# Distributional Computational Graphs: Error Bounds

arXiv: https://arxiv.org/abs/2601.16250 · HTML: https://mlsanity.com/paper/2601.16250/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 33 references that are in the map.
- First posted on arXiv 22 Jan 2026.

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

- [Directed Acyclic Graph Neural Networks](https://mlsanity.com/paper/2101.07965/) (2021)
- [The Elements of Differentiable Programming](https://mlsanity.com/paper/2403.14606/) (2024)
- [A Note on Monte Carlo Integration in High Dimensions](https://mlsanity.com/paper/2206.09036/) (2022)
- [Quantization of Probability Distributions via Divide-and-Conquer: Convergence and Error Propagation under Distributional Arithmetic Operations](https://mlsanity.com/paper/2505.15283/) (2025)
- [The Monte Carlo Method and New Device and Architectural Techniques for Accelerating It](https://mlsanity.com/paper/2508.07457/) (2025)

## Abstract (arXiv)

We study a general framework of distributional computational graphs: computational graphs whose inputs are probability distributions rather than point values. We analyze the discretization error that arises when these graphs are evaluated using finite approximations of continuous probability distributions. Such an approximation might be the result of representing a continuous real-valued distribution using a discrete representation or from constructing an empirical distribution from samples (or might be the output of another distributional computational graph). We establish non-asymptotic error bounds in terms of the Wasserstein-1 distance, without imposing structural assumptions on the computational graph.