Is the free-energy principle neurocentric?

Recently, a free-energy formulation of brain function was reviewed in relation to several other neurobiological theories (The free-energy principle: a unified brain theory? Nature Rev. Neurosci. 11, 127–138 (2010))¹. Fiorillo raises some interesting questions about the formulation from a neurocentric perspective (A neurocentric approach to Bayesian inference. Nature Rev. Neurosci. 14 Jul 2010 (doi: 10.1038/nrn2787-c1))²:

A primary function of the brain is to infer the state of the world ... to determine which motor behaviours will best promote adaptive fitness.²

The free-energy principle generalizes this by assuming that any (biological) system that conserves its form must minimize 'surprise' (maximize adaptive fitness) through exchange with its environment. 'Surprise' is simply the improbability –ln p(s|m) of sensory data s, given a model m of the environment that is entailed by the form of the system. Exchange with the environment transcends motor behaviour and could cover phototropism in plants (which expect their foliage to be deployed in sunlight) to the elaboration of dendritic processes by a neuron sampling its afferents. In all cases the system tries to sample what it expects, under a model of its world.

... the free energy approach is divorced from the biophysical reality of the nervous system ²

In fact, the approach is grounded explicitly on imperatives for biophysical systems. Furthermore, its neuronal implementation appeals to large bodies of neurophysiological and anatomical facts that often have to be summarized in tables^3,4 (Table 1). The premise of the free-energy principle is that an agent is a model of its world, and this model is determined by the agent's biophysical form and states. Mathematically, minimizing average 'surprise' (also called entropy) then becomes the same as maximizing the evidence p(s|m) for its model (that is, itself).

Table 1 Biophysical aspects of the brain that can be explained under a free-energy formulation

... the brain does not need to perform any processing step to go from information to probabilities and inference².

This assertion overlooks the fact that the mapping between environmental causes and sensory consequences is many-to-one (not bijective). This induces ambiguity — when inferring the causes of sensations⁵ — that is resolved with (Bayesian) probabilistic inference⁶. A simple example here is that 1 + 4 and 2 + 3 are both causes of 5. Alternative causes can only be represented probabilistically, with processing that integrates sensory evidence and prior expectations afforded by a (generative) model.

Surprise ... is essentially just the frequency of an event within an imaginary ensemble of states that could unfold over a long period of time.²

This is a common misconception: surprise (surprisal or self-information) is conditioned on a model and is not an attribute of a sampled (frequentist) distribution. It is –ln p(s|m) not –ln p(s). Put simply, surprise depends on predictions, which depend on a model. Agents build models to predict sensations. The model of the world (or the form of an agent) is optimum when it minimizes surprise, at which point the agent's model (or its form) stops changing and is conserved. The free-energy principle is an information-theoretic treatment of systems that conserve themselves over time and is inherently Bayesian.

... in apparent contradiction to his hypothesis animals tend to explore the least predictable sensory inputs ... ²

Do they? If animals wanted unpredictable sensations they would subject themselves to unprecedented pain. I suspect the deeper question here is how to explain itinerant (wandering or searching) behaviour while minimizing surprise⁷. This is simple to explain: agents use dynamical models (cast mathematically as equations of motion). In other words, agents expect to move through their sensory state-space (because the world is itinerant). Indeed, we have used chaotic exploration to illustrate active inference using free energy⁸ (Fig. 1).

Figure 1: The behaviour of an agent that learns to be a Lorenz attractor.

The figure shows the behaviour of an agent that learns to be a Lorenz attractor in terms of equilibrium densities (left) and exemplar trajectories (right). The top panels show the dynamics of a supervised environment that offers control of the agent's motion so that it can experience and learn itinerant (chaotic) behaviour. The middle panels show behaviour before learning, when the agent expects to be drawn to a point attractor. The lower panels show behaviour after learning, when prior expectations about the environment have been transcribed from the environment by learning under the free-energy principle. Here, learning means optimizing the expected parameters (synaptic connection strengths (μ)) of the agent's equations of motion to minimize free-energy F(s, μ). See Ref. 8 for details. Figure is reproduced, with permission, from Ref. 8 © (2010) Springer.

A truly unified brain theory will need to bridge the gap between Bayesian principles and biophysical reality ... ²

Absolutely. Hopefully, these responses affirm that the free-energy principle is fundamentally biocentric in that biophysical states encode probabilistic representations of causal structure in the world and should even apply to single neurons⁹.