Stimulus and response generalization: A stochastic model relating generalization to distance in psychological space

A mathematical model is developed in an attempt to relate errors in multiple stimulus-response situations to psychological inter-stimulus and inter response distances. The fundamental assumptions are (a) that the stimulus and response confusions go on independently of each other, (b) that the probability of a stimulus confusion is an exponential decay function of the psychological distance between the stimuli, and (c) that the probability of a response confusion is an exponential decay function of the psychological distance between the responses. The problem of the operational definition of psychological distance is considered in some detail.This paper is based upon the theoretical sections of a Ph.D. dissertation submitted to the Graduate School of Yale University and upon subsequent modification carried out on a National Academy of Sciences-National Research Council Postdoctoral Associateship at the Naval Research Laboratory. The author is particularly indebted to Drs. C. I. Hovland, R. P. Abelson, and B. S. Rosner for their generous advice and support. Helpful criticisms have also been contributed by Drs. G. A. Miller, F. A. Logan, W. D. Garvey, J. G. Holland, and H. Glaser.     

Stimulus generalization: some predictions from a model of Pavlovian conditioning.

Three experiments examined predictions generated by incorporating a common-elements account of stimulus generalization within the Rescorla-Wagner model of conditioning. All experiments employed rats in a conditioned suppression situation. Experiments 1 and 2 found that conditioning of a similar stimulus augmented the excitation controlled by a near-asymptotic target stimulus more than did further conditioning of the target itself. Prior discrimination training between the target and the similar stimulus enlarged this effect, compared with prior discrimination between the target and another dissimilar stimulus. Nonreinforced exposure of the similar stimulus prior to its reinforcement also increased the effect. Experiment 3 examined a related prediction for inhibition. After discrimination training, extinction of the previously reinforced stimulus revealed more inhibition to the previously nonreinforced stimulus when those two stimuli were more similar. These outcomes are consistent with deductions from the present model and encourage further testing of its expansion to the case of stimulus generalization.     

Stimulus generalization from feeder to response key in the acquisition of autoshaped pecking

During autoshaping, a 6-second presentation of one stimulus and a variable time 30-second presentation of a second stimulus alternated in appearance on a pigeon key. Grain always was delivered for 3 seconds at the end of the first stimulus interval. In the first experiment, autoshaped pecking of the stimulus preceding grain delivery began much sooner when that stimulus was a black vertical line on a white background and the other stimulus was green than when the opposite stimulus arrangement was used. Because these two stimuli differed in form, hue, brightness, and similarity in hue and brightness to the illumination of the raised feeder, three subsequent experiments examined whether the differential speed of autoshaping in the two groups was due to a feature-positive, feature-negative effect, a preference for brighter over darker stimuli, a simple preference for white over green, or stimulus generalization from the brightness or hue of the illuminated, raised feeder to the stimulus on the key preceding grain delivery. The data from these experiments showed that the first autoshaped key peck was most likely to be made to the stimulus of the same hue as that illuminating the feeder, regardless of whether that stimulus was positively or negatively associated with grain delivery. At least under some conditions, therefore, stimulus-generalization mediated response transfer of pecking grain in the presence of the hue illuminating the feeder to pecking the key illuminated by a similar hue appears to account for the occurrence of autoshaped key pecking.     

Stimulus generalization and the response-reinforcement contingency

Generalization gradients along a line-tilt continuum were obtained from groups of pigeons that had been trained to peck a key on different schedules of reinforcement. In Exp. I, gradients following training on a differential-reinforcement-of-low-rate (DRL) schedule proved to be much flatter than gradients following the usual 1-min variable interval (VI) training. In Exp. II, the value of the VI schedule itself was parametrically studied; Ss trained on long VI schedules (e.g., 4-min) produced much flatter gradients than Ss trained on short VI schedules (30-sec; 1-min). The results were interpreted mainly in terms of the relative control exerted by internal, proprioceptive cues on the different reinforcement schedules. Several implications of the results for other problems in the field of stimulus generalization are discussed.     

Stimulus generalization of gravity

In two experiments, squirrel monkeys were exposed to centrifugally generated, artificial gravity and trained to respond for food reinforcement at selected gravity (g) levels. Experiment I involved a single g value; in Exp. II, subjects were trained to discriminate among two or three g values. After training, generalization tests were administered over a 1.1-g to 2.1-g range. The major findings were as follows: (a) single-stimulus training yielded a linear relationship between percentage of responding and magnitude of gravity. (b) Two-valued discrimination training produced gradient peaks which were shifted from S(D) in a direction away from S(Delta). This effect was cancelled when S(D) was located equidistant between two S(Delta) stimuli. (c) Gradient form was independent of the S(D)-S(Delta) difference, but related to continuum location and/or intensity of discriminative stimuli.     

Stimulus generalization of excitation and inhibition

Five sign-tracking experiments with pigeons investigated the breadth of stimulus generalization of excitatory and inhibitory conditioning. Using a compound stimulus test procedure, these experiments found evidence for a narrower generalization of associative strength in excitation than in inhibition. They also found a narrower associative gradient with a more strongly conditioned excitatory stimulus, although this did not seem to account for the difference between exciters and inhibitors. These results confirm earlier findings comparing generalization after acquisition and extinction and raise various theoretical issues about generalization.     

Stimulus generalization: the ordering and spacing of test stimuli

Twenty-four pigeons learned a successive discrimination between 500 mmu (S+) and 574 mmu (S-). When tested in extinction, some birds received stimuli around S+, with no S- presentations. These birds showed a positive peak shift, with maximum responding not at 550 mmu, but displaced to 538 mmu and 544 mmu. Other birds were tested with stimuli around S-, with no S+ presentations. These birds showed a negative shift, with least responding not at 574 mmu, but at 586 mmu. Though the first group was tested around S+ and the second around S-, total responding between groups did not differ. When retested on the other half of the continuum, however, birds that had gone from the S+ half to the S- half responded fewer times than those that had gone from the S- half to the S+ half. In a second experiment, reducing stimulus spacing from 6 mmu to 2 mmu produced flatter gradients and decreased the amount of positive shift. In a third experiment, birds were tested across the whole continuum with stimuli presented in serial order. A sequence from 538 mmu to 586 mmu produced no responding after the first part of the session; a sequence from 586 mmu to 538 mmu produced responding throughout the session.     

Stimulus generalization of schedule-induced polydipsia

Five rats were exposed to an intradimensional discrimination by associating two tones of different frequency with the components of a multiple random-time 30-sec, extinction schedule of food presentation. After schedule-induced polydipsia developed and the intermittent schedule of food presentation established stable differential licking rates during the stimuli associated with the multiple schedule, a stimulus generalization test was conducted. When generalization testing was conducted by presenting stimuli that varied on the frequency dimension during the random-time 30-sec component of the multiple schedule, all five rats demonstrated moderately sloping symmetrical gradients. Thus, schedule-induced polydipsia can be brought under the control of stimuli other than the food pellet.     

Stimulus generalization of excitation and inhibition

Five sign-tracking experiments with pigeons investigated the breadth of stimulus generalization of excitatory and inhibitory conditioning. Using a compound stimulus test procedure, these experiments found evidence for a narrower generalization of associative strength in excitation than in inhibition. They also found a narrower associative gradient with a more strongly conditioned excitatory stimulus, although this did not seem to account for the difference between exciters and inhibitors. These results confirm earlier findings comparing generalization after acquisition and extinction and raise various theoretical issues about generalization.