Supporting information.

Fig A. Improvement on test set loss saturates as the number of transition matrices increases. (a) Test set loss as training proceeded. Shaded area denotes ±1 standard deviation computed over eight runs with random initialization for each K. K = 1 shows the performance of the single-layer model. (b) Best test loss as K increases. Error bars denote ±1 standard deviation. Fig B. Cue-triggered recall is cue-specific. Four examples of cue-specific sequence recall by the associative memory model after training on different sequences, when given the first frame as the cue. In each quadrant: top: the original image sequence; bottom: cue-triggered recall of the stored sequence. Fig C. Prediction error threshold robustly finds changes of dynamics. (a) The distribution of first-level prediction errors in the two-level DPC model on the Moving MNIST training set. The red dashed line denotes the threshold ρ = 0.73, where the cumulative density reaches 0.75. (b) Examples of input sequences in the test set. The red arrows mark time steps when the first-level prediction errors exceeded ρ, corresponding to changes in input dynamics. Table A. DPC generative model parameters and values. Table B. Optimizers and learning rates used for inference and learning in the DPC experiments. Here Δ denotes the difference in r_t or r^h from before and after the current iteration of gradient descent. Table C. Memory model parameters and values. Table D. Optimizers and learning rates used for inference and learning in the memory model. Here Δ denotes the difference in m from before and after the current iteration of gradient descent. Table E. Additional parameters and values for the three-level DPC model. Table F. Additional optimizers and learning rates used for inference and learning in the three-level DPC experiments. Algorithm A. Inference & learning process. Algorithm B. Inference & learning process for the three-level DPC model.

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