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About this paper
Laurent Boué
A framework demonstrates that any dataset can be approximated by a continuous, differentiable scalar function using just one real-valued parameter. This is achieved by encoding the entire dataset into the fractional part of the single parameter, which is then decoded via iterated chaotic dynamical systems, highlighting the information capacity of real numbers and the distinction between memorization and generalization.
Key insights
- Real numbers possess an infinite capacity to encode information, allowing a single parameter to represent an entire dataset given sufficient arbitrary precision.
- The ability to fit any dataset does not imply learning or generalization; the demonstrated model performs pure memorization, explicitly encoding the data rather than inferring patterns.
- Concepts from chaos theory, such as topological conjugacy, provide elegant mathematical tools for designing functions that can encode and decode information from a single real number.
Summary by alphaXiv.
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