[2506.07578] Denoising the Future: Top-p Distributions for Moving Through Time

Computer Science > Machine Learning arXiv:2506.07578 (cs) [Submitted on 9 Jun 2025 (v1), last revised 31 Mar 2026 (this version, v4)] Title:Denoising the Future: Top-p Distributions for Moving Through Time Authors:Florian Andreas Marwitz, Ralf Möller, Magnus Bender, Marcel Gehrke View a PDF of the paper titled Denoising the Future: Top-p Distributions for Moving Through Time, by Florian Andreas Marwitz and 3 other authors View PDF HTML (experimental) Abstract:Inference in dynamic probabilistic models is a complex task involving expensive operations. In particular, for Hidden Markov Models, the whole state space has to be enumerated for advancing in time. Even states with negligible probabilities are considered, resulting in computational inefficiency and possibly increased noise due to the propagation of unlikely probability mass. We propose to denoise the future and speed up inference by using only the top-p transitions, i.e., the most probable transitions with accumulated probability p. We show that the error introduced by using only the top-p transitions is bound by $p$ and the so-called minimal mixing rate of the underlying model. We also show the same bound when using only the top-p states, which is the same, just for the states. Moreover, in our empirical evaluation, we show that we can, when using top-p transitions, expect speedups of at least an order of magnitude, while the error in terms of total variation distance is below 0.09. Using the top-p states is slower ...