Obtaining Arbitrary Prescribed Mean Field Dynamics for Recurrently Coupled Networks of Type-I Spiking Neurons with Analytically Determined Weights
A fundamental question in computational neuroscience is how to connect a network of spiking neurons to produce desired macroscopic or mean field dynamics. One possible approach is through the Neural Engineering Framework (NEF). The NEF approach requires quantities called decoders which are solved...
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2016-02-01
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| Series: | Frontiers in Computational Neuroscience |
| Subjects: | |
| Online Access: | http://journal.frontiersin.org/Journal/10.3389/fncom.2016.00015/full |
| _version_ | 1798046026041393152 |
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| author | Wilten eNicola Bryan eTripp Matthew eScott |
| author_facet | Wilten eNicola Bryan eTripp Matthew eScott |
| author_sort | Wilten eNicola |
| collection | DOAJ |
| description | A fundamental question in computational neuroscience is how to connect a network of spiking neurons to produce desired macroscopic or mean field dynamics. One possible approach is through the Neural Engineering Framework (NEF). The NEF approach requires quantities called decoders which are solved through an optimization problem requiring large matrix inversion. Here, we show how a decoder can be obtained analytically for type I and certain type II firing rates as a function of the heterogeneity of its associated neuron. These decoders generate approximants for functions that converge to the desired function in mean-squared error like 1/N, where N is the number of neurons in the network. We refer to these decoders as scale-invariant decoders due to their structure. These decoders generate weights for a network of neurons through the NEF formula for weights. These weights force the spiking network to have arbitrary and prescribed mean field dynamics. The weights generated with scale-invariant decoders all lie on low dimensional hypersurfaces asymptotically. We demonstrate the applicability of these scale-invariant decoders and weight surfaces by constructing networks of spiking theta neurons that replicate the dynamics of various well known dynamical systems such as the neural integrator, Van der Pol system and the Lorenz system. As these decoders are analytically determined and non-unique, the weights are also analytically determined and non-unique. We discuss the implications for measured weights of neuronal networks |
| first_indexed | 2024-04-11T23:30:49Z |
| format | Article |
| id | doaj.art-098ec477f0594e808f2a071035357ba3 |
| institution | Directory Open Access Journal |
| issn | 1662-5188 |
| language | English |
| last_indexed | 2024-04-11T23:30:49Z |
| publishDate | 2016-02-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Computational Neuroscience |
| spelling | doaj.art-098ec477f0594e808f2a071035357ba32022-12-22T03:57:07ZengFrontiers Media S.A.Frontiers in Computational Neuroscience1662-51882016-02-011010.3389/fncom.2016.00015178235Obtaining Arbitrary Prescribed Mean Field Dynamics for Recurrently Coupled Networks of Type-I Spiking Neurons with Analytically Determined WeightsWilten eNicola0Bryan eTripp1Matthew eScott2University of WaterlooUniversity of WaterlooUniversity of WaterlooA fundamental question in computational neuroscience is how to connect a network of spiking neurons to produce desired macroscopic or mean field dynamics. One possible approach is through the Neural Engineering Framework (NEF). The NEF approach requires quantities called decoders which are solved through an optimization problem requiring large matrix inversion. Here, we show how a decoder can be obtained analytically for type I and certain type II firing rates as a function of the heterogeneity of its associated neuron. These decoders generate approximants for functions that converge to the desired function in mean-squared error like 1/N, where N is the number of neurons in the network. We refer to these decoders as scale-invariant decoders due to their structure. These decoders generate weights for a network of neurons through the NEF formula for weights. These weights force the spiking network to have arbitrary and prescribed mean field dynamics. The weights generated with scale-invariant decoders all lie on low dimensional hypersurfaces asymptotically. We demonstrate the applicability of these scale-invariant decoders and weight surfaces by constructing networks of spiking theta neurons that replicate the dynamics of various well known dynamical systems such as the neural integrator, Van der Pol system and the Lorenz system. As these decoders are analytically determined and non-unique, the weights are also analytically determined and non-unique. We discuss the implications for measured weights of neuronal networkshttp://journal.frontiersin.org/Journal/10.3389/fncom.2016.00015/fullintegrate-and-fire neuronsmean field analysisneural engineering frameworkNeuronal heterogeneitysynaptic weightsRecurrently Coupled Networks |
| spellingShingle | Wilten eNicola Bryan eTripp Matthew eScott Obtaining Arbitrary Prescribed Mean Field Dynamics for Recurrently Coupled Networks of Type-I Spiking Neurons with Analytically Determined Weights Frontiers in Computational Neuroscience integrate-and-fire neurons mean field analysis neural engineering framework Neuronal heterogeneity synaptic weights Recurrently Coupled Networks |
| title | Obtaining Arbitrary Prescribed Mean Field Dynamics for Recurrently Coupled Networks of Type-I Spiking Neurons with Analytically Determined Weights |
| title_full | Obtaining Arbitrary Prescribed Mean Field Dynamics for Recurrently Coupled Networks of Type-I Spiking Neurons with Analytically Determined Weights |
| title_fullStr | Obtaining Arbitrary Prescribed Mean Field Dynamics for Recurrently Coupled Networks of Type-I Spiking Neurons with Analytically Determined Weights |
| title_full_unstemmed | Obtaining Arbitrary Prescribed Mean Field Dynamics for Recurrently Coupled Networks of Type-I Spiking Neurons with Analytically Determined Weights |
| title_short | Obtaining Arbitrary Prescribed Mean Field Dynamics for Recurrently Coupled Networks of Type-I Spiking Neurons with Analytically Determined Weights |
| title_sort | obtaining arbitrary prescribed mean field dynamics for recurrently coupled networks of type i spiking neurons with analytically determined weights |
| topic | integrate-and-fire neurons mean field analysis neural engineering framework Neuronal heterogeneity synaptic weights Recurrently Coupled Networks |
| url | http://journal.frontiersin.org/Journal/10.3389/fncom.2016.00015/full |
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