SERF: Towards better training of deep neural networks using log-Softplus ERror activation Function
Not on the map. Why?
Abstract (arXiv)
Activation functions play a pivotal role in determining the training dynamics and neural network performance. The widely adopted activation function ReLU despite being simple and effective has few disadvantages including the Dying ReLU problem. In order to tackle such problems, we propose a novel activation function called Serf which is self-regularized and nonmonotonic in nature. Like Mish, Serf also belongs to the Swish family of functions. Based on several experiments on computer vision (image classification and object detection) and natural language processing (machine translation, sentiment classification and multimodal entailment) tasks with different state-of-the-art architectures, it is observed that Serf vastly outperforms ReLU (baseline) and other activation functions including both Swish and Mish, with a markedly bigger margin on deeper architectures. Ablation studies further demonstrate that Serf based architectures perform better than those of Swish and Mish in varying scenarios, validating the effectiveness and compatibility of Serf with varying depth, complexity, optimizers, learning rates, batch sizes, initializers and dropout rates. Finally, we investigate the mathematical relation between Swish and Serf, thereby showing the impact of preconditioner function ingrained in the first derivative of Serf which provides a regularization effect making gradients smoother and optimization faster.
Key facts. Cited by 10 papers in the map (data through 7 Oct 2026). Builds on 27 of its 49 references that are in the map. First posted on arXiv 21 Aug 2021.
Builds on
27 of 49 references.
References · 27
- 2017Attention Is All You Needcited by 59,932
- 2015Deep Residual Learning for Image Recognitioncited by 51,809
- 2018BERT: Pre-training of Deep Bidirectional Transformers for Language Understandingcited by 40,204
- 2014Adam: A Method for Stochastic Optimizationcited by 36,960
- 2020Language Models are Few-Shot Learnerscited by 32,199
- 2020An Image is Worth 16x16 Words: Transformers for Image Recognition at Scalecited by 29,915
- 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
- 2015Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shiftcited by 6,979
- 2016Densely Connected Convolutional Networkscited by 6,691
- 2019EfficientNet: Rethinking Model Scaling for Convolutional Neural Networkscited by 6,415
- 2015Rethinking the Inception Architecture for Computer Visioncited by 5,451
- 2018MobileNetV2: Inverted Residuals and Linear Bottleneckscited by 4,773
15 more
- 2015Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classificationcited by 3,590
- 2016Gaussian Error Linear Units (GELUs)cited by 3,431
- 2016Wide Residual Networkscited by 3,057
- 2018YOLOv3: An Incremental Improvementcited by 2,652
- 2016Aggregated Residual Transformations for Deep Neural Networkscited by 2,540
- 2016Identity Mappings in Deep Residual Networkscited by 1,960
- 2021MLP-Mixer: An all-MLP Architecture for Visioncited by 1,441
- 2018ShuffleNet V2: Practical Guidelines for Efficient CNN Architecture Designcited by 1,132
- 2015Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)cited by 1,061
- 2016SqueezeNet: AlexNet-level accuracy with 50x fewer parameters and <0.5MB model sizecited by 1,054
- 2017Self-Normalizing Neural Networkscited by 591
- 2021Escaping the Big Data Paradigm with Compact Transformerscited by 261
- 2016Multi30K: Multilingual English-German Image Descriptionscited by 250
- 2019Mish: A Self Regularized Non-Monotonic Activation Functioncited by 141
- 2019ProbAct: A Probabilistic Activation Function for Deep Neural Networkscited by 12
Built on by
Citing papers per year: 2021: 1; 2022: 0; 2023: 5; 2024: 3; 2025: 1.
10 papers.
- 2021ErfAct and Pserf: Non-monotonic Smooth Trainable Activation Functionscited by 5
- 2023Gradient Domain Diffusion Models for Image Synthesiscited by 4
- 2023Compelling ReLU Networks to Exhibit Exponentially Many Linear Regions at Initialization and During Trainingcited by 4
- 2023ErfReLU: Adaptive Activation Function for Deep Neural Networkcited by 3
- 2024Probabilistic Neural Networks (PNNs) for Modeling Aleatoric Uncertainty in Scientific Machine Learningcited by 2
- 2025Implicit neural representations for end-to-end PET reconstructioncited by 2
- 2023TSSR: A Truncated and Signed Square Root Activation Function for Neural Networkscited by 1
- 2024Activation Function Optimization Scheme for Image Classificationcited by 1
- 2023STL: A Signed and Truncated Logarithm Activation Function for Neural Networkscited by 0
- 2024A New Method for Cross-Lingual-based Semantic Role Labelingcited by 0
- 2025Implicit neural representations for end-to-end PET reconstruction26 Mar 2025
- 2024Activation Function Optimization Scheme for Image Classification7 Sep 2024
- 2024A New Method for Cross-Lingual-based Semantic Role Labeling28 Aug 2024
- 2024Probabilistic Neural Networks (PNNs) for Modeling Aleatoric Uncertainty in Scientific Machine Learning21 Feb 2024
- 2023Compelling ReLU Networks to Exhibit Exponentially Many Linear Regions at Initialization and During Training29 Nov 2023
- 2023Gradient Domain Diffusion Models for Image Synthesis5 Sep 2023
- 2023TSSR: A Truncated and Signed Square Root Activation Function for Neural Networks9 Aug 2023
- 2023STL: A Signed and Truncated Logarithm Activation Function for Neural Networks31 Jul 2023
- 2023ErfReLU: Adaptive Activation Function for Deep Neural Network2 Jun 2023
- 2021ErfAct and Pserf: Non-monotonic Smooth Trainable Activation Functions9 Sep 2021