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This paper questions whether the strong performance of softmax attention in transformers stems from producing a probability distribution over inputs. Instead, we argue that softmax's effectiveness lies in its implicit regularization of the…

Machine Learning · Computer Science 2026-03-16 Hemanth Saratchandran , Jianqiao Zheng , Yiping Ji , Wenbo Zhang , Simon Lucey

Softmax is widely used in neural networks for multiclass classification, gate structure and attention mechanisms. The statistical assumption that the input is normal distributed supports the gradient stability of Softmax. However, when used…

Computer Vision and Pattern Recognition · Computer Science 2021-08-17 Shulun Wang , Bin Liu , Feng Liu

The adversarial robustness of attributions is a fundamental requirement for reliable explainability in deep learning, yet existing approaches typically rely on computationally expensive explicit regularization. In this work, we show that…

Machine Learning · Computer Science 2026-05-29 Amir Mehrpanah , Matteo Gamba , Hossein Azizpour

Recently, the robustness of deep learning models has received widespread attention, and various methods for improving model robustness have been proposed, including adversarial training, model architecture modification, design of loss…

Machine Learning · Computer Science 2023-03-23 Hao Wang , Chen Li , Jinzhe Jiang , Xin Zhang , Yaqian Zhao , Weifeng Gong

We consider learning a probabilistic classifier from partially-labelled supervision (inputs denoted with multiple possibilities) using standard neural architectures with a softmax as the final layer. We identify a bias phenomenon that can…

Machine Learning · Computer Science 2023-07-04 Zsolt Zombori , Agapi Rissaki , Kristóf Szabó , Wolfgang Gatterbauer , Michael Benedikt

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

Policy-gradient approaches to reinforcement learning have two common and undesirable overhead procedures, namely warm-start training and sample variance reduction. In this paper, we describe a reinforcement learning method based on a…

Machine Learning · Computer Science 2017-10-17 Nan Ding , Radu Soricut

Training a classifier over a large number of classes, known as 'extreme classification', has become a topic of major interest with applications in technology, science, and e-commerce. Traditional softmax regression induces a gradient cost…

Machine Learning · Statistics 2020-02-18 Robert Bamler , Stephan Mandt

Training adversarially robust discriminative (i.e., softmax) classifier has been the dominant approach to robust classification. Building on recent work on adversarial training (AT)-based generative models, we investigate using AT to learn…

Machine Learning · Computer Science 2022-12-15 Xuwang Yin

We provide two characterizations, one axiomatic and the other neuro-computational, of the dependence of choice probabilities on deadlines, within the widely used softmax representation \[ p_{t}\left( a,A\right) =\dfrac{e^{\frac{u\left(…

Theoretical Economics · Economics 2021-01-28 Simone Cerreia-Vioglio , Fabio Maccheroni , Massimo Marinacci , Aldo Rustichini

Latent categorical variables are frequently found in deep learning architectures. They can model actions in discrete reinforcement-learning environments, represent categories in latent-variable models, or express relations in graph neural…

Machine Learning · Computer Science 2026-05-14 Alessandro Manenti , Cesare Alippi

The softmax representation of probabilities for categorical variables plays a prominent role in modern machine learning with numerous applications in areas such as large scale classification, neural language modeling and recommendation…

Machine Learning · Statistics 2016-11-01 Michalis K. Titsias

Randomized smoothing is currently a state-of-the-art method to construct a certifiably robust classifier from neural networks against $\ell_2$-adversarial perturbations. Under the paradigm, the robustness of a classifier is aligned with the…

Machine Learning · Computer Science 2021-11-18 Jongheon Jeong , Sejun Park , Minkyu Kim , Heung-Chang Lee , Doguk Kim , Jinwoo Shin

Policy gradient methods are known to be highly sensitive to the choice of policy parameterization. In particular, the widely used softmax parameterization can induce ill-conditioned optimization landscapes and lead to exponentially slow…

Machine Learning · Computer Science 2026-04-02 Safwan Labbi , Daniil Tiapkin , Paul Mangold , Eric Moulines

Deep neural networks (DNNs) provide state-of-the-art results on various tasks and are widely used in real world applications. However, it was discovered that machine learning models, including the best performing DNNs, suffer from a…

Computer Vision and Pattern Recognition · Computer Science 2017-08-08 Andras Rozsa , Manuel Günther , Terrance E. Boult

Deep classifiers have achieved great success in visual recognition. However, real-world data is long-tailed by nature, leading to the mismatch between training and testing distributions. In this paper, we show that the Softmax function,…

Machine Learning · Computer Science 2020-11-24 Jiawei Ren , Cunjun Yu , Shunan Sheng , Xiao Ma , Haiyu Zhao , Shuai Yi , Hongsheng Li

Deep Neural Networks, despite their great success in diverse domains, are provably sensitive to small perturbations on correctly classified examples and lead to erroneous predictions. Recently, it was proposed that this behavior can be…

Machine Learning · Computer Science 2020-09-29 Nan Xu , Oluwaseyi Feyisetan , Abhinav Aggarwal , Zekun Xu , Nathanael Teissier

Deep convolutional neural networks (CNNs) trained with logistic and softmax losses have made significant advancement in visual recognition tasks in computer vision. When training data exhibit class imbalances, the class-wise reweighted…

Machine Learning · Computer Science 2020-03-06 Xiangrui Li , Xin Li , Deng Pan , Dongxiao Zhu

Randomized smoothing, a method to certify a classifier's decision on an input is invariant under adversarial noise, offers attractive advantages over other certification methods. It operates in a black-box and so certification is not…

Machine Learning · Computer Science 2020-06-09 Jamie Hayes

In replay-based methods for continual learning, replaying input samples in episodic memory has shown its effectiveness in alleviating catastrophic forgetting. However, the potential key factor of cross-entropy loss with softmax in causing…

Machine Learning · Computer Science 2024-01-25 Hoyong Kim , Minchan Kwon , Kangil Kim
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