## Bayesian computation in recurrent neural circuits (2004)

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Venue: | Neural Computation |

Citations: | 62 - 4 self |

### BibTeX

@ARTICLE{Rao04bayesiancomputation,

author = {Rajesh P. N. Rao},

title = {Bayesian computation in recurrent neural circuits},

journal = {Neural Computation},

year = {2004},

volume = {16},

pages = {1--38}

}

### Years of Citing Articles

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### Abstract

A large number of human psychophysical results have been successfully explained in recent years using Bayesian models. However, the neural implementation of such mod-els remains largely unclear. In this paper, we show that a network architecture com-monly used to model the cerebral cortex can implement Bayesian inference for an arbi-trary hidden Markov model. We illustrate the approach using an orientation discrimi-nation task and a visual motion detection task. In the case of orientation discrimination, we show that the model network can infer the posterior distribution over orientations and correctly estimate stimulus orientation in the presence of significant noise. In the case of motion detection, we show that the resulting model network exhibits direction selectivity and correctly computes the posterior probabilities over motion direction and position. When used to solve the well-known random dots motion discrimination task, the model generates responses that mimic the activities of evidence-accumulating neu-rons in cortical areas LIP and FEF. The framework introduced in the paper posits a new interpretation of cortical activities in terms of log posterior probabilities of stimuli occurring in the natural world. 1 1

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Citation Context ...r, it may be possible to achieve longer integration time constants by combining slow synapses (for example, NMDA synapses) with relatively strong recurrent excitation (see, for example, (Seung, 1996; =-=Wang, 2001-=-)). A particularly challenging problem is to pick recurrent weights mij such that Equation 9 holds true (the alternative of learning such weights is addressed in Section 8.1). For Equation 9 to hold t... |

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Citation Context ... Lewicki, 2002)). These psychophysical tasks range from inferring 3D structure from 2D images and judging depth from multiple cues to perception of motion and color ((Bloj, Kersten, & Hurlbert, 1999; =-=Weiss, Simoncelli, & Adelson, 2002-=-) and chapters by Mamassian et al. and Jacobs in (Rao et al., 2002)). The strength of the Bayesian approach lies in its ability to quantitatively model the interaction between prior knowledge and sens... |

66 |
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Citation Context ...eural circuit should encode probabilities in the log domain in the first place. Indeed, it has been suggested that multiplicative interactions between inputs may occur in dendrites of cortical cells (=-=Mel, 1993-=-), which could perhaps allow Equation 5 to be directly implemented in a recurrent circuit (cf. (Bridle, 1990)). However, there are several reasons why representing probabilities in the log domain coul... |

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(Show Context)
Citation Context ...ightforward linear decoding operation as described above. Several probabilistic models have also been suggested for solving specific problems in visual motion processing such as the aperture problem (=-=Simoncelli, 1993-=-; Koechlin, Anton, & Burnod, 1999; Zemel & Dayan, 1999; Ascher & Grzywacz, 2000; Freeman, Haddon, & Pasztor, 2002; Weiss & Fleet, 2002; Weiss et al., 2002). These typically rely on a prespecified bank... |

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(Show Context)
Citation Context ...an encoding model is first assumed and a Bayesian decoding model is used to estimate the stimulus x (or its distribution), given a set of responses ri (Zhang, Ginzburg, McNaughton, & Sejnowski, 1998; =-=Pouget, Zhang, Deneve, & Latham, 1998-=-; Zemel et al., 1998; Zemel & Dayan, 1999; Wu, Chen, Niranjan, & Amari, 2003). For example, in the distributional population coding (DPC) method (Zemel et al., 1998; Zemel & Dayan, 1999), the response... |

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(Show Context)
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42 |
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Citation Context ...Equation 19). The output of the model is “L” if dL(t) > c and “R” if dR(t) > c, where c is a “confidence threshold” that depends on task constraints (for example, accuracy versus speed requirements) (=-=Reddi & Carpenter, 2000-=-). Figures 12B and 12C show the responses of the two decision neurons over time for two different directions of motion and two levels of coherence. Besides correctly computing the direction of coheren... |

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- 2002
(Show Context)
Citation Context ...c problems in visual motion processing such as the aperture problem (Simoncelli, 1993; Koechlin, Anton, & Burnod, 1999; Zemel & Dayan, 1999; Ascher & Grzywacz, 2000; Freeman, Haddon, & Pasztor, 2002; =-=Weiss & Fleet, 2002-=-; Weiss et al., 2002). These typically rely on a prespecified bank of spatiotemporal filters to generate a probability distribution over velocities, which is processed according to Bayesian principles... |

34 |
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Citation Context ...Richards, 1996; Rao, Olshausen, & Lewicki, 2002)). These psychophysical tasks range from inferring 3D structure from 2D images and judging depth from multiple cues to perception of motion and color ((=-=Bloj, Kersten, & Hurlbert, 1999-=-; Weiss, Simoncelli, & Adelson, 2002) and chapters by Mamassian et al. and Jacobs in (Rao et al., 2002)). The strength of the Bayesian approach lies in its ability to quantitatively model the interact... |

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Citation Context ...e method described in this paper for implementing Equation 5. In particular, Equation 5 can be regarded as a special case of the general sum-product rule for belief propagation in a Bayesian network (=-=Jordan & Weiss, 2002-=-). Thus, in addition to incorporating “belief messages” from the previous time step and the current input as in Equation 5, a more general rule for Bayesian inference would also incorporate messages f... |

31 |
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(Show Context)
Citation Context ...sted that multiplicative interactions between inputs may occur in dendrites of cortical cells (Mel, 1993), which could perhaps allow Equation 5 to be directly implemented in a recurrent circuit (cf. (=-=Bridle, 1990-=-)). However, there are several reasons why representing probabilities in the log domain could be beneficial to a neural system: 19 (26)s• Neurons have a limited dynamic range. A logarithmic transforma... |

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