# A Unified Approach to Count-Based Weakly-Supervised Learning

arXiv: https://arxiv.org/abs/2311.13718 · HTML: https://mlsanity.com/paper/2311.13718/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 70 references that are in the map.
- First posted on arXiv 22 Nov 2023.

## Builds on (most cited first, 26 of 26)

- [Attention-based Deep Multiple Instance Learning](https://mlsanity.com/paper/1802.04712/) (2018)
- [Learning from Noisy Labels with Deep Neural Networks: A Survey](https://mlsanity.com/paper/2007.08199/) (2020)
- [Neural Probabilistic Logic Programming in DeepProbLog](https://mlsanity.com/paper/1907.08194/) (2019)
- [A Semantic Loss Function for Deep Learning with Symbolic Knowledge](https://mlsanity.com/paper/1711.11157/) (2017)
- [Positive-Unlabeled Learning with Non-Negative Risk Estimator](https://mlsanity.com/paper/1703.00593/) (2017)
- [Learning from positive and unlabeled data: a survey](https://mlsanity.com/paper/1811.04820/) (2018)
- [Multiple Instance Learning: A Survey of Problem Characteristics and Applications](https://mlsanity.com/paper/1612.03365/) (2016)
- [A Survey on Multi-view Learning](https://mlsanity.com/paper/1304.5634/) (2013)
- [Revisiting Multiple Instance Neural Networks](https://mlsanity.com/paper/1610.02501/) (2016)
- [Semantic Probabilistic Layers for Neuro-Symbolic Learning](https://mlsanity.com/paper/2206.00426/) (2022)
- [Mixture Proportion Estimation and PU Learning: A Modern Approach](https://mlsanity.com/paper/2111.00980/) (2021)
- [Self-Training with Weak Supervision](https://mlsanity.com/paper/2104.05514/) (2021)
- [On Learning from Label Proportions](https://mlsanity.com/paper/1402.5902/) (2014)
- [Learning from Label Proportions with Consistency Regularization](https://mlsanity.com/paper/1910.13188/) (2019)
- [SIMPLE: A Gradient Estimator for k-Subset Sampling](https://mlsanity.com/paper/2210.01941/) (2022)
- [Co-training for Demographic Classification Using Deep Learning from Label Proportions](https://mlsanity.com/paper/1709.04108/) (2017)
- [Neuro-Symbolic Entropy Regularization](https://mlsanity.com/paper/2201.11250/) (2022)
- [Multiple Instance Learning via Iterative Self-Paced Supervised Contrastive Learning](https://mlsanity.com/paper/2210.09452/) (2022)
- [Deep Learning from Label Proportions for Emphysema Quantification](https://mlsanity.com/paper/1807.08601/) (2018)
- [Semantic Strengthening of Neuro-Symbolic Learning](https://mlsanity.com/paper/2302.14207/) (2023)
- [Efficient Search-Based Weighted Model Integration](https://mlsanity.com/paper/1903.05334/) (2019)
- [Scaling up Hybrid Probabilistic Inference with Logical and Arithmetic Constraints via Message Passing](https://mlsanity.com/paper/2003.00126/) (2020)
- [Collapsed Inference for Bayesian Deep Learning](https://mlsanity.com/paper/2306.09686/) (2023)
- [Leveraging Unlabeled Data for Entity-Relation Extraction through Probabilistic Constraint Satisfaction](https://mlsanity.com/paper/2103.11062/) (2021)
- [Learning from Label Proportions with Instance-wise Consistency](https://mlsanity.com/paper/2203.12836/) (2022)
- [Learning from Imprecise and Fuzzy Observations: Data Disambiguation through Generalized Loss Minimization](https://mlsanity.com/paper/1305.0698/) (2013)

## Built on by (most cited first, 9 of 9)

- [A General Framework for Learning from Weak Supervision](https://mlsanity.com/paper/2402.01922/) (2024)
- [Newton Losses: Using Curvature Information for Learning with Differentiable Algorithms](https://mlsanity.com/paper/2410.19055/) (2024)
- [Deep Generative Models with Hard Linear Equality Constraints](https://mlsanity.com/paper/2502.05416/) (2025)
- [Accessible, Realistic, and Fair Evaluation of Positive-Unlabeled Learning Algorithms](https://mlsanity.com/paper/2509.24228/) (2025)
- [Weakly Supervised Segmentation as Semantic-Based Regularization](https://mlsanity.com/paper/2605.13674/) (2026)
- [ProbMoE: Differentiable Probabilistic Routing for Mixture-of-Experts](https://mlsanity.com/paper/2606.01509/) (2026)
- [Exploiting the Potential Supervision Information of Clean Samples in Partial Label Learning](https://mlsanity.com/paper/2505.09354/) (2025)
- [Learning Robust Diffusion Models from Imprecise Supervision](https://mlsanity.com/paper/2510.03016/) (2025)
- [FastBUS: A Fast Bayesian Framework for Unified Weakly-Supervised Learning](https://mlsanity.com/paper/2603.00517/) (2026)

## Abstract (arXiv)

High-quality labels are often very scarce, whereas unlabeled data with inferred weak labels occurs more naturally. In many cases, these weak labels dictate the frequency of each respective class over a set of instances. In this paper, we develop a unified approach to learning from such weakly-labeled data, which we call count-based weakly-supervised learning. At the heart of our approach is the ability to compute the probability of exactly k out of n outputs being set to true. This computation is differentiable, exact, and efficient. Building upon the previous computation, we derive a count loss penalizing the model for deviations in its distribution from an arithmetic constraint defined over label counts. We evaluate our approach on three common weakly-supervised learning paradigms and observe that our proposed approach achieves state-of-the-art or highly competitive results across all three of the paradigms.