# Training-Free Bottleneck Width Planning for Convolutional Autoencoders

arXiv: https://arxiv.org/abs/2609.30755 · HTML: https://mlsanity.com/paper/2609.30755/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 41 references that are in the map.
- First posted on arXiv 25 Sep 2026.

## Builds on (most cited first, 19 of 19)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Group Normalization](https://mlsanity.com/paper/1803.08494/) (2018)
- [EuroSAT: A Novel Dataset and Deep Learning Benchmark for Land Use and Land Cover Classification](https://mlsanity.com/paper/1709.00029/) (2017)
- [MedMNIST v2 -- A large-scale lightweight benchmark for 2D and 3D biomedical image classification](https://mlsanity.com/paper/2110.14795/) (2021)
- [Deep Learning for Classical Japanese Literature](https://mlsanity.com/paper/1812.01718/) (2018)
- [The Intrinsic Dimension of Images and Its Impact on Learning](https://mlsanity.com/paper/2104.08894/) (2021)
- [Estimating the intrinsic dimension of datasets by a minimal neighborhood information](https://mlsanity.com/paper/1803.06992/) (2018)
- [Neural Architecture Search without Training](https://mlsanity.com/paper/2006.04647/) (2020)
- [Zero-Cost Proxies for Lightweight NAS](https://mlsanity.com/paper/2101.08134/) (2021)
- [Learning Ordered Representations with Nested Dropout](https://mlsanity.com/paper/1402.0915/) (2014)
- [NAS-Bench-Suite-Zero: Accelerating Research on Zero Cost Proxies](https://mlsanity.com/paper/2210.03230/) (2022)
- [Does the Data Induce Capacity Control in Deep Learning?](https://mlsanity.com/paper/2110.14163/) (2021)
- [Stochastic Bottleneck: Rateless Auto-Encoder for Flexible Dimensionality Reduction](https://mlsanity.com/paper/2005.02870/) (2020)
- [Dimension Estimation Using Autoencoders](https://mlsanity.com/paper/1909.10702/) (2019)
- [Rate-Distortion Auto-Encoders](https://mlsanity.com/paper/1312.7381/) (2013)

## Abstract (arXiv)

Multiscale Spectral Rate-Distortion (MS-SRD) estimates the bottleneck channels required at user-supplied spatial cuts from training images and a normalized mean-squared error (NMSE) bound, without fitting a neural network. Its covariance-tail rule is exact for shared linear block-convolutional autoencoders under squared error. A nested-scale dominance result motivates reporting the activation-parameter Pareto frontier alongside the minimum-latent candidate. At NMSE <= 0.01 on thirteen grayscale datasets, its latent-size prediction has 0.84% mean absolute percentage error against nonlinear patch-autoencoder boundaries; ten predictions are exact and the remaining three differ by one channel. In a four-dataset deployable comparison, MS-SRD matches all retrospective external widths and all four selected models pass, without training a selector; a 46-fit validation grid and four Least-Volume fits each pass on two datasets. In a skip-closed U-shaped autoencoder at the same bound, five predictions are exact, nine are within one channel, and every failing prediction is one channel short. Experiments at looser bounds show progressively larger nonlinear savings.