# Large deviations for the perceptron model and consequences for active learning

arXiv: https://arxiv.org/abs/1912.03927 · HTML: https://mlsanity.com/paper/1912.03927/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Dec 2019.

## Built on by (most cited first, 7 of 7)

- [Beyond neural scaling laws: beating power law scaling via data pruning](https://mlsanity.com/paper/2206.14486/) (2022)
- [Bayes-optimal Learning of Deep Random Networks of Extensive-width](https://mlsanity.com/paper/2302.00375/) (2023)
- [Deterministic equivalent and error universality of deep random features learning](https://mlsanity.com/paper/2302.00401/) (2023)
- [An Analytical Theory of Curriculum Learning in Teacher-Student Networks](https://mlsanity.com/paper/2106.08068/) (2021)
- [Towards a statistical theory of data selection under weak supervision](https://mlsanity.com/paper/2309.14563/) (2023)
- [High-dimensional learning of narrow neural networks](https://mlsanity.com/paper/2409.13904/) (2024)
- [Influence Diagnostics in High-dimensional M-estimation: Precise Asymptotics](https://mlsanity.com/paper/2607.09250/) (2026)

## Abstract (arXiv)

Active learning is a branch of machine learning that deals with problems where unlabeled data is abundant yet obtaining labels is expensive. The learning algorithm has the possibility of querying a limited number of samples to obtain the corresponding labels, subsequently used for supervised learning. In this work, we consider the task of choosing the subset of samples to be labeled from a fixed finite pool of samples. We assume the pool of samples to be a random matrix and the ground truth labels to be generated by a single-layer teacher random neural network. We employ replica methods to analyze the large deviations for the accuracy achieved after supervised learning on a subset of the original pool. These large deviations then provide optimal achievable performance boundaries for any active learning algorithm. We show that the optimal learning performance can be efficiently approached by simple message-passing active learning algorithms. We also provide a comparison with the performance of some other popular active learning strategies.