First, we apply subspace id methods from classical control theory to learn input-controlled linear dynamical systems (key in partially observed settings). This is new for the Dynamic Mode Decomposition (DMD) literature, and the method robust to extreme partial observation (12/)

On two datasets, we apply random perturbations (noise, functions) to the true input, or utilize other task variables when performing inputDSA. We measure the correlation between the surrogate and true scores, finding that in general, inputDSA is quite robust! (8) (shoutout @oliviercodol.bsky.social)

Second: on @thomas-zhihao-luo.bsky.social recently showed that rat cortical dynamics transition from primarily input-driven to autonomous during a 2-alternative forced choice task. InputDSA corroborates this, showing that cortex becomes less input-controllable across time! (6/)

On @satpreetsingh.bsky.social ’s Deep RL fly navigation task (from @bingbrunton.bsky.social ’s lab) we show that successful models become more similar to each other across training, while unsuccessful ones diverge in inputDSA score —an Anna Karenina/universality result! (5/)

The basic idea of DSA: approximate your dynamics so that comparison is tractable. This is backed by Koopman Operator Theory and relates to work done by @wtredman.bsky.social and Igor Mezic. InputDSA naturally extends DSA—we can compare intrinsic dynamics, the effect of input, or both jointly! (3/)

Our next paper on comparing dynamical systems (with special interest to artificial and biological neural networks) is out!! Joint work with @annhuang42.bsky.social , as well as @satpreetsingh.bsky.social , @leokoz8.bsky.social , Ila Fiete, and @kanakarajanphd.bsky.social : arxiv.org/pdf/2510.25943