# Impact of Pretraining Term Frequencies on Few-Shot Reasoning

arXiv: https://arxiv.org/abs/2202.07206 · HTML: https://mlsanity.com/paper/2202.07206/

## Key facts

- Cited by 142 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 40 of its 55 references that are in the map.
- First posted on arXiv 15 Feb 2022.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 30 of 40)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [On the Opportunities and Risks of Foundation Models](https://mlsanity.com/paper/2108.07258/) (2021)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [Language Models as Knowledge Bases?](https://mlsanity.com/paper/1909.01066/) (2019)
- [Datasheets for Datasets](https://mlsanity.com/paper/1803.09010/) (2018)
- [RealToxicityPrompts: Evaluating Neural Toxic Degeneration in Language Models](https://mlsanity.com/paper/2009.11462/) (2020)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [Right for the Wrong Reasons: Diagnosing Syntactic Heuristics in Natural Language Inference](https://mlsanity.com/paper/1902.01007/) (2019)
- [The Secret Sharer: Evaluating and Testing Unintended Memorization in Neural Networks](https://mlsanity.com/paper/1802.08232/) (2018)
- [Annotation Artifacts in Natural Language Inference Data](https://mlsanity.com/paper/1803.02324/) (2018)
- [Adversarial Examples for Evaluating Reading Comprehension Systems](https://mlsanity.com/paper/1707.07328/) (2017)
- [What Neural Networks Memorize and Why: Discovering the Long Tail via Influence Estimation](https://mlsanity.com/paper/2008.03703/) (2020)
- [Documenting Large Webtext Corpora: A Case Study on the Colossal Clean Crawled Corpus](https://mlsanity.com/paper/2104.08758/) (2021)
- [Does Learning Require Memorization? A Short Tale about a Long Tail](https://mlsanity.com/paper/1906.05271/) (2019)
- [Gender Bias in Coreference Resolution](https://mlsanity.com/paper/1804.09301/) (2018)
- [Analysing Mathematical Reasoning Abilities of Neural Models](https://mlsanity.com/paper/1904.01557/) (2019)
- [Hypothesis Only Baselines in Natural Language Inference](https://mlsanity.com/paper/1805.01042/) (2018)
- [AutoPrompt: Eliciting Knowledge from Language Models with Automatically Generated Prompts](https://mlsanity.com/paper/2010.15980/) (2020)
- [Commonsense Knowledge Mining from Pretrained Models](https://mlsanity.com/paper/1909.00505/) (2019)
- [Masked Language Modeling and the Distributional Hypothesis: Order Word Matters Pre-training for Little](https://mlsanity.com/paper/2104.06644/) (2021)
- [Do NLP Models Know Numbers? Probing Numeracy in Embeddings](https://mlsanity.com/paper/1909.07940/) (2019)
- [Counterfactual Memorization in Neural Language Models](https://mlsanity.com/paper/2112.12938/) (2021)
- [Question and Answer Test-Train Overlap in Open-Domain Question Answering Datasets](https://mlsanity.com/paper/2008.02637/) (2020)
- [Injecting Numerical Reasoning Skills into Language Models](https://mlsanity.com/paper/2004.04487/) (2020)
- [End-to-End Bias Mitigation by Modelling Biases in Corpora](https://mlsanity.com/paper/1909.06321/) (2019)
- [Birds have four legs?! NumerSense: Probing Numerical Commonsense Knowledge of Pre-trained Language Models](https://mlsanity.com/paper/2005.00683/) (2020)
- [Competency Problems: On Finding and Removing Artifacts in Language Data](https://mlsanity.com/paper/2104.08646/) (2021)
- [What's in the Box? A Preliminary Analysis of Undesirable Content in the Common Crawl Corpus](https://mlsanity.com/paper/2105.02732/) (2021)
- [A Thorough Examination of the CNN/Daily Mail Reading Comprehension Task](https://mlsanity.com/paper/1606.02858/) (2016)

## Built on by (most cited first, 30 of 142)

- [Self-Instruct: Aligning Language Models with Self-Generated Instructions](https://mlsanity.com/paper/2212.10560/) (2022)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [Rethinking the Role of Demonstrations: What Makes In-Context Learning Work?](https://mlsanity.com/paper/2202.12837/) (2022)
- [When Not to Trust Language Models: Investigating Effectiveness of Parametric and Non-Parametric Memories](https://mlsanity.com/paper/2212.10511/) (2022)
- [Galactica: A Large Language Model for Science](https://mlsanity.com/paper/2211.09085/) (2022)
- [What Can Transformers Learn In-Context? A Case Study of Simple Function Classes](https://mlsanity.com/paper/2208.01066/) (2022)
- [GPT-NeoX-20B: An Open-Source Autoregressive Language Model](https://mlsanity.com/paper/2204.06745/) (2022)
- [Towards Reasoning in Large Language Models: A Survey](https://mlsanity.com/paper/2212.10403/) (2022)
- [GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2410.05229/) (2024)
- [Large Language Models Struggle to Learn Long-Tail Knowledge](https://mlsanity.com/paper/2211.08411/) (2022)
- [Language Models Are Greedy Reasoners: A Systematic Formal Analysis of Chain-of-Thought](https://mlsanity.com/paper/2210.01240/) (2022)
- [Large Language Models Are Reasoning Teachers](https://mlsanity.com/paper/2212.10071/) (2022)
- [Data Selection for Language Models via Importance Resampling](https://mlsanity.com/paper/2302.03169/) (2023)
- [Data Distributional Properties Drive Emergent In-Context Learning in Transformers](https://mlsanity.com/paper/2205.05055/) (2022)
- [Transformers as Statisticians: Provable In-Context Learning with In-Context Algorithm Selection](https://mlsanity.com/paper/2306.04637/) (2023)
- [Data Contamination: From Memorization to Exploitation](https://mlsanity.com/paper/2203.08242/) (2022)
- [Towards Understanding Chain-of-Thought Prompting: An Empirical Study of What Matters](https://mlsanity.com/paper/2212.10001/) (2022)
- [Demystifying Prompts in Language Models via Perplexity Estimation](https://mlsanity.com/paper/2212.04037/) (2022)
- [Exploring Length Generalization in Large Language Models](https://mlsanity.com/paper/2207.04901/) (2022)
- [Time Travel in LLMs: Tracing Data Contamination in Large Language Models](https://mlsanity.com/paper/2308.08493/) (2023)
- [Language models show human-like content effects on reasoning tasks](https://mlsanity.com/paper/2207.07051/) (2022)
- [Birth of a Transformer: A Memory Viewpoint](https://mlsanity.com/paper/2306.00802/) (2023)
- [Supervised Pretraining Can Learn In-Context Reinforcement Learning](https://mlsanity.com/paper/2306.14892/) (2023)
- [How well do Large Language Models perform in Arithmetic tasks?](https://mlsanity.com/paper/2304.02015/) (2023)
- [Text and Patterns: For Effective Chain of Thought, It Takes Two to Tango](https://mlsanity.com/paper/2209.07686/) (2022)
- [GrIPS: Gradient-free, Edit-based Instruction Search for Prompting Large Language Models](https://mlsanity.com/paper/2203.07281/) (2022)
- [A Survey of Deep Learning for Mathematical Reasoning](https://mlsanity.com/paper/2212.10535/) (2022)
- [Teaching Arithmetic to Small Transformers](https://mlsanity.com/paper/2307.03381/) (2023)
- [ReviewerGPT? An Exploratory Study on Using Large Language Models for Paper Reviewing](https://mlsanity.com/paper/2306.00622/) (2023)

## Abstract (arXiv)

Pretrained Language Models (LMs) have demonstrated ability to perform numerical reasoning by extrapolating from a few examples in few-shot settings. However, the extent to which this extrapolation relies on robust reasoning is unclear. In this paper, we investigate how well these models reason with terms that are less frequent in the pretraining data. In particular, we examine the correlations between the model performance on test instances and the frequency of terms from those instances in the pretraining data. We measure the strength of this correlation for a number of GPT-based language models (pretrained on the Pile dataset) on various numerical deduction tasks (e.g., arithmetic and unit conversion). Our results consistently demonstrate that models are more accurate on instances whose terms are more prevalent, in some cases above 70% (absolute) more accurate on the top 10% frequent terms in comparison to the bottom 10%. Overall, although LMs exhibit strong performance at few-shot numerical reasoning tasks, our results raise the question of how much models actually generalize beyond pretraining data, and we encourage researchers to take the pretraining data into account when interpreting evaluation results.