplars of the line patterns; Bottom: one of two possible exemplars of the checkerboard pattern)

 

 

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