Optimal computation with attractor networks

Latham, Peter E.; Pouget, Alexandre

doi:10.1016/j.jphysparis.2004.01.022

Cited by 32 publications

(39 citation statements)

References 21 publications

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“…However, it is much less clear whether any continuous attractor network could match the performance of an ideal estimator in tracking its own instantaneous attractor state. It has been shown previously that continuous attractor networks, when evolving deterministically (noise free), can estimate the location of a bump input from a sample of spikes in a Bayes-optimal way (30). The memory network faces a more difficult task because it needs to continuously estimate a state that is drifting, and its dynamics as a readout network are noisy.…”

Section: Resultsmentioning

confidence: 99%

Fundamental limits on persistent activity in networks of noisy neurons

Burak

Fiete

2012

Proc. Natl. Acad. Sci. U.S.A.

131

208

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Neural noise limits the fidelity of representations in the brain. This limitation has been extensively analyzed for sensory coding. However, in short-term memory and integrator networks, where noise accumulates and can play an even more prominent role, much less is known about how neural noise interacts with neural and network parameters to determine the accuracy of the computation. Here we analytically derive how the stored memory in continuous attractor networks of probabilistically spiking neurons will degrade over time through diffusion. By combining statistical and dynamical approaches, we establish a fundamental limit on the network’s ability to maintain a persistent state: The noise-induced drift of the memory state over time within the network is strictly lower-bounded by the accuracy of estimation of the network’s instantaneous memory state by an ideal external observer. This result takes the form of an information-diffusion inequality. We derive some unexpected consequences: Despite the persistence time of short-term memory networks, it does not pay to accumulate spikes for longer than the cellular time-constant to read out their contents. For certain neural transfer functions, the conditions for optimal sensory coding coincide with those for optimal storage, implying that short-term memory may be co-localized with sensory representation.

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Section: Resultsmentioning

confidence: 99%

Fundamental limits on persistent activity in networks of noisy neurons

Burak

Fiete

2012

Proc. Natl. Acad. Sci. U.S.A.

131

208

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“…Recent research in computational neuroscience points out the importance of continuous attractors [63,35]. Consider [22] a nonlinear neural network model…”

Section: ✷ Example 23mentioning

confidence: 99%

On partial contraction analysis for coupled nonlinear oscillators

2004

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We describe a simple but general method to analyze networks of coupled identical nonlinear oscillators, and study applications to fast synchronization, locomotion, and schooling. Specifically, we use nonlinear contraction theory to derive exact and global (rather than linearized) results on synchronization, anti-synchronization and oscillator-death. The method can be applied to coupled networks of various structures and arbitrary size. For oscillators with positive-definite diffusion coupling, it can be shown that synchronization always occur globally for strong enough coupling strengths, and an explicit upper bound on the corresponding threshold can be computed through eigenvalue analysis. The discussion also extends to the case when network structure varies abruptly and asynchronously, as in "flocks" of oscillators or dynamic elements.

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“…This parameter controls the width of the weight pattern, and as a result, the width of the pattern of activity in the basis function layer. The optimal value can be inferred from our previous analytical work (Deneve et al, 2001;Latham et al, 2003). In both object and arm tracking, we obtained optimal performance for K w equal to 3.…”

Section: Mathematical Formalizationmentioning

confidence: 71%

“…As long as sensory gains are adjusted accordingly and the condition for optimality derived by Deneve et al (1999) and Latham et al (2003) is verified, the network approximates the performance of a Kalman filter.…”

Section: Mathematical Formalizationmentioning

confidence: 92%

“…At this point, the activity in the basis function layer takes the form of a smooth hill of activity. If the network meets the condition derived by Latham et al (2003), the position of this hill corresponds to the maximum-likelihood estimate of the sensory states encoded in the initial noisy sensory inputs. The condition derived by Latham et al (2003) can be satisfied by tuning K w , the width of the lateral weights.…”

Section: Mathematical Formalizationmentioning

confidence: 99%

See 1 more Smart Citation

Optimal Sensorimotor Integration in Recurrent Cortical Networks: A Neural Implementation of Kalman Filters

Denève

Duhamel²,

Pouget³

2007

J. Neurosci.

117

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Several behavioral experiments suggest that the nervous system uses an internal model of the dynamics of the body to implement a close approximation to a Kalman filter. This filter can be used to perform a variety of tasks nearly optimally, such as predicting the sensory consequence of motor action, integrating sensory and body posture signals, and computing motor commands. We propose that the neural implementation of this Kalman filter involves recurrent basis function networks with attractor dynamics, a kind of architecture that can be readily mapped onto cortical circuits. In such networks, the tuning curves to variables such as arm velocity are remarkably noninvariant in the sense that the amplitude and width of the tuning curves of a given neuron can vary greatly depending on other variables such as the position of the arm or the reliability of the sensory feedback. This property could explain some puzzling properties of tuning curves in the motor and premotor cortex, and it leads to several new predictions.

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Optimal computation with attractor networks

Cited by 32 publications

References 21 publications

Fundamental limits on persistent activity in networks of noisy neurons

Fundamental limits on persistent activity in networks of noisy neurons

On partial contraction analysis for coupled nonlinear oscillators

Optimal Sensorimotor Integration in Recurrent Cortical Networks: A Neural Implementation of Kalman Filters

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