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Meyer-Ortmanns H. Heteroclinic networks for brain dynamics. FRONTIERS IN NETWORK PHYSIOLOGY 2023; 3:1276401. [PMID: 38020242 PMCID: PMC10663269 DOI: 10.3389/fnetp.2023.1276401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/11/2023] [Accepted: 10/16/2023] [Indexed: 12/01/2023]
Abstract
Heteroclinic networks are a mathematical concept in dynamic systems theory that is suited to describe metastable states and switching events in brain dynamics. The framework is sensitive to external input and, at the same time, reproducible and robust against perturbations. Solutions of the corresponding differential equations are spatiotemporal patterns that are supposed to encode information both in space and time coordinates. We focus on the concept of winnerless competition as realized in generalized Lotka-Volterra equations and report on results for binding and chunking dynamics, synchronization on spatial grids, and entrainment to heteroclinic motion. We summarize proposals of how to design heteroclinic networks as desired in view of reproducing experimental observations from neuronal networks and discuss the subtle role of noise. The review is on a phenomenological level with possible applications to brain dynamics, while we refer to the literature for a rigorous mathematical treatment. We conclude with promising perspectives for future research.
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Affiliation(s)
- Hildegard Meyer-Ortmanns
- School of Science, Constructor University, Bremen, Germany
- Complexity Science Hub Vienna, Vienna, Austria
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Makarov VA, Lobov SA, Shchanikov S, Mikhaylov A, Kazantsev VB. Toward Reflective Spiking Neural Networks Exploiting Memristive Devices. Front Comput Neurosci 2022; 16:859874. [PMID: 35782090 PMCID: PMC9243340 DOI: 10.3389/fncom.2022.859874] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/21/2022] [Accepted: 05/10/2022] [Indexed: 11/29/2022] Open
Abstract
The design of modern convolutional artificial neural networks (ANNs) composed of formal neurons copies the architecture of the visual cortex. Signals proceed through a hierarchy, where receptive fields become increasingly more complex and coding sparse. Nowadays, ANNs outperform humans in controlled pattern recognition tasks yet remain far behind in cognition. In part, it happens due to limited knowledge about the higher echelons of the brain hierarchy, where neurons actively generate predictions about what will happen next, i.e., the information processing jumps from reflex to reflection. In this study, we forecast that spiking neural networks (SNNs) can achieve the next qualitative leap. Reflective SNNs may take advantage of their intrinsic dynamics and mimic complex, not reflex-based, brain actions. They also enable a significant reduction in energy consumption. However, the training of SNNs is a challenging problem, strongly limiting their deployment. We then briefly overview new insights provided by the concept of a high-dimensional brain, which has been put forward to explain the potential power of single neurons in higher brain stations and deep SNN layers. Finally, we discuss the prospect of implementing neural networks in memristive systems. Such systems can densely pack on a chip 2D or 3D arrays of plastic synaptic contacts directly processing analog information. Thus, memristive devices are a good candidate for implementing in-memory and in-sensor computing. Then, memristive SNNs can diverge from the development of ANNs and build their niche, cognitive, or reflective computations.
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Affiliation(s)
- Valeri A. Makarov
- Instituto de Matemática Interdisciplinar, Universidad Complutense de Madrid, Madrid, Spain
- Department of Neurotechnologies, Research Institute of Physics and Technology, Laboratory of Stochastic Multistable Systems, Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia
| | - Sergey A. Lobov
- Department of Neurotechnologies, Research Institute of Physics and Technology, Laboratory of Stochastic Multistable Systems, Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia
- Neuroscience and Cognitive Technology Laboratory, Center for Technologies in Robotics and Mechatronics Components, Innopolis University, Innopolis, Russia
- Center For Neurotechnology and Machine Learning, Immanuel Kant Baltic Federal University, Kaliningrad, Russia
| | - Sergey Shchanikov
- Department of Neurotechnologies, Research Institute of Physics and Technology, Laboratory of Stochastic Multistable Systems, Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia
- Department of Information Technologies, Vladimir State University, Vladimir, Russia
| | - Alexey Mikhaylov
- Department of Neurotechnologies, Research Institute of Physics and Technology, Laboratory of Stochastic Multistable Systems, Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia
| | - Viktor B. Kazantsev
- Department of Neurotechnologies, Research Institute of Physics and Technology, Laboratory of Stochastic Multistable Systems, Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia
- Neuroscience and Cognitive Technology Laboratory, Center for Technologies in Robotics and Mechatronics Components, Innopolis University, Innopolis, Russia
- Center For Neurotechnology and Machine Learning, Immanuel Kant Baltic Federal University, Kaliningrad, Russia
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Lobov SA, Zharinov AI, Makarov VA, Kazantsev VB. Spatial Memory in a Spiking Neural Network with Robot Embodiment. SENSORS 2021; 21:s21082678. [PMID: 33920246 PMCID: PMC8070389 DOI: 10.3390/s21082678] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/19/2021] [Revised: 04/06/2021] [Accepted: 04/07/2021] [Indexed: 11/16/2022]
Abstract
Cognitive maps and spatial memory are fundamental paradigms of brain functioning. Here, we present a spiking neural network (SNN) capable of generating an internal representation of the external environment and implementing spatial memory. The SNN initially has a non-specific architecture, which is then shaped by Hebbian-type synaptic plasticity. The network receives stimuli at specific loci, while the memory retrieval operates as a functional SNN response in the form of population bursts. The SNN function is explored through its embodiment in a robot moving in an arena with safe and dangerous zones. We propose a measure of the global network memory using the synaptic vector field approach to validate results and calculate information characteristics, including learning curves. We show that after training, the SNN can effectively control the robot’s cognitive behavior, allowing it to avoid dangerous regions in the arena. However, the learning is not perfect. The robot eventually visits dangerous areas. Such behavior, also observed in animals, enables relearning in time-evolving environments. If a dangerous zone moves into another place, the SNN remaps positive and negative areas, allowing escaping the catastrophic interference phenomenon known for some AI architectures. Thus, the robot adapts to changing world.
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Affiliation(s)
- Sergey A. Lobov
- Neurotechnology Department, Lobachevsky State University of Nizhny Novgorod, 23 Gagarin Ave., 603950 Nizhny Novgorod, Russia; (A.I.Z.); (V.A.M.); (V.B.K.)
- Neuroscience and Cognitive Technology Laboratory, Center for Technologies in Robotics and Mechatronics Components, Innopolis University, 1 Universitetskaya Str., 420500 Innopolis, Russia
- Center For Neurotechnology and Machine Learning, Immanuel Kant Baltic Federal University, 14 Nevsky Str., 236016 Kaliningrad, Russia
- Correspondence:
| | - Alexey I. Zharinov
- Neurotechnology Department, Lobachevsky State University of Nizhny Novgorod, 23 Gagarin Ave., 603950 Nizhny Novgorod, Russia; (A.I.Z.); (V.A.M.); (V.B.K.)
| | - Valeri A. Makarov
- Neurotechnology Department, Lobachevsky State University of Nizhny Novgorod, 23 Gagarin Ave., 603950 Nizhny Novgorod, Russia; (A.I.Z.); (V.A.M.); (V.B.K.)
- Instituto de Matemática Interdisciplinar, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, 28040 Madrid, Spain
| | - Victor B. Kazantsev
- Neurotechnology Department, Lobachevsky State University of Nizhny Novgorod, 23 Gagarin Ave., 603950 Nizhny Novgorod, Russia; (A.I.Z.); (V.A.M.); (V.B.K.)
- Neuroscience and Cognitive Technology Laboratory, Center for Technologies in Robotics and Mechatronics Components, Innopolis University, 1 Universitetskaya Str., 420500 Innopolis, Russia
- Center For Neurotechnology and Machine Learning, Immanuel Kant Baltic Federal University, 14 Nevsky Str., 236016 Kaliningrad, Russia
- Lab of Neurocybernetics, Russian State Scientific Center for Robotics and Technical Cybernetics, 21 Tikhoretsky Ave., St., 194064 Petersburg, Russia
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Calvo Tapia C, Tyukin I, Makarov VA. Universal principles justify the existence of concept cells. Sci Rep 2020; 10:7889. [PMID: 32398873 PMCID: PMC7217959 DOI: 10.1038/s41598-020-64466-7] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/24/2019] [Accepted: 04/16/2020] [Indexed: 11/08/2022] Open
Abstract
The widespread consensus argues that the emergence of abstract concepts in the human brain, such as a "table", requires complex, perfectly orchestrated interaction of myriads of neurons. However, this is not what converging experimental evidence suggests. Single neurons, the so-called concept cells (CCs), may be responsible for complex tasks performed by humans. This finding, with deep implications for neuroscience and theory of neural networks, has no solid theoretical grounds so far. Our recent advances in stochastic separability of highdimensional data have provided the basis to validate the existence of CCs. Here, starting from a few first principles, we layout biophysical foundations showing that CCs are not only possible but highly likely in brain structures such as the hippocampus. Three fundamental conditions, fulfilled by the human brain, ensure high cognitive functionality of single cells: a hierarchical feedforward organization of large laminar neuronal strata, a suprathreshold number of synaptic entries to principal neurons in the strata, and a magnitude of synaptic plasticity adequate for each neuronal stratum. We illustrate the approach on a simple example of acquiring "musical memory" and show how the concept of musical notes can emerge.
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Affiliation(s)
- Carlos Calvo Tapia
- Instituto de Matemática Interdisciplinar, Faculty of Mathematics, Universidad Complutense de Madrid, Plaza de Ciencias 3, Madrid, 28040, Spain
| | - Ivan Tyukin
- University of Leicester, Department of Mathematics, University Road, LE1 7RH, United Kingdom
| | - Valeri A Makarov
- Instituto de Matemática Interdisciplinar, Faculty of Mathematics, Universidad Complutense de Madrid, Plaza de Ciencias 3, Madrid, 28040, Spain.
- Lobachevsky University of Nizhny Novgorod, Gagarin Ave. 23, Nizhny, Novgorod, 603950, Russia.
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Lobov SA, Mikhaylov AN, Shamshin M, Makarov VA, Kazantsev VB. Spatial Properties of STDP in a Self-Learning Spiking Neural Network Enable Controlling a Mobile Robot. Front Neurosci 2020; 14:88. [PMID: 32174804 PMCID: PMC7054464 DOI: 10.3389/fnins.2020.00088] [Citation(s) in RCA: 38] [Impact Index Per Article: 7.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/13/2019] [Accepted: 01/22/2020] [Indexed: 11/13/2022] Open
Abstract
Development of spiking neural networks (SNNs) controlling mobile robots is one of the modern challenges in computational neuroscience and artificial intelligence. Such networks, being replicas of biological ones, are expected to have a higher computational potential than traditional artificial neural networks (ANNs). The critical problem is in the design of robust learning algorithms aimed at building a “living computer” based on SNNs. Here, we propose a simple SNN equipped with a Hebbian rule in the form of spike-timing-dependent plasticity (STDP). The SNN implements associative learning by exploiting the spatial properties of STDP. We show that a LEGO robot controlled by the SNN can exhibit classical and operant conditioning. Competition of spike-conducting pathways in the SNN plays a fundamental role in establishing associations of neural connections. It replaces the irrelevant associations by new ones in response to a change in stimuli. Thus, the robot gets the ability to relearn when the environment changes. The proposed SNN and the stimulation protocol can be further enhanced and tested in developing neuronal cultures, and also admit the use of memristive devices for hardware implementation.
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Affiliation(s)
- Sergey A Lobov
- Neurotechnology Department, Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia.,Neuroscience and Cognitive Technology Laboratory, Center for Technologies in Robotics and Mechatronics Components, Innopolis University, Innopolis, Russia
| | - Alexey N Mikhaylov
- Neurotechnology Department, Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia
| | - Maxim Shamshin
- Neurotechnology Department, Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia
| | - Valeri A Makarov
- Neurotechnology Department, Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia.,Instituto de Matemática Interdisciplinar, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, Madrid, Spain
| | - Victor B Kazantsev
- Neurotechnology Department, Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia.,Neuroscience and Cognitive Technology Laboratory, Center for Technologies in Robotics and Mechatronics Components, Innopolis University, Innopolis, Russia
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Calvo Tapia C, Villacorta-Atienza JA, Díez-Hermano S, Khoruzhko M, Lobov S, Potapov I, Sánchez-Jiménez A, Makarov VA. Semantic Knowledge Representation for Strategic Interactions in Dynamic Situations. Front Neurorobot 2020; 14:4. [PMID: 32116635 PMCID: PMC7031254 DOI: 10.3389/fnbot.2020.00004] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2019] [Accepted: 01/14/2020] [Indexed: 11/21/2022] Open
Abstract
Evolved living beings can anticipate the consequences of their actions in complex multilevel dynamic situations. This ability relies on abstracting the meaning of an action. The underlying brain mechanisms of such semantic processing of information are poorly understood. Here we show how our novel concept, known as time compaction, provides a natural way of representing semantic knowledge of actions in time-changing situations. As a testbed, we model a fencing scenario with a subject deciding between attack and defense strategies. The semantic content of each action in terms of lethality, versatility, and imminence is then structured as a spatial (static) map representing a particular fencing (dynamic) situation. The model allows deploying a variety of cognitive strategies in a fast and reliable way. We validate the approach in virtual reality and by using a real humanoid robot.
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Affiliation(s)
- Carlos Calvo Tapia
- Facultad de CC. Matemáticas, Instituto de Matemática Interdisciplinar, Universidad Complutense de Madrid, Madrid, Spain
| | | | - Sergio Díez-Hermano
- Biomathematics Unit, Faculty of Biology, Complutense University of Madrid, Madrid, Spain
| | | | - Sergey Lobov
- N. I. Lobachevsky State University, Nizhny Novgorod, Russia
| | - Ivan Potapov
- N. I. Lobachevsky State University, Nizhny Novgorod, Russia
| | - Abel Sánchez-Jiménez
- Biomathematics Unit, Faculty of Biology, Complutense University of Madrid, Madrid, Spain
| | - Valeri A. Makarov
- Facultad de CC. Matemáticas, Instituto de Matemática Interdisciplinar, Universidad Complutense de Madrid, Madrid, Spain
- N. I. Lobachevsky State University, Nizhny Novgorod, Russia
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