Proofs: Ontologic Scalar Modulation Theorem by C.L. Vaillant
https://static1.squarespace.com/static/67b614459cffee266ad99e4b/t/6836d10c5abef746b786c315/1748422924931/Ontologic_Scalar_Modulation_Theorem.pdf Ontologic Scalar Modulation Theorem C.L. Vaillant May/25/2025 Abstract Mechanistic interpretability research seeks to reverse engineer the internal computation of neural networks into human-understandable algorithms and concepts: In this paper, we introduce an interdisciplinary theoretical framework grounded in mechanistic interpretability and enriched by cognitive science, symbolic AI, ontology, and philosophy of mind. We formalize the *Ontological Scalar Modulation Theorem*, which provides a rigorous account of how high-level semantic concepts (an **ontology**) can be represented, identified, and continuously modulated within the latent space of a learned model. Our approach offers precise mathematical definitions and structures that bridge low-level network mechanisms and high-level human-interpretable features. We illustrate the theor...