# Deep Convolutional Tables: Deep Learning without Convolutions

arXiv: https://arxiv.org/abs/2304.11706 · HTML: https://mlsanity.com/paper/2304.11706/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 50 references that are in the map.
- First posted on arXiv 23 Apr 2023.

## Builds on (most cited first, 25 of 25)

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [ShuffleNet V2: Practical Guidelines for Efficient CNN Architecture Design](https://mlsanity.com/paper/1807.11164/) (2018)
- [XNOR-Net: ImageNet Classification Using Binary Convolutional Neural Networks](https://mlsanity.com/paper/1603.05279/) (2016)
- [BinaryConnect: Training Deep Neural Networks with binary weights during propagations](https://mlsanity.com/paper/1511.00363/) (2015)
- [Quantizing deep convolutional networks for efficient inference: A whitepaper](https://mlsanity.com/paper/1806.08342/) (2018)
- [Learning Face Representation from Scratch](https://mlsanity.com/paper/1411.7923/) (2014)
- [Speeding up Convolutional Neural Networks with Low Rank Expansions](https://mlsanity.com/paper/1405.3866/) (2014)
- [Differentiable Soft Quantization: Bridging Full-Precision and Low-Bit Neural Networks](https://mlsanity.com/paper/1908.05033/) (2019)
- [Bi-Real Net: Enhancing the Performance of 1-bit CNNs With Improved Representational Capability and Advanced Training Algorithm](https://mlsanity.com/paper/1808.00278/) (2018)
- [Conditional Computation in Neural Networks for faster models](https://mlsanity.com/paper/1511.06297/) (2015)
- [Compressing Neural Networks with the Hashing Trick](https://mlsanity.com/paper/1504.04788/) (2015)
- [Towards Accurate Binary Convolutional Neural Network](https://mlsanity.com/paper/1711.11294/) (2017)
- [Training Binary Neural Networks with Real-to-Binary Convolutions](https://mlsanity.com/paper/2003.11535/) (2020)
- [Accelerating Very Deep Convolutional Networks for Classification and Detection](https://mlsanity.com/paper/1505.06798/) (2015)
- [XNOR-Net++: Improved Binary Neural Networks](https://mlsanity.com/paper/1909.13863/) (2019)
- [Shift: A Zero FLOP, Zero Parameter Alternative to Spatial Convolutions](https://mlsanity.com/paper/1711.08141/) (2017)
- [Fast Training of Convolutional Networks through FFTs](https://mlsanity.com/paper/1312.5851/) (2013)
- [Low-Rank Approximations for Conditional Feedforward Computation in Deep Neural Networks](https://mlsanity.com/paper/1312.4461/) (2013)
- [Searching for Low-Bit Weights in Quantized Neural Networks](https://mlsanity.com/paper/2009.08695/) (2020)
- [Manifold Regularized Dynamic Network Pruning](https://mlsanity.com/paper/2103.05861/) (2021)
- [Decision Forests, Convolutional Networks and the Models in-Between](https://mlsanity.com/paper/1603.01250/) (2016)
- [Searching for Network Width with Bilaterally Coupled Network](https://mlsanity.com/paper/2203.13714/) (2022)
- [LeanResNet: A Low-cost Yet Effective Convolutional Residual Networks](https://mlsanity.com/paper/1904.06952/) (2019)

## Abstract (arXiv)

We propose a novel formulation of deep networks that do not use dot-product neurons and rely on a hierarchy of voting tables instead, denoted as Convolutional Tables (CT), to enable accelerated CPU-based inference. Convolutional layers are the most time-consuming bottleneck in contemporary deep learning techniques, severely limiting their use in Internet of Things and CPU-based devices. The proposed CT performs a fern operation at each image location: it encodes the location environment into a binary index and uses the index to retrieve the desired local output from a table. The results of multiple tables are combined to derive the final output. The computational complexity of a CT transformation is independent of the patch (filter) size and grows gracefully with the number of channels, outperforming comparable convolutional layers. It is shown to have a better capacity:compute ratio than dot-product neurons, and that deep CT networks exhibit a universal approximation property similar to neural networks. As the transformation involves computing discrete indices, we derive a soft relaxation and gradient-based approach for training the CT hierarchy. Deep CT networks have been experimentally shown to have accuracy comparable to that of CNNs of similar architectures. In the low compute regime, they enable an error:speed trade-off superior to alternative efficient CNN architectures.