Embodied inference and spatial cognition

Abstract

How much about our interactions with--and experience of--our world can be deduced from basic principles? This paper reviews recent attempts to understand the self-organised behaviour of embodied agents, like ourselves, as satisfying basic imperatives for sustained exchanges with the environment. In brief, one simple driving force appears to explain many aspects of perception, action and the perception of action. This driving force is the minimisation of surprise or prediction error, which--in the context of perception--corresponds to Bayes-optimal predictive coding (that suppresses exteroceptive prediction errors) and--in the context of action--reduces to classical motor reflexes (that suppress proprioceptive prediction errors). In what follows, we look at some of the phenomena that emerge from this single principle, such as the perceptual encoding of spatial trajectories that can both generate movement (of self) and recognise the movements (of others). These emergent behaviours rest upon prior beliefs about itinerant (wandering) states of the world--but where do these beliefs come from? In this paper, we focus on the nature of prior beliefs and how they underwrite the active sampling of a spatially extended sensorium. Put simply, to avoid surprising states of the world, it is necessary to minimise uncertainty about those states. When this minimisation is implemented via prior beliefs--about how we sample the world--the resulting behaviour is remarkably reminiscent of searches seen in foraging or visual searches with saccadic eye movements.

Fig. 1

Schematic detailing the neuronal architectures that might encode posterior expectations about the states of a hierarchical generative model. This figure shows the speculative cells of origin of forward driving connections that convey prediction error from a lower area to a higher area and the backward connections that construct predictions (Mumford 1992). These predictions try to explain away prediction error in lower levels. In this scheme, the sources of forward and backward connections are superficial and deep pyramidal cells, respectively. The equations represent a generalised descent on free energy under the hierarchical models described in Friston (2008). State units are in black and error units in red. Here, neuronal populations are deployed hierarchically within three cortical areas (or macrocolumns). Within each area, the cells are shown in relation to cortical layers: supragranular (I–III) granular (IV) and infragranular (V–VI) layers

Fig. 2

This schematic summarizes the results of the simulations of action observation reported in Friston et al. (2011). The left panel pictures the brain as a forward or generative model of itinerant movement trajectories (based on a Lotka-Volterra attractor, whose states are shown as a function of time in coloured lines). This model furnishes predictions about visual and proprioceptive inputs, which prescribe movement through reflex arcs at the level of the spinal cord (insert on the lower left). The variables have the same meaning as in the previous figure. The mapping between attractor dynamics and proprioceptive consequences is modelled with Newtonian mechanics on a two jointed arm, whose extremity (red ball) is drawn to a target location (green ball) by an imaginary spring. The location of the target is prescribed (in an extrinsic frame of reference) by the currently active state in the attractor. These attractor dynamics and the mapping to an extrinsic (movement) frame of reference constitute the agent’s prior beliefs. The ensuing posterior beliefs are entrained by visual and proprioceptive sensations by prediction errors during the process of inference, as summarized in the previous figure. The resulting sequence of movements was configured to resemble handwriting and is shown as a function of location over time on the lower right (as thick grey lines). The red dots on these trajectories signify when a particular neuron or neuronal population encoding one of the hidden attractor states was active during action (left panel) and observation of the same action (right panel): More precisely, the dots indicate when responses exceeded half the maximum activity and are shown as a function of limb position. The left panel shows the responses during action and illustrates both a place-cell-like selectivity and directional selectivity for movement in an extrinsic frame of reference. The equivalent results on the right were obtained by presenting the same visual information to the agent but removing proprioceptive sensations. This can be considered as a simulation of action observation and mirror neuron-like activity

Fig. 3

This figure shows the results of simulations in which a face was presented to an agent, whose responses were simulated using the active inference scheme described in the main text. In this simulation, the agent had three internal images or hypotheses about the stimuli it might sample (an upright face, an inverted face and a rotated face). The agent was presented with an upright face and its posterior expectations were evaluated over 16 (12 ms) time bins, until the next saccade was emitted. This was repeated for eight saccades. The ensuing eye movements are shown as red dots at the location (in extrinsic coordinates) at the end of each saccade in the upper row. The corresponding sequence of eye movements is shown in the insert on the upper left, where the red circles correspond roughly to the proportion of the image sampled. These saccades are driven by prior beliefs about the direction of gaze—based upon the saliency maps in the second row. Note that these maps change with successive saccades as posterior beliefs about the hidden states, including the stimulus, become progressively more confident. Note also that salience is depleted in locations that were foveated in the previous saccade. This reflects an inhibition of return that was built into the prior beliefs. The resulting posterior beliefs provide both visual and proprioceptive predictions that suppress visual prediction errors and drive eye movements, respectively. Oculomotor responses are shown in the third row in terms of the two hidden oculomotor states corresponding to vertical and horizontal displacements. The associated portions of the image sampled (at the end of each saccade) are shown in the fourth row. The final two rows show the posterior beliefs and inferred stimulus categories, respectively. The posterior beliefs are plotted in terms of posterior expectations and the 90 % confidence interval about the true stimulus. The key thing to note here is that the expectation about the true stimulus supervenes over its competing expectations and—as a result—posterior confidence about the stimulus category increases (the confidence intervals shrink to the expectation). This illustrates the nature of evidence accumulation when selecting a hypothesis or percept the best explains sensory data. Within-saccade accumulation is evident even during the initial fixation with further stepwise decreases in uncertainty as salient information is sampled by successive saccades