# Generalizing Outside the Training Set: When Can Neural Networks Learn Identity Effects?

arXiv: https://arxiv.org/abs/2005.04330 · HTML: https://mlsanity.com/paper/2005.04330/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 May 2020.

## Built on by (most cited first, 4 of 4)

- [On the approximation capability of GNNs in node classification/regression tasks](https://mlsanity.com/paper/2106.08992/) (2021)
- [Interpreting intermediate convolutional layers of generative CNNs trained on waveforms](https://mlsanity.com/paper/2104.09489/) (2021)
- [VC dimension of Graph Neural Networks with Pfaffian activation functions](https://mlsanity.com/paper/2401.12362/) (2024)
- [Invariance, encodings, and generalization: learning identity effects with neural networks](https://mlsanity.com/paper/2101.08386/) (2021)

## Abstract (arXiv)

Often in language and other areas of cognition, whether two components of an object are identical or not determine whether it is well formed. We call such constraints identity effects. When developing a system to learn well-formedness from examples, it is easy enough to build in an identify effect. But can identity effects be learned from the data without explicit guidance? We provide a simple framework in which we can rigorously prove that algorithms satisfying simple criteria cannot make the correct inference. We then show that a broad class of algorithms including deep neural networks with standard architecture and training with backpropagation satisfy our criteria, dependent on the encoding of inputs. Finally, we demonstrate our theory with computational experiments in which we explore the effect of different input encodings on the ability of algorithms to generalize to novel inputs.