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We introduce a variational reasoning framework for language models that treats thinking traces as latent variables and optimizes them through variational inference. Starting from the evidence lower bound (ELBO), we extend it to a…

Computation and Language · Computer Science 2025-10-16 Xiangxin Zhou , Zichen Liu , Haonan Wang , Chao Du , Min Lin , Chongxuan Li , Liang Wang , Tianyu Pang

Variational inference for latent variable models is prevalent in various machine learning problems, typically solved by maximizing the Evidence Lower Bound (ELBO) of the true data likelihood with respect to a variational distribution.…

Machine Learning · Computer Science 2018-07-11 Guoqing Zheng , Yiming Yang , Jaime Carbonell

Recent work in unsupervised representation learning has focused on learning deep directed latent-variable models. Fitting these models by maximizing the marginal likelihood or evidence is typically intractable, thus a common approximation…

Machine Learning · Computer Science 2018-02-15 Alexander A. Alemi , Ben Poole , Ian Fischer , Joshua V. Dillon , Rif A. Saurous , Kevin Murphy

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

We consider the problem of parameter estimation using weakly supervised datasets, where a training sample consists of the input and a partially specified annotation, which we refer to as the output. The missing information in the annotation…

Machine Learning · Computer Science 2012-06-22 M. Pawan Kumar , Ben Packer , Daphne Koller

Recent progress in deep latent variable models has largely been driven by the development of flexible and scalable variational inference methods. Variational training of this type involves maximizing a lower bound on the log-likelihood,…

Machine Learning · Computer Science 2016-06-02 Andriy Mnih , Danilo J. Rezende

Machine learning models provide statistically impressive results which might be individually unreliable. To provide reliability, we propose an Epistemic Classifier (EC) that can provide justification of its belief using support from the…

Machine Learning · Computer Science 2020-10-20 Chitresh Bhushan , Zhaoyuan Yang , Nurali Virani , Naresh Iyer

This paper describes InfoCatVAE, an extension of the variational autoencoder that enables unsupervised disentangled representation learning. InfoCatVAE uses multimodal distributions for the prior and the inference network and then maximizes…

Machine Learning · Computer Science 2018-06-26 Edouard Pineau , Marc Lelarge

Learning useful representations of complex data has been the subject of extensive research for many years. With the diffusion of Deep Neural Networks, Variational Autoencoders have gained lots of attention since they provide an explicit…

Machine Learning · Computer Science 2020-09-15 Marco Maggipinto , Matteo Terzi , Gian Antonio Susto

Lesions or organ boundaries visible through medical imaging data are often ambiguous, thus resulting in significant variations in multi-reader delineations, i.e., the source of aleatoric uncertainty. In particular, quantifying the…

Computer Vision and Pattern Recognition · Computer Science 2022-01-19 Xiaofeng Liu , Fangxu Xing , Thibault Marin , Georges El Fakhri , Jonghye Woo

We propose a new family of optimization criteria for variational auto-encoding models, generalizing the standard evidence lower bound. We provide conditions under which they recover the data distribution and learn latent features, and…

Machine Learning · Computer Science 2017-03-01 Shengjia Zhao , Jiaming Song , Stefano Ermon

Variational Autoencoders are powerful models for unsupervised learning. However deep models with several layers of dependent stochastic variables are difficult to train which limits the improvements obtained using these highly expressive…

Machine Learning · Statistics 2016-05-30 Casper Kaae Sønderby , Tapani Raiko , Lars Maaløe , Søren Kaae Sønderby , Ole Winther

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

When used as a surrogate objective for maximum likelihood estimation in latent variable models, the evidence lower bound (ELBO) produces state-of-the-art results. Inspired by this, we consider the extension of the ELBO to a family of lower…

Recent methods for knowledge grounded dialogs generate responses by incorporating information from an external textual document. These methods do not require the exact document to be known during training and rely on the use of a retrieval…

Computation and Language · Computer Science 2022-08-16 Mayank Mishra , Dhiraj Madan , Gaurav Pandey , Danish Contractor

Unsupervised learning with functional data is an emerging paradigm of machine learning research with applications to computer vision, climate modeling and physical systems. A natural way of modeling functional data is by learning operators…

Machine Learning · Computer Science 2023-02-22 Jacob H. Seidman , Georgios Kissas , George J. Pappas , Paris Perdikaris

Deep latent variable models have achieved significant empirical successes in model-based reinforcement learning (RL) due to their expressiveness in modeling complex transition dynamics. On the other hand, it remains unclear theoretically…

Machine Learning · Computer Science 2023-03-08 Tongzheng Ren , Chenjun Xiao , Tianjun Zhang , Na Li , Zhaoran Wang , Sujay Sanghavi , Dale Schuurmans , Bo Dai

We explore the performance of latent variable models for conditional text generation in the context of neural machine translation (NMT). Similar to Zhang et al., we augment the encoder-decoder NMT paradigm by introducing a continuous latent…

Computation and Language · Computer Science 2018-12-12 Artidoro Pagnoni , Kevin Liu , Shangyan Li

This article addresses online variational estimation in state-space models. We focus on learning the smoothing distribution, i.e. the joint distribution of the latent states given the observations, using a variational approach together with…

Applications · Statistics 2024-02-06 Mathis Chagneux , Pierre Gloaguen , Sylvain Le Corff , Jimmy Olsson

Deep learning approaches process data in a layer-by-layer way with intermediate (or latent) features. We aim at designing a general solution to optimize the latent manifolds to improve the performance on classification, segmentation,…

Machine Learning · Computer Science 2025-06-03 Yida Wang , David Joseph Tan , Nassir Navab , Federico Tombari
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