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Large-scale classification of data where classes are structurally organized in a hierarchy is an important area of research. Top-down approaches that exploit the hierarchy during the learning and prediction phase are efficient for large…

Machine Learning · Computer Science 2017-06-06 Azad Naik , Huzefa Rangwala

Typical learning curves for Soft Margin Classifiers (SMCs) learning both realizable and unrealizable tasks are determined using the tools of Statistical Mechanics. We derive the analytical behaviour of the learning curves in the regimes of…

Disordered Systems and Neural Networks · Physics 2007-05-23 Sebastian Risau-Gusman , Mirta B. Gordon

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 hierarchical distribution matching (Hi-DM) approach for probabilistic shaping is described. The potential of Hi-DM in terms of trade-off between performance,complexity, and memory is illustrated through three case studies.

Information Theory · Computer Science 2020-02-20 Stella Civelli , Marco Secondini

Noisy labels pose a common challenge for training accurate deep neural networks. To mitigate label noise, prior studies have proposed various robust loss functions to achieve noise tolerance in the presence of label noise, particularly…

Machine Learning · Computer Science 2025-08-05 Jialiang Wang , Xiong Zhou , Deming Zhai , Junjun Jiang , Xiangyang Ji , Xianming Liu

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

In this paper, we introduce a threshold-based framework for multiclass classification that generalizes the standard argmax rule. This is done by replacing the probabilistic interpretation of softmax outputs with a geometric one on the…

Machine Learning · Computer Science 2025-12-02 Francesco Marchetti , Edoardo Legnaro , Sabrina Guastavino

Hierarchical optimization refers to problems with interdependent decision variables and objectives, such as minimax and bilevel formulations. While various algorithms have been proposed, existing methods and analyses lack adaptivity in…

Machine Learning · Computer Science 2025-10-27 Xiaochuan Gong , Jie Hao , Mingrui Liu

Traditional Multi-level Hierarchical Classification (MLHC) classifiers often rely on backbone models with $n$ independent output layers. This structure tends to overlook the hierarchical relationships between classes, leading to…

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

The Bootstrap method application in simulation supposes that value of random variables are not generated during the simulation process but extracted from available sample populations. In the case of Hierarchical Bootstrap the function of…

Artificial Intelligence · Computer Science 2013-03-29 A. Andronov , M. Fioshin

Hierarchical text classification (HTC) assigns documents to multiple levels of a pre-defined taxonomy. Automated patent subject classification represents one of the hardest HTC scenarios because of domain knowledge difficulty and a huge…

Computation and Language · Computer Science 2025-10-09 Lekang Jiang , Wenjun Sun , Stephan Goetz

The multiplication of matrices is an important arithmetic operation in computational mathematics. In the context of hierarchical matrices, this operation can be realized by the multiplication of structured block-wise low-rank matrices,…

Numerical Analysis · Mathematics 2018-05-24 Jürgen Dölz , Helmut Harbrecht , Michael D. Multerer

In order to learn quickly with few samples, meta-learning utilizes prior knowledge learned from previous tasks. However, a critical challenge in meta-learning is task uncertainty and heterogeneity, which can not be handled via globally…

Machine Learning · Computer Science 2019-11-19 Huaxiu Yao , Ying Wei , Junzhou Huang , Zhenhui Li

Estimating how well a machine learning model performs during inference is critical in a variety of scenarios (for example, to quantify uncertainty, or to choose from a library of available models). However, the standard accuracy estimate of…

Computer Vision and Pattern Recognition · Computer Science 2021-10-07 Xuechen Zhang , Samet Oymak , Jiasi Chen

Deep learning has significantly advanced time series forecasting through its powerful capacity to capture sequence relationships. However, training these models with the Mean Square Error (MSE) loss often results in over-smooth predictions,…

Machine Learning · Computer Science 2024-12-25 Yanru Sun , Zongxia Xie , Dongyue Chen , Emadeldeen Eldele , Qinghua Hu

Federated Learning (FL) allows a number of agents to participate in training a global machine learning model without disclosing locally stored data. Compared to traditional distributed learning, the heterogeneity (non-IID) of the agents…

Machine Learning · Computer Science 2022-06-23 Bin Yang , Thomas Carette , Masanobu Jimbo , Shinya Maruyama

Ensuring the reliability of automated decision-making based on neural networks will be crucial as Artificial Intelligence systems are deployed more widely in critical situations. This paper proposes a new approach for measuring confidence…

Machine Learning · Computer Science 2025-05-01 Daniel Sikar , Artur d'Avila Garcez , Tillman Weyde

Loss functions play a key role in training superior deep neural networks. In convolutional neural networks (CNNs), the popular cross entropy loss together with softmax does not explicitly guarantee minimization of intra-class variance or…

Computer Vision and Pattern Recognition · Computer Science 2019-04-26 XiaoBin Li , WeiQiang Wang

This paper discusses the application of L1-regularized maximum entropy modeling or SL1-Max [9] to multiclass categorization problems. A new modification to the SL1-Max fast sequential learning algorithm is proposed to handle conditional…

Machine Learning · Computer Science 2007-05-23 Patrick Haffner , Steven Phillips , Rob Schapire