Pyramidal neuron as two-layer neural network. Poirazi, P., Brannon, T., & Mel, B. W Neuron, 37(6):989-99, 2003. abstract bibtex The pyramidal neuron is the principal cell type in the mammalian forebrain, but its function remains poorly understood. Using a detailed compartmental model of a hippocampal CA1 pyramidal cell, we recorded responses to complex stimuli consisting of dozens of high-frequency activated synapses distributed throughout the apical dendrites. We found the cell's firing rate could be predicted by a simple formula that maps the physical components of the cell onto those of an abstract two-layer "neural network." In the first layer, synaptic inputs drive independent sigmoidal subunits corresponding to the cell's several dozen long, thin terminal dendrites. The subunit outputs are then summed within the main trunk and cell body prior to final thresholding. We conclude that insofar as the neural code is mediated by average firing rate, a two-layer neural network may provide a useful abstraction for the computing function of the individual pyramidal neuron.
@Article{Poirazi2003a,
author = {Panayiota Poirazi and Terrence Brannon and Bartlett W Mel},
journal = {Neuron},
title = {Pyramidal neuron as two-layer neural network.},
year = {2003},
number = {6},
pages = {989-99},
volume = {37},
abstract = {The pyramidal neuron is the principal cell type in the mammalian forebrain,
but its function remains poorly understood. Using a detailed compartmental
model of a hippocampal CA1 pyramidal cell, we recorded responses
to complex stimuli consisting of dozens of high-frequency activated
synapses distributed throughout the apical dendrites. We found the
cell's firing rate could be predicted by a simple formula that maps
the physical components of the cell onto those of an abstract two-layer
"neural network." In the first layer, synaptic inputs drive independent
sigmoidal subunits corresponding to the cell's several dozen long,
thin terminal dendrites. The subunit outputs are then summed within
the main trunk and cell body prior to final thresholding. We conclude
that insofar as the neural code is mediated by average firing rate,
a two-layer neural network may provide a useful abstraction for the
computing function of the individual pyramidal neuron.},
keywords = {Computing Methodologies, Human, Language, Learning, Mental Processes, Models, Theoretical, Stochastic Processes, Support, U.S. Gov't, Non-P.H.S., Cognition, Linguistics, Neural Networks (Computer), Practice (Psychology), Non-U.S. Gov't, Memory, Psychological, Task Performance and Analysis, Time Factors, Visual Perception, Adult, Attention, Discrimination Learning, Female, Male, Short-Term, Mental Recall, Orientation, Pattern Recognition, Visual, Perceptual Masking, Reading, Concept Formation, Form Perception, Animals, Corpus Striatum, Shrews, P.H.S., Visual Cortex, Visual Pathways, Acoustic Stimulation, Auditory Cortex, Auditory Perception, Cochlea, Ear, Gerbillinae, Glycine, Hearing, Neurons, Space Perception, Strychnine, Adolescent, Decision Making, Reaction Time, Astrocytoma, Brain Mapping, Brain Neoplasms, Cerebral Cortex, Electric Stimulation, Electrophysiology, Epilepsy, Temporal Lobe, Evoked Potentials, Frontal Lobe, Noise, Parietal Lobe, Scalp, Child, Language Development, Psycholinguistics, Brain, Perception, Speech, Vocalization, Animal, Discrimination (Psychology), Hippocampus, Rats, Calcium, Chelating Agents, Excitatory Postsynaptic Potentials, Glutamic Acid, Guanosine Diphosphate, In Vitro, Neuronal Plasticity, Pyramidal Cells, Receptors, AMPA, Metabotropic Glutamate, N-Methyl-D-Aspartate, Somatosensory Cortex, Synapses, Synaptic Transmission, Thionucleotides, Action Potentials, Calcium Channels, L-Type, Electric Conductivity, Entorhinal Cortex, Neurological, Long-Evans, Infant, Mathematics, Statistics, Probability Learning, Problem Solving, Psychophysics, Association Learning, Child Psychology, Habituation (Psychophysiology), Probability Theory, Analysis of Variance, Semantics, Symbolism, Behavior, Eye Movements, Macaca mulatta, Prefrontal Cortex, Cats, Dogs, Haplorhini, Photic Stimulation, Electroencephalography, Nervous System Physiology, Darkness, Grasshoppers, Light, Membrane Potentials, Neural Inhibition, Afferent, Picrotoxin, Vision, Deoxyglucose, Injections, Microspheres, Neural Pathways, Rhodamines, Choice Behavior, Speech Perception, Verbal Learning, Dominance, Cerebral, Fixation, Ocular, Language Tests, Random Allocation, Comparative Study, Saguinus, Sound Spectrography, Species Specificity, Audiometry, Auditory Threshold, Calibration, Data Interpretation, Statistical, Anesthesia, General, Electrodes, Implanted, Pitch Perception, Sound Localization, Paired-Associate Learning, Serial Learning, Auditory, Age Factors, Motion Perception, Brain Injuries, Computer Simulation, Blindness, Psychomotor Performance, Color Perception, Signal Detection (Psychology), Judgment, ROC Curve, Regression Analysis, Music, Probability, Arm, Cerebrovascular Disorders, Hemiplegia, Movement, Muscle, Skeletal, Myoclonus, Robotics, Magnetoencephalography, Phonetics, Software, Speech Production Measurement, Epilepsies, Partial, Laterality, Stereotaxic Techniques, Germany, Speech Acoustics, Verbal Behavior, Child Development, Instinct, Brain Stem, Coma, Diagnosis, Differential, Hearing Disorders, Hearing Loss, Central, Neuroma, Acoustic, Dendrites, Down-Regulation, Patch-Clamp Techniques, Wistar, Up-Regulation, Aged, Aphasia, Middle Aged, Cones (Retina), Primates, Retina, Retinal Ganglion Cells, Tympanic Membrane, Cell Communication, Extremities, Biological, Motor Activity, Rana catesbeiana, Spinal Cord, Central Nervous System, Motion, Motor Cortex, Intelligence, Macaca fascicularis, Adoption, Critical Period (Psychology), France, Korea, Magnetic Resonance Imaging, Multilingualism, Auditory Pathways, Cochlear Nerve, Loudness Perception, Neural Conduction, Sensory Thresholds, Sound, Language Disorders, Preschool, Generalization (Psychology), Vocabulary, Biophysics, Nerve Net, Potassium Channels, Sodium Channels, 12670427},
}
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We found the cell's firing rate could be predicted by a simple formula that maps the physical components of the cell onto those of an abstract two-layer \"neural network.\" In the first layer, synaptic inputs drive independent sigmoidal subunits corresponding to the cell's several dozen long, thin terminal dendrites. The subunit outputs are then summed within the main trunk and cell body prior to final thresholding. We conclude that insofar as the neural code is mediated by average firing rate, a two-layer neural network may provide a useful abstraction for the computing function of the individual pyramidal neuron.","keywords":"Computing Methodologies, Human, Language, Learning, Mental Processes, Models, Theoretical, Stochastic Processes, Support, U.S. Gov't, Non-P.H.S., Cognition, Linguistics, Neural Networks (Computer), Practice (Psychology), Non-U.S. Gov't, Memory, Psychological, Task Performance and Analysis, Time Factors, Visual Perception, Adult, Attention, Discrimination Learning, Female, Male, Short-Term, Mental Recall, Orientation, Pattern Recognition, Visual, Perceptual Masking, Reading, Concept Formation, Form Perception, Animals, Corpus Striatum, Shrews, P.H.S., Visual Cortex, Visual Pathways, Acoustic Stimulation, Auditory Cortex, Auditory Perception, Cochlea, Ear, Gerbillinae, Glycine, Hearing, Neurons, Space Perception, Strychnine, Adolescent, Decision Making, Reaction Time, Astrocytoma, Brain Mapping, Brain Neoplasms, Cerebral Cortex, Electric Stimulation, Electrophysiology, Epilepsy, Temporal Lobe, Evoked Potentials, Frontal Lobe, Noise, Parietal Lobe, Scalp, Child, Language Development, Psycholinguistics, Brain, Perception, Speech, Vocalization, Animal, Discrimination (Psychology), Hippocampus, Rats, Calcium, Chelating Agents, Excitatory Postsynaptic Potentials, Glutamic Acid, Guanosine Diphosphate, In Vitro, Neuronal Plasticity, Pyramidal Cells, Receptors, AMPA, Metabotropic Glutamate, N-Methyl-D-Aspartate, Somatosensory Cortex, Synapses, Synaptic Transmission, Thionucleotides, Action Potentials, Calcium Channels, L-Type, Electric Conductivity, Entorhinal Cortex, Neurological, Long-Evans, Infant, Mathematics, Statistics, Probability Learning, Problem Solving, Psychophysics, Association Learning, Child Psychology, Habituation (Psychophysiology), Probability Theory, Analysis of Variance, Semantics, Symbolism, Behavior, Eye Movements, Macaca mulatta, Prefrontal Cortex, Cats, Dogs, Haplorhini, Photic Stimulation, Electroencephalography, Nervous System Physiology, Darkness, Grasshoppers, Light, Membrane Potentials, Neural Inhibition, Afferent, Picrotoxin, Vision, Deoxyglucose, Injections, Microspheres, Neural Pathways, Rhodamines, Choice Behavior, Speech Perception, Verbal Learning, Dominance, Cerebral, Fixation, Ocular, Language Tests, Random Allocation, Comparative Study, Saguinus, Sound Spectrography, Species Specificity, Audiometry, Auditory Threshold, Calibration, Data Interpretation, Statistical, Anesthesia, General, Electrodes, Implanted, Pitch Perception, Sound Localization, Paired-Associate Learning, Serial Learning, Auditory, Age Factors, Motion Perception, Brain Injuries, Computer Simulation, Blindness, Psychomotor Performance, Color Perception, Signal Detection (Psychology), Judgment, ROC Curve, Regression Analysis, Music, Probability, Arm, Cerebrovascular Disorders, Hemiplegia, Movement, Muscle, Skeletal, Myoclonus, Robotics, Magnetoencephalography, Phonetics, Software, Speech Production Measurement, Epilepsies, Partial, Laterality, Stereotaxic Techniques, Germany, Speech Acoustics, Verbal Behavior, Child Development, Instinct, Brain Stem, Coma, Diagnosis, Differential, Hearing Disorders, Hearing Loss, Central, Neuroma, Acoustic, Dendrites, Down-Regulation, Patch-Clamp Techniques, Wistar, Up-Regulation, Aged, Aphasia, Middle Aged, Cones (Retina), Primates, Retina, Retinal Ganglion Cells, Tympanic Membrane, Cell Communication, Extremities, Biological, Motor Activity, Rana catesbeiana, Spinal Cord, Central Nervous System, Motion, Motor Cortex, Intelligence, Macaca fascicularis, Adoption, Critical Period (Psychology), France, Korea, Magnetic Resonance Imaging, Multilingualism, Auditory Pathways, Cochlear Nerve, Loudness Perception, Neural Conduction, Sensory Thresholds, Sound, Language Disorders, Preschool, Generalization (Psychology), Vocabulary, Biophysics, Nerve Net, Potassium Channels, Sodium Channels, 12670427","bibtex":"@Article{Poirazi2003a,\n author = {Panayiota Poirazi and Terrence Brannon and Bartlett W Mel},\n journal = {Neuron},\n title = {Pyramidal neuron as two-layer neural network.},\n year = {2003},\n number = {6},\n pages = {989-99},\n volume = {37},\n abstract = {The pyramidal neuron is the principal cell type in the mammalian forebrain,\n\tbut its function remains poorly understood. Using a detailed compartmental\n\tmodel of a hippocampal CA1 pyramidal cell, we recorded responses\n\tto complex stimuli consisting of dozens of high-frequency activated\n\tsynapses distributed throughout the apical dendrites. We found the\n\tcell's firing rate could be predicted by a simple formula that maps\n\tthe physical components of the cell onto those of an abstract two-layer\n\t\"neural network.\" In the first layer, synaptic inputs drive independent\n\tsigmoidal subunits corresponding to the cell's several dozen long,\n\tthin terminal dendrites. The subunit outputs are then summed within\n\tthe main trunk and cell body prior to final thresholding. We conclude\n\tthat insofar as the neural code is mediated by average firing rate,\n\ta two-layer neural network may provide a useful abstraction for the\n\tcomputing function of the individual pyramidal neuron.},\n keywords = {Computing Methodologies, Human, Language, Learning, Mental Processes, Models, Theoretical, Stochastic Processes, Support, U.S. Gov't, Non-P.H.S., Cognition, Linguistics, Neural Networks (Computer), Practice (Psychology), Non-U.S. Gov't, Memory, Psychological, Task Performance and Analysis, Time Factors, Visual Perception, Adult, Attention, Discrimination Learning, Female, Male, Short-Term, Mental Recall, Orientation, Pattern Recognition, Visual, Perceptual Masking, Reading, Concept Formation, Form Perception, Animals, Corpus Striatum, Shrews, P.H.S., Visual Cortex, Visual Pathways, Acoustic Stimulation, Auditory Cortex, Auditory Perception, Cochlea, Ear, Gerbillinae, Glycine, Hearing, Neurons, Space Perception, Strychnine, Adolescent, Decision Making, Reaction Time, Astrocytoma, Brain Mapping, Brain Neoplasms, Cerebral Cortex, Electric Stimulation, Electrophysiology, Epilepsy, Temporal Lobe, Evoked Potentials, Frontal Lobe, Noise, Parietal Lobe, Scalp, Child, Language Development, Psycholinguistics, Brain, Perception, Speech, Vocalization, Animal, Discrimination (Psychology), Hippocampus, Rats, Calcium, Chelating Agents, Excitatory Postsynaptic Potentials, Glutamic Acid, Guanosine Diphosphate, In Vitro, Neuronal Plasticity, Pyramidal Cells, Receptors, AMPA, Metabotropic Glutamate, N-Methyl-D-Aspartate, Somatosensory Cortex, Synapses, Synaptic Transmission, Thionucleotides, Action Potentials, Calcium Channels, L-Type, Electric Conductivity, Entorhinal Cortex, Neurological, Long-Evans, Infant, Mathematics, Statistics, Probability Learning, Problem Solving, Psychophysics, Association Learning, Child Psychology, Habituation (Psychophysiology), Probability Theory, Analysis of Variance, Semantics, Symbolism, Behavior, Eye Movements, Macaca mulatta, Prefrontal Cortex, Cats, Dogs, Haplorhini, Photic Stimulation, Electroencephalography, Nervous System Physiology, Darkness, Grasshoppers, Light, Membrane Potentials, Neural Inhibition, Afferent, Picrotoxin, Vision, Deoxyglucose, Injections, Microspheres, Neural Pathways, Rhodamines, Choice Behavior, Speech Perception, Verbal Learning, Dominance, Cerebral, Fixation, Ocular, Language Tests, Random Allocation, Comparative Study, Saguinus, Sound Spectrography, Species Specificity, Audiometry, Auditory Threshold, Calibration, Data Interpretation, Statistical, Anesthesia, General, Electrodes, Implanted, Pitch Perception, Sound Localization, Paired-Associate Learning, Serial Learning, Auditory, Age Factors, Motion Perception, Brain Injuries, Computer Simulation, Blindness, Psychomotor Performance, Color Perception, Signal Detection (Psychology), Judgment, ROC Curve, Regression Analysis, Music, Probability, Arm, Cerebrovascular Disorders, Hemiplegia, Movement, Muscle, Skeletal, Myoclonus, Robotics, Magnetoencephalography, Phonetics, Software, Speech Production Measurement, Epilepsies, Partial, Laterality, Stereotaxic Techniques, Germany, Speech Acoustics, Verbal Behavior, Child Development, Instinct, Brain Stem, Coma, Diagnosis, Differential, Hearing Disorders, Hearing Loss, Central, Neuroma, Acoustic, Dendrites, Down-Regulation, Patch-Clamp Techniques, Wistar, Up-Regulation, Aged, Aphasia, Middle Aged, Cones (Retina), Primates, Retina, Retinal Ganglion Cells, Tympanic Membrane, Cell Communication, Extremities, Biological, Motor Activity, Rana catesbeiana, Spinal Cord, Central Nervous System, Motion, Motor Cortex, Intelligence, Macaca fascicularis, Adoption, Critical Period (Psychology), France, Korea, Magnetic Resonance Imaging, Multilingualism, Auditory Pathways, Cochlear Nerve, Loudness Perception, Neural Conduction, Sensory Thresholds, Sound, Language Disorders, Preschool, Generalization (Psychology), Vocabulary, Biophysics, Nerve Net, Potassium Channels, Sodium Channels, 12670427},\n}\n\n","author_short":["Poirazi, P.","Brannon, T.","Mel, B. 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