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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

This article studies the Fisher-Rao gradient, also referred to as the natural gradient, of the evidence lower bound (ELBO) which plays a central role in generative machine learning. It reveals that the gap between the evidence and its lower…

Machine Learning · Computer Science 2025-10-02 Nihat Ay , Jesse van Oostrum , Adwait Datar

Decomposition of the evidence lower bound (ELBO) objective of VAE used for density estimation revealed the deficiency of VAE for representation learning and suggested ways to improve the model. In this paper, we investigate whether we can…

Machine Learning · Computer Science 2022-11-22 Fahim Faisal Niloy , M. Ashraful Amin , AKM Mahbubur Rahman , Amin Ahsan Ali

Model-based reinforcement learning (RL) is considered to be a promising approach to reduce the sample complexity that hinders model-free RL. However, the theoretical understanding of such methods has been rather limited. This paper…

Machine Learning · Computer Science 2021-02-16 Yuping Luo , Huazhe Xu , Yuanzhi Li , Yuandong Tian , Trevor Darrell , Tengyu Ma

While Deep Neural Networks (DNNs) achieve remarkable performance, their tendency to produce overconfident predictions. Evidential Deep Learning (EDL) mitigates this by formulating predictions as a Dirichlet distribution over class…

Machine Learning · Computer Science 2026-05-27 Jiawei Tang , Xinyan Du , Hui Liu , Junhui Hou , Yuheng Jia

A key challenge in applying reinforcement learning (RL) to diffusion large language models (dLLMs) lies in the intractability of their likelihood functions, which are essential for the RL objective, necessitating corresponding approximation…

Machine Learning · Computer Science 2025-10-15 Nianyi Lin , Jiajie Zhang , Lei Hou , Juanzi Li

Standard variational lower bounds used to train latent variable models produce biased estimates of most quantities of interest. We introduce an unbiased estimator of the log marginal likelihood and its gradients for latent variable models…

Machine Learning · Computer Science 2020-07-14 Yucen Luo , Alex Beatson , Mohammad Norouzi , Jun Zhu , David Duvenaud , Ryan P. Adams , Ricky T. Q. Chen

One of the challenges in training generative models such as the variational auto encoder (VAE) is avoiding posterior collapse. When the generator has too much capacity, it is prone to ignoring latent code. This problem is exacerbated when…

Machine Learning · Computer Science 2019-10-30 Talip Ucar

Deep latent variable models learn condensed representations of data that, hopefully, reflect the inner workings of the studied phenomena. Unfortunately, these latent representations are not statistically identifiable, meaning they cannot be…

Machine Learning · Statistics 2025-06-02 Stas Syrota , Yevgen Zainchkovskyy , Johnny Xi , Benjamin Bloem-Reddy , Søren Hauberg

The evidence lower bound (ELBO) is one of the most central objectives for probabilistic unsupervised learning. For the ELBOs of several generative models and model classes, we here prove convergence to entropy sums. As one result, we…

Machine Learning · Statistics 2025-01-17 Jan Warnken , Dmytro Velychko , Simon Damm , Asja Fischer , Jörg Lücke

How can we perform efficient inference and learning in directed probabilistic models, in the presence of continuous latent variables with intractable posterior distributions, and large datasets? We introduce a stochastic variational…

Machine Learning · Statistics 2022-12-13 Diederik P Kingma , Max Welling

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

Unsupervised learning aims at the discovery of hidden structure that drives the observations in the real world. It is essential for success in modern machine learning. Latent variable models are versatile in unsupervised learning and have…

Machine Learning · Computer Science 2016-06-13 Furong Huang

A trade-off exists between reconstruction quality and the prior regularisation in the Evidence Lower Bound (ELBO) loss that Variational Autoencoder (VAE) models use for learning. There are few satisfactory approaches to deal with a balance…

Machine Learning · Computer Science 2019-09-10 Shuyu Lin , Stephen Roberts , Niki Trigoni , Ronald Clark

Variational Autoencoders (VAEs) have become a cornerstone in generative modeling and representation learning within machine learning. This paper explores a nuanced aspect of VAEs, focusing on interpreting the Kullback-Leibler (KL)…

Machine Learning · Computer Science 2024-06-25 Mariano Rivera

Auto-encoding Variational Bayes (AEVB) is a powerful and general algorithm for fitting latent variable models (a promising direction for unsupervised learning), and is well-known for training the Variational Auto-Encoder (VAE). In this…

Machine Learning · Computer Science 2022-08-17 Yang Zhi-Han

Binary Neural Networks (BiNNs), which employ single-bit precision weights, have emerged as a promising solution to reduce memory usage and power consumption while maintaining competitive performance in large-scale systems. However, training…

Quantum Physics · Physics 2025-11-18 Luca Nepote , Alix Lhéritier , Nicolas Bondoux , Marios Kountouris , Maurizio Filippone

Machine unlearning (MU) is to make a well-trained model behave as if it had never been trained on specific data. In today's over-parameterized models, dominated by neural networks, a common approach is to manually relabel data and fine-tune…

Machine Learning · Computer Science 2025-07-21 Ruikai Yang , Mingzhen He , Zhengbao He , Youmei Qiu , Xiaolin Huang

Variational Autoencoders (VAEs) have been shown to be remarkably effective in recovering model latent spaces for several computer vision tasks. However, currently trained VAEs, for a number of reasons, seem to fall short in learning…

Machine Learning · Computer Science 2021-07-27 Chandrajit Bajaj , Avik Roy , Haoran Zhang

Variational autoencoders (VAEs) are a standard framework for inducing latent variable models that have been shown effective in learning text representations as well as in text generation. The key challenge with using VAEs is the {\it…

Machine Learning · Computer Science 2020-05-01 Serhii Havrylov , Ivan Titov