# RACH-Space: Reconstructing Adaptive Convex Hull Space with Applications in Weak Supervision

arXiv: https://arxiv.org/abs/2307.04870 · HTML: https://mlsanity.com/paper/2307.04870/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 35 references that are in the map.
- First posted on arXiv 10 Jul 2023.

## Builds on (most cited first, 17 of 17)

- [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)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [On the Opportunities and Risks of Foundation Models](https://mlsanity.com/paper/2108.07258/) (2021)
- [Data Programming: Creating Large Training Sets, Quickly](https://mlsanity.com/paper/1605.07723/) (2016)
- [Training Complex Models with Multi-Task Weak Supervision](https://mlsanity.com/paper/1810.02840/) (2018)
- [Fast and Three-rious: Speeding Up Weak Supervision with Triplet Methods](https://mlsanity.com/paper/2002.11955/) (2020)
- [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)
- [Self-Training with Weak Supervision](https://mlsanity.com/paper/2104.05514/) (2021)
- [Weakly Supervised Disentanglement by Pairwise Similarities](https://mlsanity.com/paper/1906.01044/) (2019)
- [Incremental Knowledge Base Construction Using DeepDive](https://mlsanity.com/paper/1502.00731/) (2015)
- [Learning Hyper Label Model for Programmatic Weak Supervision](https://mlsanity.com/paper/2207.13545/) (2022)
- [Learning from Multiple Noisy Partial Labelers](https://mlsanity.com/paper/2106.04530/) (2021)
- [Constrained Labeling for Weakly Supervised Learning](https://mlsanity.com/paper/2009.07360/) (2020)
- [The limit shape of convex hull peeling](https://mlsanity.com/paper/1805.08278/) (2018)
- [Ground Truth Inference for Weakly Supervised Entity Matching](https://mlsanity.com/paper/2211.06975/) (2022)

## Abstract (arXiv)

We introduce RACH-Space, an algorithm for labelling unlabelled data in weakly supervised learning, given incomplete, noisy information about the labels. RACH-Space offers simplicity in implementation without requiring hard assumptions on data or the sources of weak supervision, and is well suited for practical applications where fully labelled data is not available. Our method is built upon a geometrical interpretation of the space spanned by the set of weak signals. We also analyze the theoretical properties underlying the relationship between the convex hulls in this space and the accuracy of our output labels, bridging geometry with machine learning. Empirical results demonstrate that RACH-Space works well in practice and compares favorably to the best existing label models for weakly supervised learning.