Grounding Large Language Models with Tensor Network Coefficients to Force Deterministic Data Analysis

Large language models are mathematically probabilistic, rendering their output potentially inaccurate. These LLM hallucinations grow as data becomes increasingly entangled or complex. This paper introduces a new computational methodology for natual-language based data analysis. It is defined as "AURA". The methods and structure of AURA develops the foundation for a data analysis and evaluation workspace or integration that eliminates this probabilistic problem entirely. The AURA methodology defines all statistical relationships within a given dataset through a deterministic tensor network mechanism. It then constructs Hamiltonian values from inter-column Pearson correlations. Solving the Hamiltonian yields the same statistical relationships as the original dataset. The resulting verified coefficients are passed to the LLM's context window, creating a deterministic environment for the LLM to operate within. Consequentially, computational reproducibility of every cited number becomes possible. The systematic implementation or interface consists of four required components. The Translation Ledger maintains an auditable recording of all compilations for human verification and recordings for when possibilities for deterministic deviations become present (inaccuracy is yielded through data quality issues or ambiguous user queries). Schema Aware Context standardizes column metadata during natural language query composition for contextual narrative building alongside deterministic coefficient coupling. Deterministic Render Blocks present dynamic, auditable outputs with dual SLA receipts. Lastly, the Iteration Chain stacks queries into a traceable drill-down history. 2.6 million rows were tested across 15 distinct validation tests, which are outlined in this paper. The computational methods herein achieved zero correlation difference against independent NumPy/SciPy ground truth. The system will be presented as a Dynsell Quantum Research service, which will demonstrate the full breadth of this research.