# QML-HCS: A Hypercausal Quantum Machine Learning Framework for Non-Stationary Environments

arXiv: https://arxiv.org/abs/2511.17624 · HTML: https://mlsanity.com/paper/2511.17624/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 23 references that are in the map.
- First posted on arXiv 18 Nov 2025.

## Builds on (most cited first, 10 of 10)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Towards Causal Representation Learning](https://mlsanity.com/paper/2102.11107/) (2021)
- [DoWhy: An End-to-End Library for Causal Inference](https://mlsanity.com/paper/2011.04216/) (2020)
- [CausalML: Python Package for Causal Machine Learning](https://mlsanity.com/paper/2002.11631/) (2020)
- [TensorFlow Quantum: A Software Framework for Quantum Machine Learning](https://mlsanity.com/paper/2003.02989/) (2020)
- [Convex Geometry and Duality of Over-parameterized Neural Networks](https://mlsanity.com/paper/2002.11219/) (2020)
- [Causal Structure Learning: a Combinatorial Perspective](https://mlsanity.com/paper/2206.01152/) (2022)
- [Causal Discovery and Forecasting in Nonstationary Environments with State-Space Models](https://mlsanity.com/paper/1905.10857/) (2019)
- [Model Based Explanations of Concept Drift](https://mlsanity.com/paper/2303.09331/) (2023)
- [Quantum-Inspired Machine Learning: a Survey](https://mlsanity.com/paper/2308.11269/) (2023)

## Abstract (arXiv)

QML-HCS is a research-grade framework for constructing and analyzing quantum-inspired machine learning models operating under hypercausal feedback dynamics. Hypercausal refers to AI systems that leverage extended, deep, or nonlinear causal relationships (expanded causality) to reason, predict, and infer states beyond the capabilities of traditional causal models. Current machine learning and quantum-inspired systems struggle in non-stationary environments, where data distributions drift and models lack mechanisms for continuous adaptation, causal stability, and coherent state updating. QML-HCS addresses this limitation through a unified computational architecture that integrates quantum-inspired superposition principles, dynamic causal feedback, and deterministic-stochastic hybrid execution to enable adaptive behavior in changing environments. The framework implements a hypercausal processing core capable of reversible transformations, multipath causal propagation, and evaluation of alternative states under drift. Its architecture incorporates continuous feedback to preserve causal consistency and adjust model behavior without requiring full retraining. QML-HCS provides a reproducible and extensible Python interface backed by efficient computational routines, enabling experimentation in quantum-inspired learning, causal reasoning, and hybrid computation without the need for specialized hardware. A minimal simulation demonstrates how a hypercausal model adapts to a sudden shift in the input distribution while preserving internal coherence. This initial release establishes the foundational architecture for future theoretical extensions, benchmarking studies, and integration with classical and quantum simulation platforms.