Equilibria of the Rescorla--Wagner model

By David Danks. 2003

202 citations recorded by the source corpus.

The Rescorla-Wagner model has been a leading theory of animal causal induction for nearly 30 years, and human causal induction for the past 15 years. Recent theories (especially Psychol. Rev. 104 (1997) 367) have provided alternative explanations of how people draw causal conclusions from covariational data. However, theoretical attempts to compare the Rescorla-Wagner model with more recent models have been hampered by the fact that the Rescorla-Wagner model is an algorthimic theory, while the model recent theories are all computational. This paper provides a detailed derivation of the long-run behaviour of the Rescorla-Wagner model under a wide range of parameters and experimental setups, so that the model can be compared with computational theories. It also shows that the model agrees with competing theories on a wider range of cases than had previously been thought. The paper concludes by showing how recently suggested modification of the Rescorla-Wagner model impact the long-run behavior of the model.

Subfields: Cognitive Neuroscience, Developmental and Educational Psychology, Social Psychology

View Paper: https://www.semanticscholar.org/paper/ee237ef73f5af7dad18ca946efc878ede65fa791

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Citations in the corpus

Causal Learning (2012, methodology): “For situations involving only one varying cue, its mean weight at equilibrium according to the RW algorithm has been shown to equal ΔP if the value of β remains the same when the US is present and when it is absent for the λ values just mentioned (Chapman & Robins, 1990; Danks, 2003).”
Demythologizing the word frequency effect: A discriminative learning perspective (2010, methodology): “Connections from the form layer to the semantic layer are estimated using the equilibrium equations for discriminative learning (Danks, 2003) as defined by the Rescorla-Wagner equations (Wagner & Rescorla, 1972).”
A theory of causal learning in children: causal maps and Bayes nets. (2004, unknown): “The RW process is often compared with other learning theories through its long run behavior, or equilibria (Cheng, 1997; Danks, 2003).”
A visual analytics approach to understanding cycling behaviour (2012, unknown): “…boundaries on the hypothesis search space, ﬁrst introduced by Muggleton (1995) as part of the Progol system, and are built from one random positive example, background knowledge (a set of clauses that describe what is known) and language bias (a set of clauses that deﬁne how clauses can be built).”
The Myth of Cognitive Decline: Non-Linear Dynamics of Lifelong Learning (2014, methodology): “…of cues (it's a mild day in the hills, and there is not a cloud in the sky), our cognitive systems actively learn to expect that some events will not occur (on hearing a distant rumbling, the idea of thunder is not entertained; Rescorla, 1968, 1988; Danks, 2003; Ramscar, Dye, & McCauley, 2013b).”
Children's causal inferences from indirect evidence: Backwards blocking and Bayesian reasoning in preschoolers (2004, background): “…prior knowledge applicable to the current situation (as in the case of beliefs and desires above), to relatively general assumptions about causality (e.g., that causes precede effects – a piece of knowledge that potentially discriminates which events are causes and which events are effects).”
Intuitive theories as grammars for causal inference (2007, background): “There has not been a widespread effort to propose and test principled domain-general frameworks for modeling theory-based induction of causal structure, as there has been for more bottom-up associative accounts (Rescorla & Wagner, 1972; Cheng & Novick, 1990; Cheng, 1997; Lober & Shanks, 2000; Danks,”
Structure and strength in causal induction. (2005, unknown): “…value of the weight given to the cause C when the causal induction task is modeled with a linear associator trained using the Rescorla-Wagner (Rescorla & Wagner, 1972) learning rule (Cheng, 1997; Cheng & Holyoak, 1995; Chapman & Robbins, 1990; Danks, 2003; Wasserman, Elek, Chatlosh & Baker, 1993).”
An amorphous model for morphological processing in visual comprehension based on naive discriminative learning. (2011, methodology): “Dashed lines represent the stable-state association strength obtained with the equilibrium equations of Danks (2003).”
Error and expectation in language learning: The curious absence of mouses in adult speech (2013, methodology): “…with similar principles embodied in a wide range of learning models, in which equivalent simulations could be implemented (see e.g. Barlow 2001, Courville et al. 2006, Danks 2003, Dayan & Daw 2008, Gallistel 2003, Kruschke 2008, McLaren & Mackintosh 2000, Pearce & Hall 1980, Sutton & Barto 1998).”
Effects of primary and secondary morphological family size in monolingual and bilingual word processing (2014, methodology): “The NDR model actually estimates the association strengths (weights) of cues (lett rs and letter bigrams) to outcomes (meanings) by means of the equilibrium equations for the Rescorla-Wagner equations derived by Danks (2003), obviating the need to simulate the learning process step by step.”
Making choices in Russian: pros and cons of statistical methods for rival forms (2013, methodology): “This type of model makes use of a two-335 layer network, the weights of which are estimated using the equilibrium 336 equations of Danks (2003) for the Rescorla-Wagner equations (Rescorla and 337 Wagner 1972) that summarize and bring together a wide body of results on 338 animal and human learning.”