# ConformalLayers: A non-linear sequential neural network with associative layers

arXiv: https://arxiv.org/abs/2110.12108 · HTML: https://mlsanity.com/paper/2110.12108/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 26 references that are in the map.
- First posted on arXiv 23 Oct 2021.

## Builds on (most cited first, 14 of 14)

- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [You Only Look Once: Unified, Real-Time Object Detection](https://mlsanity.com/paper/1506.02640/) (2015)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Hyperband: A Novel Bandit-Based Approach to Hyperparameter Optimization](https://mlsanity.com/paper/1603.06560/) (2016)
- [Quantized Neural Networks: Training Neural Networks with Low Precision Weights and Activations](https://mlsanity.com/paper/1609.07061/) (2016)
- [Exploiting Linear Structure Within Convolutional Networks for Efficient Evaluation](https://mlsanity.com/paper/1404.0736/) (2014)
- [Deconstructing Lottery Tickets: Zeros, Signs, and the Supermask](https://mlsanity.com/paper/1905.01067/) (2019)
- [Searching for Activation Functions](https://mlsanity.com/paper/1710.05941/) (2017)
- [SqueezeDet: Unified, Small, Low Power Fully Convolutional Neural Networks for Real-Time Object Detection for Autonomous Driving](https://mlsanity.com/paper/1612.01051/) (2016)
- [RNNPool: Efficient Non-linear Pooling for RAM Constrained Inference](https://mlsanity.com/paper/2002.11921/) (2020)
- [Associative Convolutional Layers](https://mlsanity.com/paper/1906.04309/) (2019)

## Abstract (arXiv)

Convolutional Neural Networks (CNNs) have been widely applied. But as the CNNs grow, the number of arithmetic operations and memory footprint also increase. Furthermore, typical non-linear activation functions do not allow associativity of the operations encoded by consecutive layers, preventing the simplification of intermediate steps by combining them. We present a new activation function that allows associativity between sequential layers of CNNs. Even though our activation function is non-linear, it can be represented by a sequence of linear operations in the conformal model for Euclidean geometry. In this domain, operations like, but not limited to, convolution, average pooling, and dropout remain linear. We take advantage of associativity to combine all the "conformal layers" and make the cost of inference constant regardless of the depth of the network.