System Dynamics (84,990 frames)

Now that the prediction feedback mechanism and arousal have been written, I’ve been able to do some early tests to see what the system’s behaviour is like. Right now I’ve only been running short tests of one day/night cycle. So the degree of learning from the predictor is quite low.

This test is implemented as the system is expected to work, where ongoing external stimulus adds noise to the predictor feedback loop. The dynamics are quite simple now, where the three system states (dreaming, mind-wandering and waking) are all discrete and mutually exclusive. Mind-wandering and dreaming are both identical, where the current state of activation is the initial input to the predictor. While the system continues to mind-wander or dream, the next state is the predictor output combined with external stimulus activation. Mind-wandering is triggered by a lack of arousal (change over time) in external stimulus and dreaming is triggered by the circadian clock. As hard thresholds are used to trigger mind-wandering and dreaming, there are some oscillations between states due to the noisy arousal and / or brightness. Following is the system state plotted over time, the subtle dynamics are difficult to see because of the large number of frames.


The longest continuous waking period is 107 frames with a mean of 4 frames. For mind-wandering, the longest continuous period is 436 frames with a mean of 21 frames. From the plot above it can be seen that is a brief waking period during sleep, and waking is about to begin near the end of the test (when sun is about to rise). The dreams are expectedly quite long, with a max of 26505 frames and a mean of 4125 frames. To get a better look at the dynamics, here is a zoomed in version where we see the transition between waking and dreaming:


Note an initial short lapse into dreaming during a period of predominantly mind-wandering and occasional waking. One can clearly see the different character of prediction feedback vs waking (even including the ongoing combination of external stimulus and predictions), in the following state plot (scaled from 84,990 pixels wide to 10,000). Rows are the state of each precept, columns time. White indicates a precept is activation, and black when not activated. Note the clear switch of state during dreaming initiated by the brief waking period:


The system is almost entirely in a mind-wandering (40,196 frames) or dreaming (37,127 frames) state, with waking (7,645 frames) appearing more like punctuation. This is not unexpected, since the system is only awake when there is external arousal. A more dynamic setting would lead to different results. In this case, prediction learning will be a lot slower, but also that the states being learned from will include the greatest arousal. I am currently running another test where the external stimulus does not effect the predictor feedback. This will give me a better sense of the how periodic or static dreams and mind-wandering are. After that, and it will be time for another long test processing the whole data-set.

I have noticed that the ephemeral quality of the percepts means that it’s unlikely that we would see a clear replay of daily events in any intelligible form. This could be solved with more learning, or more percepts, but it is clear that the images produced during mind-wandering and dreaming are quite sparse in comparison to waking.