# Aggregating time-series and image data: functors and double functors

arXiv: https://arxiv.org/abs/2504.05274 · HTML: https://mlsanity.com/paper/2504.05274/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 39 references that are in the map.
- First posted on arXiv 7 Apr 2025.

## Builds on (most cited first, 7 of 7)

- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Simplified State Space Layers for Sequence Modeling](https://mlsanity.com/paper/2208.04933/) (2022)
- [Hypergraph Categories](https://mlsanity.com/paper/1806.08304/) (2018)
- [Time-warping invariants of multidimensional time series](https://mlsanity.com/paper/1906.05823/) (2019)
- [Tropical time series, iterated-sums signatures and quasisymmetric functions](https://mlsanity.com/paper/2009.08443/) (2020)
- [Polygraphs: From Rewriting to Higher Categories](https://mlsanity.com/paper/2312.00429/) (2023)

## Abstract (arXiv)

Aggregation of time-series or image data over subsets of the domain is a fundamental task in data science. We show that many known aggregation operations can be interpreted as (double) functors on appropriate (double) categories. Such functorial aggregations are amenable to parallel implementation via straightforward extensions of Blelloch's parallel scan algorithm. In addition to providing a unified viewpoint on existing operations, it allows us to propose new aggregation operations for time-series and image data.