Abstract
Abstract
In a spiking network with Boltzmann stationary distribution, design is energy-function design. For the winnertake-all encoding of weighted shortest path, correctness needs two conditions, not one, and we give both. Ordering requires the length-bias coefficient λ = 2bk + D + c to vanish. Discrimination does not follow: equal-activity configurations the couplings cannot distinguish from a path leave only the continuity scale c to separate them. Required c is a ratio, not a depth law, reproduced over 1,027 instances at 8.6% median error and within 16% on with held families. At the customary c = 4, counting microstates at B = 2wmax, 13.4% clear, one in forty at the size normally run. And on most instances the path is not the cheapest configuration: disjoint cycle sets carry an extra continuity pair, and raising c favors them. What excludes them is the terminal drive, outside the energy function.