# Automated discovery of symbolic laws governing skill acquisition from naturally occurring data

arXiv: https://arxiv.org/abs/2404.05689 · HTML: https://mlsanity.com/paper/2404.05689/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 60 references that are in the map.
- First posted on arXiv 8 Apr 2024.

## Builds on (most cited first, 6 of 6)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Discovering Symbolic Models from Deep Learning with Inductive Biases](https://mlsanity.com/paper/2006.11287/) (2020)
- [On the Expressive Power of Deep Neural Networks](https://mlsanity.com/paper/1606.05336/) (2016)
- [Physics-informed learning of governing equations from scarce data](https://mlsanity.com/paper/2005.03448/) (2020)

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

- [PoE-World: Compositional World Modeling with Products of Programmatic Experts](https://mlsanity.com/paper/2505.10819/) (2025)
- [EduPlanner: LLM-Based Multi-Agent Systems for Customized and Intelligent Instructional Design](https://mlsanity.com/paper/2504.05370/) (2025)
- [Symbolic regression via MDLformer-guided search: from minimizing prediction error to minimizing description length](https://mlsanity.com/paper/2411.03753/) (2024)
- [A Survey of Models for Cognitive Diagnosis: New Developments and Future Directions](https://mlsanity.com/paper/2407.05458/) (2024)
- [DisenGCD: A Meta Multigraph-assisted Disentangled Graph Learning Framework for Cognitive Diagnosis](https://mlsanity.com/paper/2410.17564/) (2024)
- [Beyond Accuracy and Complexity: The Effective Information Criterion for Structurally Stable Symbolic Regression](https://mlsanity.com/paper/2509.21780/) (2025)
- [SA-GAT-SR: Self-Adaptable Graph Attention Networks with Symbolic Regression for high-fidelity material property prediction](https://mlsanity.com/paper/2505.00625/) (2025)

## Abstract (arXiv)

Skill acquisition is a key area of research in cognitive psychology as it encompasses multiple psychological processes. The laws discovered under experimental paradigms are controversial and lack generalizability. This paper aims to unearth the laws of skill learning from large-scale training log data. A two-stage algorithm was developed to tackle the issues of unobservable cognitive states and algorithmic explosion in searching. Initially a deep learning model is employed to determine the learner's cognitive state and assess the feature importance. Subsequently, symbolic regression algorithms are utilized to parse the neural network model into algebraic equations. Experimental results show the algorithm can accurately restore preset laws within a noise range in continuous feedback settings. When applied to Lumosity training data, the method outperforms traditional and recent models in fitness terms. The study reveals two new forms of skill acquisition laws and reaffirms some previous findings.