Theory of Hallucinations based on Equivariance

Equivariance is an important feature in machine learning, including language models. It ensures that any sequences of phrases with the same meanings are interpreted consistently. For example, the sentence 'There is a cat on the table' should be interpreted by language models as it is, regardless of variations in its token-level expression. Building on this insight, I propose a new theory suggesting that insufficient equivariance in language models can lead to hallucinations. According to this theory, which is both intuitive and novel, language models trained on relatively small datasets tend to misinterpret input texts and/or generate incorrect texts (i.e., hallucinations). To test this theory, I developed a toy model known as 'dancing men', which is a character-level substitution cipher. Additionally, I propose a novel technique based on the T5 (Text To Text Transfer Transformer) model to efficiently decipher these codes without relying on frequency analysis. I have found that this T5 model can almost completely solve the cipher, demonstrating its ability to acquire equivariance in this frame. This method could be scaled up to word-level and sentence-level substitution ciphers, analogous to large language models without tokenizers or dictionaries. This scalability makes it suitable for investigating the proposed link between inadequate equivariance acquisition and the emergence of hallucinations.