Spatiotemporal Computations of an Excitable and Plastic Brain: Neuronal Plasticity Leads to Noise-Robust and Noise-Constructive Computations
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{"title"=>"Spatiotemporal Computations of an Excitable and Plastic Brain: Neuronal Plasticity Leads to Noise-Robust and Noise-Constructive Computations", "type"=>"journal", "authors"=>[{"first_name"=>"Hazem", "last_name"=>"Toutounji", "scopus_author_id"=>"24529246900"}, {"first_name"=>"Gordon", "last_name"=>"Pipa", "scopus_author_id"=>"7801435498"}], "year"=>2014, "source"=>"PLoS Computational Biology", "identifiers"=>{"pmid"=>"24651447", "doi"=>"10.1371/journal.pcbi.1003512", "sgr"=>"84897439146", "scopus"=>"2-s2.0-84897439146", "issn"=>"15537358", "pui"=>"372738389"}, "id"=>"809a55cd-7fc9-318e-b385-be337a4af9b3", "abstract"=>"Author SummaryThe world is not perceived as a chain of segmented sensory still lifes. Instead, it appears that the brain is capable of integrating the temporal dependencies of the incoming sensory stream with the spatial aspects of that input. It then transfers the resulting whole in a useful manner, in order to reach a coherent and causally sound image of our physical surroundings, and to act within it. These spatiotemporal computations are made possible through a cluster of local and coexisting adaptation mechanisms known collectively as neuronal plasticity. While this role is widely known and supported by experimental evidence, no unifying theory of how the brain, through the interaction of plasticity mechanisms, gets to represent spatiotemporal computations in its spatiotemporal activity. In this paper, we aim at such a theory. We develop a rigorous mathematical formalism of spatiotemporal representations within the input-driven dynamics of cortical networks. We demonstrate that the interaction of two of the most common plasticity mechanisms, intrinsic and synaptic plasticity, leads to representations that allow for spatiotemporal computations. We also show that these representations are structured to tolerate noise and to even benefit from it.", "link"=>"http://www.mendeley.com/research/spatiotemporal-computations-excitable-plastic-brain-neuronal-plasticity-leads-noiserobust-noiseconst", "reader_count"=>66, "reader_count_by_academic_status"=>{"Professor > Associate Professor"=>5, "Librarian"=>1, "Researcher"=>17, "Student > Doctoral Student"=>6, "Student > Ph. D. Student"=>17, "Student > Master"=>10, "Student > Bachelor"=>4, "Professor"=>6}, "reader_count_by_user_role"=>{"Professor > Associate Professor"=>5, "Librarian"=>1, "Researcher"=>17, "Student > Doctoral Student"=>6, "Student > Ph. D. Student"=>17, "Student > Master"=>10, "Student > Bachelor"=>4, "Professor"=>6}, "reader_count_by_subject_area"=>{"Engineering"=>2, "Unspecified"=>1, "Mathematics"=>2, "Agricultural and Biological Sciences"=>20, "Medicine and Dentistry"=>3, "Neuroscience"=>10, "Arts and Humanities"=>1, "Physics and Astronomy"=>8, "Psychology"=>2, "Computer Science"=>16, "Linguistics"=>1}, "reader_count_by_subdiscipline"=>{"Engineering"=>{"Engineering"=>2}, "Medicine and Dentistry"=>{"Medicine and Dentistry"=>3}, "Neuroscience"=>{"Neuroscience"=>10}, "Physics and Astronomy"=>{"Physics and Astronomy"=>8}, "Psychology"=>{"Psychology"=>2}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>20}, "Computer Science"=>{"Computer Science"=>16}, "Linguistics"=>{"Linguistics"=>1}, "Mathematics"=>{"Mathematics"=>2}, "Unspecified"=>{"Unspecified"=>1}, "Arts and Humanities"=>{"Arts and Humanities"=>1}}, "reader_count_by_country"=>{"Austria"=>1, "Netherlands"=>1, "Poland"=>1, "United Kingdom"=>1, "Chile"=>1, "Switzerland"=>1, "Germany"=>8, "Spain"=>1}, "group_count"=>0}

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/1427658"], "description"=>"<p>(A) The dynamics of a recurrent network that is trained by homeostatic and synaptic plasticity and driven by a Markovian input. Each layer corresponds to one input. The layer illustrates a two-dimensional projection of the phase space of the autonomous (semi-)dynamical system associated with that input. A layer that corresponds to the spontaneous activity (SA) is added for completeness. Due to the interaction of synaptic and homeostatic plasticity, each of these (semi-)dynamical systems has two dynamic regimes: an input-insensitive dynamic regime that is shared by all the layers and that captures the temporal structure of the input, and an input-sensitive dynamic regime that contains a single periodic attractor. The input-sensitive attractor depends on the layer and is close to one of the vertexes of the input-insensitive attractor. The network is excited by the exemplary input sequence . The red cross refers to the initial conditions that are chosen within the input-sensitive dynamics. Given the input sequence, the network dynamics follows the meta-transient that is illustrated by the arrows between the different layers. For instance, when the network is excited by the input <i>B</i>, the network activity approaches the <i>B</i>-attractor within the corresponding layer. When <i>C</i> follows, a bifurcation occurs, where the <i>B</i>-attractor becomes unstable and the <i>C</i>-attractor becomes stable. The meta-transient approaches the <i>C</i>-attractor from the direction of the unstable <i>B</i>-attractor. When <i>C</i> is preceded by the less common input <i>A</i>, the <i>C</i>-attractor is approached differently, such that the distance to it is bigger than in the case of the most common transition . (B) Noise-robust computations are a result of the interaction between synaptic and homeostatic intrinsic plasticity. Synaptic plasticity leads to high separability and intrinsic plasticity to redundancy. These effects lead to a neural code that allows a higher margin of noise and alternative representations of computations, thus facilitating noise-robustness.</p>", "links"=>[], "tags"=>["neuroscience", "computational neuroscience", "Circuit models", "Learning and memory", "Neural homeostasis", "neural networks", "Nonlinear dynamics", "driven", "networks", "endowed", "synaptic", "homeostatic", "emergence", "noise-robust", "spatiotemporal"], "article_id"=>968045, "categories"=>["Biological Sciences", "Mathematics"], "users"=>["Hazem Toutounji", "Gordon Pipa"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1003512.g008", "stats"=>{"downloads"=>0, "page_views"=>9, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Schematics_of_the_driven_dynamics_of_networks_endowed_by_synaptic_and_homeostatic_plasticity_and_the_emergence_of_noise_robust_spatiotemporal_computations_/968045", "title"=>"Schematics of the driven dynamics of networks endowed by synaptic and homeostatic plasticity, and the emergence of noise-robust spatiotemporal computations.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-03-20 02:43:45"}
  • {"files"=>["https://ndownloader.figshare.com/files/1427643"], "description"=>"<p>(A) An exemplary recurrent neural network of 12 neurons. The network state has a 4-Winner-Take-All (4WTA) nonlinear dynamics, where the 4 neurons with the highest membrane potential fire and the rest are silent. The membrane potential is the sum of the recurrent afferents and the external drive . It is also depolarized (hyperpolarized) with decreasing (increasing) excitability threshold . The recurrent network can also be subject to <i>noise</i>, while reserving the 4WTA dynamics: when a neuron fails to spike due to noise, another fires instead. (B) The recurrent network is adapted by two plasticity mechanisms. The excitability threshold is modulated by <b><i>i</i></b><i>ntrinsic </i><b><i>p</i></b><i>lasticity</i> (IP), the recurrent afferents by <b><i>s</i></b><i>pike-</i><b><i>t</i></b><i>iming-</i><b><i>d</i></b><i>ependent synaptic </i><b><i>p</i></b><i>lasticity</i> (STDP). (C) The external drive consists of discrete symbols that follow a certain stochastic dynamics, and each projects to a corresponding <b><i>r</i></b><i>eceptive </i><b><i>f</i></b><i>ield</i> (RF). The exemplary drive is a 3-symbols Markov chain that allows a probability for <i>noisy</i> transitions, i.e. . (D) Linear functions of the network state parametrized by output weights fitted to (possibly nonlinear) target functions of sequences of the external drive. (E) Nonlinear information-theoretic quantities are measured: network state entropy and the mutual information of the network state and input sequence . (F) Analysis of the appearance and disappearance of attractors due to the external drive within the network as an input-driven dynamical system.</p>", "links"=>[], "tags"=>["neuroscience", "computational neuroscience", "Circuit models", "Learning and memory", "Neural homeostasis", "neural networks", "Nonlinear dynamics", "recurrent", "methods", "analyzing", "computational"], "article_id"=>968030, "categories"=>["Biological Sciences", "Mathematics"], "users"=>["Hazem Toutounji", "Gordon Pipa"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1003512.g001", "stats"=>{"downloads"=>1, "page_views"=>14, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Overview_of_the_recurrent_network_model_and_the_methods_for_analyzing_its_computational_capabilities_/968030", "title"=>"Overview of the recurrent network model and the methods for analyzing its computational capabilities.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-03-20 02:43:45"}
  • {"files"=>["https://ndownloader.figshare.com/files/1427651"], "description"=>"<p>Bootstrapped median relative change from the noiseless performance of 100 networks trained with both STDP and IP on (A) the memory task RAND x 4, (B) the prediction task Markov-85, and (C) the nonlinear task Parity-3. High perturbation of is applied at the end of the plasticity phase. Error bars correspond to the and the percentiles. Noise level is the probability of a bit flip in the network state, that is, the probability of one of the spiking neurons at time step to become silent, while a silent neuron fires instead. The shaded area indicates the ratio of noisy spikes which is measured in comparison to the noiseless SIP-RNs. The green line indicates the median and the orange lines the and the percentiles of the noisy spikes ratio.</p>", "links"=>[], "tags"=>["neuroscience", "computational neuroscience", "Circuit models", "Learning and memory", "Neural homeostasis", "neural networks", "Nonlinear dynamics", "achieved", "synaptic", "intrinsic"], "article_id"=>968038, "categories"=>["Biological Sciences", "Mathematics"], "users"=>["Hazem Toutounji", "Gordon Pipa"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1003512.g006", "stats"=>{"downloads"=>1, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Noise_robustness_is_achieved_through_the_interaction_of_synaptic_and_intrinsic_plasticity_/968038", "title"=>"Noise-robustness is achieved through the interaction of synaptic and intrinsic plasticity.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-03-20 02:43:45"}
  • {"files"=>["https://ndownloader.figshare.com/files/1427647"], "description"=>"<p>100 networks are trained by STDP and IP simultaneously on (A) the memory task RAND x 4, (B) the prediction task Markov-85, and (C) the nonlinear task Parity-3 with increasing perturbation level: (yellow), (orange), and (red). Error bars indicate standard error of the mean. The red line marks chance level. The -axis shows the input time-lag. Negative time-lags indicate the past, and positive ones, the future. (D) Network state entropy and (E) the mutual information with the three most recent RAND x 4 inputs at the end of the plasticity phase for different perturbation levels. Values are averaged over 50 networks and estimated from 5000 samples for each network. Error bars indicate standard error of the mean.</p>", "links"=>[], "tags"=>["neuroscience", "computational neuroscience", "Circuit models", "Learning and memory", "Neural homeostasis", "neural networks", "Nonlinear dynamics"], "article_id"=>968034, "categories"=>["Biological Sciences", "Mathematics"], "users"=>["Hazem Toutounji", "Gordon Pipa"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1003512.g004", "stats"=>{"downloads"=>1, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Post_plasticity_perturbation_/968034", "title"=>"Post-plasticity perturbation.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-03-20 02:43:45"}
  • {"files"=>["https://ndownloader.figshare.com/files/1427660", "https://ndownloader.figshare.com/files/1427661", "https://ndownloader.figshare.com/files/1427662", "https://ndownloader.figshare.com/files/1427663", "https://ndownloader.figshare.com/files/1427664", "https://ndownloader.figshare.com/files/1427665", "https://ndownloader.figshare.com/files/1427666"], "description"=>"<div><p>It is a long-established fact that neuronal plasticity occupies the central role in generating neural function and computation. Nevertheless, no unifying account exists of how neurons in a recurrent cortical network learn to compute on temporally and spatially extended stimuli. However, these stimuli constitute the norm, rather than the exception, of the brain's input. Here, we introduce a geometric theory of learning spatiotemporal computations through neuronal plasticity. To that end, we rigorously formulate the problem of neural representations as a relation in space between stimulus-induced neural activity and the asymptotic dynamics of excitable cortical networks. Backed up by computer simulations and numerical analysis, we show that two canonical and widely spread forms of neuronal plasticity, that is, spike-timing-dependent synaptic plasticity and intrinsic plasticity, are both necessary for creating neural representations, such that these computations become realizable. Interestingly, the effects of these forms of plasticity on the emerging neural code relate to properties necessary for both combating and utilizing noise. The neural dynamics also exhibits features of the most likely stimulus in the network's spontaneous activity. These properties of the spatiotemporal neural code resulting from plasticity, having their grounding in nature, further consolidate the biological relevance of our findings.</p></div>", "links"=>[], "tags"=>["neuroscience", "computational neuroscience", "Circuit models", "Learning and memory", "Neural homeostasis", "neural networks", "Nonlinear dynamics", "computations", "excitable", "neuronal", "plasticity", "leads", "noise-robust", "noise-constructive"], "article_id"=>968047, "categories"=>["Biological Sciences", "Mathematics"], "users"=>["Hazem Toutounji", "Gordon Pipa"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1003512.s001", "https://dx.doi.org/10.1371/journal.pcbi.1003512.s002", "https://dx.doi.org/10.1371/journal.pcbi.1003512.s003", "https://dx.doi.org/10.1371/journal.pcbi.1003512.s004", "https://dx.doi.org/10.1371/journal.pcbi.1003512.s005", "https://dx.doi.org/10.1371/journal.pcbi.1003512.s006", "https://dx.doi.org/10.1371/journal.pcbi.1003512.s007"], "stats"=>{"downloads"=>1, "page_views"=>19, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Spatiotemporal_Computations_of_an_Excitable_and_Plastic_Brain_Neuronal_Plasticity_Leads_to_Noise_Robust_and_Noise_Constructive_Computations_/968047", "title"=>"Spatiotemporal Computations of an Excitable and Plastic Brain: Neuronal Plasticity Leads to Noise-Robust and Noise-Constructive Computations", "pos_in_sequence"=>0, "defined_type"=>4, "published_date"=>"2014-03-20 02:43:45"}
  • {"files"=>["https://ndownloader.figshare.com/files/1427656"], "description"=>"<p>Average classification performance of 100 networks trained with both STDP and IP on (A) the memory task RAND x 4, (B) the prediction task Markov-85, and (C) the nonlinear task Parity-3 for increasing levels of noise and no perturbation at the end of the plasticity phase (). (D) Network state entropy and (E) the mutual information with the three most recent RAND x 4 inputs at the end of the plasticity phase for different levels of noise. Values are averaged over 50 networks and estimated from 5000 samples for each network. (A–E) Noise levels are applied during the plasticity, training, and testing phases. They indicate the probability of a bit flip in the network state, that is, the probability of one of the <i>k</i> spiking neurons at time step to become silent, while silent neuron to fire instead. . Error bars indicate standard error of the mean.</p>", "links"=>[], "tags"=>["neuroscience", "computational neuroscience", "Circuit models", "Learning and memory", "Neural homeostasis", "neural networks", "Nonlinear dynamics", "rendered", "constructive", "synaptic", "intrinsic", "plasticity"], "article_id"=>968043, "categories"=>["Biological Sciences", "Mathematics"], "users"=>["Hazem Toutounji", "Gordon Pipa"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1003512.g007", "stats"=>{"downloads"=>0, "page_views"=>14, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Noise_at_certain_levels_is_rendered_constructive_when_synaptic_and_intrinsic_plasticity_interact_/968043", "title"=>"Noise at certain levels is rendered constructive when synaptic and intrinsic plasticity interact.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-03-20 02:43:45"}
  • {"files"=>["https://ndownloader.figshare.com/files/1427650"], "description"=>"<p>The three dimensions correspond to the first three principal components (PCs) of the network activity. (A) Highly-overlapping order-1 volumes of representation of an IP-RN. (B) Input-insensitive global attractor of a SP-RN that corresponds to a minimal code. (C) With no perturbed (), a SIP-RN dynamics also converges to an input-insensitive attractor and exhibits a minimal code. (D) Approximate visualization of order-1 volumes of representation of a SIP-RN. The approximation uses the means and the standard deviations of the corresponding coordinates of the network activity in the principal components space as the center and semi-axes lengths of ellipsoids. Arrows correspond to the transitions from one input symbol to the other. Their thickness symbolizes the probability of a transition, which reflects the Markov-85 transition probability. The collection of volumes of representation and the arrows show the perturbation set within which the nonautonomous attractor resides. (E) Order-2 volumes of representation of a SIP-RN also approximated using the mean and standard deviations of coordinates. Order-2 volumes are more exact approximations to the order-1 representations according to the volumes' inclusion property. The correspondence is clarified by using similar color coding. (F) Autonomous periodic attractors of a SIP-RN, each belonging to one of the autonomous semi-dynamical systems associated with one Markov-85 input. For clarity, no arrows are drawn between the vertexes of an attractor.</p>", "links"=>[], "tags"=>["neuroscience", "computational neuroscience", "Circuit models", "Learning and memory", "Neural homeostasis", "neural networks", "Nonlinear dynamics", "networks", "representations"], "article_id"=>968037, "categories"=>["Biological Sciences", "Mathematics"], "users"=>["Hazem Toutounji", "Gordon Pipa"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1003512.g005", "stats"=>{"downloads"=>0, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Plasticity_effects_on_networks_dynamics_and_input_representations_under_the_prediction_task_input_/968037", "title"=>"Plasticity effects on networks dynamics and input representations under the prediction task input.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-03-20 02:43:45"}
  • {"files"=>["https://ndownloader.figshare.com/files/1427646"], "description"=>"<p>(A) Network state entropy and (B) the mutual information with the three most recent RAND x 4 inputs as they develop through the plasticity phase for SP-RNs (green), IP-RNs (blue), and SIP-RNs (orange). Mutual information for IP-RNs is estimated from 500000 time steps, and is averaged over 5 networks only. Other values are averaged over 50 networks and estimated from 100000 samples for each network. Error bars indicate standard error of the mean.</p>", "links"=>[], "tags"=>["neuroscience", "computational neuroscience", "Circuit models", "Learning and memory", "Neural homeostasis", "neural networks", "Nonlinear dynamics", "entropy"], "article_id"=>968033, "categories"=>["Biological Sciences", "Mathematics"], "users"=>["Hazem Toutounji", "Gordon Pipa"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1003512.g003", "stats"=>{"downloads"=>0, "page_views"=>12, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Network_state_entropy_and_the_mutual_information_with_input_/968033", "title"=>"Network state entropy and the mutual information with input.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-03-20 02:43:45"}
  • {"files"=>["https://ndownloader.figshare.com/files/1427644"], "description"=>"<p>100 networks are trained by STDP and IP simultaneously (orange), IP alone (blue), STDP alone (green), or are nonplastic (gray). Optimal linear classifiers are then trained to perform (A) the memory task RAND x 4, (B) the prediction task Markov-85, and (C) the nonlinear task Parity-3. Nonplastic networks have their weights trained by STDP and then randomly shuffled, so that they have the same weight and threshold distributions as SP-RNs. However, due to the shuffling, their weight matrices carry no structure. Error bars indicate standard error of the mean. The red line marks chance level. The <i>x</i>-axis shows the input time-lag. Negative time-lags indicate the past, and positive ones, the future.</p>", "links"=>[], "tags"=>["neuroscience", "computational neuroscience", "Circuit models", "Learning and memory", "Neural homeostasis", "neural networks", "Nonlinear dynamics", "classification"], "article_id"=>968031, "categories"=>["Biological Sciences", "Mathematics"], "users"=>["Hazem Toutounji", "Gordon Pipa"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1003512.g002", "stats"=>{"downloads"=>0, "page_views"=>2, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Average_classification_performance_/968031", "title"=>"Average classification performance.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-03-20 02:43:45"}

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Relative Metric

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