  In this paper we generalize and extend an idea of low-rank adaptation (LoRA)
of large language models (LLMs) based on Transformer architecture. Widely used
LoRA-like methods of fine-tuning LLMs are based on matrix factorization of
gradient update. We introduce LoTR, a novel approach for parameter-efficient
fine-tuning of LLMs which represents a gradient update to parameters in a form
of tensor decomposition. Low-rank adapter for each layer is constructed as a
product of three matrices, and tensor structure arises from sharing left and
right multipliers of this product among layers. Simultaneous compression of a
sequence of layers with low-rank tensor representation allows LoTR to archive
even better parameter efficiency then LoRA especially for deep models.
Moreover, the core tensor does not depend on original weight dimension and can
be made arbitrary small, which allows for extremely cheap and fast downstream
fine-tuning.
