Real-world signals occupy compact low-variability regions in functional space, supplying a topological basis for perception, identifiability, and generalization from few examples.
for everyε >0 there existsδ >0 such that for allt 1, t2 ∈[0, T]: |t1 −t 2|< δ⇒ |f(s, θ)(t 1)−f(s, θ)(t 2)|< ε
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The Blueprints of Intelligence: A Functional-Topological Foundation for Perception and Representation
Real-world signals occupy compact low-variability regions in functional space, supplying a topological basis for perception, identifiability, and generalization from few examples.