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Optimal prediction with resource constraints using the information bottleneck
Fig 6
Representations learned on underdamped systems can be transferred to other types of motion, while representations learned on overdamped systems cannot be easily transferred.
(a) Here, we consider the information bottleneck bound curve (black) for a stimulus with underlying parameters, (ζ, Δt). For some particular level of 
, we obtain a mapping, 
that extracts some predictive information, denoted 
, about a stimulus with parameters (ζ, Δt). Keeping that mapping fixed, we determine the amount of predictive information for dynamics with new parameters (ζ′, Δt′), denoted by 
. (b) One-dimensional slices of 
in the (ζ′, Δt′) plane: 
versus ζ′ for Δt′ = 1. 
(top), and versus Δt′ for ζ′ = 1. Parameters are set to (ζ = 1, Δt = 1), 
. (c) Two-dimensional map of 
versus (ζ′, Δt′) (same parameters as b). (d) Overall transferability of the mapping. The heatmap of (c) is integrated over ζ′ and Δt′ and normalized by the integral of 
. We see that mappings learned from underdamped systems at late times yield high levels of predictive information for a wide range of parameters, while mappings learned from overdamped systems are not generally useful.
doi: https://doi.org/10.1371/journal.pcbi.1008743.g006