# Conditional Teaching Size

arXiv: https://arxiv.org/abs/2107.07038 · HTML: https://mlsanity.com/paper/2107.07038/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 43 references that are in the map.
- First posted on arXiv 29 Jun 2021.

## Builds on (most cited first, 16 of 16)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Curriculum Learning: A Survey](https://mlsanity.com/paper/2101.10382/) (2021)
- [Curriculum Learning by Transfer Learning: Theory and Experiments with Deep Networks](https://mlsanity.com/paper/1802.03796/) (2018)
- [Generative Teaching Networks: Accelerating Neural Architecture Search by Learning to Generate Synthetic Training Data](https://mlsanity.com/paper/1912.07768/) (2019)
- [Policy Teaching via Environment Poisoning: Training-time Adversarial Attacks against Reinforcement Learning](https://mlsanity.com/paper/2003.12909/) (2020)
- [Learning Compositional Rules via Neural Program Synthesis](https://mlsanity.com/paper/2003.05562/) (2020)
- [SOLOIST: Building Task Bots at Scale with Transfer Learning and Machine Teaching](https://mlsanity.com/paper/2005.05298/) (2020)
- [Curriculum Learning of Multiple Tasks](https://mlsanity.com/paper/1412.1353/) (2014)
- [An Overview of Machine Teaching](https://mlsanity.com/paper/1801.05927/) (2018)
- [Iterative Machine Teaching](https://mlsanity.com/paper/1705.10470/) (2017)
- [A Sequential Self Teaching Approach for Improving Generalization in Sound Event Recognition](https://mlsanity.com/paper/2007.00144/) (2020)
- [Preference-based Teaching](https://mlsanity.com/paper/1702.02047/) (2017)
- [Conversation Learner -- A Machine Teaching Tool for Building Dialog Managers for Task-Oriented Dialog Systems](https://mlsanity.com/paper/2004.04305/) (2020)
- [Perspective Plane Program Induction from a Single Image](https://mlsanity.com/paper/2006.14708/) (2020)

## Abstract (arXiv)

Recent research in machine teaching has explored the instruction of any concept expressed in a universal language. In this compositional context, new experimental results have shown that there exist data teaching sets surprisingly shorter than the concept description itself. However, there exists a bound for those remarkable experimental findings through teaching size and concept complexity that we further explore here. As concepts are rarely taught in isolation we investigate the best configuration of concepts to teach a given set of concepts, where those that have been acquired first can be reused for the description of new ones. This new notion of conditional teaching size uncovers new insights, such as the interposition phenomenon: certain prior knowledge generates simpler compatible concepts that increase the teaching size of the concept that we want to teach. This does not happen for conditional Kolmogorov complexity. Furthermore, we provide an algorithm that constructs optimal curricula based on interposition avoidance. This paper presents a series of theoretical results, including their proofs, and some directions for future work. New research possibilities in curriculum teaching in compositional scenarios are now wide open to exploration.