# A Self-Supervised Framework for Function Learning and Extrapolation

arXiv: https://arxiv.org/abs/2106.07369 · HTML: https://mlsanity.com/paper/2106.07369/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 54 references that are in the map.
- First posted on arXiv 14 Jun 2021.

## Builds on (most cited first, 23 of 23)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [Neural Processes](https://mlsanity.com/paper/1807.01622/) (2018)
- [Unsupervised Feature Extraction by Time-Contrastive Learning and Nonlinear ICA](https://mlsanity.com/paper/1605.06336/) (2016)
- [Unsupervised Scalable Representation Learning for Multivariate Time Series](https://mlsanity.com/paper/1901.10738/) (2019)
- [Unsupervised Representation Learning for Time Series with Temporal Neighborhood Coding](https://mlsanity.com/paper/2106.00750/) (2021)
- [DreamCoder: Growing generalizable, interpretable knowledge with wake-sleep Bayesian program learning](https://mlsanity.com/paper/2006.08381/) (2020)
- [VideoMoCo: Contrastive Video Representation Learning with Temporally Adversarial Examples](https://mlsanity.com/paper/2103.05905/) (2021)
- [Gaussian Process Kernels for Pattern Discovery and Extrapolation](https://mlsanity.com/paper/1302.4245/) (2013)
- [Building machines that adapt and compute like brains](https://mlsanity.com/paper/1711.04203/) (2017)
- [Structure Discovery in Nonparametric Regression through Compositional Kernel Search](https://mlsanity.com/paper/1302.4922/) (2013)
- [Sequence-to-Sequence Contrastive Learning for Text Recognition](https://mlsanity.com/paper/2012.10873/) (2020)
- [TimeNet: Pre-trained deep recurrent neural network for time series classification](https://mlsanity.com/paper/1706.08838/) (2017)
- [Learning Representations that Support Extrapolation](https://mlsanity.com/paper/2007.05059/) (2020)
- [The Variational Gaussian Process](https://mlsanity.com/paper/1511.06499/) (2015)
- [Improving Clinical Predictions through Unsupervised Time Series Representation Learning](https://mlsanity.com/paper/1812.00490/) (2018)
- [Differentiable Compositional Kernel Learning for Gaussian Processes](https://mlsanity.com/paper/1806.04326/) (2018)
- [Function Contrastive Learning of Transferable Meta-Representations](https://mlsanity.com/paper/2010.07093/) (2020)
- [The Human Kernel](https://mlsanity.com/paper/1510.07389/) (2015)

## Built on by (most cited first, 2 of 2)

- [Beyond Transformers for Function Learning](https://mlsanity.com/paper/2304.09979/) (2023)
- [A Group Theoretic Analysis of the Symmetries Underlying Base Addition and Their Learnability by Neural Networks](https://mlsanity.com/paper/2507.10678/) (2025)

## Abstract (arXiv)

Understanding how agents learn to generalize -- and, in particular, to extrapolate -- in high-dimensional, naturalistic environments remains a challenge for both machine learning and the study of biological agents. One approach to this has been the use of function learning paradigms, which allow peoples' empirical patterns of generalization for smooth scalar functions to be described precisely. However, to date, such work has not succeeded in identifying mechanisms that acquire the kinds of general purpose representations over which function learning can operate to exhibit the patterns of generalization observed in human empirical studies. Here, we present a framework for how a learner may acquire such representations, that then support generalization -- and extrapolation in particular -- in a few-shot fashion. Taking inspiration from a classic theory of visual processing, we construct a self-supervised encoder that implements the basic inductive bias of invariance under topological distortions. We show the resulting representations outperform those from other models for unsupervised time series learning in several downstream function learning tasks, including extrapolation.