Pre-training acts as an implicit compressor of the average NLP task — Aghajanyan et al.'s proposed mechanism for why larger, better-pretrained models have lower intrinsic dimension

Aghajanyan, Zettlemoyer & Gupta ("Intrinsic Dimensionality Explains the Effectiveness of Language Model Fine-Tuning," arXiv:2012.13255) propose a mechanism for why fine-tuning a pretrained language model has very low intrinsic dimension (claim-aghajanyan-2020-fine-tuning-low-intrinsic-dimension): pre-training itself acts as an implicit compressor. They interpret the intrinsic parameter vector of a fine-tuning run as encoding the task, and its dimension d as "the minimal description length of the task within the framework dictated by the pre-trained representations," and hypothesize "that pre-training is implicitly lowering the intrinsic dimensionality of the average NLP task, and therefore compress the minimal description length of those same tasks."

They test this directly, retraining RoBERTa-Base from scratch and measuring intrinsic dimension across pre-training checkpoints on six datasets: "the intrinsic dimensionality of RoBERTa-Base monotonically decreases as we continue pre-training" — a result they note is surprising precisely because "the language model does not have access to downstream datasets" while pre-training. Extending the measurement across a dozen-plus released models of varying size (BERT, RoBERTa, BART, Electra, ALBERT, XLNet, T5, XLM-R) on MRPC, they report: "we see a strong general trend that as the number of parameters increases, the intrinsic dimension of fine-tuning on MRPC decreases." Their own gloss: "the more parameters we have in the model, the less we need to represent a task."

This mechanism is the answer half of question-intrinsic-dimension-falls-with-model-scale-adaptation: larger, better-pretrained models don't need more information to specify a fine-tune because pre-training has already compressed the "average task" into the representation. Whether the same intrinsic-dimension trend continues to hold at far larger scale is tested separately in claim-hu-2021-lora-gpt3-175b-intrinsic-rank-one-or-two. See also entity-armen-aghajanyan and entity-intrinsic-dimension.