# Fast and Three-rious: Speeding Up Weak Supervision with Triplet Methods

arXiv: https://arxiv.org/abs/2002.11955 · HTML: https://mlsanity.com/paper/2002.11955/

## Key facts

- Cited by 98 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Feb 2020.

## Built on by (most cited first, 30 of 98)

- [DataComp: In search of the next generation of multimodal datasets](https://mlsanity.com/paper/2304.14108/) (2023)
- [Ask Me Anything: A simple strategy for prompting language models](https://mlsanity.com/paper/2210.02441/) (2022)
- [Language Models Enable Simple Systems for Generating Structured Views of Heterogeneous Data Lakes](https://mlsanity.com/paper/2304.09433/) (2023)
- [WRENCH: A Comprehensive Benchmark for Weak Supervision](https://mlsanity.com/paper/2109.11377/) (2021)
- [A Survey on Programmatic Weak Supervision](https://mlsanity.com/paper/2202.05433/) (2022)
- [Language Models in the Loop: Incorporating Prompting into Weak Supervision](https://mlsanity.com/paper/2205.02318/) (2022)
- [Theoretical Analysis of Weak-to-Strong Generalization](https://mlsanity.com/paper/2405.16043/) (2024)
- [End-to-End Weak Supervision](https://mlsanity.com/paper/2107.02233/) (2021)
- [Smoothie: Label Free Language Model Routing](https://mlsanity.com/paper/2412.04692/) (2024)
- [To Aggregate or Not? Learning with Separate Noisy Labels](https://mlsanity.com/paper/2206.07181/) (2022)
- [Universalizing Weak Supervision](https://mlsanity.com/paper/2112.03865/) (2021)
- [Co-training Improves Prompt-based Learning for Large Language Models](https://mlsanity.com/paper/2202.00828/) (2022)
- [Shrinking the Generation-Verification Gap with Weak Verifiers](https://mlsanity.com/paper/2506.18203/) (2025)
- [Weak-to-Strong Generalization Through the Data-Centric Lens](https://mlsanity.com/paper/2412.03881/) (2024)
- [Training Subset Selection for Weak Supervision](https://mlsanity.com/paper/2206.02914/) (2022)
- [DP-SSL: Towards Robust Semi-supervised Learning with A Few Labeled Samples](https://mlsanity.com/paper/2110.13740/) (2021)
- [Shoring Up the Foundations: Fusing Model Embeddings and Weak Supervision](https://mlsanity.com/paper/2203.13270/) (2022)
- [skweak: Weak Supervision Made Easy for NLP](https://mlsanity.com/paper/2104.09683/) (2021)
- [Learning Hyper Label Model for Programmatic Weak Supervision](https://mlsanity.com/paper/2207.13545/) (2022)
- [Creating Training Sets via Weak Indirect Supervision](https://mlsanity.com/paper/2110.03484/) (2021)
- [Weakly Supervised Veracity Classification with LLM-Predicted Credibility Signals](https://mlsanity.com/paper/2309.07601/) (2023)
- [The Road to Artificial SuperIntelligence: A Comprehensive Survey of Superalignment](https://mlsanity.com/paper/2412.16468/) (2024)
- [CARE: Confounder-Aware Aggregation for Reliable LLM Evaluation](https://mlsanity.com/paper/2603.00039/) (2026)
- [SQLens: An End-to-End Framework for Error Detection and Correction in Text-to-SQL](https://mlsanity.com/paper/2506.04494/) (2025)
- [Losses over Labels: Weakly Supervised Learning via Direct Loss Construction](https://mlsanity.com/paper/2212.06921/) (2022)
- [Nemo: Guiding and Contextualizing Weak Supervision for Interactive Data Programming](https://mlsanity.com/paper/2203.01382/) (2022)
- [Lifting Weak Supervision To Structured Prediction](https://mlsanity.com/paper/2211.13375/) (2022)
- [WeakSAM: Segment Anything Meets Weakly-supervised Instance-level Recognition](https://mlsanity.com/paper/2402.14812/) (2024)
- [The ALCHEmist: Automated Labeling 500x CHEaper Than LLM Data Annotators](https://mlsanity.com/paper/2407.11004/) (2024)
- [Label Propagation with Weak Supervision](https://mlsanity.com/paper/2210.03594/) (2022)

## Abstract (arXiv)

Weak supervision is a popular method for building machine learning models without relying on ground truth annotations. Instead, it generates probabilistic training labels by estimating the accuracies of multiple noisy labeling sources (e.g., heuristics, crowd workers). Existing approaches use latent variable estimation to model the noisy sources, but these methods can be computationally expensive, scaling superlinearly in the data. In this work, we show that, for a class of latent variable models highly applicable to weak supervision, we can find a closed-form solution to model parameters, obviating the need for iterative solutions like stochastic gradient descent (SGD). We use this insight to build FlyingSquid, a weak supervision framework that runs orders of magnitude faster than previous weak supervision approaches and requires fewer assumptions. In particular, we prove bounds on generalization error without assuming that the latent variable model can exactly parameterize the underlying data distribution. Empirically, we validate FlyingSquid on benchmark weak supervision datasets and find that it achieves the same or higher quality compared to previous approaches without the need to tune an SGD procedure, recovers model parameters 170 times faster on average, and enables new video analysis and online learning applications.