Variational ecology and the physics of sentient systems

Abstract

This paper addresses the challenges faced by multiscale formulations of the variational (free energy) approach to dynamics that obtain for large-scale ensembles. We review a framework for modelling complex adaptive control systems for multiscale free energy bounding organism-niche dynamics, thereby integrating the modelling strategies and heuristics of variational neuroethology with a broader perspective on the ecological nestedness of biotic systems. We extend the multiscale variational formulation beyond the action-perception loops of individual organisms by appealing to the variational approach to niche construction to explain the dynamics of coupled systems constituted by organisms and their ecological niche. We suggest that the statistical robustness of living systems is inherited, in part, from their eco-niches, as niches help coordinate dynamical patterns across larger spatiotemporal scales. We call this approach variational ecology. We argue that, when applied to cultural animals such as humans, variational ecology enables us to formulate not just a physics of individual minds, but also a physics of interacting minds across spatial and temporal scales - a physics of sentient systems that range from cells to societies.

Keywords: Evolutionary systems theory; Free energy principle; Niche construction; Physics of the mind; Variational ecology; Variational neuroethology.

Fig. 1

The Markov blanket. These schematics illustrate the partition of states into internal (μ) and hidden or external states (η) that are separated by a MB – comprising sensory (s) and active states (a). The upper panel shows this partition as it would be applied to action and perception in the brain; where active and internal states minimise a free energy functional of sensory states. The ensuing self-organisation of internal states then corresponds to perception, while action couples brain states back to external states. The lower panel shows exactly the same dependencies but rearranged so that the internal states are associated with the intracellular states of a cell, while the sensory states become the surface states of the cell membrane overlying active states (e.g., the actin filaments of the cytoskeleton).

Fig. 2

Explanatory scope of variational approach. Variational neuroethology leverages the FEP to explain the adaptive free energy bounding dynamics of living systems across spatial and temporal scales. Here we indicate some of the scales at which these dynamics unfold. Given the intrinsic correlation between spatial and temporal scales, the phase space described here is populated mostly along its diagonal. Adapted from .

Fig. 3

Blankets of blankets. This schematic figure illustrates the recursive architecture by which successively larger (and slower) scale dynamics arise from subordinate levels. Starting at the bottom of the figure (lower panel) we can consider an ensemble of vector states (here nine). The conditional dependencies among these vector states then define a particular partition of into particles (upper panels). Crucially, this partition equips each particle with a bipartition into blanket and internal states, where blanket states comprise active (red) and sensory states (magenta). The behaviour of each particle can now be summarised in terms of (slow) eigenmodes or mixtures of its blanket states to produce vector states at the next level or scale. These constitute an ensemble of vector states and the process starts again. The upper panels illustrate the bipartition for a single particle (left panel) and an ensemble of particles; i.e., the particular partition per se (right panel). The insets on top illustrate the implicit self-similarity in moving from one scale to the next using. In this figure, Ω ⋅ b denotes a linear mixture of blanket states specified by the principal eigenvectors of their Jacobian. Because the corresponding eigenvalues play the role of Lyapunov exponents, the resulting mixtures correspond to slow or unstable dynamical modes of activity.

Fig. 4

Self-assembly and active inference. This figure shows the results of a simulation of morphogenesis under active inference reported in . This simulation used a gradient descent on variational free energy using a simple ensemble of eight cells; each of which had the same (pluripotential) generative model. This generative model predicted what each cell would sense and signal (chemotactically) for any given location in a ‘target morphology’ (lower middle panel – extracellular target signal; in other words, what each agent would expect to sense if it were at a particular location). By actively moving around, all the cells minimised their variational free energy (i.e., surprise) by inferring where they were, in relation to others. Because variational free energy is an extensive quantity, the free energy minimising arrangement of the ensemble is the target morphology. In other words, every cell has to ‘find its place’, at which point each cell minimises its own surprise about the signals it senses (because it knows its place) and the ensemble minimises the total free energy. The upper panels show the time courses of expectations about its place in the morphology (upper left), the associated active states mediating migration and signal expression (upper middle) and the resulting trajectories; projected onto the first (vertical) direction – and colour-coded to show differentiation (upper right). These trajectories progressively minimise total free energy (lower left panel). The lower right panel shows the ensuing configuration. Here, the trajectory is shown in small circles (for each time step). The insert corresponds to the target configuration. Please see for further details.

Fig. 5

Bayesian mechanics and active inference. This graphic summarises the belief updating scheme in the minimisation of variational free energy and expected free energy , , . In the first step (circles on the left), discrete actions solicit a sensory outcome (i.e., in the parlance of the SIF, a solicitation) used to form approximate posterior beliefs about states of the world. This belief updating involves the minimisation of free energy under a set of plausible policies (blue panel – Perceptual inference). Note that free energy F(π,s) includes Markovian dependencies among hidden states. This reflects the fact that the generative model is a Markov decision process. In the second step (green panel – Policy selection), the approximate posterior beliefs from the first step are used to evaluate expected free energy F(π,τ) and subsequent beliefs about action. These beliefs correspond to the epistemic and pragmatic affordances that underwrite policy selection. Note that the free energy per se is a function of sensory states, given a policy. In contrast, the expected free energy is a function of the policy. The construct of affordance in active inference corresponds to inferences about action on the environment, which are selected in terms of competing policies via the minimisation of expected free energy. The variables in this figure correspond to those in Fig. 1. Here, a policy π comprises a sequence of actions; the expression Q(η|π) denotes beliefs about hidden states given a particular policy; and Q(π) denotes posterior beliefs about the policy that is currently being pursued by the agent. Free energy is the difference between complexity and accuracy, while expected free energy can be decomposed into expected complexity (i.e., complexity cost or risk) and expected inaccuracy (i.e., ambiguity). Risk can be regarded as the (KL) divergence (D) between beliefs about future states under a particular policy and prior preferences about states. Ambiguity denotes the loss of a definitive mapping between external states and observed sensory states (quantified as entropy, H). Alternatively, expected free energy can be decomposed into epistemic and pragmatic affordance. Posterior beliefs about policies depend on their expected free energy. Crucially, these posterior beliefs include the free energy evaluated during perceptual inference. This has several interesting consequences from our perspective. This construction means that the agent has to infer the policy that it is currently pursuing and verify its predictions in light of sensory evidence. This is possible because the beliefs about actions that are encoded by internal states are distinct from the active states of the agent's MB. Free energy per se provides evidence that a particular policy is being pursued. In this scheme, agents (will appear to) entertain beliefs about their own behaviour, endowing them with what is defined as intentionality of goal directed behaviour under active inference. In effect, this enables agents to author their own sensorium in a fashion that has close connections with niche construction: see main text and . See for technical discussion. Figure from .

Fig. 6

A particular partition. This schematic figure illustrates a partition of vectors states (small coloured balls) into particles (comprising nine vectors), where each particle (π) has six blanket states (red and magenta for active and sensory states respectively) and three internal states (cyan). The upper panel summarises the operators used to create a particular partition. We start by forming an adjacency matrix that characterises the coupling between different vectors states. In this example, the adjacency matrix is based upon the Jacobian and implicitly the flow of vector states. The resulting adjacency matrix defines a MB forming matrix (B), which identifies the children, parents, and parents of the children. The same adjacency matrix is used to form a graph Laplacian (L) that is used to define neighbouring (i.e., coupled) internal states. One first identifies a set of internal states using the graph Laplacian. Here, the j-th subset of internal states at the level i are chosen based upon dense coupling with the vector state with the largest graph Laplacian. Closely coupled internal states are then selected from the columns of the graph Laplacian that exceed some threshold. In practice, the examples used later specify the number of internal states desired for each level of the hierarchical decomposition. Having identified a new set of internal states (that are not members of any particle that has been identified so far) its MB is recovered using the MB forming matrix. The internal and blanket states then constitute a new particle, which is added to the list of particles identified. This procedure is repeated until all vector states have been accounted for. In the example here, we have already identified four particles and the procedure adds a fifth (top) particle to the list of particles; thereby accounting for nine of the remaining vector states.