Criticality Analysis: Bio-inspired Nonlinear Data Representation

TL;DR

The paper addresses how arbitrary data with varying scales can be represented in a biologically plausible, deterministic manner. It introduces Criticality Analysis (CA), a bio-inspired framework that uses Rate Control of Chaos (RCC) controlled nonlinear oscillators arranged as a deterministic reservoir to generate scale-free, dynamic representations. Through experiments on Iris, Wine, and Bonemarrow datasets, with Berry and Wu oscillator models, dynamic normalization, and dynamic Hebbian learning, the authors show that deterministic perturbations yield phase-space trajectories that cluster by class and preserve persistent feature relations. Key contributions include a training-light reservoir representation that is size-invariant, supports simple linear readouts, and offers a biologically relevant approach to data representation with potential applications in ML and biosystems. It provides a foundation for biologically plausible information processing and a scalable, deterministic alternative for dynamic data representation in machine learning contexts.

Abstract

The representation of arbitrary data in a biological system is one of the most elusive elements of biological information processing. The often logarithmic nature of information in amplitude and frequency presented to biosystems prevents simple encapsulation of the information contained in the input. Criticality Analysis (CA) is a bio-inspired method of information representation within a controlled self-organised critical system that allows scale-free representation. This is based on the concept of a reservoir of dynamic behaviour in which self-similar data will create dynamic nonlinear representations. This unique projection of data preserves the similarity of data within a multidimensional neighbourhood. The input can be reduced dimensionally to a projection output that retains the features of the overall data, yet has much simpler dynamic response. The method depends only on the rate control of chaos applied to the underlying controlled models, that allows the encoding of arbitrary data, and promises optimal encoding of data given biological relevant networks of oscillators. The CA method allows for a biologically relevant encoding mechanism of arbitrary input to biosystems, creating a suitable model for information processing in varying complexity of organisms and scale-free data representation for machine learning.

Figures (7)

• Figure 1: A First 12 samples of the Iris data set as presented to the 4 oscillator network. B Total $M$ resulting from the perturbations caused by the Iris dataset of the network. C Total $F$ versus $M$ of the 4 oscillator Iris perturbed network showing different dynamic domains representing categories. D Maxima of $F$ versus $M$ of the figure in panel C demonstrating possible linear separation bounderies. E Iris perturbed phase space plot of $F$ versus $M$ of the 64 oscillator network, showing size independent constant representation of the data. F Phase space plot of the maxima of the 64 oscillator Iris perturbed network, showing consistent representation of the data.
• Figure 2: A Evolution in time of 12 samples from the Iris data set input to a network of oscillators with dynamic Hebbian learning. B Phase space plot of the total $F$ versus $M$ of all the Iris samples, showing changes in dynamic response due to the perturbations causing adaptive learning. C Maxima of total $F$ versus $M$ of all the Iris samples in the network, showing poor separation on amplitude. D Median frequency of the total $F$ versus the maximal $M$ showing that separation is possible due to the changing dynamics of the orbits, as is shown in panel A.
• Figure 3: A Orbits of 5 samples of the first class in the Iris data set as represented by the read-out unit 7 in time. B Orbits of 5 samples of the second class in the Iris data set as represented by unit 7 in time. C Same as previous panels, but for the third class. D Phase space plot of the maxima of total $F$ and $M$ of the six reservoir units (i.e. excluding the read-out units, 7 and 8).
• Figure 4: A Phase space plot of the maximal $f$ and $m$ from the read out unit 7. B Phase space plot of the maximal $f$ versus the median frequency of $m$ of unit 7. C Phase space plot of the maximal $f$ and $m$ of the read out unit 8. D Phase space plot of unit 8, showing maximal $f$ versus the median frequency of $m$.
• Figure 5: A Network of four Wu oscillators with Iris data input, showing the evolution of 20 samples with total $W$ of the network. The network does not oscillated and converges to steady states, as shown in the plot where the transients end at a specific value of total $W$. B Phase space representation of the maximal total $Z$ versus $W$ showing the steady state representations in two dimensions allowing separation. C Three dimensional representation of the maxima of total $Y$, $Z$ and $W$, with the Iris data presented to the four Wu oscillator network, showing different representation in multiple dimensions.