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Sequence-to-sequence models are a powerful workhorse of NLP. Most variants employ a softmax transformation in both their attention mechanism and output layer, leading to dense alignments and strictly positive output probabilities. This…

Computation and Language · Computer Science 2019-06-14 Ben Peters , Vlad Niculae , André F. T. Martins

We reinterpret the final Large Language Model (LLM) softmax classifier as an Energy-Based Model (EBM), decomposing the sequence-to-sequence probability chain into multiple interacting EBMs at inference. This principled approach allows us to…

Artificial Intelligence · Computer Science 2026-03-04 Adrian Robert Minut , Hazem Dewidar , Iacopo Masi

Matching is one of the most widely used study designs for adjusting for measured confounders in observational studies. However, unmeasured confounding may exist and cannot be removed by matching. Therefore, a sensitivity analysis is…

Methodology · Statistics 2024-01-17 Jeffrey Zhang , Dylan Small , Siyu Heng

The problem of publishing privacy-guaranteed data for hypothesis testing is studied using the maximal leakage (ML) as a metric for privacy and the type-II error exponent as the utility metric. The optimal mechanism (random mapping) that…

Information Theory · Computer Science 2017-04-12 Jiachun Liao , Lalitha Sankar , Flavio P. Calmon , Vincent Y. F. Tan

Two-sample network hypothesis testing is an important inference task with applications across diverse fields such as medicine, neuroscience, and sociology. Many of these testing methodologies operate under the implicit assumption that the…

Methodology · Statistics 2024-05-28 Ayushi Saxena , Vince Lyzinski

Active learning aims to obtain a classifier of high accuracy by using fewer label requests in comparison to passive learning by selecting effective queries. Many active learning methods have been developed in the past two decades, which…

Machine Learning · Computer Science 2016-08-08 Cem Orhan , Öznur Taştan

Attention is a core component of transformer architecture, whether encoder-only, decoder-only, or encoder-decoder model. However, the standard softmax attention often produces noisy probability distribution, which can impair effective…

Computation and Language · Computer Science 2025-11-11 Dhananjay Ram , Wei Xia , Stefano Soatto

Self-training is a well-known approach for semi-supervised learning. It consists of iteratively assigning pseudo-labels to unlabeled data for which the model is confident and treating them as labeled examples. For neural networks, softmax…

Machine Learning · Computer Science 2024-04-04 Ambroise Odonnat , Vasilii Feofanov , Ievgen Redko

Effective Uncertainty Quantification (UQ) represents a key aspect for reliable deployment of Large Language Models (LLMs) in automated decision-making and beyond. Yet, for LLM generation with multiple choice structure, the state-of-the-art…

Machine Learning · Computer Science 2025-11-18 Ramzi Dakhmouche , Adrien Letellier , Hossein Gorji

Linear attention has attracted interest as a computationally efficient approximation to softmax attention, especially for long sequences. Recent studies have explored distilling softmax attention in pre-trained Transformers into linear…

Machine Learning · Computer Science 2025-07-08 Naoki Nishikawa , Rei Higuchi , Taiji Suzuki

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

Two-tower neural networks are a popular architecture for the retrieval stage in recommender systems. These models are typically trained with a softmax loss over the item catalog. However, in web-scale settings, the item catalog is often…

Information Retrieval · Computer Science 2025-07-29 Kirill Khrylchenko , Vladimir Baikalov , Sergei Makeev , Artem Matveev , Sergei Liamaev

We revisit the problem of sketching using approximate leverage scores for matrix least squares problems of the form $\| AX - B \|_F^2$ where the design matrix $A \in \mathbb{R}^{N \times r}$ is tall and skinny with $N \gg r$. We derive the…

Numerical Analysis · Mathematics 2026-03-31 Brett W. Larsen , Tamara G. Kolda

The success of Large Language Models (LLMs) relies heavily on the huge amount of pre-training data learned in the pre-training phase. The opacity of the pre-training process and the training data causes the results of many benchmark tests…

Computation and Language · Computer Science 2025-03-03 Shiwen Ni , Xiangtao Kong , Chengming Li , Xiping Hu , Ruifeng Xu , Jia Zhu , Min Yang

We study a Bayesian binary sequential hypothesis testing problem with multiple large language models (LLMs). Each LLM $j$ has per-query cost $c_j>0$, random waiting time with mean $\mu_j>0$ and sub-Gaussian tails, and \emph{asymmetric}…

Data Structures and Algorithms · Computer Science 2026-04-03 Guokai Li , Alys Liang , Mo Liu , Murray Lei , Stefanus Jasin , Fenghua Yang , Preet Baxi

This paper considers an ML inspired approach to hypothesis testing known as classifier/classification-accuracy testing ($\mathsf{CAT}$). In $\mathsf{CAT}$, one first trains a classifier by feeding it labeled synthetic samples generated by…

Statistics Theory · Mathematics 2025-11-25 Patrik Róbert Gerber , Yanjun Han , Yury Polyanskiy

Cross-level interactions among fixed effects in linear mixed models (also known as multilevel models) are often complicated by the variances stemming from random effects and residuals. When these variances change across clusters, tests of…

Methodology · Statistics 2022-03-18 Ting Wang , Edgar C. Merkle , Joaquin A. Anguera , Brandon M. Turner

The softmax layer in neural machine translation is designed to model the distribution over mutually exclusive tokens. Machine translation, however, is intrinsically uncertain: the same source sentence can have multiple semantically…

Computation and Language · Computer Science 2022-05-03 Felix Stahlberg , Shankar Kumar

Machine learning models are central to people's lives and impact society in ways as fundamental as determining how people access information. The gravity of these models imparts a responsibility to model developers to ensure that they are…

Applications · Statistics 2020-07-13 Cyrus DiCiccio , Sriram Vasudevan , Kinjal Basu , Krishnaram Kenthapadi , Deepak Agarwal

In this paper, we propose a new method for calculating the output layer in neural machine translation systems. The method is based on predicting a binary code for each word and can reduce computation time/memory requirements of the output…

Computation and Language · Computer Science 2017-04-25 Yusuke Oda , Philip Arthur , Graham Neubig , Koichiro Yoshino , Satoshi Nakamura
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