Compacttaskrepresentationsasanormativemodel forhigher-orderbrainactivity: Supplementary material

Each column Φ i thus defines the direction in history space that componentzi is representing. Ifthere areNz independent relevant directions in the history space, every component has to code for aseparate direction, thus effectively increasing the noise. Furthermore, both degeneracies will scale up the system state to effectively scale down the relative size of the transition noiseσt, thereby pushing the system's dynamic range tohavezmax asan upper bound. Here, we first describe howsuch asystem has to focus on relevant information only in order to increase the precision in the representation of this relevantinformation (Fig.1A).Second, weillustrate howasystem mayalsoincrease precision by ignoringtiminginformation,ifirrelevant(Fig.1B). Let us consider a single state dimensionµ(zi) = φ>i h, where φ>i is thei'th row ofΦ and h is a history.