Talking to Blackbox: Explainability Through P+NP=1
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The interpretability of complex AI systems remains one of the most critical challenges for modern machine learning, particularly when dealing with blackbox models such as deep neural networks and large language models (LLMs). While current Explainable AI (XAI) techniques — notably SHAP and LIME — provide local or feature-based insights, they often rely on additive approximations that fail to capture the underlying epistemic dynamics or the structural reasoning of models. This paper introduces Talking to Blackbox, a framework that proposes a new paradigm of XAI, inspired by complexity theory and the symbolic principle P + NP = 1. We conceptualize a blackbox model as an interplay between interpretable elements (P) and latent complexity (NP), where P + NP = 1 serves as a heuristic principle for balancing transparency and computational depth. Instead of forcing full visibility, Talking to Blackbox constructs explanatory tokens from model inputs and intermediate states, mapping them to epistemic fields — such as Heuristic Physics (hPhy), Collapse Mathematics (cMth), and Intention Flow (iFlw). Through these fields, the framework iteratively transforms NP opacity into P clarity, producing dynamic narratives of explainability measured by the evolving metric α(t). A proof-of-concept simulation using a weather forecasting blackbox demonstrates how raw variables (e.g., pressure, temperature, humidity) can be translated into narrative tokens (“falling pressure,” “high humidity”), which are processed to generate a human-readable explanation of the prediction. Although this approach does not aim to formally prove P = NP, it employs the P + NP = 1 hypothesis as a conceptual bridge between complexity and intelligibility. By complementing existing techniques like SHAP and LIME, our architecture emphasizes interpretability not as a static attribution but as a dialogue with the model, revealing the flow of reasoning rather than isolated feature contributions. This conceptual framework builds upon prior works on heuristic convergence [2], [3], proposing a new epistemic approach to XAI that integrates complexity theory, symbolic reasoning, and narrative structures.