# Causal Future Prediction in a Minkowski Space-Time

arXiv: https://arxiv.org/abs/2008.09154 · HTML: https://mlsanity.com/paper/2008.09154/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Aug 2020.

## Built on by (most cited first, 3 of 3)

- [Next-Gen Machine Learning Supported Diagnostic Systems for Spacecraft](https://mlsanity.com/paper/2106.05659/) (2021)
- [Mixed moving average field guided learning for spatio-temporal data](https://mlsanity.com/paper/2301.00736/) (2023)
- [Causality-Induced Positional Encoding for Transformer-Based Representation Learning of Non-Sequential Features](https://mlsanity.com/paper/2509.16629/) (2025)

## Abstract (arXiv)

Estimating future events is a difficult task. Unlike humans, machine learning approaches are not regularized by a natural understanding of physics. In the wild, a plausible succession of events is governed by the rules of causality, which cannot easily be derived from a finite training set. In this paper we propose a novel theoretical framework to perform causal future prediction by embedding spatiotemporal information on a Minkowski space-time. We utilize the concept of a light cone from special relativity to restrict and traverse the latent space of an arbitrary model. We demonstrate successful applications in causal image synthesis and future video frame prediction on a dataset of images. Our framework is architecture- and task-independent and comes with strong theoretical guarantees of causal capabilities.