Exploring Alternatives to Softmax Function
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Abstract (arXiv)
Softmax function is widely used in artificial neural networks for multiclass classification, multilabel classification, attention mechanisms, etc. However, its efficacy is often questioned in literature. The log-softmax loss has been shown to belong to a more generic class of loss functions, called spherical family, and its member log-Taylor softmax loss is arguably the best alternative in this class. In another approach which tries to enhance the discriminative nature of the softmax function, soft-margin softmax (SM-softmax) has been proposed to be the most suitable alternative. In this work, we investigate Taylor softmax, SM-softmax and our proposed SM-Taylor softmax, an amalgamation of the earlier two functions, as alternatives to softmax function. Furthermore, we explore the effect of expanding Taylor softmax up to ten terms (original work proposed expanding only to two terms) along with the ramifications of considering Taylor softmax to be a finite or infinite series during backpropagation. Our experiments for the image classification task on different datasets reveal that there is always a configuration of the SM-Taylor softmax function that outperforms the normal softmax function and its other alternatives.
Key facts. Cited by 16 papers in the map (data through 7 Oct 2026). First posted on arXiv 23 Nov 2020.
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Citing papers per year: 2021: 1; 2022: 1; 2023: 4; 2024: 5; 2025: 4; 2026: 1.
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- 2024The Hedgehog & the Porcupine: Expressive Linear Attentions with Softmax Mimicrycited by 119
- 2023Low-Cost High-Power Membership Inference Attackscited by 99
- 2022SimA: Simple Softmax-free Attention for Vision Transformerscited by 32
- 2024The Fine-Grained Complexity of Gradient Computation for Training Large Language Modelscited by 30
- 2024ConSmax: Hardware-Friendly Alternative Softmax with Learnable Parameterscited by 14
- 2025Fast RoPE Attention: Combining the Polynomial Method and Fast Fourier Transformcited by 9
- 2024Rethinking Attention: Polynomial Alternatives to Softmax in Transformerscited by 8
- 2021Escaping the Gradient Vanishing: Periodic Alternatives of Softmax in Attention Mechanismcited by 7
- 2024TaylorShift: Shifting the Complexity of Self-Attention from Squared to Linear (and Back) using Taylor-Softmaxcited by 6
- 2025Parallel Sequence Modeling via Generalized Spatial Propagation Networkcited by 4
- 2023A Neural Network Based Choice Model for Assortment Optimizationcited by 3
- 2025Adaptive Temperature Based on Logits Correlation in Knowledge Distillationcited by 2
4 more
- 2025Untangling Component Imbalance in Hybrid Linear Attention Conversion Methodscited by 2
- 2023Unleashing the power of Neural Collapse for Transferability Estimationcited by 1
- 2023Classified as unknown: A novel Bayesian neural networkcited by 0
- 2026Is Softmax Loss All You Need? A Principled Analysis of Softmax-family Losscited by 0
- 2026Is Softmax Loss All You Need? A Principled Analysis of Softmax-family Loss30 Jan 2026
- 2025Untangling Component Imbalance in Hybrid Linear Attention Conversion Methods7 Oct 2025
- 2025Fast RoPE Attention: Combining the Polynomial Method and Fast Fourier Transform17 May 2025
- 2025Adaptive Temperature Based on Logits Correlation in Knowledge Distillation12 Mar 2025
- 2025Parallel Sequence Modeling via Generalized Spatial Propagation Network21 Jan 2025
- 2024Rethinking Attention: Polynomial Alternatives to Softmax in Transformers24 Oct 2024
- 2024TaylorShift: Shifting the Complexity of Self-Attention from Squared to Linear (and Back) using Taylor-Softmax5 Mar 2024
- 2024The Fine-Grained Complexity of Gradient Computation for Training Large Language Models7 Feb 2024
- 2024The Hedgehog & the Porcupine: Expressive Linear Attentions with Softmax Mimicry6 Feb 2024
- 2024ConSmax: Hardware-Friendly Alternative Softmax with Learnable Parameters31 Jan 2024
- 2023Low-Cost High-Power Membership Inference Attacks6 Dec 2023
- 2023Unleashing the power of Neural Collapse for Transferability Estimation9 Oct 2023
4 more
- 2023A Neural Network Based Choice Model for Assortment Optimization10 Aug 2023
- 2023Classified as unknown: A novel Bayesian neural network31 Jan 2023
- 2022SimA: Simple Softmax-free Attention for Vision Transformers17 Jun 2022
- 2021Escaping the Gradient Vanishing: Periodic Alternatives of Softmax in Attention Mechanism16 Aug 2021
- 2023Low-Cost High-Power Membership Inference Attackscited by 99
- 2023Low-Cost High-Power Membership Inference Attacks6 Dec 2023
- 2024The Hedgehog & the Porcupine: Expressive Linear Attentions with Softmax Mimicrycited by 119
- 2022SimA: Simple Softmax-free Attention for Vision Transformerscited by 32
- 2024The Fine-Grained Complexity of Gradient Computation for Training Large Language Modelscited by 30
- 2024ConSmax: Hardware-Friendly Alternative Softmax with Learnable Parameterscited by 14
- 2025Fast RoPE Attention: Combining the Polynomial Method and Fast Fourier Transformcited by 9
- 2024Rethinking Attention: Polynomial Alternatives to Softmax in Transformerscited by 8
- 2021Escaping the Gradient Vanishing: Periodic Alternatives of Softmax in Attention Mechanismcited by 7
- 2024TaylorShift: Shifting the Complexity of Self-Attention from Squared to Linear (and Back) using Taylor-Softmaxcited by 6
- 2025Parallel Sequence Modeling via Generalized Spatial Propagation Networkcited by 4
- 2023A Neural Network Based Choice Model for Assortment Optimizationcited by 3
- 2025Adaptive Temperature Based on Logits Correlation in Knowledge Distillationcited by 2
- 2025Untangling Component Imbalance in Hybrid Linear Attention Conversion Methodscited by 2
12 most cited of 15 All 15 (JSON)
- 2026Is Softmax Loss All You Need? A Principled Analysis of Softmax-family Loss30 Jan 2026
- 2025Untangling Component Imbalance in Hybrid Linear Attention Conversion Methods7 Oct 2025
- 2025Fast RoPE Attention: Combining the Polynomial Method and Fast Fourier Transform17 May 2025
- 2025Adaptive Temperature Based on Logits Correlation in Knowledge Distillation12 Mar 2025
- 2025Parallel Sequence Modeling via Generalized Spatial Propagation Network21 Jan 2025
- 2024Rethinking Attention: Polynomial Alternatives to Softmax in Transformers24 Oct 2024
- 2024TaylorShift: Shifting the Complexity of Self-Attention from Squared to Linear (and Back) using Taylor-Softmax5 Mar 2024
- 2024The Fine-Grained Complexity of Gradient Computation for Training Large Language Models7 Feb 2024
- 2024The Hedgehog & the Porcupine: Expressive Linear Attentions with Softmax Mimicry6 Feb 2024
- 2024ConSmax: Hardware-Friendly Alternative Softmax with Learnable Parameters31 Jan 2024
- 2023Unleashing the power of Neural Collapse for Transferability Estimation9 Oct 2023
- 2023A Neural Network Based Choice Model for Assortment Optimization10 Aug 2023
12 newest of 15 All 15 (JSON)