Natural computation measured as a reduction of complexity

Chaos: An Interdisciplinary Journal of Nonlinear Science

Joller

2011

Self Cite

Complex noiseless dynamical systems can be represented in a compressed manner by unstable periodic orbits. It is unknown, however, how to use this technique to obtain a suitable notion of similarity among them, how to extend such an approach to more general complex networks, and how to apply such a method in the important case of noisy systems. Our approach provides a solution to these questions. For a proof-of-concept, we consider Drosophila's precopulatory courtship, where our method reveals the existence of a complex grammar (similar to those found in complex physical systems and in language), leading to the conclusion that the observed grammar is very unlikely the product of chance. Complex noiseless dynamical systems can be represented in a compressed manner by unstable periodic orbits. It is unknown, however, how to use this technique to obtain a suitable notion of similarity among them, how to extend such an approach to more general complex networks, and how to apply such a method in the important case of noisy systems. Our approach provides a solution to these questions. For a proof-of-concept, we consider Drosophila's precopulatory courtship, where our method reveals the existence of a complex grammar (similar to those found in complex physical systems and in language), leading to the conclusion that the observed grammar is very unlikely the product of chance. Complex networks are usually described in terms of abstract network structures, where a node often comes equipped with a rule characterizing its local activity, or by using Markov random walks models. For their understanding, however, intermediate scales may play a distinguished role. This is the case if measures characterizing the network as a whole are too crude for providing the desired insights and if the local node dynamics do not provide an overview of the network. We formulate here in precise mathematical terms such as intermediate, mesoscopic, description of the network, based on periodic orbits as the mesoscopic observables. From these observables, we develop a method for measuring the similarity of graphs, a challenge of great importance that seems not to have been solved in the generality put forward here. An obvious typical application of our approach would be, e.g., the characterization of behavior, with robotics motion planning or the characterization of animal courtship behavior as prominent examples. Animal courtship, which we chose as the real-world testing case of our approach, is a puzzling phenomenon. Its function and purpose have largely remained unexplained, not least because of the generally large and complex underlying network structure and the lack of methods able to deal with such situations. The driving biological questions that we wish to answer here are: Could it be that during courtship, nontrivial information about a prospective mate is conveyed? And if so, how is this information organized and what purpose could it serve? The proposed approach provides partial answers to these questions. We verify that Dro...

Section: Graph Fundamentalsmentioning

confidence: 99%

Mesocopic comparison of complex networks based on periodic orbits

Chaos: An Interdisciplinary Journal of Nonlinear Science

Joller

2011

Self Cite

“…This sort of "computation" as "the ability to transmit, store and modify information" 14 (which then has been claimed to be optimal at edge-ofchaos) has a different meaning from a computation seen as the step of simplifying, i.e., destroying, information. 17 Despite the links that have been drawn between edgeof-chaos and avalanche criticality 18,19 previously, the precise relationship between avalanche and edge-of-chaos criticality is still not settled. While we are not aware of contradicting evidence, a few studies have exhibited simultaneous occurrence of both phase transitions, 6,20 but these studies were based on rather simple network models, with nodes having no intrinsic dynamics.…”

Section: Introductionmentioning

confidence: 99%

“…This is indeed the case at the system's transition from stable to chaotic dynamics, which is characterized by a vanishing largest Lyapunov exponent. Unfortunately, in the sense of computation as a reduction of complexity of prediction, 17 such a "reservoir" is not actually computing; it rather serves as a high-dimensional representation space of spatiotemporal input patterns, from which the readout neurons can sample and perform the computation. This sort of "computation" as "the ability to transmit, store and modify information" 14 (which then has been claimed to be optimal at edge-ofchaos) has a different meaning from a computation seen as the step of simplifying, i.e., destroying, information.…”

Section: Introductionmentioning

confidence: 99%

Avalanche and edge-of-chaos criticality do not necessarily co-occur in neural networks

Kanders

Lorimer

Chaos: An Interdisciplinary Journal of Nonlinear Science

2017

There are indications that for optimizing neural computation, neural networks may operate at criticality. Previous approaches have used distinct fingerprints of criticality, leaving open the question whether the different notions would necessarily reflect different aspects of one and the same instance of criticality, or whether they could potentially refer to distinct instances of criticality. In this work, we choose avalanche criticality and edge-of-chaos criticality and demonstrate for a recurrent spiking neural network that avalanche criticality does not necessarily entrain dynamical edge-of-chaos criticality. This suggests that the different fingerprints may pertain to distinct phenomena. In biological neural networks, scale-free avalanches of neuronal firing events have suggested that such networks might preferably operate at criticality, in particular, since theoretical studies of artificial neural networks and of cellular automata have highlighted some potential computational benefits of such a state. In these studies, notions of either edge-of-chaos criticality or avalanche criticality were adhered to. Here, using a recurrent neural network of more realistic neurons compared with what has been considered previously, we scrutinize whether these two manifestations of criticality are necessarily co-occurring. Based on a realistic paradigm of neural networks, we show that a positive largest Lyapunov exponent-indicating chaotic dynamics of the networkis conserved as we tune the network from subcritical to critical and to supercritical avalanche behavior. This demonstrates that avalanche criticality does not necessarily co-occur with edge-of-chaos criticality.

“…5). Whereas in the ground state the prediction of the evolution of the system is extremely difficult, for the tuned system this is much simpler [39], which is coexpressed by an increased computation (measured as the reduction of the complexity of prediction of the system [40]) after learning. Since the specific heat diverges (½ðd 2 SðεÞ=dε 2 Þ ¼ 0 and there is no latent heat trace, the ground-state system would indeed be at the critical point.…”

mentioning

confidence: 99%

Auditory Power-Law Activation Avalanches Exhibit a Fundamental Computational Ground State

Gomez

2016

Phys. Rev. Lett.

The cochlea provides a biological information-processing paradigm that we are only beginning to understand in its full complexity. Our work reveals an interacting network of strongly nonlinear dynamical nodes, on which even a simple sound input triggers subnetworks of activated elements that follow power-law size statistics ("avalanches"). From dynamical systems theory, power-law size distributions relate to a fundamental ground state of biological information processing. Learning destroys these power laws. These results strongly modify the models of mammalian sound processing and provide a novel methodological perspective for understanding how the brain processes information.