Illustration of Neocybernetic Equilibria

Introduction

This simulation visualizes dynamic attractors, emergent models, of data in a multidimensional tension space. To simplify the presentation, a few dozen tension samples index a complex environment. The emergent models determine processes that can be used to represent and estimate tension intensities, cybernetic equilibria. The simulation is based on cybernetic systems where perceptions x are linear (and optionally sparse) balancing transformations of effective tensions ū and emergent models phi are adapted towards local matching of mutual cybernetic information . In other words, perceptions are superpositions of dampening responses to time dependent external perturbing fields. Responses are coupled to effective fields via emergent (average) interactions between response superpositions and effective fields.

The simulation demonstrates this local strategy resulting in emergent system level properties such as:

Elastic resilience. The system reacts by generalized diffusion to restore dynamic balance.
Adaptive robustness and emergent models. The models orient themselves to span the principal subspace of the tension distribution, reflecting relevant patterns and filtering noise.
Optimal regulation. Multidimensional tension space is attenuated by implicit model-based control as tension excitation is partially consumed for model activity.

Initially only two cybernetic systems (in blue) driven by two-dimensional tension samples (light dots) are shown. Tension samples are attenuated (light lines) by implicit tension use, which gives an estimate (black circle) of the current tensions (black disks at mouse position). The systems interact only via their environment, but still as a whole enact functionally interesting structures. See “controls” tab and more animations below the demo to learn more.

Explore the Interactive Demo

Higher-Dimensional Examples

The simulation presents only 1–5 models in a 2–5-dimensional tension space. Useful results are obtained in higher-dimensional spaces. The spaces can be composed of any kind of finite data (for example, augmented with delayed and otherwise transformed tensions), but perhaps it is most illustrative to present a few examples where the structure of the tension space is intuitively clear: using images as multidimensional tensions. Each example below is initiated with random models in the tension space that is determined by image data.

Digits A – 10 emergent models of a 256-dimensional tension space with 500 tension samples. Tension samples consist of handwritten digits presented as 16×16=256-dimensional vectors. The models seem to orient themselves to represent clusters in the tension space.
Digits B – 40 emergent models of a 256-dimensional tension space with 500 tension samples. Tension samples consist of the same handwritten digits as above. An example tension (bottom right) can be reconstructed (bottom rightmost) by adding together active models. Only a few emergent models are active for each tension sample (activity is not visualized in the animation), and different models can be shared across representations – the distributed code is sparse and different models tend to respond to different strokes.
Faces – 30 emergent models of a 560-dimensional tension space with 1965 tension samples. An example tension (bottom left) can be reconstructed (bottom right) by a linear combination of active models representing facial expressions (30 almost orthogonal vectors, each 28×20=560-dimensional).
Digits C – 100 sharing emergent models of a 1024-dimensional tension space with 8940 tension samples. Tension samples consist of handwritten digits presented as 32×32=1024-dimensional vectors. This time the coupling coefficient matrix Q has also non-diagonal elements so that the models respond also to their spatial, planar neighbours.
Digits D – 100 sharing emergent models of 1024- and 10-dimensional tension spaces with 8940 tension samples. Tension samples consist of the same handwritten digits as in the previous case. In addition to non-diagonal Q here also class label information is used: there is a 10-dimensional parallel tension space indexing whether the current sample is a number 0–9, and the models respond simultaneously to both spaces. Thus the models reflect also additional type information instead of only the tension space structure. The results can be used, for example, for Partial Least Squares (PLS) / Canonical Correlation Analysis (CCA) like subspace regression, in a distributed, regularized and sparse way.

In addition, among recent developments is to use complex values for representing tension magnitude and phase together, allowing modeling of tension space change tensions in the same framework.

Update: Now you can test run the algorithm in R environment for statistical computing: pca.r, sca.r, csca.r. A more thorough tutorial may be prepared later. In the meantime, lectures on elementary cybernetics, especially lecture 4 and later, discusses cybernetic equilibria, and some summaries are available too.

Applications

Neocybernetics may offer new possibilities for research and development of complex systems, i.a. bioinspired and hyperdimensional computing. See lectures and publications elsewhere on this site for examples on:

Statistical methods applied in soft sensors, sensor fusion, and calibration
Emergence of behaviors applied in parameter optimization of industrial systems
Idea of “fractal robustness” applied in redesign and analysis of a power plant grid

Systems biology, modeling of genetic and metabolic systems using dynamic models
Biodiversity in ecologies and economies, and estimating their qualitative behaviors
Structured models for neural and cognitive systems, and new languages for them

Crossing the boundaries of qualitative and quantitative methods in the behavioral and social sciences
Systems theoretical contributions to (mathematical) natural philosophy

Neocybernetic Proposal

As a summary, studies on neocybernetics suggest that mostly everything is information (covariation) – the essence of perceived stable structures consists of attractors of dynamic processes governed by modeling and entropy pursuit in the tension space. Life could then be characterized – in a more general way than the common understanding as the germline – as the drive towards fractal balance of functions in various environments.