# ToL: A Tensor of List-Based Unified Computation Model

arXiv: https://arxiv.org/abs/2212.10740 · HTML: https://mlsanity.com/paper/2212.10740/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 28 references that are in the map.
- First posted on arXiv 21 Dec 2022.

## Builds on (most cited first, 5 of 5)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [On the expressive power of query languages for matrices](https://mlsanity.com/paper/1709.08359/) (2017)
- [Expressive power of linear algebra query languages](https://mlsanity.com/paper/2010.13717/) (2020)
- [Data Motifs: A Lens Towards Fully Understanding Big Data and AI Workloads](https://mlsanity.com/paper/1808.08512/) (2018)

## Abstract (arXiv)

Previous computation models either have equivalent abilities in representing all computations but fail to provide primitive operators for programming complex algorithms or lack generalized expression ability to represent newly-added computations. This article presents a unified computation model with generalized expression ability and a concise set of primitive operators for programming high-level algorithms. We propose a unified data abstraction -- Tensor of List, and offer a unified computation model based on Tensor of List, which we call the ToL model (in short, ToL). ToL introduces five atomic computations that can represent any elementary computation by finite composition, ensured with strict formal proof. Based on ToL, we design a pure-functional language -- ToLang. ToLang provides a concise set of primitive operators that can be used to program complex big data and AI algorithms. Our evaluations show ToL has generalized expression ability and a built-in performance indicator, born with a strictly defined computation metric -- elementary operation count (EOPs), consistent with FLOPs within a small error range.