# Neural scaling laws for an uncertain world

arXiv: https://arxiv.org/abs/1607.04886 · HTML: https://mlsanity.com/paper/1607.04886/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jul 2016.

## Built on by (most cited first, 1 of 1)

- [DeepSITH: Efficient Learning via Decomposition of What and When Across Time Scales](https://mlsanity.com/paper/2104.04646/) (2021)

## Abstract (arXiv)

Autonomous neural systems must efficiently process information in a wide range of novel environments, which may have very different statistical properties. We consider the problem of how to optimally distribute receptors along a one-dimensional continuum consistent with the following design principles. First, neural representations of the world should obey a neural uncertainty principle---making as few assumptions as possible about the statistical structure of the world. Second, neural representations should convey, as much as possible, equivalent information about environments with different statistics. The results of these arguments resemble the structure of the visual system and provide a natural explanation of the behavioral Weber-Fechner law, a foundational result in psychology. Because the derivation is extremely general, this suggests that similar scaling relationships should be observed not only in sensory continua, but also in neural representations of ``cognitive' one-dimensional quantities such as time or numerosity.