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The Variational AutoEncoder (VAE) learns simultaneously an inference and a generative model, but only one of these models can be learned at optimum, this behaviour is associated to the ELBO learning objective, that is optimised by a…

Machine Learning · Computer Science 2020-11-10 Vincenzo Crescimanna , Bruce Graham

The InfoNCE objective, originally introduced for contrastive representation learning, has become a popular choice for mutual information (MI) estimation, despite its indirect connection to MI. In this paper, we demonstrate why InfoNCE…

Machine Learning · Computer Science 2025-10-31 J. Jon Ryu , Pavan Yeddanapudi , Xiangxiang Xu , Gregory W. Wornell

Inference in both brains and machines can be formalized by optimizing a shared objective: maximizing the evidence lower bound (ELBO) in machine learning, or minimizing variational free energy (F) in neuroscience (ELBO = -F). While this…

Artificial Intelligence · Computer Science 2025-10-27 Hadi Vafaii , Dekel Galor , Jacob L. Yates

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

Unnormalised latent variable models are a broad and flexible class of statistical models. However, learning their parameters from data is intractable, and few estimation techniques are currently available for such models. To increase the…

Machine Learning · Statistics 2019-02-26 Benjamin Rhodes , Michael Gutmann

Contrastive learning has emerged as a cornerstone of unsupervised representation learning across vision, language, and graph domains, with InfoNCE as its dominant objective. Despite its empirical success, the theoretical underpinnings of…

Machine Learning · Computer Science 2025-11-18 Ge Cheng , Shuo Wang , Yun Zhang

In recent years, several unsupervised, "contrastive" learning algorithms in vision have been shown to learn representations that perform remarkably well on transfer tasks. We show that this family of algorithms maximizes a lower bound on…

Machine Learning · Computer Science 2020-06-08 Mike Wu , Chengxu Zhuang , Milan Mosse , Daniel Yamins , Noah Goodman

In variational inference (VI), an approximation of the posterior distribution is selected from a family of distributions through numerical optimization. With the most common variational objective function, known as the evidence lower bound…

Machine Learning · Statistics 2025-01-15 Declan McNamara , Jackson Loper , Jeffrey Regier

Bayesian Inference and Information Bottleneck are the two most popular objectives for neural networks, but they can be optimised only via a variational lower bound: the Variational Information Bottleneck (VIB). In this manuscript we show…

Machine Learning · Computer Science 2020-03-10 Vincenzo Crescimanna , Bruce Graham

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

Information bottleneck (IB) principle [1] has become an important element in information-theoretic analysis of deep models. Many state-of-the-art generative models of both Variational Autoencoder (VAE) [2; 3] and Generative Adversarial…

Computer Vision and Pattern Recognition · Computer Science 2019-12-06 Slava Voloshynovskiy , Mouad Kondah , Shideh Rezaeifar , Olga Taran , Taras Holotyak , Danilo Jimenez Rezende

In self-supervised contrastive learning, a widely-adopted objective function is InfoNCE, which uses the heuristic cosine similarity for the representation comparison, and is closely related to maximizing the Kullback-Leibler (KL)-based…

Machine Learning · Computer Science 2024-02-16 Yiwei Lu , Guojun Zhang , Sun Sun , Hongyu Guo , Yaoliang Yu

Masked autoencoders (MAEs) represent a prominent self-supervised learning paradigm in computer vision. Despite their empirical success, the underlying mechanisms of MAEs remain insufficiently understood. Recent studies have attempted to…

Computer Vision and Pattern Recognition · Computer Science 2025-02-28 Tao Huang , Yanxiang Ma , Shan You , Chang Xu

A key advance in learning generative models is the use of amortized inference distributions that are jointly trained with the models. We find that existing training objectives for variational autoencoders can lead to inaccurate amortized…

Machine Learning · Computer Science 2018-05-31 Shengjia Zhao , Jiaming Song , Stefano Ermon

User intentions are typically formalized as evaluation rewards to be maximized when fine-tuning language models (LMs). Existing alignment methods, such as Direct Preference Optimization (DPO), are mainly tailored for pairwise preference…

Machine Learning · Computer Science 2024-10-31 Huayu Chen , Guande He , Lifan Yuan , Ganqu Cui , Hang Su , Jun Zhu

Amortised inference enables scalable learning of sequential latent-variable models (LVMs) with the evidence lower bound (ELBO). In this setting, variational posteriors are often only partially conditioned. While the true posteriors depend,…

Machine Learning · Computer Science 2021-03-18 Justin Bayer , Maximilian Soelch , Atanas Mirchev , Baris Kayalibay , Patrick van der Smagt

A framework to boost the efficiency of Bayesian inference in probabilistic programs is introduced by embedding a sampler inside a variational posterior approximation. We call it the refined variational approximation. Its strength lies both…

Machine Learning · Computer Science 2020-02-25 Victor Gallego , David Rios Insua

We present a new statistical learning paradigm for Boltzmann machines based on a new inference principle we have proposed: the latent maximum entropy principle (LME). LME is different both from Jaynes maximum entropy principle and from…

Machine Learning · Computer Science 2012-12-12 Shaojun Wang , Dale Schuurmans , Fuchun Peng , Yunxin Zhao

Disentanglement learning aims to construct independent and interpretable latent variables in which generative models are a popular strategy. InfoGAN is a classic method via maximizing Mutual Information (MI) to obtain interpretable latent…

Machine Learning · Computer Science 2021-10-05 Hongxiang Jiang , Jihao Yin , Xiaoyan Luo , Fuxiang Wang

Variational Autoencoder is a scalable method for learning latent variable models of complex data. It employs a clear objective that can be easily optimized. However, it does not explicitly measure the quality of learned representations. We…

Machine Learning · Computer Science 2020-05-29 Andriy Serdega , Dae-Shik Kim
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