Variational autoencoder loss. Kingma and Max Welling in 2013.
Variational autoencoder loss Mar 19, 2018 · A variational autoencoder (VAE) provides a probabilistic manner for describing an observation in latent space. 6. VAEs use variational inference to create a probabilistic latent space. 52% and the embeddings from different classes are overlapped at many spots, as shown in Fig. Variational Autoencoders with Keras and MNIST # Authors: Charles Kenneth Fisher, Raghav Kansal Adapted from this notebook. Oct 17, 2024 · Intrusion Detection Systems (IDS) face significant challenges in detecting minority class attacks within imbalanced network traffic, where traditional methods often struggle to maintain high accuracy without sacrificing key performance metrics like precision and recall. An autoencoder consists of two networks – an encoder, which maps an image to a latent variable, and a decoder, which plays the role of the Mar 15, 2025 · Autoencoders have become a fundamental technique in deep learning (DL), significantly enhancing representation learning across various domains, including image processing, anomaly detection, and generative modelling. A special emphasis will be placed on the Gaussian The loss function of the variational autoencoder is the negative log-likelihood with a regularizer. The use of the variational Autoencoder has revolutionized the field of generative modeling by allowing for the generation of new data points by sampling from the learned latent space. We understand AE. My data can be thought of as an image of length 100, width 2, and it has 2 channels (100, 2, 2) def construct_ae(input_shape May 30, 2025 · Explore Variational Autoencoder (VAE) architecture, covering its components, training, mathematical foundations, and applications in Generative AI. Warm-up: Variational Autoencoding We Feb 25, 2024 · The construction of a Variational Autoencoder (VAE) involves designing the encoder and decoder structures and defining an appropriate loss function to optimize the model. Jul 21, 2019 · This tutorial derives the variational lower bound loss function of the standard variational autoencoder in the instance of a gaussian latent prior and gaussian approximate posterior, under which assumptions the Kullback-Leibler term in the variations lower bound has a closed form solution. Thus, rather than building an encoder which outputs a single value to describe each latent state attribute, we'll formulate our encoder to describe a probability distribution A simple tutorial of Variational AutoEncoder (VAE) models. By default, pixel-by-pixel measurement like L2 loss, or logistic regression loss is used to measure the difference between reconstructed and original images. The basic framework of a variational autoencoder. Mar 27, 2025 · While analyzing the loss function of the variational autoencoder (VAE) model, I noticed that the Kullback-Leibler (KL) loss term has a nice… Apr 25, 2023 · In this article we will be implementing variational autoencoders from scratch, in python. In Convolutional VAE model, the encoder and decodes has two-dimensional Convolutional layers with variational layer length. Reconstruction Loss: This loss measures the difference between the original data and the data reconstructed through the VAE. Second, we might want to measure the likelihood that a new vector x ∗ was created by this probability Feb 4, 2018 · Optimizing purely for reconstruction loss For example, training an autoencoder on the MNIST dataset, and visualizing the encodings from a 2D latent space reveals the formation of distinct clusters Jul 24, 2024 · For the poor model generalization and low diagnostic efficiency of fault diagnosis under imbalanced distributions, a novel fault diagnosis method using variational autoencoder generation adversaria Aug 12, 2018 · The idea of Variational Autoencoder (Kingma & Welling, 2014), short for VAE, is actually less similar to all the autoencoder models above, but deeply rooted in the methods of variational bayesian and graphical model. Covers the ELBO objective, reparameterization trick, loss scaling, gradient behaviors, and experiments with MNIST showing the reconstruction-KL trade-off across latent dimensionalities. e, the sum of reconstruction error and KL divergence. My loss function is the classical one, i. Mar 7, 2024 · The encoder generates the latent variable. Variational Autoencoder Variational autoencoder (VAE) makes assumptions about the probability distribution of the data and tries to learn a better approximation of it. We will verify the assump-tion and also demonstrate quantitatively how much the re-construction loss is underestimated in the experiment sec-tion. Therefore, we can assume the reconstruction loss term is underestimated, which will potentially breaks the balance between recon-struction loss and KL loss in (1). Loss with Gaussian Distributions Recall from the setup of our Variational Autoencoder model that we have defined the latent vector as living in two-dimensional space following a multivariate Gaussian distribution. In a recent work, Dai and Jun 28, 2024 · A Variational Autoencoder (VAE) is an extended form of an autoencoder that learns a more meaningful latent space representation through a probabilistic approach. This study introduces the XIDINTFL-VAE framework, which leverages Class-Wise Focal Loss (CWFL) and Variational AutoEncoder (a) Triplet Loss (b) Variational autoencoder loss Figure 3. Jun 7, 2018 · Where as the tensorflow tutorial for variational autoencoder uses binary cross-entropy for measuring the reconstruction loss. Mar 17, 2022 · I have some perplexities about the implementation of Variational autoencoder loss. In addition, we will familiarize ourselves with the Keras sequential GUI as well as how to Dec 27, 2023 · What are Variational Autoencoders (VAEs)? Autoencoders are ingenious, unsupervised learning mechanisms capable of learning efficient data representations. Our model is first tested on MNIST data set. Jan 28, 2020 · Fig 3. It also turns out that MLE is widely being used in generative models like Variational Autoencoders (VAE) and Diffusion models (DDPM). Let us agree on the claim for now. In this tutorial, we derive the variational lower bound loss function of the standard variational autoencoder. 3 I'm working with a Variational Autoencoder and I have seen that there are people who uses MSE Loss and some people who uses BCE Loss, does anyone know if one is more correct that the another and why? As far as I understand, if you assume that the latent space vector of the VAE follows a Gaussian distribution, you should use MSE Loss. , 2013) Vector Quantized Variational AutoEncoder (VQ-VAE, A. Correctly balancing these two components is a delicate issue, easily resulting in poor generative behaviours. What is a variational autoencoder? To get an understanding of a VAE, we'll first start from a simple network and add parts step by step. published a paper Auto-Encoding Variational Bayes. The variational autoencoder adds an additional component to the loss function, preventing Q(zjX) from col-lapsing to a dirac distribution: speci cally, we try to bring each Q(zjX) close to the prior P(z) distribution by minimizing their Kullback-Leibler divergence KL(Q(zjX)jjP(z)). They used for generating new data such as creating realistic images or text. P. We do so in the instance of a gaussian latent prior and gaussian approximate posterior, under which assumptions the Kullback-Leibler term in the variational lower bound has a closed form solution. Jun 13, 2019 · I have implemented a Variational Autoencoder in Pytorch that works on SMILES strings (String representations of molecular structures). Nov 11, 2023 · In this blog post, we’ll embark on an enlightening exploration of loss functions in the simple autoencoder, and later in another blogs we will cover other models like variational autoencoder Nov 20, 2022 · The loss function in VAE consists of reproduction loss and the Kullback–Leibler (KL) divergence. What is a Variational Autoencoder (VAE)? Variational Autoencoders (VAEs) are a powerful type of neural network and a generative model that extends traditional autoencoders by learning a probabilistic representation of data. As a bonus point, I’ll show you how by imposing a special role to some of Jul 9, 2018 · I have the following function which is supposed to autoencode my data. Can some please tell me WHY, based on the same dataset with same values (they are all numerical values which in effect represent pixel values) they use R2-loss/MSE-loss for the autoencoder and Binary-Cross-Entropy loss The loss function used to train an undercomplete autoencoder is called reconstruction loss, as it is a check of how well the image has been reconstructed from the input data. There are two main reasons for modelling distributions. An autoencoder is a type of model that is trained to replicate its input by transforming the input to a lower dimensional space (the encoding step) and reconstructing the input Visualising the reconstructed inputs would definitely be a good place to start while debugging this scenario. Learning curve We carried out t-SNE embedding for the mean vector, which is projected into two dimensional . Based off of Latent space interpolation Aug 13, 2024 · Explore Variational Autoencoders (VAEs) in this comprehensive guide. Variational AutoEncoder (VAE, D. We'll assume that each image is generated from some unseen latent code zzz, and there's an underlying distribution of latents p(zp(zp(z). Apr 9, 2025 · Short Introduction to Variational Autoencoders A Variational Autoencoder (VAE) is kind of like a regular autoencoder — but with a probabilistic twist. Jul 24, 2024 · Download Citation | Fault diagnosis using variational autoencoder GAN and focal loss CNN under unbalanced data | For the poor model generalization and low diagnostic efficiency of fault diagnosis Nov 29, 2022 · This document is meant to give a practical introduction to different variations around Autoencoders for generating data, namely plain AutoEncoder (AE) in Section 3, Variational AutoEncoders (VAE) in Section 4 and Conditional Variational AutoEncoders (CVAE) in Section 6. We have a dataset of images, xxx. Variational inference. Aug 12, 2023 · The variational autoencoder (VAE) is thus simply an autoencoder supplemented with an inductive prior that the latent distribution Z should fit into a pre-selected family of handpicked probability distributions. In a normal autoencoder, there is a possibility for Feb 9, 2020 · In this tutorial, we will derive the variational lower bound loss function of the standard variational autoencoder. sum(1 + logvar - mu. Variational Autoencoders Variational Autoencoder Overview Sampling from a Variational Autoencoder The Log-Var Trick The Variational Autoencoder Loss Function A Variational Autoencoder for Handwritten Digits in PyTorch A Variational Autoencoder for Face Images in PyTorch VAEs and Latent Space Arithmetic Variational autoencoders were introduced to address different deficiencies of this architecture, which we will cover. 2 Autoencoder Learning We learn the weights in an autoencoder using the same tools that we previously used for supervised learning, namely (stochastic) gradient descent of a multi-layer neural network to minimize a loss function. Mar 14, 2023 · Variational autoencoders (VAEs) are a family of deep generative models with use cases that span many applications, from image processing to bioinformatics. Mar 7, 2018 · More importantly, how do we weight latent loss with reconstruction loss when summing together for the final loss? Is it just trial and error? or is there some theory (or at least rule of thumb) for it? A Res-Net Style VAE with an adjustable perceptual loss using a pre-trained vgg19. VAEs have an additional layer containing a mean vector and standard deviation vector. They are used for generative modeling, meaning they can generate new data samples similar to the training data. 5 * torch. Variational Autoencoder Loss Function The loss function of a variational autoencoder combines the following two components − Reconstruction Loss The reconstruction loss is used to make sure that the decoder can accurately reconstruct the input from the latent space representation received from hidden layer. In this post, we present the mathematical theory behind VAEs, which Oct 2, 2023 · A Deep Dive into Variational Autoencoder with PyTorch In this tutorial, we dive deep into the fascinating world of Variational Autoencoders (VAEs). Variational Autoencoders (VAE) The goal of variational autoencoders is to constrain the latent space of an autoencoder so that it can be sampled from. Since generative models are usually evaluated with metrics such as the Frechet Inception Distance (FID) that compare the 8. There are two complimentary ways of viewing the VAE: as a probabilistic model that is fit using variational Bayesian inference, or as a type of autoencoding neural network. Apr 19, 2023 · The loss function for a VAE is typically composed of two parts: the reconstruction loss (similar to the traditional autoencoder loss) and the KL divergence loss. Mar 6, 2025 · In my previous blog, we explored maximum likelihood estimation (MLE) and how it can be used to derive commonly used loss functions. It uses stochastic gradient descent to optimize and learn the distribution of latent variables. Help Understanding Reconstruction Loss In Variational Autoencoder Ask Question Asked 7 years, 10 months ago Modified 5 years, 4 months ago Oct 9, 2025 · 3. In Bayesian machine learning, the posterior distribution is typically computationally intractable, hence Loss function for VAE The loss function of a Variational Autoencoder (VAE) is composed of two main parts: Reconstruction Loss and KL Divergence. exp(),dim=1) return recon_loss + KLD After having noticed problems in my loss convergence, even in simple tasks of 1d vectors reconstruction, I started googling around and I have Aug 1, 2023 · Let's derive some things related to variational auto-encoders (VAEs). May 7, 2021 · 由於AutoEncoder在訓練時，每筆數據皆為單一狀況，可以視為數據為Independent，在數字1及數字7中間的變化難以預計。但VAE則不相同，由於Encode向量中有加入Noise，所以數字1及數字7中間Encode向量需要同時還原回1及7，Loss計算時會使Model取一個中間值，使計算數字1及數字7時的Loss最小。因為以上原因，所以 Aug 16, 2024 · This notebook demonstrates how to train a Variational Autoencoder (VAE) (1, 2) on the MNIST dataset. Nov 2, 2024 · The β-VAE (beta Variational Autoencoder) is a modification of the traditional VAE that introduces a hyperparameter, β (beta), to balance the trade-off between the reconstruction loss and the KL . The result is the “variational autoencoder. Mar 3, 2024 · A comprehensive guide to implementing Variational Autoencoders (VAEs) in PyTorch. When trained to output the same string as the input, the loss does not decrease between epochs. Like all autoencoders, the variational autoencoder is primarily used for unsupervised learning of hidden representations. One straightforward method of discovering such a mapping is the autoencoder. Learning Goals # The goals of this notebook is to learn how to code a variational autoencoder in Keras. At its heart, a VAE still has the same structural components as a traditional autoencoder: an encoder and a decoder. Consequently, the Variational Autoencoder (VAE) finds itself in a delicate balance between the latent loss and the reconstruction loss. e How should I intuitively understand the KL divergence loss in variational autoencoders? [duplicate] Ask Question Asked 6 years, 8 months ago Modified 6 years ago Aug 5, 2016 · In this post, I'll go over the variational autoencoder, a type of network that solves these two problems. Although the reconstruction loss can be anything depending on the input and output, we will use an L1 loss to depict the term (also called the norm loss) represented by: Nov 28, 2023 · We learn the weights in an autoencoder using the same tools that we previously used for supervised learning, namely (stochastic) gradient descent of a multi-layer neural network to minimize a loss function. When you are saying the loss is too high during training, check which loss is too high, is it the reconstruction loss (MSE here) or the KL Divergence. In machine learning, a variational autoencoder (VAE) is an artificial neural network architecture introduced by Diederik P. Variational Autoencoder loss function — Image by Author As mentioned before, the latent vector is sampled from the encoder-generated distribution before feeding it to the decoder. So, let's make the model layer by layer so we can gain better insights about the model Apr 15, 2021 · As you mentioned, MSE is used to measure the difference between the original and generated images. Jul 21, 2019 · Variational Autoencoders (VAE) are one important example where variational inference is utilized. Feb 19, 2025 · Understanding the Evidence Lower Bound (ELBO) Loss in Variational Autoencoders Variational Autoencoders (VAEs) are generative models that leverage probabilistic graphical models and deep learning Oct 16, 2022 · As the name suggests, that tutorial provides examples of how to implement various kinds of autoencoders in Keras, including the variational autoencoder (VAE) 1. Because there are no global representations that are shared by all datapoints, we can decompose the loss function into only terms that depend on a single datapoint l i li. However, the goal of a variational autoencoder is not to reconstruct the original input; it’s to generate new samples that resemble the original input. For traditional vanilla VAE, the metric accuracy is 74. In this blog, we will explore how the loss function of Variational Autoencoders are derived. The following code is essentially copy-and-pasted from above, with a single term added added to the loss (autoencoder. The parameters of both the encoder and decoder networks are updated using a single pass of ordinary backprop. This approach, which we call Triplet based Variational Autoencoder (TVAE), allows us to capture more fine-grained information in the embedding. Oord et. May 3, 2020 · Variational AutoEncoder Author: fchollet Date created: 2020/05/03 Last modified: 2024/04/24 Description: Convolutional Variational AutoEncoder (VAE) trained on MNIST digits. MSE loss can be used as an additional term, which is done in CycleGAN, where the authors use LSGAN loss and cycle-consistent loss, which is MSE-like loss. Kingma et. I have tried removing the KL Divergence loss and sampling and training only the simple autoencoder. In terms of probability, the encoder is = encoder = encoder’s posterior given the input X we fix a parameterization of the posterior, and have the encoder spit out the parameters according to input Now think about what happens if we train only with reconstruction loss A smaller latent loss implies a limited encoding of information that would otherwise enhance the reconstruction loss. pow(2) - logvar. But during training, the loss function always reach to NaN, so it cant update through backward. kl). VAE is rooted in Bayesian inference, i. Learn their theoretical concept, architecture, applications, and implementation with PyTorch. There are many differences between Variational Autoencoder and Standard autoencoder but the main difference is that in variational autoencoder you are trying to predict mean and standard deviation of the latent variable Z instead of predicting Z directly. This is the one I’ve been using so far: def vae_loss(recon_loss, mu, logvar): KLD = -0. This paper was an extension of the original idea of Auto-Encoder primarily to learn the useful distribution of the data. We will discuss hyperparameters, training, and loss-functions. Apr 15, 2019 · The variational autoencoder We can fix these issues by making two changes to the autoencoder. We’ll start by unraveling the foundational concepts, exploring the roles of the encoder and decoder, and drawing comparisons between the traditional Convolutional Autoencoder (CAE) and the VAE. VAEs are latent variable generative Apr 26, 2021 · Variational Autoencoder ( VAE ) came into existence in 2013, when Diederik et al. Hence, this architecture is known as a variational autoencoder (VAE). Aug 29, 2017 · I'm experimenting with Keras (Tensorflow backend) and Variational Autoencoder. Suppose we have a distribution z z and we want to generate the observation x x from it. Jan 27, 2022 · Here, we can see that the distribution is not separable and quite skewed for different values, that's why we use KL-divergence loss in the above variational autoencoder. ” First, we map each point x in our dataset to a low-dimensional vector of means μ (x) and variances σ (x) 2 for a diagonal multivariate Gaussian distribution. The KL divergence is a metric used to measure the distance between two probability distributions. To generate data that strongly represents observations in a collection of data, you can use a variational autoencoder. This encourages the model to preserve the original content. [2] In addition to being seen as an autoencoder neural network architecture, variational autoencoders can also be studied within the May 14, 2020 · In order to train the variational autoencoder, we only need to add the auxillary loss in our training algorithm. , 2017) The features are learned by triplet loss on the mean vectors of VAE in conjunction with reconstruction loss of VAE. Code is implemented with tensorflow and keras This example shows how to train a deep learning variational autoencoder (VAE) to generate images. First, we might want to draw samples (generate) from the distribution to create new plausible values of x. Then, using neural network to learn these two distributions gives us the variational autoencoder where we use another simple distribution q (zjx) to ap-proximate the posterior distribution p (zjx) which is intractable in most of time. Dec 30, 2024 · A step-by-step guide to implementing a β-VAE in PyTorch, covering the encoder, decoder, loss function, and latent space interpolation. Jul 8, 2024 · A comprehensive guide on the concepts and PyTorch implementation of variational autoencoder. Oct 9, 2025 · Variational Autoencoder Mathematics behind Variational Autoencoder Variational autoencoder uses KL-divergence as its loss function the goal of this is to minimize the difference between a supposed distribution and original distribution of dataset. May 13, 2025 · As a variational target, it merges reconstruction loss with KL divergence, ensuring accurate data recreation while maintaining proper latent space representation. An common way of describing a neural network is an approximation of some function we wish to model. This helps in limiting Nov 11, 2018 · In the previous post of this series I introduced the Variational Autoencoder (VAE) framework, and explained the theory behind it. Unlike regular autoencoders that create fixed representations, VAEs create probability distributions. Evidence Lower Bound (ELBO) First, we'll state some assumptions. 1. Mar 31, 2025 · What is a Variational Autoencoder? Variational Autoencoders (VAEs) are a type of artificial neural network architecture that combines the power of autoencoders with probabilistic methods. Simple framework for implementation of the KL loss annealing schedule on any Variational Autoencoder (VAE) with an autoregressive decoder. Jul 23, 2025 · Convolutional Variational Autoencoder (CVAE) As we know Autoencoders used to have three layers which are Encoding layer, bottleneck or latent space layer and decoder or output layer. Jan 28, 2020 · The goal of the variational autoencoder (VAE) is to learn a probability distribution P r (x) over a multi-dimensional variable x. A VAE is a probabilistic take on the autoencoder, a model which takes high dimensional input data and compresses it into a smaller representation. This repository contains the implementations of following VAE families. al. Oct 16, 2022 · Figure 3. Introduction This story is built on top of my previous story: A Simple AutoEncoder and Latent Space Visualization with PyTorch Apr 22, 2019 · The first one will be how to use autoencoder with a sequence of data by building an LSTM network and the second use case is a called Variational Autoencoder (VAE) which is mainly used in Generative Models and generating data or images. May 12, 2024 · Additionally, the loss function of the variational autoencoder includes an additional KL divergence term in addition to the reconstruction loss. We call q (zjx) inference model or recognition model or an encoder or an approximated posterior. You could also consider looking into the BetaVAE, it applies a stronger constraint on the latent bottleneck. In this loss, you take the sum along the dimension of the latent variable: the larger the dimension of the latent variables in your autoencoder, the larger this loss will be. Mar 20, 2024 · Variational Autoencoder (VAE) [12, 24] has become a popular generative model, allowing us to formalize this problem in the framework of probabilistic graphical models with latent variables. This paper provides a comprehensive review of autoencoder architectures, from their inception and fundamental concepts to advanced implementations such as adversarial autoencoders Hi everyone, I'm trying to rebuild the VAE as in the the paper Deep Feature Consistent Variational Encoder but for larger images (160 x 320 x 1). 4(a). What are autoencoders and what purpose they serve Autoencoder is a neural architecture that consists of Abstract Tutorial: Deriving the Standard Variational Autoencoder (VAE) Loss Function Reconstruction loss alone is sufficient to optimize most autoencoders, whose sole goal is a learning compressed representation of input data that’s conducive to accurate reconstruction. However, traditional autoencoders often grapple with rigid structures that limit their ability to capture intricate nuances and generate diverse outputs. What is Variational AE? Basically a AE, but a generative model The encoder parameterizes a distribution and not just a point estimate Hence, probabilistic non-linear dimensionality reduction Feb 22, 2020 · Let’s jump back into variational inference and defining the cost function with ELBO. A smaller latent loss implies a limited encoding of information that would otherwise enhance the reconstruction loss. In this post I’ll explain the VAE in more detail, or in other words – I’ll provide some code After reading this post, you’ll understand the technical details needed to implement VAE. [1] It is part of the families of probabilistic graphical models and variational Bayesian methods. Kingma and Max Welling in 2013. It is an alternative to traditional variational autoencoders that is fast to train, stable, easy to implement, and leads to improved unsupervised feature learning. A Tutorial on Information Maximizing Variational Autoencoders (InfoVAE) Shengjia Zhao This tutorial discusses MMD variational autoencoders (MMD-VAE in short), a member of the InfoVAE family. Nov 3, 2021 · The loss function is then the sum of these two losses. We'd Autoencoders vs. Unlike a traditional autoencoder, which maps the input onto a latent vector, a VAE maps the input data into the parameters of a probability Mar 27, 2024 · A variational autoencoder is a type of generative neural network architecture. Variational Autoencoder was inspired by the methods of the variational bayesian and graphical model. Oct 17, 2025 · A variational autoencoder-generative adversarial network (VAE-GAN) is a hybrid neural network model that combines the best features of a VAE and a GAN to generate better results. Continue to help good content that is interesting, well-researched, and useful, rise to the top! To gain full voting privileges, Feb 18, 2020 · In the loss function of Variational Autoencoders there is a well known tension between two components: the reconstruction loss, improving the quality of the resulting images, and the Kullback-Leibler divergence, acting as a regularizer of the latent space. encoder. Feb 23, 2020 · In this article, we highlight what appears to be major issue of Variational Autoencoders, evinced from an extensive experimentation with different network architectures and datasets: the variance of generated data is significantly lower than that of training data. Variational Auto-Encoders The core problem in latent variable modelling is that the latent variables are never observed, so the mapping p (x | z) is not defined by the data. Oct 4, 2024 · A Variational Autoencoder (VAE) is like a special machine that learns to organize these LEGO bricks into a smaller, more manageable box called the latent space. Dec 31, 2022 · Variational AutoEncoder, and a bit KL Divergence, with PyTorch I. jeabjjqrclwqwsdjevrqdaqpnnhvezgocmphsldmgnlwfrhpddpcosyjuhsuzrhmtsewzpbsfzrlxqjamy