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We present a novel technique for constructing differentiable order-type operations, including soft ranking, soft top-k selection, and soft permutations. Our approach leverages an efficient closed-form formula for the inverse of the function…

Artificial Intelligence · Computer Science 2025-09-04 Łukasz Struski , Michał B. Bednarczyk , Igor T. Podolak , Jacek Tabor

A recommender system generates personalized recommendations for a user by computing the preference score of items, sorting the items according to the score, and filtering top-K items with high scores. While sorting and ranking items are…

Information Retrieval · Computer Science 2020-12-08 Hyunsung Lee , Yeongjae Jang , Jaekwang Kim , Honguk Woo

Knapsack and Top-k operators are useful for selecting discrete subsets of variables. However, their integration into neural networks is challenging as they are piecewise constant, yielding gradients that are zero almost everywhere. In this…

Machine Learning · Computer Science 2026-01-30 Germain Vivier-Ardisson , Michaël E. Sander , Axel Parmentier , Mathieu Blondel

Cascade ranking is widely used for large-scale top-k selection problems in online advertising and recommendation systems, and learning-to-rank is an important way to optimize the models in cascade ranking. Previous works on learning-to-rank…

Machine Learning · Computer Science 2024-02-22 Yunli Wang , Zhiqiang Wang , Jian Yang , Shiyang Wen , Dongying Kong , Han Li , Kun Gai

Decision Trees (DTs) are widely used in safety-critical domains such as medical diagnosis, valued for their interpretability and effectiveness on tabular data. However, training accurate oblique DTs is challenging due to complex…

Machine Learning · Computer Science 2026-05-11 Subrat Prasad Panda , Blaise Genest , Arvind Easwaran

We propose Top-N-Rank, a novel family of list-wise Learning-to-Rank models for reliably recommending the N top-ranked items. The proposed models optimize a variant of the widely used discounted cumulative gain (DCG) objective function which…

Information Retrieval · Computer Science 2018-12-20 Junjie Liang , Jinlong Hu , Shoubin Dong , Vasant Honavar

The top-k operation, i.e., finding the k largest or smallest elements from a collection of scores, is an important model component, which is widely used in information retrieval, machine learning, and data mining. However, if the top-k…

Machine Learning · Computer Science 2020-02-19 Yujia Xie , Hanjun Dai , Minshuo Chen , Bo Dai , Tuo Zhao , Hongyuan Zha , Wei Wei , Tomas Pfister

The top-k operator returns a sparse vector, where the non-zero values correspond to the k largest values of the input. Unfortunately, because it is a discontinuous function, it is difficult to incorporate in neural networks trained…

Machine Learning · Computer Science 2023-06-06 Michael E. Sander , Joan Puigcerver , Josip Djolonga , Gabriel Peyré , Mathieu Blondel

To adapt large language models (LLMs) to ranking tasks, existing list-wise methods, represented by list-wise Direct Preference Optimization (DPO), focus on optimizing partial-order or full-order list ranking consistency for LLMs to enhance…

Information Retrieval · Computer Science 2025-06-03 Shihao Cai , Chongming Gao , Yang Zhang , Wentao Shi , Jizhi Zhang , Keqin Bao , Qifan Wang , Fuli Feng

The top-k classification accuracy is one of the core metrics in machine learning. Here, k is conventionally a positive integer, such as 1 or 5, leading to top-1 or top-5 training objectives. In this work, we relax this assumption and…

Machine Learning · Computer Science 2022-06-16 Felix Petersen , Hilde Kuehne , Christian Borgelt , Oliver Deussen

In this paper, we investigate the recommendation task in the most common scenario with implicit feedback (e.g., clicks, purchases). State-of-the-art methods in this direction usually cast the problem as to learn a personalized ranking on a…

Information Retrieval · Computer Science 2020-12-29 Yan Gao , Jiafeng Guo , Yanyan Lan , Huaming Liao

Top-k query processing finds a list of k results that have largest scores w.r.t the user given query, with the assumption that all the k results are independent to each other. In practice, some of the top-k results returned can be very…

Databases · Computer Science 2012-08-02 Lu Qin , Jeffrey Xu Yu , Lijun Chang

Many complicated real-world tasks can be broken down into smaller, more manageable parts, and planning with prior knowledge extracted from these simplified pieces is crucial for humans to make accurate decisions. However, replicating this…

Artificial Intelligence · Computer Science 2024-05-21 Jingqing Ruan , Kaishen Wang , Qingyang Zhang , Dengpeng Xing , Bo Xu

Many complex multi-target prediction problems that concern large target spaces are characterised by a need for efficient prediction strategies that avoid the computation of predictions for all targets explicitly. Examples of such problems…

Information Retrieval · Computer Science 2018-03-06 Michiel Stock , Krzysztof Dembczynski , Bernard De Baets , Willem Waegeman

Sorting an array is a fundamental routine in machine learning, one that is used to compute rank-based statistics, cumulative distribution functions (CDFs), quantiles, or to select closest neighbors and labels. The sorting function is…

Machine Learning · Computer Science 2019-11-05 Marco Cuturi , Olivier Teboul , Jean-Philippe Vert

Cascade Ranking is a prevalent architecture in large-scale top-k selection systems like recommendation and advertising platforms. Traditional training methods focus on single-stage optimization, neglecting interactions between stages.…

Information Retrieval · Computer Science 2025-06-05 Yunli Wang , Zhen Zhang , Zhiqiang Wang , Zixuan Yang , Yu Li , Jian Yang , Shiyang Wen , Peng Jiang , Kun Gai

Over the past few years, as large language models have ushered in an era of intelligence emergence, there has been an intensified focus on scaling networks. Currently, many network architectures are designed manually, often resulting in…

Computer Vision and Pattern Recognition · Computer Science 2024-05-14 Kai Liu , Ruohui Wang , Jianfei Gao , Kai Chen

Learning to Rank (LTR) algorithms are usually evaluated using Information Retrieval metrics like Normalised Discounted Cumulative Gain (NDCG) or Mean Average Precision. As these metrics rely on sorting predicted items' scores (and thus, on…

Information Retrieval · Computer Science 2021-05-25 Przemysław Pobrotyn , Radosław Białobrzeski

We consider the Top-$K$ selection problem, which aims to identify the largest $K$ elements in an array. Top-$K$ selection arises in many machine learning algorithms and often becomes a bottleneck on accelerators, which are optimized for…

Machine Learning · Computer Science 2026-05-14 Yashas Samaga , Varun Yerram , Spandana Raj Babbula , Prateek Jain , Praneeth Netrapalli

In decision-making problems with limited training data, policy functions approximated using deep neural networks often exhibit suboptimal performance. An alternative approach involves learning a world model from the limited data and…

Machine Learning · Computer Science 2024-08-05 Dixant Mittal , Wee Sun Lee
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