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Softmax loss is widely used in deep neural networks for multi-class classification, where each class is represented by a weight vector, a sample is represented as a feature vector, and the feature vector has the largest projection on the…

Computer Vision and Pattern Recognition · Computer Science 2017-05-30 Yuhui Yuan , Kuiyuan Yang , Chao Zhang

In deep learning classifiers, the cost function usually takes the form of a combination of SoftMax and CrossEntropy functions. The SoftMax unit transforms the scores predicted by the model network into assessments of the degree…

Machine Learning · Computer Science 2023-11-29 Wladyslaw Skarbek

We study the tradeoff between computational effort and classification accuracy in a cascade of deep neural networks. During inference, the user sets the acceptable accuracy degradation which then automatically determines confidence…

Machine Learning · Computer Science 2020-11-12 Konstantin Berestizshevsky , Guy Even

We present an approach to accelerate Neural Field training by efficiently selecting sampling locations. While Neural Fields have recently become popular, it is often trained by uniformly sampling the training domain, or through handcrafted…

Computer Vision and Pattern Recognition · Computer Science 2023-12-04 Shakiba Kheradmand , Daniel Rebain , Gopal Sharma , Hossam Isack , Abhishek Kar , Andrea Tagliasacchi , Kwang Moo Yi

Random Fourier features provide a way to tackle large-scale machine learning problems with kernel methods. Their slow Monte Carlo convergence rate has motivated the research of deterministic Fourier features whose approximation error can…

Machine Learning · Computer Science 2021-10-20 Frederiek Wesel , Kim Batselier

This note considers softmax parameter estimation when little/no labeled training data is available, but a priori information about the relative geometry of class label log-odds boundaries is available. It is shown that `data-free' softmax…

Machine Learning · Statistics 2018-08-29 Nisar Ahmed

Softmax is popular normalization method used in machine learning. Deep learning solutions like Transformer or BERT use the softmax function intensively, so it is worthwhile to optimize its performance. This article presents our methodology…

Mathematical Software · Computer Science 2019-05-28 Jacek Czaja , Michal Gallus , Tomasz Patejko , Jian Tang

We propose the use of low bit-depth Sigma-Delta and distributed noise-shaping methods for quantizing the Random Fourier features (RFFs) associated with shift-invariant kernels. We prove that our quantized RFFs -- even in the case of $1$-bit…

Machine Learning · Computer Science 2022-04-14 Jinjie Zhang , Harish Kannan , Alexander Cloninger , Rayan Saab

The Softmax bottleneck was first identified in language modeling as a theoretical limit on the expressivity of Softmax-based models. Being one of the most widely-used methods to output probability, Softmax-based models have found a wide…

Machine Learning · Computer Science 2021-10-12 Ying-Chen Lin

Enabling machine learning classifiers to defer their decision to a downstream expert when the expert is more accurate will ensure improved safety and performance. This objective can be achieved with the learning-to-defer framework which…

Machine Learning · Computer Science 2023-11-03 Yuzhou Cao , Hussein Mozannar , Lei Feng , Hongxin Wei , Bo An

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 problem of heterogeneous clients in federated learning has recently drawn a lot of attention. Spectral model sharding, i.e., partitioning the model parameters into low-rank matrices based on the singular value decomposition, has been…

Machine Learning · Computer Science 2024-11-01 Denis Korzhenkov , Christos Louizos

The key factor in implementing machine learning algorithms in decision-making situations is not only the accuracy of the model but also its confidence level. The confidence level of a model in a classification problem is often given by the…

Machine Learning · Statistics 2024-05-02 Masanari Kimura , Hiroki Naganuma

As the vocabulary size of modern word-based language models becomes ever larger, many sampling-based training criteria are proposed and investigated. The essence of these sampling methods is that the softmax-related traversal over the…

Computation and Language · Computer Science 2021-06-18 Yingbo Gao , David Thulke , Alexander Gerstenberger , Khoa Viet Tran , Ralf Schlüter , Hermann Ney

The margin-based softmax loss functions greatly enhance intra-class compactness and perform well on the tasks of face recognition and object classification. Outperformance, however, depends on the careful hyperparameter selection. Moreover,…

Computer Vision and Pattern Recognition · Computer Science 2019-12-18 JT Wu , L. Wang

Softmax distributions are widely used in machine learning, including Large Language Models (LLMs), where the attention unit uses softmax distributions. We abstract the attention unit as the softmax model, where given a vector input, the…

Machine Learning · Statistics 2025-06-02 Yuzhou Gu , Zhao Song , Junze Yin

The kernel embedding algorithm is an important component for adapting kernel methods to large datasets. Since the algorithm consumes a major computation cost in the testing phase, we propose a novel teacher-learner framework of learning…

Machine Learning · Statistics 2017-12-08 Jianqiao Wangni , Jingwei Zhuo , Jun Zhu

Building upon recent advances in entropy-regularized optimal transport, and upon Fenchel duality between measures and continuous functions , we propose a generalization of the logistic loss that incorporates a metric or cost between…

Machine Learning · Statistics 2019-05-16 Arthur Mensch , Mathieu Blondel , Gabriel Peyré

In recent years, the softmax model and its fast approximations have become the de-facto loss functions for deep neural networks when dealing with multi-class prediction. This loss has been extended to language modeling and recommendation,…

Machine Learning · Statistics 2019-09-19 Ugo Tanielian , Flavian Vasile

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