# Tom: Leveraging trend of the observed gradients for faster convergence

arXiv: https://arxiv.org/abs/2109.03820 · HTML: https://mlsanity.com/paper/2109.03820/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 50 references that are in the map.
- First posted on arXiv 7 Sep 2021.

## Builds on (most cited first, 28 of 28)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [Feature Pyramid Networks for Object Detection](https://mlsanity.com/paper/1612.03144/) (2016)
- [You Only Look Once: Unified, Real-Time Object Detection](https://mlsanity.com/paper/1506.02640/) (2015)
- [Squeeze-and-Excitation Networks](https://mlsanity.com/paper/1709.01507/) (2017)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [DeepLab: Semantic Image Segmentation with Deep Convolutional Nets, Atrous Convolution, and Fully Connected CRFs](https://mlsanity.com/paper/1606.00915/) (2016)
- [SSD: Single Shot MultiBox Detector](https://mlsanity.com/paper/1512.02325/) (2015)
- [Fast R-CNN](https://mlsanity.com/paper/1504.08083/) (2015)
- [Aggregated Residual Transformations for Deep Neural Networks](https://mlsanity.com/paper/1611.05431/) (2016)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [Rich feature hierarchies for accurate object detection and semantic segmentation](https://mlsanity.com/paper/1311.2524/) (2013)
- [ShuffleNet: An Extremely Efficient Convolutional Neural Network for Mobile Devices](https://mlsanity.com/paper/1707.01083/) (2017)
- [MnasNet: Platform-Aware Neural Architecture Search for Mobile](https://mlsanity.com/paper/1807.11626/) (2018)
- [On the Convergence of Adam and Beyond](https://mlsanity.com/paper/1904.09237/) (2019)
- [Spatial Pyramid Pooling in Deep Convolutional Networks for Visual Recognition](https://mlsanity.com/paper/1406.4729/) (2014)
- [Highway Networks](https://mlsanity.com/paper/1505.00387/) (2015)
- [Efficient parametrization of multi-domain deep neural networks](https://mlsanity.com/paper/1803.10082/) (2018)
- [The Unusual Effectiveness of Averaging in GAN Training](https://mlsanity.com/paper/1806.04498/) (2018)
- [Clockwork Convnets for Video Semantic Segmentation](https://mlsanity.com/paper/1608.03609/) (2016)
- [STFCN: Spatio-Temporal FCN for Semantic Video Segmentation](https://mlsanity.com/paper/1608.05971/) (2016)
- [See More Than Once -- Kernel-Sharing Atrous Convolution for Semantic Segmentation](https://mlsanity.com/paper/1908.09443/) (2019)

## Abstract (arXiv)

The success of deep learning can be attributed to various factors such as increase in computational power, large datasets, deep convolutional neural networks, optimizers etc. Particularly, the choice of optimizer affects the generalization, convergence rate, and training stability. Stochastic Gradient Descent (SGD) is a first order iterative optimizer that updates the gradient uniformly for all parameters. This uniform update may not be suitable across the entire training phase. A rudimentary solution for this is to employ a fine-tuned learning rate scheduler which decreases learning rate as a function of iteration. To eliminate the dependency of learning rate schedulers, adaptive gradient optimizers such as AdaGrad, AdaDelta, RMSProp, Adam employ a parameter-wise scaling term for learning rate which is a function of the gradient itself. We propose Tom (Trend over Momentum) optimizer, which is a novel variant of Adam that takes into account of the trend which is observed for the gradients in the loss landscape traversed by the neural network. In the proposed Tom optimizer, an additional smoothing equation is introduced to address the trend observed during the process of optimization. The smoothing parameter introduced for the trend requires no tuning and can be used with default values. Experimental results for classification datasets such as CIFAR-10, CIFAR-100 and CINIC-10 image datasets show that Tom outperforms Adagrad, Adadelta, RMSProp and Adam in terms of both accuracy and has a faster convergence. The source code is publicly made available at https://github.com/AnirudhMaiya/Tom