We establish and build theoretical and numerical connections between the theories and methods of integrated information and algorithmic complexity. We introduce a method for estimating integrated information performing a programmability test rooted in algorithmic information dynamics quantifying the change in program size of a system subject to perturbations. Our method is based on the idea that simple rules of causal dynamical systems can shorten the calculation needed to estimate integrated information whereas program-size descriptions of non-integrated systems subject to perturbations, whose parts are causally disconnected (cannot be explained from each other or do not follow from each other) behave differently. On the basis of the perturbation test , we demonstrate how a system can be regarded as providing its own explanations for its own behavioursomething today highly sought in machine learning, helping us infer causal properties of a system while, if integrated, reducing the number of calculations required. We expect this approach to contribute toward a better understanding of integrated informationand of its connections to other, more established areas of science, such as dynamical systems and algorithmic information theory, and to help avoid some of the current abuses (e.g. relating \phi to lossless compression algorithms such as LZW) and limitations arising from the bottleneck principle which other approaches to \phi have been heavily subject to .
The concept of information has emerged as a language in its own right, bridging several disciplines that analyze natural phenomena and man-made systems. Integrated information has been introduced as a metric to quantify the amount of information generated by a system beyond the information generated by its elements. Yet, this intriguing notion comes with the price of being prohibitively expensive to calculate, since the calculations require an exponential number of sub-divisions of a system. Here we introduce a novel framework to connect algorithmic randomness and integrated information and a numerical method for estimating integrated information using a perturbation test rooted in algorithmic information dynamics . This method quantifies the change in program size of a system when subjected to a perturbation. The intuition behind is that if an object is random then random perturbations have little to no effect to what happens when a shorter program but when an object has the ability to move in both directions (towards or away from randomness) it will be shown to be better integrated as a measure of sophistication telling apart randomness and simplicity from structure. We show that an object with a high integrated information value is also more compressible, and is, therefore, more sensitive to perturbations. We find that such a perturbation test quantifying compression sensitivity provides a system with a means to extract explanations--causal accounts--of its own behaviour. Our technique can reduce the number of calculations to arrive at some bounds or estimations, as the algorithmic perturbation test guides an efficient search for estimating integrated information. Our work sets the stage for a systematic exploration of connections between algorithmic complexity and integrated information at the level of both theory and practice .
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We establish and build theoretical and numerical connections between the theories and methods of integrated information and algorithmic complexity. We introduce a
The concept of information has emerged as a language in its own right, bridging several disciplines that analyze natural phenomena and man-made systems. Integrated information has been introduced as a metric to quantify the amount of information generated by a system beyond the information generated by its elements. Yet, this intriguing notion comes with the price of being prohibitively expensive to calculate, since the calculations require an exponential number of sub-divisions of a system. Here we introduce a novel framework to connect algorithmic randomness and integrated information and a numerical
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performing a programmability
using a perturbation
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quantifying
. This method quantifies
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subject to perturbations. Our method is based on the idea that simple rules of causal dynamical systems can shorten the calculation needed to estimate integrated information whereas program-size descriptions of non-integrated systems subject to perturbations, whose parts are causally disconnected (cannot be explained from each other or do not follow from each other) behave differently. On the basis of the perturbation test , we demonstrate how a system can be regarded as providing its own explanations for its own behavioursomething today highly sought in machine learning, helping us infer causal properties of a system while, if integrated, reducing
when subjected to a perturbation. The intuition behind is that if an object is random then random perturbations have little to no effect to what happens when a shorter program but when an object has the ability to move in both directions (towards or away from randomness) it will be shown to be better integrated as a measure of sophistication telling apart randomness and simplicity from structure. We show that an object with a high integrated information value is also more compressible, and is, therefore, more sensitive to perturbations. We find that such a perturbation test quantifying compression sensitivity provides a system with a means to extract explanations--causal accounts--of its own behaviour. Our technique can reduce
R
required. We expect this approach to contribute toward a better understanding of integrated informationand of its connections to other, more established areas of science, such as dynamical systems and algorithmic information theory, and to help avoid some of the current abuses (e.g. relating \phi to lossless compression algorithms such as LZW) and limitations arising from the bottleneck principle which other approaches to \phi have been heavily subject to
to arrive at some bounds or estimations, as the algorithmic perturbation test guides an efficient search for estimating integrated information. Our work sets the stage for a systematic exploration of connections between algorithmic complexity and integrated information at the level of both theory and practice