The Feigin-Tipunin algorithm is a combinatorial and iterative algorithm introduced by the speaker recently to construct and study log VA(-module)s that have the q-series valued quantum invariant of 3-mfds called homological block introduced by S. Gukov et al. as their characters. The key point is that at each step of the iteration, a geometric representation theory can be used as in the usual Feigin-Tipunin construction, so that the representation theory of the log-VA can be studied without having to examine its complicated algebraic structure. In this talk, after describing the speaker's previous work, it will be explained that if the FT algorithm can be applied to a certain lattice VOA-module, we can construct a log VA-module with the homological block of the (N+2)-Seifert 3-mfd as its character.
How much information do the outputs of language models contain about their inputs? We investigate this problem in two scenarios, recovering text inputs from the outputs of embeddings from sentence embedders and next-token probability outputs from language models. In both cases, our methods are able to fully recover some inputs given just the model output.