Summary of Rademacher Complexity Of Neural Odes Via Chen-fliess Series, by Joshua Hanson et al.
Rademacher Complexity of Neural ODEs via Chen-Fliess Series
by Joshua Hanson, Maxim Raginsky
First submitted to arxiv on: 30 Jan 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); Systems and Control (eess.SY); Optimization and Control (math.OC)
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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 A new framework is proposed in this paper, framing continuous-depth neural ODE models as single-layer, infinite-width nets using the Chen-Fliess series expansion for nonlinear ODEs. The approach leverages the signature of the control input to represent infinite-dimensional paths as a sequence of tensors and iterated Lie derivatives of the output function with respect to vector fields in the controlled ODE model. This allows for compact expressions to be derived for the Rademacher complexity of ODE models, which map an initial condition to a scalar output at some terminal time. The result is straightforwardly analyzed due to the single-layer architecture. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper shows how special kinds of computer models can be broken down into simpler parts. It’s like taking a big puzzle and breaking it into smaller pieces that are easier to understand. These models are called ODEs, or ordinary differential equations. The authors use a special tool to help them analyze these models and make predictions about what will happen in the future. They also show how this new framework can be used to measure how well these models do at making accurate predictions. |
