Simplicial complexes

Field dynamics provides a continuous analogue of the down-up walk on simplicial complexes. This talk introduces the process and explains applications to discrete sampling, including independent sets on graphs of unbounded degree up to the critical point.

…composed of simplexes, known as “simplicial compl

Relational invariance---a network’s ability to capture the geometric relationships between input patterns abstracted away from explicit external variables---has the potential to enable robustness and generalizability in neural networks. Previous work from our group has shown that a combinatorial neuronal code preserves the relational geometry of acoustic stimuli in the songbird brain. Here we show that combinatorial codes in autoencoding spiking neural networks (SNNs) can maintain relational invariance and display a hierarchical structure that optimizes the network’s internal representation. B

…and embedding these connections in a simplicial complex. Simplicial complexes are