Simulating Overall and Trial-by-Trial Effects in Response Selection with a Biologically-plausible Connectionist Network

Simulating Overall and Trial-by-Trial Effects in Response Selection with a Biologically-plausible Connectionist Network Blair C. Armstrong (b.armstrong@bcbl.eu) Basque Center on Cognition, Brain, and Language Paseo Mikeletegi 69, San Sebastian, 20009 Spain David C. Plaut (plaut@cmu.edu) Department of Psychology and Center for the Neural Basis of Cognition, Carnegie Mellon University 5000 Forbes Avenue, Pittsburgh, PA 15213 USA Abstract principles which can, by virtue of the domain-general nature of the framework, have wide-spread implications for domains well beyond response selection (e.g., semantic cognition). Past work by Ratcliff, Van Zandt, and McKoon (1999) pro- vides some initial insight into the performance of connec- tionist models of 2AFC tasks relative to that of the diffu- sion model in simulating performance in a numerosity judg- ment task. In this task, participants were presented with a 10×10 array which was filled with a number of asterisks sam- pled from two overlapping distributions with ‘low’ and ‘high’ mean numbers of asterisks, and made responses indicating which distribution they believed had been sampled from to generate the stimulus. The model comparisons revealed that the connectionist models failed to capture important aspects of the behavioral data (e.g., latency-accuracy functions, trial- by-trial adaptive effects). To address some of these limitations, Usher and McClel- land (2001) introduced a revised connectionist formalism in the leaky, competing accumulator model. Changes in this model included explicit constraints on the sign of the weights between competing units and from the underlying source of evidence that drives the response units, and the use of a threshold-linear activation function that is not differentiable at all points in time. A critical implication of the latter change is that it violates the mathematical principles that underlie standard gradient descent learning algorithms such as back- propagation (Hinton, 1989). Collectively, these changes ren- dered the accumulator functionally analogous to the diffusion model, and generally showed identical or superior fits to that model. This notwithstanding, a fundamental issue with this type of domain-specific connectionist model is what strengths of the standard connectionist framework were given up dur- ing model development. In particular, the disconnect between these models and standard connectionist learning algorithms prevents these models from being effortlessly extended to other response selection tasks—let alone cognitive process- ing and learning in other domains. An alternative approach to developing improved connec- tionist models of response selection is to focus, instead, on improving the domain-general assumptions of the frame- work. One way to do this that is independent of the partic- ular constraints needed to simulate response selection is to more accurately instantiate the known connectivity and pro- cessing characteristics of the brain. For instance, neurons Ratcliff, Van Zandt, and McKoon (1999, Psych. Rev.) claim that connectionist models fail to simulate many aspects of how individuals select one of two possible responses. Here, these claims are re-evaluated via computational and behavioral in- vestigations of an extended version of the original numeros- ity judgment task. The results of the experiment indicate that some of the empirical effects that the models failed to cap- ture do not generalize and were likely due to idiosyncratic as- pects of the original methodology. The simulations show that a more biologically-plausible model captures the bulk of the new effects, including some trial-by-trial adaptive effects that are outside the scope of models tested against aggregate data, and emergent asymptotic stability that has previously required an explicit leak parameter. Keywords: response selection, decision making, connection- ism, numerosity judgment, overall and trial-by-trial effects Understanding how one of multiple candidate responses is selected in a given task is a long-standing and critical issue in cognitive science, and is one of the earliest domains to have been investigated with computational models. To date, much of the work has focused on the sub-issue of how individu- als perform in tasks in which they must rapidly select one of two possible responses (i.e., speeded two-alternative forced- choice tasks; 2AFC tasks). This has led to the development of several models that can be fit to data from 2AFC tasks with a high degree of precision (e.g., the diffusion model; Ratcliff, 1978). One of several key limitations of these models, how- ever, is that they are highly domain-specific and are not nat- urally extendable to studying other intuitively related issues, such as ‘closed-set’ response selection tasks involving three or more pre-specified candidate responses, or ‘open-set’ re- sponse selection tasks which require the production of novel responses such as nonword naming. These models are also often fit to aggregated data and do not explain how the deci- sion system adapts over time based on its past experiences. One possible avenue for addressing these limitations is the development of a connectionist model of response selection, given the connectionist framework’s grounding in domain- general learning, representation, and processing principles that are drawn from systems and cellular neuroscience. Not only might such a model be able to explain the overall and adaptive effects in 2AFC tasks, it should also be readily ex- tendable to the other response tasks described previously. Moreover, insofar as connectionist models fail in these en- deavors, this can serve to guide the development of improved