Internal models and the construction of time: generalizing from state estimation to trajectory estimation to address temporal features of perception, including temporal illusions.

Grush, R.
Journal of Neural Engineering, 2:S209, 2005
URL, Google Scholar


The question of whether time is its own best representation is explored. Though there is theoretical debate between proponents of internal models and embedded cognition proponents (e.g. Brooks R 1991 Artificial Intelligence 47 139—59) concerning whether the world is its own best model, proponents of internal models are often content to let time be its own best representation. This happens via the time update of the model that simply allows the model’s state to evolve along with the state of the modeled domain. I argue that this is neither necessary nor advisable. I show that this is not necessary by describing how internal modeling approaches can be generalized to schemes that explicitly represent time by maintaining trajectory estimates rather than state estimates. Though there are a variety of ways this could be done, I illustrate the proposal with a scheme that combines filtering, smoothing and prediction to maintain an estimate of the modeled domain’s trajectory over time. I show that letting time be its own representation is not advisable by showing how trajectory estimation schemes can provide accounts of temporal illusions, such as apparent motion, that pose serious difficulties for any scheme that lets time be its own representation.


The author argues based on temporal illusions that perceptual states correspond to smoothed trajectories where smoothing is meant as in the context of a Kalman smoother. In particular, temporal illusions such as the flash-lag effect and the cutaneous rabbit show that stimuli later in time can influence the perception of earlier stimuli. However, it seems that this is only the case for temporally very close stimuli (within 100ms). Thus, Grush suggests that stimuli are internally represented as trajectories including past and future states. However, the representation of the past states in the trajectory is also updated when new sensory evidence is collected (the observations, or rather the states, are smoothed). This idea has actually already been suggested by Rao, Eagleman and Sejnowski (2001) as stated by the author, but here he additionally postulates that also some of the future states are represented in the trajectory to account for apparent motion effects (where a motion is continued in the head when the stimulus disappears).

It’s an interesting account of temporal aspects in perceptions, but note that he develops things for the perceptual level, which does not necessarily let us draw conclusions for processing on the sensory level. Also, his discussion on whether Rao et al’s account of a fixed-lag smoother can be true is interesting, though he didn’t entirely convince me that fixed-lag perception is not what is happening in the brain. Wouldn’t instantaneous updating of the perceptual trajectory mean that at some point our perception changes, but during the illusions people report coherent motion. Ok, it could be that we just don’t “remember” our previous perception after it’s updated, but it still sounds counterintuitive. I don’t think that the apparent motion illusions are a good argument for representing future states, because other mechanisms could be responsible for that.

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