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Invariants of Behavior pp 141–175Cite as

Attractor Landscapes and the Invariants of Behavior

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Part of the book series: Springer Series in Cognitive and Neural Systems ((SSCNS,volume 1))

Abstract

This chapter introduces an explanatory middleman, the concept of an attractor landscape. It is used to show what is an invariant of behavior: an abstract representation of a functional mechanism. With an experiment in the evolution of active tracking, recurrent neural networks are evolved that enable agents to track a moving object in a simulated environment. The invariant behavior, i.e., the functional mechanism implemented by agents, is a two-dimensional version of the well-known – from cybernetics – negative feedback, which subsumes an ample range of both simple and complex organismic functions. I will (1) show how, despite extreme variability in network structures, constancy of behavior reflects invariant features of the attractor landscapes, (2) show that behavioral function only exists as a potential, until it is evoked, and (3) show that even networks with radically different attractors may implement the same embodied function, as long as these networks possess certain invariant features of the attractor landscape. This chapter also addresses constancy arising from level crossing, convergence, as variable activity patterns have their dimensions effectively reduced at the level of actuators. I will show how attractors are made equivalent through convergence. How the ongoingness of behavior appears as the attractor landscape is explored through organism–environment interaction. This will lead to the concept of a “metatransient,” with respect to which we show effectively what it means for an organism, to implicitly represent the coupling between the organism and its environment.

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Notes

  1. 1.

    Parameterizations are meant in the manner that has become usual in the dynamical systems literature, in which parameters are variables that change slowly with respect to the dynamics of the network.

  2. 2.

    It is helpful to be aware that “qualitatively distinct dynamic behavior” might lead to qualitatively similar agent behavior, which might be a source of ambiguity (see Sect. 8.4.6.2).

  3. 3.

    The idea that readout units sample different aspects of the same attractor is analogous to the approach of liquid state machines or echo state networks (dynamic reservoir networks) [19], with the difference that their attractors are generated randomly to satisfy certain requirements for complex dynamics, whereas our attractors are incrementally evolved. This difference results from the role of the attractors, in which we think that there are attractors that are more apt to solve some kinds of problems, and that artificial evolution is a good method to beget them.

  4. 4.

    This does not mean, however, that all the agent may reach every coexisting attractor during behavior, since the possible states are also bounded by the possible history of interactions.

  5. 5.

    Consider when the ball is subject to gravity, with the velocity on the vertical axis, even if the head locks its position to the ball, thereby keeping a constant input pattern, it must nevertheless accelerate downward.

  6. 6.

    The internal states of the hidden layer are inherited across parameterizations.

  7. 7.

    These input patterns were obtained with the same network operating under 500-Hz update frequency, so the differences between steps would be tiny. Note that this test would not have been possible if the network had not been robust to different update frequencies.

  8. 8.

    Note that this reflexive depiction of behavior does not need to mean it is stereotypical. In The Structure of Behavior, Merleau-Ponty [22] makes a case for the inadequacy of a physiological theory of behavior based on reflexes, since a quantitative change of the stimulus induces a qualitative change in behavior. But as we have seen in our case, even a small quantitative difference in stimulus may invoke a qualitatively different reaction, not bijective with the stimulus.

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  1. Okinawa Institute of Science and Technology, Okinawa, Japan

    Mario Negrello

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  1. Mario Negrello
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Correspondence to Mario Negrello .

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Negrello, M. (2011). Attractor Landscapes and the Invariants of Behavior. In: Invariants of Behavior. Springer Series in Cognitive and Neural Systems, vol 1. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8804-1_8

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