A Mathematical Exploration of Why Language Models Help Solve Downstream
Tasks
- URL: http://arxiv.org/abs/2010.03648v2
- Date: Wed, 14 Apr 2021 17:59:14 GMT
- Title: A Mathematical Exploration of Why Language Models Help Solve Downstream
Tasks
- Authors: Nikunj Saunshi, Sadhika Malladi, Sanjeev Arora
- Abstract summary: Autoregressive language models, pretrained using large text corpora to do well on next word prediction, have been successful at solving many downstream tasks.
This paper initiates a mathematical study of this phenomenon for the downstream task of text classification.
- Score: 35.046596668631615
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Autoregressive language models, pretrained using large text corpora to do
well on next word prediction, have been successful at solving many downstream
tasks, even with zero-shot usage. However, there is little theoretical
understanding of this success. This paper initiates a mathematical study of
this phenomenon for the downstream task of text classification by considering
the following questions: (1) What is the intuitive connection between the
pretraining task of next word prediction and text classification? (2) How can
we mathematically formalize this connection and quantify the benefit of
language modeling? For (1), we hypothesize, and verify empirically, that
classification tasks of interest can be reformulated as sentence completion
tasks, thus making language modeling a meaningful pretraining task. With a
mathematical formalization of this hypothesis, we make progress towards (2) and
show that language models that are $\epsilon$-optimal in cross-entropy
(log-perplexity) learn features that can linearly solve such classification
tasks with $\mathcal{O}(\sqrt{\epsilon})$ error, thus demonstrating that doing
well on language modeling can be beneficial for downstream tasks. We
experimentally verify various assumptions and theoretical findings, and also
use insights from the analysis to design a new objective function that performs
well on some classification tasks.
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