Thus, fMRI BOLD activity reflects an indirect, noisy measure ofneural activity,mismatched toneural timescales byseveral orders ofmagnitude.

Theperformance ofneural networksonhigh-dimensional datadistributions suggests that it may be possible to parameterize a representation of agiven highdimensional function with controllably small errors, potentially outperforming standard interpolation methods. We demonstrate, both theoretically and numerically, that this is indeed the case. We map the parameters of a neural network to a system of particles relaxing with an interaction potential determined by the lossfunction.

Behavior is shaped by various factors operating across different timescales.

A central challenge of representing natural signals, such as speech and music, is that they are structured across many different timescales (Chomsky and Halle, 1968; Lerdahl and Jackendoff, 1985; Hickokand Poeppel, 2007).

Wecanseethis as the slope of the update function changes (middle row of Figure 1), these green lines correspond tothelocations givenbythearrowsinthetoprow.

Inthisworkweconstruct interpretable multi-timescale representations by forcing individual units in an LSTMLM to integrate information over specific temporal scales.