Cognitive psychology focuses on study of higher mental functions with particular emphasis on the ways in which people acquire knowledge and use it to shape and understand their experience in the world. This figures indicates key foci of cognitive psychology. Cognitive psychology is the school of psychology that examines internal mental processes such as problem solving, memory, and language. It had its foundations in the Gestalt psychology o f Max Wertheimer, Wolfgang Köhler, and Kurt Koffka, and in the work of Jean Piaget, who studied intellectual development in children. Cognitive psychologists are interested in how people understand, diagnose, and solve problems, concerning themselves with the mental processes which mediate between stimulus and response. Cognitive theory contends that solutions to problems take the form of algorithms—rules that are not necessarily understood but promise a solution, or heuristics—rules that are understood but that do not always guarantee solutions. In other instances, solutions may be found through insight, a sudden awareness of relationships.
Cognitive psychology focuses on study of higher mental functions with particular emphasis on the ways in which people acquire knowledge and use it to shape and understand their experience in the world. This figures indicates key foci of cognitive psychology. Cognitive psychology is the school of psychology that examines internal mental processes such as problem solving, memory, and language. It had its foundations in the Gestalt psychology o f Max Wertheimer, Wolfgang Köhler, and Kurt Koffka, and in the work of Jean Piaget, who studied intellectual development in children. Cognitive psychologists are interested in how people understand, diagnose, and solve problems, concerning themselves with the mental processes which mediate between stimulus and response. Cognitive theory contends that solutions to problems take the form of algorithms—rules that are not necessarily understood but promise a solution, or heuristics—rules that are understood but that do not always guarantee solutions. In other instances, solutions may be found through insight, a sudden awareness of relationships.
Despite their inseparability, the three paradigms are distinct from one another because they represent separate areas of competence. Theory is concerned with the ability to describe and prove relationships among objects. Abstraction is concerned with the ability to use those relationships to make predictions that can be compared with the world. Design is concerned with the ability to implement specific instances of those relationships and use them to perform useful actions. Applied mathematicians, computational scientists, and design engineers generally do not have interchangeable skills. Moreover, in computing we tend to study computational aids that support people engaged in informationtransforming processes. On the design side, for example, sophisticated VLSI design and simulation systems enable the efficient and correct design of microcircuitry, and programming environments enable the efficient design of software. On the modeling side, supercomputers evaluate mathematical models and make predictions about the world, and networks help disseminate findings from scientific experiments. On the theory side, computers help prove theorems, check the consistency of specifications, check for counterexamples, and demonstrate test cases. Computing sits at the crossroads among the central processes of applied mathematics, science, and engineering. The three processes are of equal-and fundamental- importance in the discipline, which is a unique blend of interaction among theory, abstraction, and design. The binding forces are a common interest in experimentation and design as information transformers, a common interest in computational support of the stages of those processes, and a common interest in efficiency. The fundamental question underlying all of computing is, “What can be (efficiently) automated?”
Despite their inseparability, the three paradigms are distinct from one another because they represent separate areas of competence. Theory is concerned with the ability to describe and prove relationships among objects. Abstraction is concerned with the ability to use those relationships to make predictions that can be compared with the world. Design is concerned with the ability to implement specific instances of those relationships and use them to perform useful actions. Applied mathematicians, computational scientists, and design engineers generally do not have interchangeable skills. Moreover, in computing we tend to study computational aids that support people engaged in informationtransforming processes. On the design side, for example, sophisticated VLSI design and simulation systems enable the efficient and correct design of microcircuitry, and programming environments enable the efficient design of software. On the modeling side, supercomputers evaluate mathematical models and make predictions about the world, and networks help disseminate findings from scientific experiments. On the theory side, computers help prove theorems, check the consistency of specifications, check for counterexamples, and demonstrate test cases. Computing sits at the crossroads among the central processes of applied mathematics, science, and engineering. The three processes are of equal-and fundamental- importance in the discipline, which is a unique blend of interaction among theory, abstraction, and design. The binding forces are a common interest in experimentation and design as information transformers, a common interest in computational support of the stages of those processes, and a common interest in efficiency. The fundamental question underlying all of computing is, “What can be (efficiently) automated?”
Cognitive psychology focuses on study of higher mental functions with particular emphasis on the ways in which people acquire knowledge and use it to shape and understand their experience in the world. This figures indicates key foci of cognitive psychology. Cognitive psychology is the school of psychology that examines internal mental processes such as problem solving, memory, and language. It had its foundations in the Gestalt psychology o f Max Wertheimer, Wolfgang Köhler, and Kurt Koffka, and in the work of Jean Piaget, who studied intellectual development in children. Cognitive psychologists are interested in how people understand, diagnose, and solve problems, concerning themselves with the mental processes which mediate between stimulus and response. Cognitive theory contends that solutions to problems take the form of algorithms—rules that are not necessarily understood but promise a solution, or heuristics—rules that are understood but that do not always guarantee solutions. In other instances, solutions may be found through insight, a sudden awareness of relationships.
Thus, neurons are simulated in a “clock-driven” fashion whereas synapses are simulated in an “event-driven” fashion. As a first step toward cognitive computation, an interesting question is whether one can simulate a mammalian-scale cortical model in near real-time on an existing computer system? What are the memory, computation, and communication costs for achieving such a simulation? Memory: To achieve near real-time simulation times, the state of all neurons and synapses must fit in the random access memory of the system. Since synapses far outnumber the neurons, the total available memory divided by the number of bytes per synapse limits the number of synapses that can be modeled. We need to store state for 448 billion synapses and 55 million neurons where later being negligible in comparison to the former. Communication: Let us assume that, on an average, each neuron fires once a second. Each neuron connects to 8,000 other neurons, and, hence, each neuron would generate 8,000 spikes (“messages’) per second. This amounts to a total of 448 billion messages per second. Computation: Let us assume that, on an average, each neuron fires once a second. In this case, on an average, each synapse would be activated twice—once when its pre-synaptic neuron fires and once when its post-synaptic neuron fires. This amounts to 896 billion synaptic updates per second. Let us assume that the state of each neuron is updated every millisecond. This amounts to 55 billion neuronal updates per second. Once again, synapses seem to dominate the computational cost. The key observation is that synapses dominate all the three costs! Let us now take a state-of-the-art supercomputer BlueGene/L with 32,768 processors, 256 megabytes of memory per processor (a total of 8 terabytes), and 1.05 gigabytes per second of in/out communication bandwidth per node. To meet the above three constraints, if one can design data structure and algorithms that require no more than 16 byes of storage per synapse, 175 Flops per synapse per second, and 66 bytes per spike message, then one can hope for a rat-scale, near real-time simulation. Can such a software infrastructure be put together? This is exactly the challenge that our paper addresses. Specifically, we have designed and implemented a massively parallel cortical simulator, C2, designed to run on distributed memory multiprocessors that incorporates several algorithmic enhancements: (a) a computationally efficient way to simulate neurons in a clock-driven (&quot;synchronous&quot;) and synapses in an event-driven(&quot;asynchronous&quot;) fashion; (b) a memory efficient representation to compactly represent the state of the simulation; (c) a communication efficient way to minimize the number of messages sent by aggregating them in several ways and by mapping message exchanges between processors onto judiciously chosen MPI primitives for synchronization. Furthermore, the simulator incorporated (a) carefully selected computationally efficient models of phenomenological spiking neurons from the literature; (b) carefully selected models of spike-timing dependent synaptic plasticity for synaptic updates; (c) axonal delays; (d) 80% excitatory neurons and 20% inhibitory neurons; and (e) a certain random graph of neuronal interconnectivity.
The term “neuron” was coined by Heinrich Wilhelm Gottfried von Waldeyer-Hartz in 1891 to capture the discrete information processing units of the brain. The junctions between two neurons were termed “synapses” by Sir Charles Sherrington in 1897. Information flows only along one direction through a synapse, thus we talk about a “pre-synaptic” and a “post-synaptic” neuron. Neurons, when activated by sufficient input received via synapses, emit “spikes” that are delivered to those synapses that the neuron is pre-synaptic to. Neurons can be either “excitatory” or “inhibitory.”
Thus, neurons are simulated in a “clock-driven” fashion whereas synapses are simulated in an “event-driven” fashion. As a first step toward cognitive computation, an interesting question is whether one can simulate a mammalian-scale cortical model in near real-time on an existing computer system? What are the memory, computation, and communication costs for achieving such a simulation? Memory: To achieve near real-time simulation times, the state of all neurons and synapses must fit in the random access memory of the system. Since synapses far outnumber the neurons, the total available memory divided by the number of bytes per synapse limits the number of synapses that can be modeled. We need to store state for 448 billion synapses and 55 million neurons where later being negligible in comparison to the former. Communication: Let us assume that, on an average, each neuron fires once a second. Each neuron connects to 8,000 other neurons, and, hence, each neuron would generate 8,000 spikes (“messages’) per second. This amounts to a total of 448 billion messages per second. Computation: Let us assume that, on an average, each neuron fires once a second. In this case, on an average, each synapse would be activated twice—once when its pre-synaptic neuron fires and once when its post-synaptic neuron fires. This amounts to 896 billion synaptic updates per second. Let us assume that the state of each neuron is updated every millisecond. This amounts to 55 billion neuronal updates per second. Once again, synapses seem to dominate the computational cost. The key observation is that synapses dominate all the three costs! Let us now take a state-of-the-art supercomputer BlueGene/L with 32,768 processors, 256 megabytes of memory per processor (a total of 8 terabytes), and 1.05 gigabytes per second of in/out communication bandwidth per node. To meet the above three constraints, if one can design data structure and algorithms that require no more than 16 byes of storage per synapse, 175 Flops per synapse per second, and 66 bytes per spike message, then one can hope for a rat-scale, near real-time simulation. Can such a software infrastructure be put together? This is exactly the challenge that our paper addresses. Specifically, we have designed and implemented a massively parallel cortical simulator, C2, designed to run on distributed memory multiprocessors that incorporates several algorithmic enhancements: (a) a computationally efficient way to simulate neurons in a clock-driven (&quot;synchronous&quot;) and synapses in an event-driven(&quot;asynchronous&quot;) fashion; (b) a memory efficient representation to compactly represent the state of the simulation; (c) a communication efficient way to minimize the number of messages sent by aggregating them in several ways and by mapping message exchanges between processors onto judiciously chosen MPI primitives for synchronization. Furthermore, the simulator incorporated (a) carefully selected computationally efficient models of phenomenological spiking neurons from the literature; (b) carefully selected models of spike-timing dependent synaptic plasticity for synaptic updates; (c) axonal delays; (d) 80% excitatory neurons and 20% inhibitory neurons; and (e) a certain random graph of neuronal interconnectivity.
Thus, neurons are simulated in a “clock-driven” fashion whereas synapses are simulated in an “event-driven” fashion. As a first step toward cognitive computation, an interesting question is whether one can simulate a mammalian-scale cortical model in near real-time on an existing computer system? What are the memory, computation, and communication costs for achieving such a simulation? Memory: To achieve near real-time simulation times, the state of all neurons and synapses must fit in the random access memory of the system. Since synapses far outnumber the neurons, the total available memory divided by the number of bytes per synapse limits the number of synapses that can be modeled. We need to store state for 448 billion synapses and 55 million neurons where later being negligible in comparison to the former. Communication: Let us assume that, on an average, each neuron fires once a second. Each neuron connects to 8,000 other neurons, and, hence, each neuron would generate 8,000 spikes (“messages’) per second. This amounts to a total of 448 billion messages per second. Computation: Let us assume that, on an average, each neuron fires once a second. In this case, on an average, each synapse would be activated twice—once when its pre-synaptic neuron fires and once when its post-synaptic neuron fires. This amounts to 896 billion synaptic updates per second. Let us assume that the state of each neuron is updated every millisecond. This amounts to 55 billion neuronal updates per second. Once again, synapses seem to dominate the computational cost. The key observation is that synapses dominate all the three costs! Let us now take a state-of-the-art supercomputer BlueGene/L with 32,768 processors, 256 megabytes of memory per processor (a total of 8 terabytes), and 1.05 gigabytes per second of in/out communication bandwidth per node. To meet the above three constraints, if one can design data structure and algorithms that require no more than 16 byes of storage per synapse, 175 Flops per synapse per second, and 66 bytes per spike message, then one can hope for a rat-scale, near real-time simulation. Can such a software infrastructure be put together? This is exactly the challenge that our paper addresses. Specifically, we have designed and implemented a massively parallel cortical simulator, C2, designed to run on distributed memory multiprocessors that incorporates several algorithmic enhancements: (a) a computationally efficient way to simulate neurons in a clock-driven (&quot;synchronous&quot;) and synapses in an event-driven(&quot;asynchronous&quot;) fashion; (b) a memory efficient representation to compactly represent the state of the simulation; (c) a communication efficient way to minimize the number of messages sent by aggregating them in several ways and by mapping message exchanges between processors onto judiciously chosen MPI primitives for synchronization. Furthermore, the simulator incorporated (a) carefully selected computationally efficient models of phenomenological spiking neurons from the literature; (b) carefully selected models of spike-timing dependent synaptic plasticity for synaptic updates; (c) axonal delays; (d) 80% excitatory neurons and 20% inhibitory neurons; and (e) a certain random graph of neuronal interconnectivity.
Thus, neurons are simulated in a “clock-driven” fashion whereas synapses are simulated in an “event-driven” fashion. As a first step toward cognitive computation, an interesting question is whether one can simulate a mammalian-scale cortical model in near real-time on an existing computer system? What are the memory, computation, and communication costs for achieving such a simulation? Memory: To achieve near real-time simulation times, the state of all neurons and synapses must fit in the random access memory of the system. Since synapses far outnumber the neurons, the total available memory divided by the number of bytes per synapse limits the number of synapses that can be modeled. We need to store state for 448 billion synapses and 55 million neurons where later being negligible in comparison to the former. Communication: Let us assume that, on an average, each neuron fires once a second. Each neuron connects to 8,000 other neurons, and, hence, each neuron would generate 8,000 spikes (“messages’) per second. This amounts to a total of 448 billion messages per second. Computation: Let us assume that, on an average, each neuron fires once a second. In this case, on an average, each synapse would be activated twice—once when its pre-synaptic neuron fires and once when its post-synaptic neuron fires. This amounts to 896 billion synaptic updates per second. Let us assume that the state of each neuron is updated every millisecond. This amounts to 55 billion neuronal updates per second. Once again, synapses seem to dominate the computational cost. The key observation is that synapses dominate all the three costs! Let us now take a state-of-the-art supercomputer BlueGene/L with 32,768 processors, 256 megabytes of memory per processor (a total of 8 terabytes), and 1.05 gigabytes per second of in/out communication bandwidth per node. To meet the above three constraints, if one can design data structure and algorithms that require no more than 16 byes of storage per synapse, 175 Flops per synapse per second, and 66 bytes per spike message, then one can hope for a rat-scale, near real-time simulation. Can such a software infrastructure be put together? This is exactly the challenge that our paper addresses. Specifically, we have designed and implemented a massively parallel cortical simulator, C2, designed to run on distributed memory multiprocessors that incorporates several algorithmic enhancements: (a) a computationally efficient way to simulate neurons in a clock-driven (&quot;synchronous&quot;) and synapses in an event-driven(&quot;asynchronous&quot;) fashion; (b) a memory efficient representation to compactly represent the state of the simulation; (c) a communication efficient way to minimize the number of messages sent by aggregating them in several ways and by mapping message exchanges between processors onto judiciously chosen MPI primitives for synchronization. Furthermore, the simulator incorporated (a) carefully selected computationally efficient models of phenomenological spiking neurons from the literature; (b) carefully selected models of spike-timing dependent synaptic plasticity for synaptic updates; (c) axonal delays; (d) 80% excitatory neurons and 20% inhibitory neurons; and (e) a certain random graph of neuronal interconnectivity.
Thus, neurons are simulated in a “clock-driven” fashion whereas synapses are simulated in an “event-driven” fashion. As a first step toward cognitive computation, an interesting question is whether one can simulate a mammalian-scale cortical model in near real-time on an existing computer system? What are the memory, computation, and communication costs for achieving such a simulation? Memory: To achieve near real-time simulation times, the state of all neurons and synapses must fit in the random access memory of the system. Since synapses far outnumber the neurons, the total available memory divided by the number of bytes per synapse limits the number of synapses that can be modeled. We need to store state for 448 billion synapses and 55 million neurons where later being negligible in comparison to the former. Communication: Let us assume that, on an average, each neuron fires once a second. Each neuron connects to 8,000 other neurons, and, hence, each neuron would generate 8,000 spikes (“messages’) per second. This amounts to a total of 448 billion messages per second. Computation: Let us assume that, on an average, each neuron fires once a second. In this case, on an average, each synapse would be activated twice—once when its pre-synaptic neuron fires and once when its post-synaptic neuron fires. This amounts to 896 billion synaptic updates per second. Let us assume that the state of each neuron is updated every millisecond. This amounts to 55 billion neuronal updates per second. Once again, synapses seem to dominate the computational cost. The key observation is that synapses dominate all the three costs! Let us now take a state-of-the-art supercomputer BlueGene/L with 32,768 processors, 256 megabytes of memory per processor (a total of 8 terabytes), and 1.05 gigabytes per second of in/out communication bandwidth per node. To meet the above three constraints, if one can design data structure and algorithms that require no more than 16 byes of storage per synapse, 175 Flops per synapse per second, and 66 bytes per spike message, then one can hope for a rat-scale, near real-time simulation. Can such a software infrastructure be put together? This is exactly the challenge that our paper addresses. Specifically, we have designed and implemented a massively parallel cortical simulator, C2, designed to run on distributed memory multiprocessors that incorporates several algorithmic enhancements: (a) a computationally efficient way to simulate neurons in a clock-driven (&quot;synchronous&quot;) and synapses in an event-driven(&quot;asynchronous&quot;) fashion; (b) a memory efficient representation to compactly represent the state of the simulation; (c) a communication efficient way to minimize the number of messages sent by aggregating them in several ways and by mapping message exchanges between processors onto judiciously chosen MPI primitives for synchronization. Furthermore, the simulator incorporated (a) carefully selected computationally efficient models of phenomenological spiking neurons from the literature; (b) carefully selected models of spike-timing dependent synaptic plasticity for synaptic updates; (c) axonal delays; (d) 80% excitatory neurons and 20% inhibitory neurons; and (e) a certain random graph of neuronal interconnectivity.
On a historical note, in 1956, a team of IBM researchers simulated 512 neurons ( N. Rochester, J. H. Holland, L. H. Haibt, and W. L. Duda, Tests on a Cell Assembly Theory of the Action of the Brain Using a Large Digital Computer, IRE Transaction of Information Theory, IT-2, pp. 80-93, September 1956. ). Our results represent a judicious intersection between computer science which defines the region of feasibility in terms of available computing resources today, and neuroscience which defines the region of desirability in terms of biological details that one would like to add. At any given point in time, to get a particular scale of simulation at a particular simulation speed, one must balance between feasibility and desirability. Thus, our results demonstrate that a non-empty intersection between these two regions exists today at rat-scale, at near real-time and at a certain complexity of simulations. This intersection will continue to expand over time. As more biological richness is added, correspondingly more resources will be required to accommodate the model in memory and to maintain reasonable simulation times. The value of the current simulator is in the fact that it permits almost interactive, large-scale simulation, and, hence, allows us to explore a wide space of parameters in trying to uncover (“guess”) the function of the cerebral cortex. Furthermore, understanding and harnessing dynamics of such large-scale networks is a tremendously exciting frontier. We hope that C2 will become the linear accelerator of cognitive computing.
On a historical note, in 1956, a team of IBM researchers simulated 512 neurons ( N. Rochester, J. H. Holland, L. H. Haibt, and W. L. Duda, Tests on a Cell Assembly Theory of the Action of the Brain Using a Large Digital Computer, IRE Transaction of Information Theory, IT-2, pp. 80-93, September 1956. ). Our results represent a judicious intersection between computer science which defines the region of feasibility in terms of available computing resources today, and neuroscience which defines the region of desirability in terms of biological details that one would like to add. At any given point in time, to get a particular scale of simulation at a particular simulation speed, one must balance between feasibility and desirability. Thus, our results demonstrate that a non-empty intersection between these two regions exists today at rat-scale, at near real-time and at a certain complexity of simulations. This intersection will continue to expand over time. As more biological richness is added, correspondingly more resources will be required to accommodate the model in memory and to maintain reasonable simulation times. The value of the current simulator is in the fact that it permits almost interactive, large-scale simulation, and, hence, allows us to explore a wide space of parameters in trying to uncover (“guess”) the function of the cerebral cortex. Furthermore, understanding and harnessing dynamics of such large-scale networks is a tremendously exciting frontier. We hope that C2 will become the linear accelerator of cognitive computing.
On a historical note, in 1956, a team of IBM researchers simulated 512 neurons ( N. Rochester, J. H. Holland, L. H. Haibt, and W. L. Duda, Tests on a Cell Assembly Theory of the Action of the Brain Using a Large Digital Computer, IRE Transaction of Information Theory, IT-2, pp. 80-93, September 1956. ). Our results represent a judicious intersection between computer science which defines the region of feasibility in terms of available computing resources today, and neuroscience which defines the region of desirability in terms of biological details that one would like to add. At any given point in time, to get a particular scale of simulation at a particular simulation speed, one must balance between feasibility and desirability. Thus, our results demonstrate that a non-empty intersection between these two regions exists today at rat-scale, at near real-time and at a certain complexity of simulations. This intersection will continue to expand over time. As more biological richness is added, correspondingly more resources will be required to accommodate the model in memory and to maintain reasonable simulation times. The value of the current simulator is in the fact that it permits almost interactive, large-scale simulation, and, hence, allows us to explore a wide space of parameters in trying to uncover (“guess”) the function of the cerebral cortex. Furthermore, understanding and harnessing dynamics of such large-scale networks is a tremendously exciting frontier. We hope that C2 will become the linear accelerator of cognitive computing.
On a historical note, in 1956, a team of IBM researchers simulated 512 neurons ( N. Rochester, J. H. Holland, L. H. Haibt, and W. L. Duda, Tests on a Cell Assembly Theory of the Action of the Brain Using a Large Digital Computer, IRE Transaction of Information Theory, IT-2, pp. 80-93, September 1956. ). Our results represent a judicious intersection between computer science which defines the region of feasibility in terms of available computing resources today, and neuroscience which defines the region of desirability in terms of biological details that one would like to add. At any given point in time, to get a particular scale of simulation at a particular simulation speed, one must balance between feasibility and desirability. Thus, our results demonstrate that a non-empty intersection between these two regions exists today at rat-scale, at near real-time and at a certain complexity of simulations. This intersection will continue to expand over time. As more biological richness is added, correspondingly more resources will be required to accommodate the model in memory and to maintain reasonable simulation times. The value of the current simulator is in the fact that it permits almost interactive, large-scale simulation, and, hence, allows us to explore a wide space of parameters in trying to uncover (“guess”) the function of the cerebral cortex. Furthermore, understanding and harnessing dynamics of such large-scale networks is a tremendously exciting frontier. We hope that C2 will become the linear accelerator of cognitive computing.
Thus, neurons are simulated in a “clock-driven” fashion whereas synapses are simulated in an “event-driven” fashion. As a first step toward cognitive computation, an interesting question is whether one can simulate a mammalian-scale cortical model in near real-time on an existing computer system? What are the memory, computation, and communication costs for achieving such a simulation? Memory: To achieve near real-time simulation times, the state of all neurons and synapses must fit in the random access memory of the system. Since synapses far outnumber the neurons, the total available memory divided by the number of bytes per synapse limits the number of synapses that can be modeled. We need to store state for 448 billion synapses and 55 million neurons where later being negligible in comparison to the former. Communication: Let us assume that, on an average, each neuron fires once a second. Each neuron connects to 8,000 other neurons, and, hence, each neuron would generate 8,000 spikes (“messages’) per second. This amounts to a total of 448 billion messages per second. Computation: Let us assume that, on an average, each neuron fires once a second. In this case, on an average, each synapse would be activated twice—once when its pre-synaptic neuron fires and once when its post-synaptic neuron fires. This amounts to 896 billion synaptic updates per second. Let us assume that the state of each neuron is updated every millisecond. This amounts to 55 billion neuronal updates per second. Once again, synapses seem to dominate the computational cost. The key observation is that synapses dominate all the three costs! Let us now take a state-of-the-art supercomputer BlueGene/L with 32,768 processors, 256 megabytes of memory per processor (a total of 8 terabytes), and 1.05 gigabytes per second of in/out communication bandwidth per node. To meet the above three constraints, if one can design data structure and algorithms that require no more than 16 byes of storage per synapse, 175 Flops per synapse per second, and 66 bytes per spike message, then one can hope for a rat-scale, near real-time simulation. Can such a software infrastructure be put together? This is exactly the challenge that our paper addresses. Specifically, we have designed and implemented a massively parallel cortical simulator, C2, designed to run on distributed memory multiprocessors that incorporates several algorithmic enhancements: (a) a computationally efficient way to simulate neurons in a clock-driven (&quot;synchronous&quot;) and synapses in an event-driven(&quot;asynchronous&quot;) fashion; (b) a memory efficient representation to compactly represent the state of the simulation; (c) a communication efficient way to minimize the number of messages sent by aggregating them in several ways and by mapping message exchanges between processors onto judiciously chosen MPI primitives for synchronization. Furthermore, the simulator incorporated (a) carefully selected computationally efficient models of phenomenological spiking neurons from the literature; (b) carefully selected models of spike-timing dependent synaptic plasticity for synaptic updates; (c) axonal delays; (d) 80% excitatory neurons and 20% inhibitory neurons; and (e) a certain random graph of neuronal interconnectivity.
Thus, neurons are simulated in a “clock-driven” fashion whereas synapses are simulated in an “event-driven” fashion. As a first step toward cognitive computation, an interesting question is whether one can simulate a mammalian-scale cortical model in near real-time on an existing computer system? What are the memory, computation, and communication costs for achieving such a simulation? Memory: To achieve near real-time simulation times, the state of all neurons and synapses must fit in the random access memory of the system. Since synapses far outnumber the neurons, the total available memory divided by the number of bytes per synapse limits the number of synapses that can be modeled. We need to store state for 448 billion synapses and 55 million neurons where later being negligible in comparison to the former. Communication: Let us assume that, on an average, each neuron fires once a second. Each neuron connects to 8,000 other neurons, and, hence, each neuron would generate 8,000 spikes (“messages’) per second. This amounts to a total of 448 billion messages per second. Computation: Let us assume that, on an average, each neuron fires once a second. In this case, on an average, each synapse would be activated twice—once when its pre-synaptic neuron fires and once when its post-synaptic neuron fires. This amounts to 896 billion synaptic updates per second. Let us assume that the state of each neuron is updated every millisecond. This amounts to 55 billion neuronal updates per second. Once again, synapses seem to dominate the computational cost. The key observation is that synapses dominate all the three costs! Let us now take a state-of-the-art supercomputer BlueGene/L with 32,768 processors, 256 megabytes of memory per processor (a total of 8 terabytes), and 1.05 gigabytes per second of in/out communication bandwidth per node. To meet the above three constraints, if one can design data structure and algorithms that require no more than 16 byes of storage per synapse, 175 Flops per synapse per second, and 66 bytes per spike message, then one can hope for a rat-scale, near real-time simulation. Can such a software infrastructure be put together? This is exactly the challenge that our paper addresses. Specifically, we have designed and implemented a massively parallel cortical simulator, C2, designed to run on distributed memory multiprocessors that incorporates several algorithmic enhancements: (a) a computationally efficient way to simulate neurons in a clock-driven (&quot;synchronous&quot;) and synapses in an event-driven(&quot;asynchronous&quot;) fashion; (b) a memory efficient representation to compactly represent the state of the simulation; (c) a communication efficient way to minimize the number of messages sent by aggregating them in several ways and by mapping message exchanges between processors onto judiciously chosen MPI primitives for synchronization. Furthermore, the simulator incorporated (a) carefully selected computationally efficient models of phenomenological spiking neurons from the literature; (b) carefully selected models of spike-timing dependent synaptic plasticity for synaptic updates; (c) axonal delays; (d) 80% excitatory neurons and 20% inhibitory neurons; and (e) a certain random graph of neuronal interconnectivity.
Nencki 2010 Day1
1.
Dariusz Plewczynski, PhD
ICM, University of Warsaw
D.Plewczynski@icm.edu.pl
czwartek, 25 marca 2010
2.
Cognitive Computing
From Brain Modelling to Large
Scale Machine Learning
Dariusz Plewczynski, PhD
ICM, University of Warsaw
D.Plewczynski@icm.edu.pl
czwartek, 25 marca 2010
4.
What is Cognition?
1. Cognoscere latin: "to know" or "to recognize"
2. Cognition is a general term for all forms of
knowing (e.g. attending, remembering,
reasoning and understanding concepts, facts,
propositions, and rules).
3. Cognitive processes refers to the processing of
information, applying knowledge, and changing
preferences.
4. Cognitive psychology is the study of cognition.
5. Cognitive science is an interdisciplinary field
that extends the principles of cognitive
psychology to other systems that manipulate
information.
6. Cognitive Informatics studies the natural
intelligence and internal information processing
mechanisms of the brain, as well as the
processes involved in perception and cognition.
http://en.wikiversity.org/wiki/Cognition
czwartek, 25 marca 2010
6.
Cognitive Psychology
• focuses on study of higher mental
functions with particular emphasis on
the ways in which people acquire
knowledge and use it to shape and
understand their experience in the
world.
• examines internal mental processes
such as problem solving, memory, and
language.
• How people understand, diagnose,
and solve problems, the mental
processes, which mediate between
stimulus and response in the form of
algorithmic or heuristics rules.
http://en.wikiversity.org/wiki/Cognitive_psychology
czwartek, 25 marca 2010
8.
Cognitive Science
The interdisciplinary study of mind or the
study of thought. It embraces multiple
research disciplines, including psychology,
artificial intelligence, philosophy,
neuroscience, linguistics, anthropology,
sociology and biology.
It relies on varying scientific methodology
(e.g. behavioral experimentation,
computational simulations, neuro-imaging,
statistical analyses), and spans many
levels of analysis of the mind (from low-
level learning and decision mechanisms to
high-level logic and planning, from neural
circuitry to modular brain organization,
etc.).
http://en.wikiversity.org/wiki/Cognitive_science
czwartek, 25 marca 2010
10.
Cognitive Computing?
we know now what is cognition
at least more or less ...
czwartek, 25 marca 2010
11.
Cognitive Computing?
we know now what is cognition
at least more or less ...
... but where is the computing ?
czwartek, 25 marca 2010
12.
Computing
Computing as a discipline, Denning 1989, Computer
czwartek, 25 marca 2010
13.
Computing
The discipline of computing is the systematic study of
algorithmic processes that describe and transform information:
theory, analysis, design, efficiency, implementation, application.
Instances of theory may appear at every stage of abstraction
and design, instances of modeling at every stage of theory
and design, and instances of design at
every stage of theory and abstraction.
Computing as a discipline, Denning 1989, Computer
czwartek, 25 marca 2010
15.
Cognitive Informatics
An emerging discipline that studies the
natural intelligence and internal
information processing mechanisms of the
brain, as well as the processes involved in
perception and cognition.
It provides a coherent set of fundamental
theories, and contemporary mathematics,
which form the foundation for most
information- and knowledge-based
science and engineering disciplines such
as computer science, cognitive science,
neuropsychology, systems science,
cybernetics, software engineering, and
knowledge engineering.
http://en.wikiversity.org/wiki/Cognitive_informatics
czwartek, 25 marca 2010
16.
How the brain works?
David Marr (1945-1980) three levels of analysis:
the problem (computational level)
the strategy (algorithmic level)
how it’s actually done by networks of neurons
(implementational level)
P. Latham
P. Dayan
czwartek, 25 marca 2010
17.
Simulating the Brain
neuron introduced by Heinrich von Waldeyer-Hartz 1891
http://en.wikipedia.org/wiki/Neuron
czwartek, 25 marca 2010
18.
Simulating the Brain
synapse introduced by Charles Sherrington 1897
http://en.wikipedia.org/wiki/Synapse
czwartek, 25 marca 2010
19.
How the brain works?
neocortex (cognition)
6 layers
~30 cm
~0.5 cm
subcortical structures
(emotions, reward,
homeostasis, much much
more)
P. Latham
P. Dayan
czwartek, 25 marca 2010
20.
How the brain works?
Cortex vs CPU numbers:
1 mm^2
1 mm3 of cortex: 1 mm2 of a CPU:
50,000 neurons 1 million transistors
10000 connections/neuron 2 connections/transistor
(=> 500 million connections) (=> 2 million connections)
4 km of axons .002 km of wire
whole brain (2 kg): whole CPU:
1011 neurons 109 transistors
1015 connections 2*109 connections
8 million km of axons 2 km of wire
P. Latham
P. Dayan
czwartek, 25 marca 2010
21.
How the brain really learns?
Time & Learning:
You have about 1015 synapses.
If it takes 1 bit of information to set a synapse, you need 1015
bits to set all of them.
30 years ≈ 109 seconds.
To set 1/10 of your synapses in 30 years, you must absorb
100,000 bits/second.
Learning in the brain is almost completely unsupervised!
P. Latham
P. Dayan
czwartek, 25 marca 2010
22.
Neuronal Simulators
Software Packages:
Neuron http://www.neuron.yale.edu/neuron/
NEST http://www.nest-initiative.org/
Brian http://www.briansimulator.org/
Genesis http://genesis-sim.org/
...
czwartek, 25 marca 2010
24.
Brain Resolution
WBE levels of interest:
An informal poll among WBE workshop in 2008 attendees
produced a range of estimates where the required resolution
for Whole Brain Emulation (WBE) is. The consensus
appeared to be level 4‐6. Two participants were more
optimistic about high level models, while two suggested that
elements on level 8‐9 may be necessary at least initially (but
that the bulk of mature emulation, once the basics were
understood, could occur on level 4‐5). To achieve emulation
on this level, the consensus was that 5×5×50 nm scanning
resolution would be needed. This roadmap will hence focus
on level 4‐6 models, while being open for that deeper levels
may turn out to be needed. A. Sandberg, N. Bostrom
czwartek, 25 marca 2010
25.
Something Smaller
Mammalian thalamo-cortical
System by E. Izhikevich:
The simulation of a model that has the size of the human
brain: a detailed large-scale thalamocortical model based on
experimental measures in several mammalian species.
The model exhibits behavioral regimes of normal brain activity that
were not explicitly built-in but emerged spontaneously as the result of
interactions among anatomical and dynamic processes. It describes
spontaneous activity, sensitivity to changes in individual neurons,
emergence of waves and rhythms, and functional connectivity on
different scales.
E. Izhikevich
czwartek, 25 marca 2010
26.
and Less Complicated
IEEE TRANSACTIONS ON NEURAL NETWORKS, VOL. 15, NO. 5, SEPTEMBER 2004
E. Izhikevich
czwartek, 25 marca 2010
27.
Our Goal: Cognitive Networks
Cognitive networks CN are inspired by
brain structure and performed cognitive functions
CN put together single machine learning units connected via an
interconnections. The goal is to understand the learning as the
spatiotemporal information processing and storing capability of
such networks (Meta-Learning!).
1. Space: for every LU (learning unit):
a. For every time step:
i. Update the state of each LU using changed training data
ii. If the LU learning was performed with success,
generate an event for each coupling that the LU is
post-event coupled to and pre-event coupled to.
2. Time: For every TC (time coupling):
When it receives a pre- or post-event,
update its state and, if necessary, the state of the post-event LUs
czwartek, 25 marca 2010
28.
Uwe Koch &
Stephane Spieser
Pawel G Sadowski, Tom
Dariusz Plewczyński Kathryn S Lilley
darman@icm.edu.pl Marcin von Grotthuss
Krzysztof Ginalski
Leszek Rychlewski
Adrian Tkacz
Jan Komorowski & Marcin
Kierczak
Lucjan Wyrwicz
czwartek, 25 marca 2010
29.
Brainstorming
(static consensus learning)
Uwe Koch &
Stephane Spieser
Pawel G Sadowski, Tom
Dariusz Plewczyński Kathryn S Lilley
darman@icm.edu.pl Marcin von Grotthuss
Krzysztof Ginalski
Leszek Rychlewski
Adrian Tkacz
Jan Komorowski & Marcin
Kierczak
Lucjan Wyrwicz
czwartek, 25 marca 2010
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