A Mathematical Exploration of Why Language Models Help Solve Downstream Tasks

By Nikunj Saunshi, Sadhika Malladi, Sanjeev Arora. 2020

93 citations recorded by the source corpus.

Autoregressive language models pretrained on large corpora have been successful at solving downstream tasks, even with zero-shot usage. However, there is little theoretical justification for their success. This paper considers the following questions: (1) Why should learning the distribution of natural language help with downstream classification tasks? (2) Why do features learned using language modeling help solve downstream tasks with linear classifiers? For (1), we hypothesize, and verify empirically, that classification tasks of interest can be reformulated as next word prediction tasks, thus making language modeling a meaningful pretraining task. For (2), we analyze properties of the cross-entropy objective to show that $\epsilon$-optimal language models in cross-entropy (log-perplexity) learn features that are $\mathcal{O}(\sqrt{\epsilon})$-good on natural linear classification tasks, thus demonstrating mathematically that doing well on language modeling can be beneficial for downstream tasks. We perform experiments to verify assumptions and validate theoretical results. Our theoretical insights motivate a simple alternative to the cross-entropy objective that performs well on some linear classification tasks.

Subfields: Large Language Models, Natural Language Processing, Statistical Learning Theory

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Citations in the corpus

Learning To Retrieve Prompts for In-Context Learning (2021, background): “Saunshi et al. (2021) suggests that by conditioning on a prompt, the task of predicting the next word approaches linear separability.”
Why Do Pretrained Language Models Help in Downstream Tasks? An Analysis of Head and Prompt Tuning (2021, unknown): “Our work contrasts with prior theoretical work [28], which assumes that downstream labels are recoverable via a linear head applied to the conditional token probabilities, and analyze how errors in pretraining or model misspecification propagate downstream.”
Self-Supervised Representation Learning: Introduction, advances, and challenges (2021, unknown): “…to only instance discrimination methods [48], another that primarily considers how SSRL learns useful representations for natural language tasks [49], and finally, a paper that makes use of conditional independence to further elucidate how masked prediction pretext tasks lead to useful…”
Differentiable Prompt Makes Pre-trained Language Models Better Few-shot Learners (2021, background): “(ii) DART has the same task setting as large-scale language model pre-training and has a small theoretical upper bound for downstream classification tasks [36].”
Fine-Tuning Language Models with Just Forward Passes (2023, background): “Past works [83, 67] have demonstrated how the inclusion of a suitable prompt ensures the fine-tuning objective is closely related to the pre-training one.”
Training Trajectories of Language Models Across Scales (2022, background): “For zero-shot inference, Saunshi et al. (2020) mathematically shows that doing well in language modeling benefits downstream tasks.”