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About this paper
Bruno Gavranović
This research introduces a 2-categorical framework to distinguish between operationally distinct but denotationally equivalent systems modeled by lenses and optics. It formalizes how lens composition implicitly employs recomputation, akin to gradient checkpointing, while optic composition explicitly manages internal states, offering a method to analyze inherent space-time tradeoffs.
Key insights
- Lens composition naturally implements a space-time tradeoff similar to gradient checkpointing, prioritizing memory efficiency by recomputing intermediate results.
- Optic composition, by allowing explicit choice of internal state, offers a different tradeoff that prioritizes speed through storing intermediate data.
- Higher category theory provides the necessary framework to formally distinguish between denotationally equivalent but operationally disparate system implementations.
Summary by alphaXiv.
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