# LIME: Learning Inductive Bias for Primitives of Mathematical Reasoning

arXiv: https://arxiv.org/abs/2101.06223 · HTML: https://mlsanity.com/paper/2101.06223/

## Key facts

- Cited by 46 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 76 references that are in the map.
- First posted on arXiv 15 Jan 2021.

## Builds on (most cited first, 30 of 42)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [XLNet: Generalized Autoregressive Pretraining for Language Understanding](https://mlsanity.com/paper/1906.08237/) (2019)
- [fairseq: A Fast, Extensible Toolkit for Sequence Modeling](https://mlsanity.com/paper/1904.01038/) (2019)
- [PEGASUS: Pre-training with Extracted Gap-sentences for Abstractive Summarization](https://mlsanity.com/paper/1912.08777/) (2019)
- [Cross-lingual Language Model Pretraining](https://mlsanity.com/paper/1901.07291/) (2019)
- [Effective Approaches to Attention-based Neural Machine Translation](https://mlsanity.com/paper/1508.04025/) (2015)
- [SpanBERT: Improving Pre-training by Representing and Predicting Spans](https://mlsanity.com/paper/1907.10529/) (2019)
- [Unified Language Model Pre-training for Natural Language Understanding and Generation](https://mlsanity.com/paper/1905.03197/) (2019)
- [Generative Language Modeling for Automated Theorem Proving](https://mlsanity.com/paper/2009.03393/) (2020)
- [MASS: Masked Sequence to Sequence Pre-training for Language Generation](https://mlsanity.com/paper/1905.02450/) (2019)
- [Analysing Mathematical Reasoning Abilities of Neural Models](https://mlsanity.com/paper/1904.01557/) (2019)
- [Deep Learning for Symbolic Mathematics](https://mlsanity.com/paper/1912.01412/) (2019)
- [Learning a SAT Solver from Single-Bit Supervision](https://mlsanity.com/paper/1802.03685/) (2018)
- [What Can Neural Networks Reason About?](https://mlsanity.com/paper/1905.13211/) (2019)
- [The Lean mathematical library](https://mlsanity.com/paper/1910.09336/) (2019)
- [Learning to Prove Theorems via Interacting with Proof Assistants](https://mlsanity.com/paper/1905.09381/) (2019)
- [Guiding High-Performance SAT Solvers with Unsat-Core Predictions](https://mlsanity.com/paper/1903.04671/) (2019)
- [Graph Representations for Higher-Order Logic and Theorem Proving](https://mlsanity.com/paper/1905.10006/) (2019)
- [GamePad: A Learning Environment for Theorem Proving](https://mlsanity.com/paper/1806.00608/) (2018)
- [Premise Selection for Theorem Proving by Deep Graph Embedding](https://mlsanity.com/paper/1709.09994/) (2017)
- [TacticToe: Learning to Prove with Tactics](https://mlsanity.com/paper/1804.00596/) (2018)
- [INT: An Inequality Benchmark for Evaluating Generalization in Theorem Proving](https://mlsanity.com/paper/2007.02924/) (2020)
- [Exploration of Neural Machine Translation in Autoformalization of Mathematics in Mizar](https://mlsanity.com/paper/1912.02636/) (2019)
- [Enhancing the Transformer with Explicit Relational Encoding for Math Problem Solving](https://mlsanity.com/paper/1910.06611/) (2019)

## Built on by (most cited first, 30 of 46)

- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [LeanDojo: Theorem Proving with Retrieval-Augmented Language Models](https://mlsanity.com/paper/2306.15626/) (2023)
- [Exploiting Programmatic Behavior of LLMs: Dual-Use Through Standard Security Attacks](https://mlsanity.com/paper/2302.05733/) (2023)
- [Language models show human-like content effects on reasoning tasks](https://mlsanity.com/paper/2207.07051/) (2022)
- [Pretrained Transformers as Universal Computation Engines](https://mlsanity.com/paper/2103.05247/) (2021)
- [Proof Artifact Co-training for Theorem Proving with Language Models](https://mlsanity.com/paper/2102.06203/) (2021)
- [A Survey of Deep Learning for Mathematical Reasoning](https://mlsanity.com/paper/2212.10535/) (2022)
- [Large Language Models as Analogical Reasoners](https://mlsanity.com/paper/2310.01714/) (2023)
- [Unveiling Transformers with LEGO: a synthetic reasoning task](https://mlsanity.com/paper/2206.04301/) (2022)
- [Vision Transformers provably learn spatial structure](https://mlsanity.com/paper/2210.09221/) (2022)
- [NaturalProofs: Mathematical Theorem Proving in Natural Language](https://mlsanity.com/paper/2104.01112/) (2021)
- [Language Models Can Teach Themselves to Program Better](https://mlsanity.com/paper/2207.14502/) (2022)
- [Exposing Attention Glitches with Flip-Flop Language Modeling](https://mlsanity.com/paper/2306.00946/) (2023)
- [Lean-STaR: Learning to Interleave Thinking and Proving](https://mlsanity.com/paper/2407.10040/) (2024)
- [A Survey on Deep Learning for Theorem Proving](https://mlsanity.com/paper/2404.09939/) (2024)
- [On the generalization of language models from in-context learning and finetuning: a controlled study](https://mlsanity.com/paper/2505.00661/) (2025)
- [Foundation Metrics for Evaluating Effectiveness of Healthcare Conversations Powered by Generative AI](https://mlsanity.com/paper/2309.12444/) (2023)
- [Insights into Pre-training via Simpler Synthetic Tasks](https://mlsanity.com/paper/2206.10139/) (2022)
- [Symbolic Behaviour in Artificial Intelligence](https://mlsanity.com/paper/2102.03406/) (2021)
- [Unsupervised Neural Machine Translation with Generative Language Models Only](https://mlsanity.com/paper/2110.05448/) (2021)
- [TRIGO: Benchmarking Formal Mathematical Proof Reduction for Generative Language Models](https://mlsanity.com/paper/2310.10180/) (2023)
- [Mathematical Language Models: A Survey](https://mlsanity.com/paper/2312.07622/) (2023)
- [ExPT: Synthetic Pretraining for Few-Shot Experimental Design](https://mlsanity.com/paper/2310.19961/) (2023)
- [Decrypting Cryptic Crosswords: Semantically Complex Wordplay Puzzles as a Target for NLP](https://mlsanity.com/paper/2104.08620/) (2021)
- [Through the Lens of Core Competency: Survey on Evaluation of Large Language Models](https://mlsanity.com/paper/2308.07902/) (2023)
- [General Intelligence Requires Reward-based Pretraining](https://mlsanity.com/paper/2502.19402/) (2025)
- [A Survey on Mathematical Reasoning and Optimization with Large Language Models](https://mlsanity.com/paper/2503.17726/) (2025)
- [Procedural Pretraining: Warming Up Language Models with Abstract Data](https://mlsanity.com/paper/2601.21725/) (2026)
- [A Survey in Mathematical Language Processing](https://mlsanity.com/paper/2205.15231/) (2022)

## Abstract (arXiv)

While designing inductive bias in neural architectures has been widely studied, we hypothesize that transformer networks are flexible enough to learn inductive bias from suitable generic tasks. Here, we replace architecture engineering by encoding inductive bias in the form of datasets. Inspired by Peirce's view that deduction, induction, and abduction are the primitives of reasoning, we design three synthetic tasks that are intended to require the model to have these three abilities. We specifically design these tasks to be synthetic and devoid of mathematical knowledge to ensure that only the fundamental reasoning biases can be learned from these tasks. This defines a new pre-training methodology called "LIME" (Learning Inductive bias for Mathematical rEasoning). Models trained with LIME significantly outperform vanilla transformers on four very different large mathematical reasoning benchmarks. Unlike dominating the computation cost as traditional pre-training approaches, LIME requires only a small fraction of the computation cost of the typical downstream task. The code for generating LIME tasks is available at https://github.com/tonywu95/LIME.