Fig. 3: Overcoming inflexible decision boundaries by increasing the input multiplicity hyperparameter M.
From: Limits on the computational expressivity of non-equilibrium biophysical processes
A Plot of the learned classification functions π1(F) and π2(F) shown as colored density plots over the input force space. On top of this, scatter plots show the dataset, colored by assigned class, which was used to train the network. Solid lines show the contour π1(F) = 1/2 in blue and π2(F) = 1/2 in orange; note that these are approximately overlapping. The network shown in Fig. 1E is used for all classification tasks in this figure. B, C Same as A, but for different classification tasks. D Schematic illustration of the monotonicity constraint. E Plots illustrating that increasing M from 1 to 2 allows for non-monotonic dependence of a steady-state occupation on an input driving force. F Same as panel C, but for the network in Fig. 1E, which also includes driving along the dashed arrows (M = 2). G Schematic illustration of a recently designed synthetic chemical band-pass system using multiple input binding42. A drug binds through a high-affinity pathway to activate a protein and through a second, low-affinity pathway to deactivate the protein, leading to a non-monotonic dependence of activation on the drug.
