Simple Neural Networks That Optimize Decisions

Brown, Eric; Gao, Juan; Holmes, Philip; Bogacz, Rafał; Gilzenrat, Mark S.; Cohen, Jonathan D.

doi:10.1142/s0218127405012478

Cited by 85 publications

(85 citation statements)

References 40 publications

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“…For networks with underlying linear dynamics and both a reset nonlinearity and a finite dynamic range on neuronal responses, our results are consistent with the optimality of perfectly tuned attractor networks. Similarly, we note that the perfectly tuned attractor network (integrator) was found in a recent study to be the optimal architecture for storing the running total of a continuously presented input in which noise likewise started with the arrival of the signal (Brown et al, 2005). …”

Section: Discussionsupporting

confidence: 54%

Noise Tolerance of Attractor and Feedforward Memory Models

Lim

Goldman

2012

Neural Computation

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In short-term memory networks, transient stimuli are represented by patterns of neural activity that persist long after stimulus offset. Here, we compare the performance of two prominent classes of memory networks, feedback-based attractor networks and feedforward networks, in conveying information about the amplitude of a briefly presented stimulus in the presence of gaussian noise. Using Fisher information as a metric of memory performance, we find that the optimal form of network architecture depends strongly on assumptions about the forms of nonlinearities in the network. For purely linear networks, we find that feedforward networks outperform attractor networks because noise is continually removed from feedforward networks when signals exit the network; as a result, feedforward networks can amplify signals they receive faster than noise accumulates over time. By contrast, attractor networks must operate in a signal-attenuating regime to avoid the buildup of noise. However, if the amplification of signals is limited by a finite dynamic range of neuronal responses or if noise is reset at the time of signal arrival, as suggested by recent experiments, we find that attractor networks can out-perform feedforward ones. Under a simple model in which neurons have a finite dynamic range, we find that the optimal attractor networks are forgetful if there is no mechanism for noise reduction with signal arrival but nonforgetful (perfect integrators) in the presence of a strong reset mechanism. Furthermore, we find that the maximal Fisher information for the feedforward and attractor networks exhibits power law decay as a function of time and scales linearly with the number of neurons. These results highlight prominent factors that lead to trade-offs in the memory performance of networks with different architectures and constraints, and suggest conditions under which attractor or feedforward networks may be best suited to storing information about previous stimuli.

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Section: Discussionsupporting

confidence: 54%

Noise Tolerance of Attractor and Feedforward Memory Models

Lim

Goldman

2012

Neural Computation

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“…This formulation is equivalent to a firing rate model via a linear transformation (Grossberg, 1988; Brown et al, 2005), and reductions to one-dimensional drift diffusion and Ornstein-Uhlenbeck systems can be made in appropriate parameter ranges (Brown and Holmes, 2001; Bogacz et al, 2006). …”

Section: Methodsmentioning

confidence: 99%

Sequential Effects in Two-Choice Reaction Time Tasks: Decomposition and Synthesis of Mechanisms

et al. 2009

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Performance on serial tasks is influenced by first-and higher-order sequential effects, respectively due to the immediately previous and earlier trials. As response-to-stimulus interval (RSI) increases, the pattern of reaction times transits from a benefit-only mode, traditionally ascribed to automatic facilitation (AF), to a cost-benefit mode, due to strategic expectancy (SE). To illuminate the sources of such effects, we develop a connectionist network of two mutually-inhibiting neural decision units subject to feedback from previous trials. A study of separate biasing mechanisms shows that residual decision unit activity can lead only to first-order AF, but higher-order AF can result from strategic priming mediated by conflict-monitoring, which we instantiate in two distinct versions. A further mechanism mediates expectation-related biases that grow during RSI toward saturation levels determined by weighted repetition (or alternation) sequence lengths. Equipped with these mechanisms, the network, consistent with known neurophysiology, accounts for several sets of behavioral data over a wide range of RSIs. The results also suggest that practice speeds up all the mechanisms rather than adjusting their relative strengths.

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“…DDM has proven to be quite successful with accounting for behavioral data [47, 69], and more recent monkey’s accuracy and reaction time in the RDM task [65, 30]. DDM can be considered as a normative theory, since it is the continuous-time equivalent of the sequential probability-ratio test (SPRT), which is the optimal procedure for making binary choices under uncertainty in the sense that it minimizes the mean decision time among all tests for a given error rate [10, 6]. …”

Section: Interplay Between Normative Theory and Neural Circuit Mechanismmentioning

confidence: 99%

Neural dynamics and circuit mechanisms of decision-making

Wang

2012

Current Opinion in Neurobiology

128

113

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In this review, I briefly summarize current neurobiological studies of decision-making that bear on two general themes. The first focuses on the nature of neural representation and dynamics in a decision circuit. Experimental and computational results suggest that ramping-to-threshold in the temporal domain and trajectory of population activity in the state space represent a duality of perspectives on a decision process. Moreover, a decision circuit can display several different dynamical regimes, such as the ramping mode and the jumping mode with distinct defining properties. The second is concerned with the relationship between biologically-based mechanistic models and normative-type models. A fruitful interplay between experiments and these models at different levels of abstraction have enabled investigators to pose increasingly refined questions and gain new insights into the neural basis of decision-making. In particular, recent work on multi-alternative decisions suggests that deviations from rational models of choice behavior can be explained by established neural mechanisms.

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Simple Neural Networks That Optimize Decisions

Cited by 85 publications

References 40 publications

Noise Tolerance of Attractor and Feedforward Memory Models

Noise Tolerance of Attractor and Feedforward Memory Models

Sequential Effects in Two-Choice Reaction Time Tasks: Decomposition and Synthesis of Mechanisms

Neural dynamics and circuit mechanisms of decision-making

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