Many perceptual processes and neural computations, such as speech recognition, motor control and learning, depend on the ability to measure and mark the passage of time. However, the processes that make such temporal judgements possible are unknown. A number of different hypothetical mechanisms have been advanced, all of which depend on the known, temporally predictable evolution of a neural or psychological state, possibly through oscillations or the gradual decay of a memory trace. Alternatively, judgements of elapsed time might be based on observations of temporally structured, but stochastic processes. Such processes need not be specific to the sense of time; typical neural and sensory processes contain at least some statistical structure across a range of time scales. Here, we investigate the statistical properties of an estimator of elapsed time which is based on a simple family of stochastic process.

Many perceptual processes and neural computations, such as speech recognition, motor control and learning, depend on the ability to measure and mark the passage of time. However, the processes that make such temporal judgements possible are unknown. A number of different hypothetical mechanisms have been advanced, all of which depend on the known, temporally predictable evolution of a neural or psychological state, possibly through oscillations or the gradual decay of a memory trace. Alternatively, judgements of elapsed time might be based on observations of temporally structured, but stochastic processes. Such processes need not be specific to the sense of time; typical neural and sensory processes contain at least some statistical structure across a range of time scales. Here, we investigate the statistical properties of an estimator of elapsed time which is based on a simple family of stochastic process.

Many perceptual processes and neural computations, such as speech recognition, motor control and learning, depend on the ability to measure and mark the passage of time. However, the processes that make such temporal judgements possible are unknown. A number of different hypothetical mechanisms have been advanced, all of which depend on the known, temporally predictable evolution of a neural orpsychological state, possibly through oscillations or the gradual decay of a memory trace. Alternatively, judgements of elapsed time might be based on observations oftemporally structured, but stochastic processes. Such processes need not be specific to the sense of time; typical neural and sensory processes contain at least some statistical structure across a range of time scales. Here, we investigate the statistical properties of an estimator of elapsed time which is based on a simple family of stochastic process.

We study a population decoding paradigm in which the maximum likelihood inference is based on an unfaithful decoding model (UMLI). This is usually the case for neural population decoding because the encoding process of the brain is not exactly known, or because a simplified decoding model is preferred for saving computational cost. We consider an unfaithful decoding model which neglects the pairwise correlation between neuronal activities, and prove that UMLI is asymptotically efficient when the neuronal correlation is uniform or of limited-range. The performance of UMLI is compared with that of the maximum likelihood inference based on a faithful model and that of the center of mass decoding method. It turns out that UMLI has advantages of decreasing the computational complexity remarkablely and maintaining a high-level decoding accuracy at the same time. The effect of correlation on the decoding accuracy is also discussed.

We study a population decoding paradigm in which the maximum likelihood inferenceis based on an unfaithful decoding model (UMLI). This is usually the case for neural population decoding because the encoding process of the brain is not exactly known, or because a simplified decoding modelis preferred for saving computational cost. We consider an unfaithful decoding model which neglects the pairwise correlation between neuronal activities, and prove that UMLI is asymptotically efficient whenthe neuronal correlation is uniform or of limited-range. The performance of UMLI is compared with that of the maximum likelihood inference based on a faithful model and that of the center of mass decoding method.It turns out that UMLI has advantages of decreasing the computational complexity remarkablely and maintaining a high-level decoding accuracy at the same time. The effect of correlation on the decoding accuracy is also discussed.

Coarse codes are widely used throughout the brain to encode sensory and motor variables. Methods designed to interpret these codes, such as population vector analysis, are either inefficient, i.e., the variance of the estimate is much larger than the smallest possible variance, or biologically implausible, like maximum likelihood. Moreover, these methods attempt to compute a scalar or vector estimate of the encoded variable. Neurons are faced with a similar estimation problem. They must read out the responses of the presynaptic neurons, but, by contrast, they typically encode the variable with a further population code rather than as a scalar. We show how a nonlinear recurrent network can be used to perform these estimation in an optimal way while keeping the estimate in a coarse code format. This work suggests that lateral connections in the cortex may be involved in cleaning up uncorrelated noise among neurons representing similar variables.

Coarse codes are widely used throughout the brain to encode sensory and motor variables. Methods designed to interpret these codes, such as population vector analysis, are either inefficient, i.e., the variance of the estimate is much larger than the smallest possible variance, or biologically implausible, like maximum likelihood. Moreover, these methods attempt to compute a scalar or vector estimate of the encoded variable. Neurons are faced with a similar estimation problem. They must read out the responses of the presynaptic neurons, but, by contrast, they typically encode the variable with a further population code rather than as a scalar. We show how a nonlinear recurrent network can be used to perform these estimation in an optimal way while keeping the estimate in a coarse code format. This work suggests that lateral connections in the cortex may be involved in cleaning up uncorrelated noise among neurons representing similar variables.

Coarse codes are widely used throughout the brain to encode sensory andmotor variables. Methods designed to interpret these codes, such as population vector analysis, are either inefficient, i.e., the variance of the estimate is much larger than the smallest possible variance,or biologically implausible, like maximum likelihood. Moreover, these methods attempt to compute a scalar or vector estimate of the encoded variable. Neurons are faced with a similar estimationproblem. They must read out the responses of the presynaptic neurons, but, by contrast, they typically encode the variable with a further population code rather than as a scalar. We show how a nonlinear recurrent network can be used to perform theseestimation in an optimal way while keeping the estimate in a coarse code format. This work suggests that lateral connections inthe cortex may be involved in cleaning up uncorrelated noise among neurons representing similar variables.