Neural Networks with Anticipation: Problems and Prospects
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The document discusses the use of anticipation in neural networks, exploring its implications in various fields such as control theory, biology, and societal models. It introduces the concept of anticipation and its types, providing mathematical formulations and examples related to network behavior. The research directions outlined include abstract mathematical investigations, model applications, and the exploration of real-world systems like traffic and socio-economic dynamics.
![ANTICIPATION
The anticipation property is that the individual
makes a decision accounting the future states of
the system [1].
One of the consequences is that the accounting
for an anticipatory property leads to advanced
mathematical models. Since 1992 starting from
cellular automata the incursive relation had been
introduced by D. Dubois for the case when
„the values of of state X(t+1) at time t+1 depends
on values X(t-i) at time t-i, i=1,2,…, the value X(t)
at time t and the value X(t+j) at time t+j, j=1,2,…
as the function of command vector p‟ [1].](https://image.slidesharecdn.com/07-aacimp02partanticipat-100821115443-phpapp02/85/Neural-Networks-with-Anticipation-Problems-and-Prospects-5-320.jpg)
![“In the same way, the hyperincursion is an
extension of the hyper recursion in which several
different solutions can be generated at each time
step” [1, p.98].
According [1] the anticipation may be of „weak‟ type
(with predictive model for future states of system,
the case which had been considered by R. Rosen)
and of „strong‟ type when the system cannot make
predictions.](https://image.slidesharecdn.com/07-aacimp02partanticipat-100821115443-phpapp02/85/Neural-Networks-with-Anticipation-Problems-and-Prospects-7-320.jpg)
Neural Networks with Anticipation: Problems and Prospects
- 1. NEURAL NETWORKS WITH ANTICIPATION: PROBLEMS AND PROSPECTS Alexander MAKARENKO Institute for Applied System Analysis at National Technical University of Ukraine (KPI)
- 2. INTRODUCTION Nonlinear networks science (problems and effects): stability bifurcations chaos sinchronisation turbulence chimera states
- 3. MODELS AND SYSTEMS (RECENTLY): coupled oscillators coupled maps neural networks cellular automata o.d.e. system ……… MAINLY of NEUTRAL or WITH DELAY
- 4. ANTICIPATION Neural network learning (Sutton, Barto, 1982) Control theory (Pyragas, 2000?) Neuroscience (1970-1980,… , 2009) Traffic investigations and models (1980, …, 2008) Biology (R. Rosen, 1950- 60- ….) Informatics, physics, cellular automata, etc. (D. Dubois, 1982 - ….) Models of society (Makarenko, 1998 - …)
- 5. ANTICIPATION The anticipation property is that the individual makes a decision accounting the future states of the system [1]. One of the consequences is that the accounting for an anticipatory property leads to advanced mathematical models. Since 1992 starting from cellular automata the incursive relation had been introduced by D. Dubois for the case when „the values of of state X(t+1) at time t+1 depends on values X(t-i) at time t-i, i=1,2,…, the value X(t) at time t and the value X(t+j) at time t+j, j=1,2,… as the function of command vector p‟ [1].
- 6. ANTICIPATION In the simplest cases of discrete systems this leads to the formal dynamic equations (for the case of discrete time t=0, 1, ..., n, ... and finite number of elements M): si (t 1) Gi ({si (t )},...,{si (t g (i))}, R), where R is the set of external parameters (environment, control), {si(t)} the state of the system at a moment of time t (i=1, 2, …, M), g(i) horizon of forecasting, {G} set of nonlinear functions for evolution of the elements states.
- 7. “In the same way, the hyperincursion is an extension of the hyper recursion in which several different solutions can be generated at each time step” [1, p.98]. According [1] the anticipation may be of „weak‟ type (with predictive model for future states of system, the case which had been considered by R. Rosen) and of „strong‟ type when the system cannot make predictions.
- 8. HOPFIELD TYPE NETWORK WITH ANTICIPATION
- 9. SOME EXAMPLES OF MODELS x j (n 1) f w ji xi (n) w ji xi (n 1) N N x j (n 1) f (1 ) w ji xi (n) w ji xi (n 1) i1 i1
- 10. EXAMPLE OF ACTIVATION FUNCTION 0, якщо x 0 f ( x) x, якщо x [0,1) 1, якщо x 1
- 11. Network with 2 coupled neurons Single-valued periodicity
- 12. Neuronert with 2 neuroons 1,2 Multi-valued ciclicity 1 0,8 2 нейрон 0,6 0,4 0,2 0 -0,2 0 0,2 0,4 0,6 0,8 1 1,2 -0,2 1 нейрон
- 13. Netework with 6 neurons. Ciclicity
- 14. Network with 8 neurons
- 15. The influence on anticipation parameter
- 17. RESEARCH DIRECTIONS I. General investigations of abstract mathematical objects: Definitions of regimes: Periodicity; Chaos; Solitons; Chimera states; Bifurcations; Attractors; Etc.
- 18. RESEARCH DIRECTIONS II. Investigation of concrete models and solutions In artificial neural networks In cellular automata In coupled maps Solitons, traveling waves Self-organization Collapses Etc.
- 19. RESEARCH DIRECTIONS III. Interpretations and applications Traffic modeling Crowds movement Socio- economical systems Control applications Neuroscience Conscious problem Physics IT
- 20. REFERENCES 1. Dubois D. Generation of fractals from incursive automata, digital diffusion and wave equation systems. BioSystems, 43 (1997) 97-114. 2 Makarenko A., Goldengorin B. , Krushinski D. Game „Life‟ with Anticipation Property. Proceed. ACRI 2008, Lecture Notes Computer Science, N. 5191, Springer, Berlin-Heidelberg, 2008. p. 77-82 3. B. Goldengorin, D.Krushinski, A. Makarenko Synchronization of Movement for Large – Scale Crowd. In: Recent Advances in Nonlinear Dynamics and Synchronization: Theory and applications. Eds. Kyamakya K., Halang W.A., Unger H., Chedjou J.C., Rulkov N.F.. Li Z., Springer, Berlin/Heidelberg, 2009 277 – 303 4. Makarenko A., Stashenko A. (2006) Some two- steps discrete-time anticipatory models with „boiling‟ multivaluedness. AIP Conference Proceedings, vol.839, ed. Daniel M. Dubois, USA, pp.265-272.