  The performance of Large Language Models has achieved superhuman breadth with
unprecedented depth. At the same time, the language models are mostly black box
models and the underlying mechanisms for performance have been evaluated using
synthetic or mechanistic schemes. We extend current mechanistic schemes to
incorporate Logic, memory, and nuances of Language such as latent structure.
The proposed framework is called LOLAMEME and we provide two instantiations of
LOLAMEME: LoLa and MeMe languages. We then consider two generative language
model architectures: transformer-based GPT-2 and convolution-based Hyena. We
propose the hybrid architecture T HEX and use LOLAMEME framework is used to
compare three architectures. T HEX outperforms GPT-2 and Hyena on select tasks.
