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When making a decision, one must first accumulate evidence, often over time, and then select the appropriate action. Here, we present a neural model of decision making that can perform both evidence accumulation and action selection optimally. More specifically, we show that, given a Poisson-like distribution of spike counts, biological neural networks can accumulate evidence without loss of information through linear integration of neural activity and can select the most likely action through attractor dynamics. This holds for arbitrary correlations, any tuning curves, continuous and discrete variables, and sensory evidence whose reliability varies over time. Our model predicts that the neurons in the lateral intraparietal cortex involved in evidence accumulation encode, on every trial, a probability distribution which predicts the animal’s performance. We present experimental evidence consistent with this prediction and discuss other predictions applicable to more general settings.

Simple perceptual tasks have laid the groundwork for understanding the neurobiology of decision-making. Here, we examined this foundation to explain how decision-making circuitry adjusts in the face of a more difficult task. We measured behavioral and physiological responses of monkeys on a two-and four-choice direction-discrimination decision task. For both tasks, firing rates in the lateral intraparietal area appeared to reflect the accumulation of evidence for or against each choice. Evidence accumulation began at a lower firing rate for the four-choice task, but reached a common level by the end of the decision process. The larger excursion suggests that the subjects required more evidence before making a choice. Furthermore, on both tasks, we observed a time-dependent rise in firing rates that may impose a deadline for deciding. These physiological observations constitute an effective strategy for handling increased task difficulty. The differences appear to explain subjects' accuracy and reaction times. Organisms face decisions of varying complexity. In simple decisions, perceptual observations allow an animal to choose between action and inaction, or between two alternative actions. These are simple instances of complex cognitive processes, which may require additional information from the environment or from memory. The ability to delay a response to consider incoming information is a hallmark of higher brain function. Decisions between two choices in a perceptual-motion task 1-3 demonstrate mechanisms of decision-making. In the task, humans or monkeys reported the net direction of motion in a patch of moving random dots. In the reaction-time version 2 , subjects communicated their decision with a saccade when they were ready. This version identifies the period when subjects are accumulating evidence for a decision, but have not yet committed to an alternative. How rapidly evidence accumulates depends on the strength of motion. The process ends when the evidence reaches a threshold or bound corresponding to one alternative. These 'bounded accumulation of evidence' models encompass multiple mechanisms that have been proposed to explain choice and decision time 1,4,5 . Several observations are consistent with the idea that evidence accumulates to a bound. First, a formal model of bounded accumulation accounts quantitatively for subjects' speed and accuracy Because two-alternative choice tasks are simple, they may offer limited insight into decision-making in general; organisms regularly face decisions with multiple alternatives. Here, we compare responses on a four-choice decision task with a two-choice task. Our results argue that the bounded accumulation framework can be extended to explain more complex decisions, and they begin to reveal how decision-making circuitry adjusts to increasingly difficult decisions. RESULTS Behavior Two monkeys were trained on a two-choice and a four-choice motiondiscrimination task Like accuracy, decision speed also depended on both motion strength and the number of choices. Reaction times were longer on the four-choice task 10 . These differences were largest at lower motion strengths, but were significant at all motion strengths (P o 0.01; We measured responses on an additional condition with two targets, spaced 901 apart

The authors present a new model of free recall on the basis of M. W. Howard and M. J. Kahana’s (2002a) temporal context model and M. Usher and J. L. McClelland’s (2001) leaky-accumulator decision model. In this model, contextual drift gives rise to both short-term and long-term recency effects, and contextual retrieval gives rise to short-term and long-term contiguity effects. Recall decisions are controlled by a race between competitive leaky accumulators. The model captures the dynamics of immediate, delayed, and continual distractor free recall, demonstrating that dissociations between short- and long-term recency can naturally arise from a model in which an internal contextual state is used as the sole cue for retrieval across time scales.

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When faced with choices between two sources of reward, animals can rapidly adjust their rates of responding to each so that overall reinforcement increases. Herrnstein's 'matching law' provides a simple description of the equilibrium state of this choice allocation process: animals reallocate behavior so that relative rates of responding equal, or match, the relative rates of reinforcement obtained for each response. Herrnstein and colleagues proposed 'melioration' as a dynamical process for achieving this equilibrium, but left details of its operation unspecified. Here we examine a way of filling in the details that links the decision making and operant conditioning literatures and extends choice proportion predictions into predictions about inter-response times. Our approach implements melioration in an adaptive version of the drift diffusion model (DDM), which is widely used in decision making research to account for response time distributions. When the drift parameter of the DDM is 0 and its threshold parameters are inversely proportional to reward rates, its choice proportions dynamically track a state of exact matching. A DDM with fixed thresholds and drift that is determined by differences in reward rates can produce similar, but not identical, results. We examine the choice probability and inter-response time predictions of these models, separately and in combination, and the possible implications for brain organization provided by neural network implementations of them. Results suggest that melioration and matching may derive from synapses that estimate reward rates by a process of leaky integration, and that link together the input and output stages of a two-stage stimulusresponse mechanism. Introduction For much of the twentieth century, psychological research on choice and simple decision making was typically carried out within one of two separate traditions. One is the behaviorist tradition, emerging from the work of Thorndike and Pavlov and exemplified by operant conditioning experiments with animals

The Eriksen task is a classical paradigm that explores the e®ects of competing sensory inputs on response tendencies, and the nature of selective attention in controlling these processes. In this task, con°icting °anker stimuli interfere with the processing of a central target, especially on short reaction-time trials. This task has been modeled by neural networks and more recently by a normative Bayesian account. Here, we analyze the dynamics of the Bayesian models, which are nonlinear, coupled discrete-time dynamical systems, by considering simpli¯ed, approximate systems that are linear and decoupled. Analytical solutions of these allow us to describe how posterior probabilities and psychometric functions depend upon model parameters. We compare our results with numerical simulations of the original models and show that the agreement is rather good. We also investigate the continuum limits of these simpli¯ed dynamical systems, and demonstrate that Bayesian updating is closely related to a drift-di®usion process, whose implementation in neural network models has been extensively studied.

Abstract — This paper investigates the effect of coupling in a collective decision-making scenario, in which the task is to correctly identify a (noisy) stimulus between two known al-ternatives. Multiple interconnected decision-making units, each represented by a Drift-Diffusion Model (DDM), accumulate evidence toward a decision. A number of different graph topolo-gies among the DDM’s are considered, and their effect on the accuracy of the decision is investigated. It is deduced that, for the same stimuli, the average of the collected evidence increases linearly with time toward the correct decision regardless of the communication topology. However, the uncertainty associated with the process is affected by the interconnection graph, implying that certain topologies are better than others. I.