Theory of Hallucinations based on Equivariance

This study aims to acquire knowledge for creating very large language models that are immune to hallucinations. Hallucinations in contemporary large language models are often attributed to a misunderstanding of real-world social relationships. Therefore, I hypothesize that very large language models capable of thoroughly grasping all these relationships will be free from hallucinations. Additionally, I propose that certain types of equivariant language models are adept at learning and understanding these relationships. Building on this, I have developed a specialized cross-entropy error function to create a hallucination scale for language models, which measures their extent of equivariance acquisition. Utilizing this scale, I tested language models for their ability to acquire character-level equivariance. In particular, I introduce and employ a novel technique based on T5 (Text To Text Transfer Transformer) that efficiently understands permuted input texts without the need for explicit dictionaries to convert token IDs (integers) to texts (strings). This T5 model demonstrated a moderate ability to acquire character-level equivariance. Additionally, I discovered scale laws that can aid in developing hallucination-free language models at the character level. This methodology can be extended to assess equivariance acquisition at the word level, paving the way for very large language models that can comprehensively understand relationships and, consequently, avoid hallucinations.