# Representation Learning by Learning to Count

arXiv: https://arxiv.org/abs/1708.06734 · HTML: https://mlsanity.com/paper/1708.06734/

## Key facts

- Cited by 120 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Aug 2017.

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- [Understanding Cross-Domain Few-Shot Learning Based on Domain Similarity and Few-Shot Difficulty](https://mlsanity.com/paper/2202.01339/) (2022)
- [Can Vision Transformers Learn without Natural Images?](https://mlsanity.com/paper/2103.13023/) (2021)
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## Abstract (arXiv)

We introduce a novel method for representation learning that uses an artificial supervision signal based on counting visual primitives. This supervision signal is obtained from an equivariance relation, which does not require any manual annotation. We relate transformations of images to transformations of the representations. More specifically, we look for the representation that satisfies such relation rather than the transformations that match a given representation. In this paper, we use two image transformations in the context of counting: scaling and tiling. The first transformation exploits the fact that the number of visual primitives should be invariant to scale. The second transformation allows us to equate the total number of visual primitives in each tile to that in the whole image. These two transformations are combined in one constraint and used to train a neural network with a contrastive loss. The proposed task produces representations that perform on par or exceed the state of the art in transfer learning benchmarks.