Jordi Piñero, Ricard Solé; Statistical physics of liquid brains.

Experts from article

Liquid neural networks (or ‘liquid brains’) are a widespread class of cognitive living networks characterized by a common feature: the agents (ants or immune cells, for example) move in space. Thus, no fixed, long-term agent-agent connections are maintained, in contrast with standard neural systems.

Network interactions in liquid versus solid brains. The three case studies analysed in this paper are shown, with examples of the agents involved in each case.

(a) Standard neural networks involve spatially localized cells connected through synaptic weights. In contrast with this architecture, liquid brains, including

(b) ant colonies and

© the IS include mobile agents (or cell subsets) interacting in space and time with no fixed pairwise weights. A schematic of each case study is outlined in the row below. Standard neural networks are defined in terms of connected excitable elements that can be roughly classified in active (firing) and inactive (quiescent) neurons, here indicated as filled and open circles, respectively

(d). The wiring matrix remains basically the same in terms of topology (who is connected with whom) but will be modified in strength due to experience. By contrast, ant colonies must be represented by disconnected graphs

(e) where interactions are possible within a given spatial range, here indicated by means of the grey circle. The IS allows several representations of the interactions, but in many cases it is the molecular interaction between epitopes (strings of symbols in (f)) that truly represents the underlying liquid brain dynamics.

Ant colonies also involve collectives of interacting individuals that can be modeled as on/off activity - e.g. engaged in a task or not. However, the physical location of such mobile agents change over time: the colony is ‘liquid’. Thus, interactions are now extended to a spatiotemporal embedding, with agents interacting at a certain location in one instant and then moving on to other locations to continue interacting with each other. This particularity will constrain the system's adaptive properties in a non-trivial manner. Within the liquid realm, we can still characterize two paradigms: given their relative mobility and signal transmissivity (see below) insect colonies are strongly affected by the locality of their interactions, whereas ISs are highly mobile, such that a well-mixed approach might accurately represent their overall dynamics.

Other types of organisms, such as the slime mould Physarum, solve some classes of optimization problems by using a different form of fluid organization [13], although in this case there is no neural substrate. Systems of this kind are able to solve minimization problems on a network [14].

Jordi Piñero, Ricard Solé; Statistical physics of liquid brains. Phil. Trans. R. Soc. B 10 June 2019; 374 (1774): 20180376. https://doi.org/10.1098/rstb.2018.0376