# A Discrete Hard EM Approach for Weakly Supervised Question Answering

arXiv: https://arxiv.org/abs/1909.04849 · HTML: https://mlsanity.com/paper/1909.04849/

## Key facts

- Cited by 78 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Sep 2019.

## Built on by (most cited first, 30 of 78)

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- [Recent Advances in Text-to-SQL: A Survey of What We Have and What We Expect](https://mlsanity.com/paper/2208.10099/) (2022)
- [One Question Answering Model for Many Languages with Cross-lingual Dense Passage Retrieval](https://mlsanity.com/paper/2107.11976/) (2021)
- [UnitedQA: A Hybrid Approach for Open Domain Question Answering](https://mlsanity.com/paper/2101.00178/) (2021)
- [A Survey on Table Question Answering: Recent Advances](https://mlsanity.com/paper/2207.05270/) (2022)
- [Evidentiality-guided Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2112.08688/) (2021)
- [Learning Math Reasoning from Self-Sampled Correct and Partially-Correct Solutions](https://mlsanity.com/paper/2205.14318/) (2022)
- [Ever: Mitigating Hallucination in Large Language Models through Real-Time Verification and Rectification](https://mlsanity.com/paper/2311.09114/) (2023)
- [R2-D2: A Modular Baseline for Open-Domain Question Answering](https://mlsanity.com/paper/2109.03502/) (2021)
- [An Efficient Memory-Augmented Transformer for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2210.16773/) (2022)
- [Capturing Row and Column Semantics in Transformer Based Question Answering over Tables](https://mlsanity.com/paper/2104.08303/) (2021)
- [ReasTAP: Injecting Table Reasoning Skills During Pre-training via Synthetic Reasoning Examples](https://mlsanity.com/paper/2210.12374/) (2022)
- [Rider: Reader-Guided Passage Reranking for Open-Domain Question Answering](https://mlsanity.com/paper/2101.00294/) (2021)
- [Dual Reader-Parser on Hybrid Textual and Tabular Evidence for Open Domain Question Answering](https://mlsanity.com/paper/2108.02866/) (2021)
- [What's in a Name? Answer Equivalence For Open-Domain Question Answering](https://mlsanity.com/paper/2109.05289/) (2021)
- [Modeling Multi-hop Question Answering as Single Sequence Prediction](https://mlsanity.com/paper/2205.09226/) (2022)
- [Weakly-Supervised Hierarchical Models for Predicting Persuasive Strategies in Good-faith Textual Requests](https://mlsanity.com/paper/2101.06351/) (2021)
- [Narrative Question Answering with Cutting-Edge Open-Domain QA Techniques: A Comprehensive Study](https://mlsanity.com/paper/2106.03826/) (2021)
- [Grow-and-Clip: Informative-yet-Concise Evidence Distillation for Answer Explanation](https://mlsanity.com/paper/2201.05088/) (2022)
- [Neural Knowledge Bank for Pretrained Transformers](https://mlsanity.com/paper/2208.00399/) (2022)
- [Refiner: Restructure Retrieval Content Efficiently to Advance Question-Answering Capabilities](https://mlsanity.com/paper/2406.11357/) (2024)
- [RAS: Retrieval-And-Structuring for Knowledge-Intensive LLM Generation](https://mlsanity.com/paper/2502.10996/) (2025)
- [TempRetriever: Fusion-based Temporal Dense Passage Retrieval for Time-Sensitive Questions](https://mlsanity.com/paper/2502.21024/) (2025)
- [Chaining Simultaneous Thoughts for Numerical Reasoning](https://mlsanity.com/paper/2211.16482/) (2022)

## Abstract (arXiv)

Many question answering (QA) tasks only provide weak supervision for how the answer should be computed. For example, TriviaQA answers are entities that can be mentioned multiple times in supporting documents, while DROP answers can be computed by deriving many different equations from numbers in the reference text. In this paper, we show it is possible to convert such tasks into discrete latent variable learning problems with a precomputed, task-specific set of possible "solutions" (e.g. different mentions or equations) that contains one correct option. We then develop a hard EM learning scheme that computes gradients relative to the most likely solution at each update. Despite its simplicity, we show that this approach significantly outperforms previous methods on six QA tasks, including absolute gains of 2--10%, and achieves the state-of-the-art on five of them. Using hard updates instead of maximizing marginal likelihood is key to these results as it encourages the model to find the one correct answer, which we show through detailed qualitative analysis.