相关论文: On the Convergence of the ELBO to Entropy Sums

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…

The central objective function of a variational autoencoder (VAE) is its variational lower bound (the ELBO). Here we show that for standard (i.e., Gaussian) VAEs the ELBO converges to a value given by the sum of three entropies: the…

Standard probabilistic sparse coding assumes a Laplace prior, a linear mapping from latents to observables, and Gaussian observable distributions. We here derive a solely entropy-based learning objective for the parameters of standard…

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…

Various lower bounds are established for the entropy of sums, products and their combinations. First, we derive a prime-field analogue of a version of the entropy power inequality established by Tao over torsion-free groups. Next, we prove…

We prove that the evidence lower bound (ELBO) employed by variational auto-encoders (VAEs) admits non-trivial solutions having constant posterior variances under certain mild conditions, removing the need to learn variances in the encoder.…

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…

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,…

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.…

When training large models on limited data, avoiding overfitting is paramount. Common grid search or smarter search methods rely on expensive separate runs for each candidate hyperparameter, while carving out a validation set that reduces…

The Evidence Lower Bound (ELBO) is a quantity that plays a key role in variational inference. It can also be used as a criterion in model selection. However, though extremely popular in practice in the variational Bayes community, there has…

Multiple data types naturally co-occur when describing real-world phenomena and learning from them is a long-standing goal in machine learning research. However, existing self-supervised generative models approximating an ELBO are not able…

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…

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…

Traditional Variational Autoencoders (VAEs) are constrained by the limitations of the Evidence Lower Bound (ELBO) formulation, particularly when utilizing simplistic, non-analytic, or unknown prior distributions. These limitations inhibit…

The importance of Variational Autoencoders reaches far beyond standalone generative models -- the approach is also used for learning latent representations and can be generalized to semi-supervised learning. This requires a thorough…

Many crucial problems in deep learning and statistical inference are caused by a variational gap, i.e., a difference between model evidence (log-likelihood) and evidence lower bound (ELBO). In particular, in a classical VAE setting that…

Reinforcement learning with verifiable rewards (RLVR), particularly Group Relative Policy Optimization (GRPO), has advanced LLM reasoning. However, GRPO suffers from three credit assignment failures: uniform token-level granularity that…

We present a latent variable model for classification that provides a novel probabilistic interpretation of neural network softmax classifiers. We derive a variational objective to train the model, analogous to the evidence lower bound…

We combine two popular optimization approaches to derive learning algorithms for generative models: variational optimization and evolutionary algorithms. The combination is realized for generative models with discrete latents by using…