- Email: [email protected]
Structure-based modeling of schemas
Artificial Intelligence Artificial Intelligence
101 (1998) 341-343
Commentary
Structure-based
modeling of schemas P. firdi I
LkpartmentBiophysics, KFKI Reseurch Institute for Purticle and Nuclear Physics, Hungariun Academy oj Sciences, Budapest, PO. Box 49, H-1525, Hungary Received 26 January
1998; received in revised form 2.5 February
1998
The writer of this short commentary is one of the co-authors of the book by Arbib, l?rdi and Szendgothai [ 11. While The Metaphorical Bruin 2 (TMB2) provides a neural theory of functional modules (schemas), Arbib, l?rdi and Szentagothai [l] critically review and integrate the concepts of structural, functional and (much more implicit) dynamic modules. In this book we admittedly adopted a pluralist strategy: both a functionalist top-down approach and the structuralist bottom-up approach have been adopted. Though we have not mentioned it explicitly in [I], it is time to talk about a partially new topic, what I here call structure-based modeling of schemas. A few ingredients of this new approach will briefly be mentioned here.
1. Schemas versus multicompartmental
models
There are a few examples where detailed multicompartmental modeling (i.e., analyzing such as the soma and various branches each neuron as a set of multiple “compartments”, of the dendrites) leads to the understanding of the dynamic emergence of schemas. These include the analysis of central pattern generators (CPG), such as those for the lamprey spinal cord (Brodin et al. 1991) and leech heart beat (Nadim et al. [5]; Olsen et al. [5]).
2. Neural networks, (structural)
modules, schemas
Networks of neurons organized by excitatory and inhibitory synapses are structural units subject to time-dependent inputs and they also emit output signals. From a functional point of view, a single neural network may be considered sometimes as a pattern generating and/or pattern recognizing device. More often it is not a single ’ Email: [email protected]. 0004-3702/98/$19.00 0 1998 Published by Elsevier B.V. All rights reserved PII: SOOO4-3702(9X)00030-7
342
I? &Ii /Art@ial
Intelligence
101 (1998) 341-343
network but a set of cooperating neural networks that forms the structural basis of pattern generation and recognition. (Pattern generating devices are functional elements of schemas.) Consequently, while the structural organization principles of many neural centers can be understood based on the concept of modular architectonics (Szentagothai in [l]), i.e., a network made up of repetitive modular elements, there is no one-to-one correspondence between structural and functional modules.
3. Neural networks and dynamics Depending on its structure, an autonomous neural network may or may not exhibit different qualitative dynamic behavior (convergence to equilibrium, oscillation, chaos). Some architectures shows unconditional behavior, which means that the qualitative dynamics does not depend on the numerical values of synaptic strengths. The behavior of other networks can be switched from one dynamic regime to another by tuning the parameters of the network. One mechanism of tuning is synaptic plasticity, which may help to switch the dynamics between the regimes (e.g., between different oscillatory modes, or oscillation and chaos, etc. ...).
4. Network models Since the neural modeling of schemas most often requires the consideration of interacting neural centers, the proper tool seems to be not more microscopic than the singlecompartment modeling technique. Models with fixed wiring are proper tools to follow the activity dynamics on an intermediate level, while taking synaptic modification (and sometimes the dynamics of the threshold due to adaptation) into account can implement elementary developmental and learning schemas.
5. Population
models
As we have seen, structure-based bottom-up modeling has two extreme alternatives, namely multi-compartmental simulations, and simulation of networks composed of simple elements. There is an obvious trade-off between these two modeling strategies. The first method is appropriate to describe the activity patterns of single cells, small and moderately large networks based on data on detailed morphology and kinetics of voltageand calcium-dependent ion channels. The second offers a computationally efficient method for simulating large network of neurons where the details of single cell properties are neglected. To make large-scale and long-term realistic neural simulations there is a need to find a compromise between the biophysically detailed multicompartmental modeling technique, and the sometimes oversimplified network models. Statistical population theories offer a good compromise. Ventriglia [6,7] introduced a kinetic theory for describing the interaction between a population of spatially fixed neurons and a population of spikes traveling
P: hdi /Artijcial
Intelligence IO1 (lY98) 341-343
343
between the neurons. In our group (6rdi at al., Griibler et al., Barna et al.) a scale-invariant theory (and software tool) was developed, which gives the possibility to simulate the statistical behavior of large neural populations, and synchronously to monitor the behavior of an “average” single cell. There is a hope that activity propagation among neural centers may be realistically simulated, and schemas can be built from structure-based modeling.
References [ I] M.A. Arbib, P. Verdiand J. Szenmgothai, Neural Organization: Structure, Function, and Dynamics, A Bradford Book/The MIT Press, Cambridge, MA, 1997. [2] G. Bama, T. Griibler and P. Verdi, Statistical model of the hippocampal CA3 region II The population framework: model of rhythmic activity in the CA3 slice, Biol. Cybernetics (accepted). [3] P. Verdi, I. Aradi and T. Griibler, Ryhthmogenesis in single cell and population models: olfactory bulb and hippocampus, BioSystems 40 (1997) 45-53. [4] T. Grobler, G. Barna and P. Verdi, Statistical mode1 of the hippocampal CA3 region I. The single cell module: bursting model of the pyramidal cell, Biol. Cybernetics (accepted). [S] F. Nadim, O.H. Olsen, E. De Schutter and R.L. Calabrese, Modeling the leech heartbeat elemental oscillator I. Interaction of intrinsic and synaptic currents, J. Comput. Neurosci. 2 (1995) 215-235. 161 F. Ventriglia, Kinetic approach to neural systems I, Bull. Math. Biol. 36 (1974) 534-544. [7] E Ventriglia, Towards a kinetic theory of cortical-like neural fields, in: E Ventriglia (Ed.), Neural Modeling and Neural Networks, Pergamon Press, 1994, pp. 217-249. [S] P. Wallen, 0. Ekeberg, A. Lansner, L. Brodin, H. Traven and S. Grillner, A computer based model for realistic simulations of neural networks. II. The segmental network generating locomotor rhythmicity in the lamprey, J. Neurophysiol. 68 (1992) 1939-1950.
101 (1998) 341-343
Commentary
Structure-based
modeling of schemas P. firdi I
LkpartmentBiophysics, KFKI Reseurch Institute for Purticle and Nuclear Physics, Hungariun Academy oj Sciences, Budapest, PO. Box 49, H-1525, Hungary Received 26 January
1998; received in revised form 2.5 February
1998
The writer of this short commentary is one of the co-authors of the book by Arbib, l?rdi and Szendgothai [ 11. While The Metaphorical Bruin 2 (TMB2) provides a neural theory of functional modules (schemas), Arbib, l?rdi and Szentagothai [l] critically review and integrate the concepts of structural, functional and (much more implicit) dynamic modules. In this book we admittedly adopted a pluralist strategy: both a functionalist top-down approach and the structuralist bottom-up approach have been adopted. Though we have not mentioned it explicitly in [I], it is time to talk about a partially new topic, what I here call structure-based modeling of schemas. A few ingredients of this new approach will briefly be mentioned here.
1. Schemas versus multicompartmental
models
There are a few examples where detailed multicompartmental modeling (i.e., analyzing such as the soma and various branches each neuron as a set of multiple “compartments”, of the dendrites) leads to the understanding of the dynamic emergence of schemas. These include the analysis of central pattern generators (CPG), such as those for the lamprey spinal cord (Brodin et al. 1991) and leech heart beat (Nadim et al. [5]; Olsen et al. [5]).
2. Neural networks, (structural)
modules, schemas
Networks of neurons organized by excitatory and inhibitory synapses are structural units subject to time-dependent inputs and they also emit output signals. From a functional point of view, a single neural network may be considered sometimes as a pattern generating and/or pattern recognizing device. More often it is not a single ’ Email: [email protected]. 0004-3702/98/$19.00 0 1998 Published by Elsevier B.V. All rights reserved PII: SOOO4-3702(9X)00030-7
342
I? &Ii /Art@ial
Intelligence
101 (1998) 341-343
network but a set of cooperating neural networks that forms the structural basis of pattern generation and recognition. (Pattern generating devices are functional elements of schemas.) Consequently, while the structural organization principles of many neural centers can be understood based on the concept of modular architectonics (Szentagothai in [l]), i.e., a network made up of repetitive modular elements, there is no one-to-one correspondence between structural and functional modules.
3. Neural networks and dynamics Depending on its structure, an autonomous neural network may or may not exhibit different qualitative dynamic behavior (convergence to equilibrium, oscillation, chaos). Some architectures shows unconditional behavior, which means that the qualitative dynamics does not depend on the numerical values of synaptic strengths. The behavior of other networks can be switched from one dynamic regime to another by tuning the parameters of the network. One mechanism of tuning is synaptic plasticity, which may help to switch the dynamics between the regimes (e.g., between different oscillatory modes, or oscillation and chaos, etc. ...).
4. Network models Since the neural modeling of schemas most often requires the consideration of interacting neural centers, the proper tool seems to be not more microscopic than the singlecompartment modeling technique. Models with fixed wiring are proper tools to follow the activity dynamics on an intermediate level, while taking synaptic modification (and sometimes the dynamics of the threshold due to adaptation) into account can implement elementary developmental and learning schemas.
5. Population
models
As we have seen, structure-based bottom-up modeling has two extreme alternatives, namely multi-compartmental simulations, and simulation of networks composed of simple elements. There is an obvious trade-off between these two modeling strategies. The first method is appropriate to describe the activity patterns of single cells, small and moderately large networks based on data on detailed morphology and kinetics of voltageand calcium-dependent ion channels. The second offers a computationally efficient method for simulating large network of neurons where the details of single cell properties are neglected. To make large-scale and long-term realistic neural simulations there is a need to find a compromise between the biophysically detailed multicompartmental modeling technique, and the sometimes oversimplified network models. Statistical population theories offer a good compromise. Ventriglia [6,7] introduced a kinetic theory for describing the interaction between a population of spatially fixed neurons and a population of spikes traveling
P: hdi /Artijcial
Intelligence IO1 (lY98) 341-343
343
between the neurons. In our group (6rdi at al., Griibler et al., Barna et al.) a scale-invariant theory (and software tool) was developed, which gives the possibility to simulate the statistical behavior of large neural populations, and synchronously to monitor the behavior of an “average” single cell. There is a hope that activity propagation among neural centers may be realistically simulated, and schemas can be built from structure-based modeling.
References [ I] M.A. Arbib, P. Verdiand J. Szenmgothai, Neural Organization: Structure, Function, and Dynamics, A Bradford Book/The MIT Press, Cambridge, MA, 1997. [2] G. Bama, T. Griibler and P. Verdi, Statistical model of the hippocampal CA3 region II The population framework: model of rhythmic activity in the CA3 slice, Biol. Cybernetics (accepted). [3] P. Verdi, I. Aradi and T. Griibler, Ryhthmogenesis in single cell and population models: olfactory bulb and hippocampus, BioSystems 40 (1997) 45-53. [4] T. Grobler, G. Barna and P. Verdi, Statistical mode1 of the hippocampal CA3 region I. The single cell module: bursting model of the pyramidal cell, Biol. Cybernetics (accepted). [S] F. Nadim, O.H. Olsen, E. De Schutter and R.L. Calabrese, Modeling the leech heartbeat elemental oscillator I. Interaction of intrinsic and synaptic currents, J. Comput. Neurosci. 2 (1995) 215-235. 161 F. Ventriglia, Kinetic approach to neural systems I, Bull. Math. Biol. 36 (1974) 534-544. [7] E Ventriglia, Towards a kinetic theory of cortical-like neural fields, in: E Ventriglia (Ed.), Neural Modeling and Neural Networks, Pergamon Press, 1994, pp. 217-249. [S] P. Wallen, 0. Ekeberg, A. Lansner, L. Brodin, H. Traven and S. Grillner, A computer based model for realistic simulations of neural networks. II. The segmental network generating locomotor rhythmicity in the lamprey, J. Neurophysiol. 68 (1992) 1939-1950.