Summary of Hippo-prophecy: State-space Models Can Provably Learn Dynamical Systems in Context, by Federico Arangath Joseph et al.
HiPPO-Prophecy: State-Space Models can Provably Learn Dynamical Systems in Context
by Federico Arangath Joseph, Kilian Konstantin Haefeli, Noah Liniger, Caglar Gulcehre
First submitted to arxiv on: 12 Jul 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Machine Learning (stat.ML)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary This paper delves into the capabilities of State Space Models (SSMs) for in-context learning and provides a theoretical explanation for their underlying mechanism. The authors introduce a novel weight construction for SSMs, enabling them to predict the next state of any dynamical system without fine-tuning parameters. This is achieved by extending the HiPPO framework to demonstrate that continuous SSMs can approximate the derivative of any input signal. Specifically, the paper presents an explicit weight construction for continuous SSMs and provides an asymptotic error bound on the derivative approximation. The discretization of this continuous SSM yields a discrete SSM that predicts the next state. The effectiveness of the proposed parameterization is empirically demonstrated. This work is an initial step toward understanding how sequence models based on SSMs learn in context. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper studies how State Space Models (SSMs) can learn and make predictions about future states. It introduces a new way to build these models that lets them predict the next state of any system without needing to adjust their parameters. The authors also show that this approach allows SSMs to approximate the rate at which an input signal changes over time. They then demonstrate how this continuous model can be turned into a discrete one that makes accurate predictions about future states. Overall, this research is an important step in understanding how sequence models based on SSMs learn and make predictions. |
Keywords
» Artificial intelligence » Fine tuning
