Theory & Concepts

Contents

Theory & Concepts#

This section explains the theoretical foundations of QML-HCS, covering quantum principles, causal inference, and the mathematical structure behind hypercausal hybrid learning systems.

Associated Paper#

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

Hector E. Mozo

This paper introduces the theoretical foundations of QML-HCS by formalizing a hypercausal learning model for non-stationary environments. It defines the core execution semantics, including multi-branch future generation, projection policies, and continuous causal feedback mechanisms, and presents the mathematical structure used to maintain coherence and stability under distributional drift. The paper focuses on establishing the architectural and conceptual framework that informs the design and behavior of the QML-HCS software.

arXiv:2511.17624
DOI: 10.48550/arXiv.2511.17624

Pre-Temporal Model of Quantum Causal Order

Hector E. Mozo

This paper establishes the theoretical foundation for treating causal order as a continuous, quantifiable resource within computational and learning frameworks. It introduces the causal-indefiniteness measure λ(W), defined via the trace distance between a quantum process and the convex set of causally separable processes, providing a principled scalar that interpolates between indefinite and definite causal structure.

Within the context of QML-HCS, this pre-temporal formulation supplies a rigorous conceptual layer for modeling systems whose causal structure evolves over time. The measure λ(W) functions as an operational signal that can be tracked, optimized, or regularized within hypercausal learning loops, enabling QML-HCS to reason about causal consolidation, stability, and regime transitions in non-stationary environments.

In this way, the framework leverages pre-temporal causal dynamics not as an abstract phenomenon, but as a computable control variable that informs prediction, adaptation, and system-level coherence.

SSRN: 5993818
DOI: 10.2139/ssrn.5993818