Stable Autonomous Flow Matching
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916118496542720 |
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| author | Sprague, Christopher Iliffe Elofsson, Arne Azizpour, Hossein |
| author_facet | Sprague, Christopher Iliffe Elofsson, Arne Azizpour, Hossein |
| contents | In contexts where data samples represent a physically stable state, it is often assumed that the data points represent the local minima of an energy landscape. In control theory, it is well-known that energy can serve as an effective Lyapunov function. Despite this, connections between control theory and generative models in the literature are sparse, even though there are several machine learning applications with physically stable data points. In this paper, we focus on such data and a recent class of deep generative models called flow matching. We apply tools of stochastic stability for time-independent systems to flow matching models. In doing so, we characterize the space of flow matching models that are amenable to this treatment, as well as draw connections to other control theory principles. We demonstrate our theoretical results on two examples. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_05774 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stable Autonomous Flow Matching Sprague, Christopher Iliffe Elofsson, Arne Azizpour, Hossein Machine Learning Artificial Intelligence Systems and Control In contexts where data samples represent a physically stable state, it is often assumed that the data points represent the local minima of an energy landscape. In control theory, it is well-known that energy can serve as an effective Lyapunov function. Despite this, connections between control theory and generative models in the literature are sparse, even though there are several machine learning applications with physically stable data points. In this paper, we focus on such data and a recent class of deep generative models called flow matching. We apply tools of stochastic stability for time-independent systems to flow matching models. In doing so, we characterize the space of flow matching models that are amenable to this treatment, as well as draw connections to other control theory principles. We demonstrate our theoretical results on two examples. |
| title | Stable Autonomous Flow Matching |
| topic | Machine Learning Artificial Intelligence Systems and Control |
| url | https://arxiv.org/abs/2402.05774 |