# Signal Recovery from Pooling Representations

arXiv: https://arxiv.org/abs/1311.4025 · HTML: https://mlsanity.com/paper/1311.4025/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Nov 2013.

## Built on by (most cited first, 12 of 12)

- [Privacy for Free: How does Dataset Condensation Help Privacy?](https://mlsanity.com/paper/2206.00240/) (2022)
- [AdaPool: Exponential Adaptive Pooling for Information-Retaining Downsampling](https://mlsanity.com/paper/2111.00772/) (2021)
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- [Johnson-Lindenstrauss Lemma, Linear and Nonlinear Random Projections, Random Fourier Features, and Random Kitchen Sinks: Tutorial and Survey](https://mlsanity.com/paper/2108.04172/) (2021)
- [A General Framework for Robust G-Invariance in G-Equivariant Networks](https://mlsanity.com/paper/2310.18564/) (2023)
- [Injectivity capacity of ReLU gates](https://mlsanity.com/paper/2410.20646/) (2024)
- [Generalizing Aggregation Functions in GNNs:High-Capacity GNNs via Nonlinear Neighborhood Aggregators](https://mlsanity.com/paper/2202.09145/) (2022)
- [Convex Geometry of ReLU-layers, Injectivity on the Ball and Local Reconstruction](https://mlsanity.com/paper/2307.09672/) (2023)
- [Maximal function pooling with applications](https://mlsanity.com/paper/2103.01292/) (2021)
- [Hierarchical Spherical CNNs with Lifting-based Adaptive Wavelets for Pooling and Unpooling](https://mlsanity.com/paper/2205.15571/) (2022)
- [Depth Monocular Estimation with Attention-based Encoder-Decoder Network from Single Image](https://mlsanity.com/paper/2210.13646/) (2022)
- [Injectivity of ReLU-layers: Tools from Frame Theory](https://mlsanity.com/paper/2406.15856/) (2024)

## Abstract (arXiv)

In this work we compute lower Lipschitz bounds of ℓp pooling operators for p=1, 2, ∞ as well as ℓp pooling operators preceded by half-rectification layers. These give sufficient conditions for the design of invertible neural network layers. Numerical experiments on MNIST and image patches confirm that pooling layers can be inverted with phase recovery algorithms. Moreover, the regularity of the inverse pooling, controlled by the lower Lipschitz constant, is empirically verified with a nearest neighbor regression.