# A case for new neural network smoothness constraints

arXiv: https://arxiv.org/abs/2012.07969 · HTML: https://mlsanity.com/paper/2012.07969/

## Key facts

- Cited by 43 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Dec 2020.

## Built on by (most cited first, 30 of 43)

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- [The Impact of Geometric Complexity on Neural Collapse in Transfer Learning](https://mlsanity.com/paper/2405.15706/) (2024)
- [Spectral methods: crucial for machine learning, natural for quantum computers?](https://mlsanity.com/paper/2603.24654/) (2026)
- [PDE+: Enhancing Generalization via PDE with Adaptive Distributional Diffusion](https://mlsanity.com/paper/2305.15835/) (2023)
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## Abstract (arXiv)

How sensitive should machine learning models be to input changes? We tackle the question of model smoothness and show that it is a useful inductive bias which aids generalization, adversarial robustness, generative modeling and reinforcement learning. We explore current methods of imposing smoothness constraints and observe they lack the flexibility to adapt to new tasks, they don't account for data modalities, they interact with losses, architectures and optimization in ways not yet fully understood. We conclude that new advances in the field are hinging on finding ways to incorporate data, tasks and learning into our definitions of smoothness.
