Mingxue Xu

Mingxue Xu, Yao Lei Xu, Danilo P. Mandic

High-dimensional token embeddings underpin Large Language Models (LLMs), as they can capture subtle semantic information and significantly enhance the modelling of complex language patterns. However, this high dimensionality also introduces considerable model parameters and prohibitively high model storage and memory requirements, which is particularly unaffordable for low-end devices. Targeting no extra training data and insufficient computation cases, we propose a training-free model compression approach based on the Tensor-Train Decomposition (TTD), whereby each pre-trained token embedding is converted into a lower-dimensional Matrix Product State (MPS). We then comprehensively investigate the low-rank structures extracted by this approach, in terms of the compression ratio, the language task performance, and latency on a typical low-end device (i.e. Raspberry Pi). Taking GPT family models (i.e. GPT-2 and CerebrasGPT) as case studies, our approach theoretically results in $46.89\%$ fewer parameters of the entire model, with a compression ratio $39.38\times$ - $65.64\times$ for the embedding layers. With different hyperparameter choices, the model compressed with our approach can achieve a comparable language task performance to the original model with around $2.0\times$ embedding layer compression. This empirically proves the existence of low-rank structure in GPT family models, and demonstrates that about half of the parameters in the embedding layers are redundant.

Mingxue Xu, Yao Lei Xu, Danilo P. Mandic

Small Language Models (SLMs, or on-device LMs) have significantly fewer parameters than Large Language Models (LLMs). They are typically deployed on low-end devices, like mobile phones and single-board computers. Unlike LLMs, which rely on increasing model size for better generalisation, SLMs designed for edge applications are expected to have adaptivity to the deployment environments and energy efficiency given the device battery life constraints, which are not addressed in datacenter-deployed LLMs. This paper addresses these two requirements by proposing a training-free token embedding compression approach using Tensor-Train Decomposition (TTD). Each pre-trained token embedding vector is converted into a lower-dimensional Matrix Product State (MPS). We comprehensively evaluate the extracted low-rank structures across compression ratio, language task performance, latency, and energy consumption on a typical low-end device, i.e. Raspberry Pi. Taking the sub-billion parameter versions of GPT-2/Cerebres-GPT and OPT models as examples, our approach achieves a comparable language task performance to the original model with around $2.0\times$ embedding layer compression, while the energy consumption of a single query drops by half.