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Related papers: Effectiveness of MPC-friendly Softmax Replacement

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There has been a rapid advance of custom hardware (HW) for accelerating the inference speed of deep neural networks (DNNs). Previously, the softmax layer was not a main concern of DNN accelerating HW, because its portion is relatively small…

Machine Learning · Computer Science 2021-11-23 Ihor Vasyltsov , Wooseok Chang

In state-of-the-art deep learning for object recognition, SoftMax and Sigmoid functions are most commonly employed as the predictor outputs. Such layers often produce overconfident predictions rather than proper probabilistic scores, which…

Computer Vision and Pattern Recognition · Computer Science 2022-05-13 Gledson Melotti , Cristiano Premebida , Jordan J. Bird , Diego R. Faria , Nuno Gonçalves

In a multi-class classification problem, it is standard to model the output of a neural network as a categorical distribution conditioned on the inputs. The output must therefore be positive and sum to one, which is traditionally enforced…

Neural and Evolutionary Computing · Computer Science 2016-03-01 Alexandre de Brébisson , Pascal Vincent

Softmax is a standard final layer used in Neural Nets (NNs) to summarize information encoded in the trained NN and return a prediction. However, Softmax leverages only a subset of the class-specific structure encoded in the trained model…

Machine Learning · Computer Science 2019-12-09 Charles B. Delahunt , Courosh Mehanian , J. Nathan Kutz

The Softmax function is ubiquitous in machine learning, multiple previous works suggested faster alternatives for it. In this paper we propose a way to compute classical Softmax with fewer memory accesses and hypothesize that this reduction…

Performance · Computer Science 2018-07-31 Maxim Milakov , Natalia Gimelshein

The softmax function is a fundamental building block of deep neural networks, commonly used to define output distributions in classification tasks or attention weights in transformer architectures. Despite its widespread use and proven…

Machine Learning · Computer Science 2025-06-03 Wojciech Masarczyk , Mateusz Ostaszewski , Tin Sum Cheng , Tomasz Trzciński , Aurelien Lucchi , Razvan Pascanu

The Softmax function is used in the final layer of nearly all existing sequence-to-sequence models for language generation. However, it is usually the slowest layer to compute which limits the vocabulary size to a subset of most frequent…

Computation and Language · Computer Science 2019-03-25 Sachin Kumar , Yulia Tsvetkov

Meta-learning has demonstrated promising results in few-shot classification (FSC) by learning to solve new problems using prior knowledge. Bayesian methods are effective at characterizing uncertainty in FSC, which is crucial in high-risk…

Machine Learning · Computer Science 2024-10-14 Tianjun Ke , Haoqun Cao , Zenan Ling , Feng Zhou

Neural networks utilize the softmax as a building block in classification tasks, which contains an overconfidence problem and lacks an uncertainty representation ability. As a Bayesian alternative to the softmax, we consider a random…

Machine Learning · Computer Science 2020-06-30 Taejong Joo , Uijung Chung , Min-Gwan Seo

Loss functions steer the optimization direction of recommendation models and are critical to model performance, but have received relatively little attention in recent recommendation research. Among various losses, we find Softmax loss (SL)…

Machine Learning · Computer Science 2023-12-21 Junkang Wu , Jiawei Chen , Jiancan Wu , Wentao Shi , Jizhi Zhang , Xiang Wang

Evaluating the log-sum-exp function or the softmax function is a key step in many modern data science algorithms, notably in inference and classification. Because of the exponentials that these functions contain, the evaluation is prone to…

Numerical Analysis · Mathematics 2019-09-10 Pierre Blanchard , Desmond J. Higham , Nicholas J. Higham

Recently, fully-connected and convolutional neural networks have been trained to achieve state-of-the-art performance on a wide variety of tasks such as speech recognition, image classification, natural language processing, and…

Machine Learning · Computer Science 2015-02-24 Yichuan Tang

Capsule Networks (CapsNet) use the Softmax function to convert the logits of the routing coefficients into a set of normalized values that signify the assignment probabilities between capsules in adjacent layers. We show that the use of…

Computer Vision and Pattern Recognition · Computer Science 2019-03-26 Zhen Zhao , Ashley Kleinhans , Gursharan Sandhu , Ishan Patel , K. P. Unnikrishnan

Sampling-based methods, e.g., Deep Ensembles and Bayesian Neural Nets have become promising approaches to improve the quality of uncertainty estimation and robust generalization. However, they suffer from a large model size and high latency…

Machine Learning · Computer Science 2024-05-29 Ha Manh Bui , Anqi Liu

For a broad variety of critical applications, it is essential to know how confident a classification prediction is. In this paper, we discuss the drawbacks of softmax to calculate class probabilities and to handle uncertainty in Bayesian…

Machine Learning · Computer Science 2019-06-11 Christian Herta , Benjamin Voigt

Normalization methods improve both optimization and generalization of ConvNets. To further boost performance, the recently-proposed switchable normalization (SN) provides a new perspective for deep learning: it learns to select different…

Computer Vision and Pattern Recognition · Computer Science 2019-03-12 Wenqi Shao , Tianjian Meng , Jingyu Li , Ruimao Zhang , Yudian Li , Xiaogang Wang , Ping Luo

Computations for the softmax function are significantly expensive when the number of output classes is large. In this paper, we present a novel softmax inference speedup method, Doubly Sparse Softmax (DS-Softmax), that leverages sparse…

Machine Learning · Computer Science 2019-07-04 Shun Liao , Ting Chen , Tian Lin , Denny Zhou , Chong Wang

The softmax activation function plays a crucial role in the success of large language models (LLMs), particularly in the self-attention mechanism of the widely adopted Transformer architecture. However, the underlying learning dynamics that…

Machine Learning · Computer Science 2026-01-27 Yang Cao , Yingyu Liang , Zhenmei Shi , Zhao Song

In classification tasks, softmax functions are ubiquitously used as output activations to produce predictive probabilities. Such outputs only capture aleatoric uncertainty. To capture epistemic uncertainty, approximate Gaussian inference…

Machine Learning · Computer Science 2026-02-12 Bálint Mucsányi , Nathaël Da Costa , Philipp Hennig

The Softmax activation layer is a very popular Deep Neural Network (DNN) component when dealing with multi-class prediction problems. However, in DNN accelerator implementations it creates additional complexities due to the need for…

Hardware Architecture · Computer Science 2022-01-13 Raghuram S