psych 421
deefer
Chapter6.1_Cognitivescienceanddynamicalsystems-revisedfor3rdedition.pptChapter 6.1:
Cognitive science and dynamical systems
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Cognitive Science José Luis Bermúdez / Cambridge University Press 2020
Traditional CogSci
- Basic principles
Cognition is a form of information-processing
Information-processing involves manipulating representations
- PSSH and artificial neural networks incorporate different models of information-processing (mental architectures)
Cognitive Science José Luis Bermúdez / Cambridge University Press 2020
Cognitive Science José Luis Bermúdez / Cambridge University Press 2020
Dynamical systems hypothesis
• cognitive scientists should understand cognitive agents as dynamical systems embedded in their environment
• cognition is a process that evolves through time, but does not necessarily involve computation or representations
• at least not as standardly understood
• DSH sometimes offered as alternative both to PSSH and to ANNs
Cognitive Science José Luis Bermúdez / Cambridge University Press 2020
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Cognitive Science José Luis Bermúdez / Cambridge University Press 2020
Dynamical systems
(1) A dynamical system is any system that evolves over time
trivial that cognitive agents are dynamical systems
DST requires a richer notion
(2) A dynamical system is a system that can be studied using the tools of dynamical modeling
Cognitive Science José Luis Bermúdez / Cambridge University Press 2020
Cognitive Science José Luis Bermúdez / Cambridge University Press 2020
Dynamical models
- Typically use calculus to track the evolving relationship between a small number of variables over time
• difference equations (for modeling discrete time series)
• differential equations (form modeling continuous time series)
Cognitive Science José Luis Bermúdez / Cambridge University Press 2020
Cognitive Science José Luis Bermúdez / Cambridge University Press 2020
State space
- The state space of a dynamical system is a geometric way of thinking about all the possible states the system can be in
As many different dimensions as it has quantities that vary independently of each other
- The state of a system at a time can be identified with a particular set of coordinates in its state space
- The evolution of a system is its trajectory through state space from a set of initial conditions
Cognitive Science José Luis Bermúdez / Cambridge University Press 2020
Cognitive Science José Luis Bermúdez / Cambridge University Press 2020
State space of swinging pendulum
Cognitive Science José Luis Bermúdez / Cambridge University Press 2020
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Cognitive Science José Luis Bermúdez / Cambridge University Press 2020
Basins of attraction in state space
Cognitive Science José Luis Bermúdez / Cambridge University Press 2020
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Cognitive Science José Luis Bermúdez / Cambridge University Press 2020
Similarities to ANNs
ANNs count as dynamical systems
• Dimensionality of the state space given by the number of units – weight space
The process of training the network is a way of configuring the energy landscape
Information-processing in ANNs is a trajectory through unit space
Cognitive Science José Luis Bermúdez / Cambridge University Press 2020
Cognitive Science José Luis Bermúdez / Cambridge University Press 2020
Dissimilarities
- Dynamical systems theorists are typically interested in lower-dimensionality systems
i.e. fewer independently varying quantities
• The dimensions in ANNs often correspond to hidden features of the system, whereas dynamical systems theorists tend to study observable quantities
Cognitive Science José Luis Bermúdez / Cambridge University Press 2020
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Cognitive Science José Luis Bermúdez / Cambridge University Press 2020
Van Gelder’s steam engine analogy
- James Watt designed a gearing system to allow steam engines to drive a flywheel and hence produce rotational power
• Typical applications required power source to be as even as possible
• Need for a governor to regulate the speed of the flywheel
Cognitive Science José Luis Bermúdez / Cambridge University Press 2020
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Cognitive Science José Luis Bermúdez / Cambridge University Press 2020
The computational governor
1. Measure the speed of the flywheel.
Compare the actual speed S1 against the desired speed S2
If S1 = S2, return to step 1
If S1 ≠ S2 then
(a) measure the current steam pressure
(b) calculate the required alteration in steam pressure
(c) calculate the throttle adjustment to achieve that alteration
5. Make the throttle adjustment
6. Return to step 1.
Cognitive Science José Luis Bermúdez / Cambridge University Press 2020
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Cognitive Science José Luis Bermúdez / Cambridge University Press 2020
The computational governor
Representational
Computational
Sequential
Decomposable (homuncular)
Cognitive Science José Luis Bermúdez / Cambridge University Press 2020
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Cognitive Science José Luis Bermúdez / Cambridge University Press 2020
The Watt governor
- The governor regulates speed by compensating almost instantaneously when the speed of the flywheel is overshooting or undershooting
Cognitive Science José Luis Bermúdez / Cambridge University Press 2020
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Cognitive Science José Luis Bermúdez / Cambridge University Press 2020
Features
Dynamical system [behavior characterized by differential equation with fixed parameters and a small number of variables]
Real-time functioning [instantaneous adjustment]
Coupled system [interdependence between arm angle, throttle valve, and speed of flywheel]
Attractor dynamics [for any given engine speed there is an equilibrium arm angle – a region in state-space to which many different trajectories converge]
Cognitive Science José Luis Bermúdez / Cambridge University Press 2020
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Cognitive Science José Luis Bermúdez / Cambridge University Press 2020
The DST challenge
- Can the Watt governor analogy be extended to cognitive systems?
- Can we find cognitive systems which a dynamical systems model works better than a standard, computational account?
Cognitive Science José Luis Bermúdez / Cambridge University Press 2020
