In the framework of the comment above regarding the add/subtract thing, I’d also be interested in examining the function diff(s,t) = f(input+t*top_right_vec+s*cheese_vec) - f(input).
The composition claim here is saying something like diff(s,t) = diff(s,0) + diff(0,t). I’d be interested to see when this is true. It seems like your current claim is that this (approximately) holds when s<0 and t>0 and neither are too large, but maybe it holds in more or fewer scenarios. In particular, I’m surprised at the weird hard boundaries at s=0 and t=0.
In the framework of the comment above regarding the add/subtract thing, I’d also be interested in examining the function
diff(s,t) = f(input+t*top_right_vec+s*cheese_vec) - f(input).The composition claim here is saying something like
diff(s,t) = diff(s,0) + diff(0,t). I’d be interested to see when this is true. It seems like your current claim is that this (approximately) holds when s<0 and t>0 and neither are too large, but maybe it holds in more or fewer scenarios. In particular, I’m surprised at the weird hard boundaries ats=0andt=0.