Surprise response as a probe for compressed memory states
Fig 1
The naive oddball count (NOC) and the IB lossy compression models of the oddball sequence.
An illustration of the two compression models for the case of a past length of size N = 4 is shown. To be able to code any of the 16 possible sequences of 4 tones in memory that the subject heard, 4 bits of memory would be needed. (Left) The NOC model only keeps the number of oddball occurrences in the previous window in memory; i.e., the minimal sufficient statistic (see Methods). The upper plot shows the number of oddball tone occurrences n (filled red circles) and the number of standard tone occurrences N − n (empty blue circles) in the previous window for each trial, starting from trial N + 1. All plots are aligned to the stimulus sequence. The occurrence predictor (bottom plot) on each trial is n if a standard tone was played and N − n if an oddball tone was played. To be able to code the 5 alternatives of the past in memory (i.e., 0, 1, 2, 3 or 4 oddball tones out of the previous 4 tones), 2.32 bits of memory are required. (Right) The IB model keeps a fuzzy representation of the oddball counter in memory, which requires less memory usage than the NOC model due to its lower representation accuracy (with the accuracy controlled by the β parameter. see Methods for details). The upper plot illustrates a fuzzy representation m of the oddball occurrences n in the previous window, as given by IB for a high compression case (low β). The darker red represents higher p(m|n) probability. The two lower plots show two IB predictors of different compression levels (0.1 bits for the bottom plot, 2.31 bits for the middle plot). The surprise level on each trial is defined as -∑m p(m|n) log p(next tone|m) where the probabilities are defined by the IB solution for a specific compression level.