Hekaton (database)

Hekaton (also known as SQL Server In-Memory OLTP) is an in-memory database for OLTP workloads built into Microsoft SQL Server. Hekaton was designed in collaboration with Microsoft Research and was released in SQL Server 2014. Traditional RDBMS systems were designed when memory resources were expensive, and were optimized for disk storage. Hekaton is instead optimized for a working set stored entirely in main memory, but is still accessible via T-SQL like normal tables. It is fundamentally different from the "DBCC PINTABLE" feature in earlier SQL Server versions. Hekaton was announced at the Professional Association for SQL Server (PASS) conference 2012.

Language model benchmark

A language model benchmark is a standardized test designed to evaluate the performance of language models on various natural language processing tasks. These tests are intended for comparing different models' capabilities in areas such as language understanding, generation, and reasoning. Benchmarks generally consist of a dataset and corresponding evaluation metrics. The dataset provides text samples and annotations, while the metrics measure a model's performance on tasks like answering questions, text classification, and machine translation. These benchmarks are developed and maintained by academic institutions, research organizations, and industry players to track progress in the field. In addition to accuracy, the metrics can include throughput, energy efficiency, bias, trust, and sustainability. == Overview == === Types === Benchmarks may be described by the following adjectives, not mutually exclusive: Classical: These tasks are studied in natural language processing, even before the advent of deep learning. Examples include the Penn Treebank for testing syntactic and semantic parsing, as well as bilingual translation benchmarked by BLEU scores. Question answering: These tasks have a text question and a text answer, often multiple-choice. They can be open-book or closed-book. Open-book QA resembles reading comprehension questions, with relevant passages included as annotation in the question, in which the answer appears. Closed-book QA includes no relevant passages. Closed-book QA is also called open-domain question-answering. Before the era of large language models, open-book QA was more common, and understood as testing information retrieval methods. Closed-book QA became common since GPT-2 as a method to measure knowledge stored within model parameters. Omnibus: An omnibus benchmark combines many benchmarks, often previously published. It is intended as an all-in-one benchmarking solution. Reasoning: These tasks are usually in the question-answering format, but are intended to be more difficult than standard question answering. Multimodal: These tasks require processing not only text, but also other modalities, such as images and sound. Examples include OCR and transcription. Agency: These tasks are for a language-model–based software agent that operates a computer for a user, such as editing images, browsing the web, etc. Adversarial: A benchmark is "adversarial" if the items in the benchmark are picked specifically so that certain models do badly on them. Adversarial benchmarks are often constructed after state of the art (SOTA) models have saturated (achieved 100% performance) a benchmark, to renew the benchmark. A benchmark is "adversarial" only at a certain moment in time, since what is adversarial may cease to be adversarial as newer SOTA models appear. Public/Private: A benchmark might be partly or entirely private, meaning that some or all of the questions are not publicly available. The idea is that if a question is publicly available, then it might be used for training, which would be "training on the test set" and invalidate the result of the benchmark. Usually, only the guardians of the benchmark have access to the private subsets, and to score a model on such a benchmark, one must send the model weights, or provide API access, to the guardians. The boundary between a benchmark and a dataset is not sharp. Generally, a dataset contains three "splits": training, test, and validation. Both the test and validation splits are essentially benchmarks. In general, a benchmark is distinguished from a test/validation dataset in that a benchmark is typically intended to be used to measure the performance of many different models that are not trained specifically for doing well on the benchmark, while a test/validation set is intended to be used to measure the performance of models trained specifically on the corresponding training set. In other words, a benchmark may be thought of as a test/validation set without a corresponding training set. Conversely, certain benchmarks may be used as a training set, such as the English Gigaword or the One Billion Word Benchmark, which in modern language is just the negative log-likelihood loss on a pretraining set with 1 billion words. Indeed, the distinction between benchmark and dataset in language models became sharper after the rise of the pretraining paradigm, whereby a model is first trained on massive, unlabeled datasets to learn general language patterns, syntax, and knowledge (pretraining), and the base model is then adapted to specific, downstream tasks using smaller, labeled datasets (fine-tuning). === Lifecycle === Generally, the life cycle of a benchmark consists of the following steps: Inception: A benchmark is published. It can be simply given as a demonstration of the power of a new model (implicitly) that others then picked up as a benchmark, or as a benchmark that others are encouraged to use (explicitly). Growth: More papers and models use the benchmark, and the performance on the benchmark grows. Maturity, degeneration or deprecation: A benchmark may be saturated, after which researchers move on to other benchmarks. Progress on the benchmark may also be neglected as the field moves to focus on other benchmarks. Renewal: A saturated benchmark can be upgraded to make it no longer saturated, allowing further progress. === Construction === Like datasets, benchmarks are typically constructed by several methods, individually or in combination: Web scraping: Ready-made question-answer pairs may be scraped online, such as from websites that teach mathematics and programming. Conversion: Items may be constructed programmatically from scraped web content, such as by blanking out named entities from sentences, and asking the model to fill in the blank. This was used for making the CNN/Daily Mail Reading Comprehension Task. Crowd sourcing: Items may be constructed by paying people to write them, such as on Amazon Mechanical Turk. This was used for making the MCTest. === Evaluation === Generally, benchmarks are fully automated. This limits the questions that can be asked. For example, with mathematical questions, "proving a claim" would be difficult to automatically check, while "calculate an answer with a unique integer answer" would be automatically checkable. With programming tasks, the answer can generally be checked by running unit tests, with an upper limit on runtime. The benchmark scores are of the following kinds: For multiple choice or cloze questions, common scores are accuracy (frequency of correct answer), precision, recall, F1 score, etc. pass@n: The model is given n {\displaystyle n} attempts to solve each problem. If any attempt is correct, the model earns a point. The pass@n score is the model's average score over all problems. k@n: The model makes n {\displaystyle n} attempts to solve each problem, but only k {\displaystyle k} attempts out of them are selected for submission. If any submission is correct, the model earns a point. The k@n score is the model's average score over all problems. cons@n: The model is given n {\displaystyle n} attempts to solve each problem. If the most common answer is correct, the model earns a point. The cons@n score is the model's average score over all problems. Here "cons" stands for "consensus" or "majority voting". The pass@n score can be estimated more accurately by making N > n {\displaystyle N>n} attempts, and use the unbiased estimator 1 − ( N − c n ) ( N n ) {\displaystyle 1-{\frac {\binom {N-c}{n}}{\binom {N}{n}}}} , where c {\displaystyle c} is the number of correct attempts. For less well-formed tasks, where the output can be any sentence, there are the following commonly used scores including BLEU ROUGE, METEOR, NIST, word error rate, LEPOR, CIDEr, and SPICE. === Issues === error: Some benchmark answers may be wrong. ambiguity: Some benchmark questions may be ambiguously worded. subjective: Some benchmark questions may not have an objective answer at all. This problem generally prevents creative writing benchmarks. Similarly, this prevents benchmarking writing proofs in natural language, though benchmarking proofs in a formal language is possible. open-ended: Some benchmark questions may not have a single answer of a fixed size. This problem generally prevents programming benchmarks from using more natural tasks such as "write a program for X", and instead uses tasks such as "write a function that implements specification X". inter-annotator agreement: Some benchmark questions may be not fully objective, such that even people would not agree with 100% on what the answer should be. This is common in natural language processing tasks, such as syntactic annotation. shortcut: Some benchmark questions may be easily solved by an "unintended" shortcut. For example, in the SNLI benchmark, having a negative word like "not" in the second sentence is a strong signal for the "Contradiction" category, regardless of what the se

Automated machine learning

Automated machine learning (AutoML) is the process of automating the tasks of applying machine learning to real-world problems. It is the combination of automation and ML. AutoML potentially includes every stage from beginning with a raw dataset to building a machine learning model ready for deployment. AutoML was proposed as an artificial intelligence-based solution to the growing challenge of applying machine learning. The high degree of automation in AutoML aims to allow non-experts to make use of machine learning models and techniques without requiring them to become experts in machine learning. Automating the process of applying machine learning end-to-end additionally offers the advantages of producing simpler solutions, faster creation of those solutions, and models that often outperform hand-designed models. Common techniques used in AutoML include hyperparameter optimization, meta-learning and neural architecture search. == Comparison to the standard approach == In a typical machine learning application, practitioners have a set of input data points to be used for training. The raw data may not be in a form that all algorithms can be applied to. To make the data amenable for machine learning, an expert may have to apply appropriate data pre-processing, feature engineering, feature extraction, and feature selection methods. After these steps, practitioners must then perform algorithm selection and hyperparameter optimization to maximize the predictive performance of their model. If deep learning is used, the architecture of the neural network must also be chosen manually by the machine learning expert. Each of these steps may be challenging, resulting in significant hurdles to using machine learning. AutoML aims to simplify these steps for non-experts, and to make it easier for them to use machine learning techniques correctly and effectively. AutoML plays an important role within the broader approach of automating data science, which also includes challenging tasks such as data engineering, data exploration and model interpretation and prediction. == Targets of automation == Automated machine learning can target various stages of the machine learning process. Steps to automate are: Data preparation and ingestion (from raw data and miscellaneous formats) Column type detection; e.g., Boolean, discrete numerical, continuous numerical, or text Column intent detection; e.g., target/label, stratification field, numerical feature, categorical text feature, or free text feature Task detection; e.g., binary classification, regression, clustering, or ranking Feature engineering Feature selection Feature extraction Meta-learning and transfer learning Detection and handling of skewed data and/or missing values Model selection - choosing which machine learning algorithm to use, often including multiple competing software implementations Ensembling - a form of consensus where using multiple models often gives better results than any single model Hyperparameter optimization of the learning algorithm and featurization Neural architecture search Pipeline selection under time, memory, and complexity constraints Selection of evaluation metrics and validation procedures Problem checking Leakage detection Misconfiguration detection Analysis of obtained results Creating user interfaces and visualizations == Challenges and Limitations == There are a number of key challenges being tackled around automated machine learning. A big issue surrounding the field is referred to as "development as a cottage industry". This phrase refers to the issue in machine learning where development relies on manual decisions and biases of experts. This is contrasted to the goal of machine learning which is to create systems that can learn and improve from their own usage and analysis of the data. Basically, it's the struggle between how much experts should get involved in the learning of the systems versus how much freedom they should be giving the machines. However, experts and developers must help create and guide these machines to prepare them for their own learning. To create this system, it requires labor intensive work with knowledge of machine learning algorithms and system design. Additionally, other challenges include meta-learning and computational resource allocation.

80 Million Tiny Images

80 Million Tiny Images is a dataset intended for training machine-learning systems constructed by Antonio Torralba, Rob Fergus, and William T. Freeman in a collaboration between MIT and New York University. It was published in 2008. The dataset has size 760 GB. It contains 79,302,017 32×32-pixel color images, scaled down from images scraped from the World Wide Web over 8 months. The images are classified into 75,062 classes. Each class is a non-abstract noun in WordNet. Images may appear in more than one class. The dataset was motivated by non-parametric models of neural activations in the visual cortex upon seeing images. The CIFAR-10 dataset uses a subset of the images in this dataset, but with independently generated labels, as the original labels were not reliable. The CIFAR-10 set has 6000 examples of each of 10 classes, and the CIFAR-100 set has 600 examples of each of 100 non-overlapping classes. == Construction == It was first reported in a technical report in April 2007, during the middle of the construction process, when there were only 73 million images. The full dataset was published in 2008. They began with all 75,846 non-abstract nouns in WordNet, and then for each of these nouns, they scraped 7 image search engines: Altavista, Ask.com, Flickr, Cydral, Google, Picsearch, and Webshots. After 8 months of scraping, they obtained 97,245,098 images. Since they did not have enough storage, they downsized the images to 32×32 as they were scraped. After gathering, they removed images with zero variance and intra-word duplicate images, resulting in the final dataset. Out of the 75,846 nouns, only 75,062 classes had any results, so the other nouns did not appear in the final dataset. The number of images per noun follows a Zipf-like distribution, with 1056 images per noun on average. To prevent a few nouns taking up too many images, they put an upper bound of at most 3000 images per noun. == Retirement == The 80 Million Tiny Images dataset was retired from use by its creators in 2020, after a paper by researchers Abeba Birhane and Vinay Prabhu found that some of the labeling of several publicly available image datasets, including 80 Million Tiny Images, contained racist and misogynistic slurs which were causing models trained on them to exhibit racial and sexual bias. The dataset also contained offensive images. Following the release of the paper, the dataset's creators removed the dataset from distribution, and requested that other researchers not use it for further research and to delete their copies of the dataset.

Knowledge graph embedding

In representation learning, knowledge graph embedding (KGE), also called knowledge representation learning (KRL), or multi-relation learning, is a machine learning task of learning a low-dimensional representation of a knowledge graph's entities and relations while preserving their semantic meaning. Leveraging their embedded representation, knowledge graphs can be used for various applications such as link prediction, triple classification, entity recognition, clustering, and relation extraction. == Definition == A knowledge graph G = { E , R , F } {\displaystyle {\mathcal {G}}=\{E,R,F\}} is a collection of entities E {\displaystyle E} , relations R {\displaystyle R} , and facts F {\displaystyle F} . A fact is a triple ( h , r , t ) ∈ F {\displaystyle (h,r,t)\in F} that denotes a link r ∈ R {\displaystyle r\in R} between the head h ∈ E {\displaystyle h\in E} and the tail t ∈ E {\displaystyle t\in E} of the triple. Another notation that is often used in the literature to represent a triple (or fact) is ⟨ head , relation , tail ⟩ {\displaystyle \langle {\text{head}},{\text{relation}},{\text{tail}}\rangle } . This notation is called the Resource Description Framework (RDF). A knowledge graph represents the knowledge related to a specific domain; leveraging this structured representation, it is possible to infer a piece of new knowledge from it after some refinement steps. However, nowadays, people have to deal with the sparsity of data and the computational inefficiency to use them in a real-world application. The embedding of a knowledge graph is a function that translates each entity and each relation into a vector of a given dimension d {\displaystyle d} , called embedding dimension. It is even possible to embed the entities and relations with different dimensions. The embedding vectors can then be used for other tasks. A knowledge graph embedding is characterized by four aspects: Representation space: The low-dimensional space in which the entities and relations are represented. Scoring function: A measure of the goodness of a triple-embedded representation. Encoding models: The modality in which the embedded representation of the entities and relations interact with each other. Additional information: Any additional information coming from the knowledge graph that can enrich the embedded representation. Usually, an ad hoc scoring function is integrated into the general scoring function for each additional piece of information. == Embedding procedure == All algorithms for creating a knowledge graph embedding follow the same approach. First, the embedding vectors are initialized to random values. Then, they are iteratively optimized using a training set of triples. In each iteration, a batch of size b {\displaystyle b} triples is sampled from the training set, and a triple from it is sampled and corrupted—i.e., a triple that does not represent a true fact in the knowledge graph. The corruption of a triple involves substituting the head or the tail (or both) of the triple with another entity that makes the fact false. The original triple and the corrupted triple are added in the training batch, and then the embeddings are updated, optimizing a scoring function. Iteration stops when a stop condition is reached. Usually, the stop condition depends on the overfitting of the training set. At the end, the learned embeddings should have extracted semantic meaning from the training triples and should correctly predict unseen true facts in the knowledge graph. === Pseudocode === The following is the pseudocode for the general embedding procedure. algorithm Compute entity and relation embeddings input: The training set S = { ( h , r , t ) } {\displaystyle S=\{(h,r,t)\}} , entity set E {\displaystyle E} , relation set R {\displaystyle R} , embedding dimension k {\displaystyle k} output: Entity and relation embeddings initialization: the entities e {\displaystyle e} and relations r {\displaystyle r} embeddings (vectors) are randomly initialized while stop condition do S b a t c h ← s a m p l e ( S , b ) {\displaystyle S_{batch}\leftarrow sample(S,b)} // Sample a batch from the training set for each ( h , r , t ) {\displaystyle (h,r,t)} in S b a t c h {\displaystyle S_{batch}} do ( h ′ , r , t ′ ) ← s a m p l e ( S ′ ) {\displaystyle (h',r,t')\leftarrow sample(S')} // Sample a corrupted fact T b a t c h ← T b a t c h ∪ { ( ( h , r , t ) , ( h ′ , r , t ′ ) ) } {\displaystyle T_{batch}\leftarrow T_{batch}\cup \{((h,r,t),(h',r,t'))\}} end for Update embeddings by minimizing the loss function end while == Performance indicators == These indexes are often used to measure the embedding quality of a model. The simplicity of the indexes makes them very suitable for evaluating the performance of an embedding algorithm even on a large scale. Given Q {\displaystyle {\ce {Q}}} as the set of all ranked predictions of a model, it is possible to define three different performance indexes: Hits@K, MR, and MRR. === Hits@K === Hits@K or in short, H@K, is a performance index that measures the probability to find the correct prediction in the first top K model predictions. Usually, it is used k = 10 {\displaystyle k=10} . Hits@K reflects the accuracy of an embedding model to predict the relation between two given triples correctly. Hits@K = | { q ∈ Q : q < k } | | Q | ∈ [ 0 , 1 ] {\displaystyle ={\frac {|\{q\in Q:q

Yahoo Groups

Yahoo! Groups was a free-to-use system of electronic mailing lists offered by Yahoo!. Prior to February 2020, Yahoo! Groups was one of the world's largest collections of online discussion boards. It allowed members to subscribe to various groups, read subscribed discussions online, view and share photos, files and bookmarks within a group, access a group calendar, create polls for group members, and receive email notifications of new discussion topics. Some groups were simply announcement boards, to which only the group moderators could post, while others were discussion forums. Depending on each group's settings, membership could be open to everyone or only to invited or approved people. On February 1, 2020, Yahoo! removed online access to discussions and all other features except simple membership management, essentially turning all groups into mailing lists, and on October 13, 2020, it announced that Yahoo Groups would shut down completely on December 15, 2020. == History == In 1998 Yahoo! Clubs was launched as an extension of services developed by Yahoo! Messenger. In August 2000 Yahoo acquired eGroups.com. Yahoo! Groups was launched in early 2001 as an integration of technology from eGroups.com and community groups from both eGroups.com and Yahoo! Clubs. In 2001 Yahoo! deleted adult groups from its search directory, making it very difficult to locate Yahoo! groups with adult content. The Groups Updates Email feature was introduced in 2010. It summarized, in a single email, all the updates that occurred every twenty-four hours in all groups. In September 2010, a major facelift was rolled out, making Yahoo! Groups look very similar to Facebook. In December, Yahoo! Groups Japan emailed its users and posted a notice on its homepage, to announce that its service, which commenced in February 2004, would be closing on May 28, 2014. In October 2019, Yahoo! announced that all content that had been posted to Yahoo! Groups will be deleted on December 14, 2019; that date was later amended to January 31, 2020. Yahoo! announced that adding new content would be blocked on October 28, 2019. Once the content was deleted, users of Yahoo! Groups were only able to browse the group directory, request invitations and, if members of a group, send messages to that group. On October 13, 2020, Yahoo! announced they would be shutting down Yahoo! Groups on December 15, 2020. The site was closed down a few days after the advertised date, displaying a message that the service was officially shut down. This message stopped appearing at the end of January 2021 and the Yahoo! Groups web address began redirecting to the main Yahoo! page. === Criticism and controversy === On August 31, 2010, Yahoo! Groups started rolling out a major software change, which was denounced by a large number of users. The re-model was completely abandoned on January 12, 2011. == Site statistics == In August 2008, Yahoo! Group staff reported that there were 113 million users, and nine million Groups using 22 languages. In July 2010, the web analytics website Quantcast reported around 915 thousand unique visitors daily to the Yahoo! Groups website (US). In January 2011, that number had increased to 933 thousand unique visitors daily. The number did not include Yahoo! Group members who accessed the Groups site via email. In September 2010, at its "Product Runway" event, Yahoo! told reporters that Yahoo! Groups had 115 million group members and that there were 10 million Yahoo! groups. == Archives ==

Energy-based model

An energy-based model (EBM), also called Canonical Ensemble Learning (CEL) or Learning via Canonical Ensemble (LCE), is an application of canonical ensemble formulation from statistical physics for learning from data. The approach prominently appears in generative artificial intelligence. EBMs provide a unified framework for many probabilistic and non-probabilistic approaches to such learning, particularly for training graphical and other structured models. An EBM learns the characteristics of a target dataset and generates a similar but larger dataset. EBMs detect the latent variables of a dataset and generate new datasets with a similar distribution. Energy-based generative neural networks is a class of generative models, which aim to learn explicit probability distributions of data in the form of energy-based models, the energy functions of which are parameterized by modern deep neural networks. Boltzmann machines are a special form of energy-based models with a specific parametrization of the energy. == Description == For a given input x {\displaystyle x} , the model describes an energy E θ ( x ) {\displaystyle E_{\theta }(x)} such that the Boltzmann distribution P θ ( x ) = e − β E θ ( x ) Z ( θ ) {\displaystyle P_{\theta }(x)={e^{-\beta E_{\theta }(x)} \over Z(\theta )}} is a probability (density), and typically β = 1 {\displaystyle \beta =1} . Since the normalization constant: Z ( θ ) := ∫ x ∈ X e − β E θ ( x ) d x {\displaystyle Z(\theta ):=\int _{x\in X}e^{-\beta E_{\theta }(x)}dx} (also known as the partition function) depends on all the Boltzmann factors of all possible inputs x {\displaystyle x} , it cannot be easily computed or reliably estimated during training simply using standard maximum likelihood estimation. However, for maximizing the likelihood during training, the gradient of the log-likelihood of a single training example x {\displaystyle x} is given by using the chain rule: ∂ θ log ⁡ ( P θ ( x ) ) = E x ′ ∼ P θ [ ∂ θ E θ ( x ′ ) ] − ∂ θ E θ ( x ) ( ∗ ) {\displaystyle \partial _{\theta }\log \left(P_{\theta }(x)\right)=\mathbb {E} _{x'\sim P_{\theta }}[\partial _{\theta }E_{\theta }(x')]-\partial _{\theta }E_{\theta }(x)\,()} The expectation in the above formula for the gradient can be approximately estimated by drawing samples x ′ {\displaystyle x'} from the distribution P θ {\displaystyle P_{\theta }} using Markov chain Monte Carlo (MCMC). Early energy-based models, such as the 2003 Boltzmann machine by Hinton, estimated this expectation via blocked Gibbs sampling. Newer approaches make use of more efficient Stochastic Gradient Langevin Dynamics (LD), drawing samples using: x 0 ′ ∼ P 0 , x i + 1 ′ = x i ′ − α 2 ∂ E θ ( x i ′ ) ∂ x i ′ + ϵ {\displaystyle x_{0}'\sim P_{0},x_{i+1}'=x_{i}'-{\frac {\alpha }{2}}{\frac {\partial E_{\theta }(x_{i}')}{\partial x_{i}'}}+\epsilon } , where ϵ ∼ N ( 0 , α ) {\displaystyle \epsilon \sim {\mathcal {N}}(0,\alpha )} . A replay buffer of past values x i ′ {\displaystyle x_{i}'} is used with LD to initialize the optimization module. The parameters θ {\displaystyle \theta } of the neural network are therefore trained in a generative manner via MCMC-based maximum likelihood estimation: the learning process follows an "analysis by synthesis" scheme, where within each learning iteration, the algorithm samples the synthesized examples from the current model by a gradient-based MCMC method (e.g., Langevin dynamics or Hybrid Monte Carlo), and then updates the parameters θ {\displaystyle \theta } based on the difference between the training examples and the synthesized ones – see equation ( ∗ ) {\displaystyle ()} . This process can be interpreted as an alternating mode seeking and mode shifting process, and also has an adversarial interpretation. Essentially, the model learns a function E θ {\displaystyle E_{\theta }} that associates low energies to correct values, and higher energies to incorrect values. After training, given a converged energy model E θ {\displaystyle E_{\theta }} , the Metropolis–Hastings algorithm can be used to draw new samples. The acceptance probability is given by: P a c c ( x i → x ∗ ) = min ( 1 , P θ ( x ∗ ) P θ ( x i ) ) . {\displaystyle P_{acc}(x_{i}\to x^{})=\min \left(1,{\frac {P_{\theta }(x^{})}{P_{\theta }(x_{i})}}\right).} == History == The term "energy-based models" was first coined in a 2003 JMLR paper where the authors defined a generalisation of independent components analysis to the overcomplete setting using EBMs. Other early work on EBMs proposed models that represented energy as a composition of latent and observable variables. == Characteristics == EBMs demonstrate useful properties: Simplicity and stability. The EBM is the only object that needs to be designed and trained. Separate networks need not be trained to ensure balance. Adaptive computation time. An EBM can generate sharp, diverse samples or (more quickly) coarse, less diverse samples. Given infinite time, this procedure produces true samples. Flexibility. In Variational Autoencoders (VAE) and flow-based models, the generator learns a map from a continuous space to a (possibly) discontinuous space containing different data modes. EBMs can learn to assign low energies to disjoint regions (multiple modes). Adaptive generation. EBM generators are implicitly defined by the probability distribution, and automatically adapt as the distribution changes (without training), allowing EBMs to address domains where generator training is impractical, as well as minimizing mode collapse and avoiding spurious modes from out-of-distribution samples. Compositionality. Individual models are unnormalized probability distributions, allowing models to be combined through product of experts or other hierarchical techniques. == Experimental results == On image datasets such as CIFAR-10 and ImageNet 32x32, an EBM model generated high-quality images relatively quickly. It supported combining features learned from one type of image for generating other types of images. It was able to generalize using out-of-distribution datasets, outperforming flow-based and autoregressive models. EBM was relatively resistant to adversarial perturbations, behaving better than models explicitly trained against them with training for classification. == Applications == Target applications include natural language processing, robotics and computer vision. The first energy-based generative neural network is the generative ConvNet proposed in 2016 for image patterns, where the neural network is a convolutional neural network. The model has been generalized to various domains to learn distributions of videos, and 3D voxels. They are made more effective in their variants. They have proven useful for data generation (e.g., image synthesis, video synthesis, 3D shape synthesis, etc.), data recovery (e.g., recovering videos with missing pixels or image frames, 3D super-resolution, etc), data reconstruction (e.g., image reconstruction and linear interpolation ). == Alternatives == EBMs compete with techniques such as variational autoencoders (VAEs), generative adversarial networks (GANs) or normalizing flows. == Extensions == === Joint energy-based models === Joint energy-based models (JEM), proposed in 2020 by Grathwohl et al., allow any classifier with softmax output to be interpreted as energy-based model. The key observation is that such a classifier is trained to predict the conditional probability p θ ( y | x ) = e f → θ ( x ) [ y ] ∑ j = 1 K e f → θ ( x ) [ j ] for y = 1 , … , K and f → θ = ( f 1 , … , f K ) ∈ R K , {\displaystyle p_{\theta }(y|x)={\frac {e^{{\vec {f}}_{\theta }(x)[y]}}{\sum _{j=1}^{K}e^{{\vec {f}}_{\theta }(x)[j]}}}\ \ {\text{ for }}y=1,\dotsc ,K{\text{ and }}{\vec {f}}_{\theta }=(f_{1},\dotsc ,f_{K})\in \mathbb {R} ^{K},} where f → θ ( x ) [ y ] {\displaystyle {\vec {f}}_{\theta }(x)[y]} is the y-th index of the logits f → {\displaystyle {\vec {f}}} corresponding to class y. Without any change to the logits it was proposed to reinterpret the logits to describe a joint probability density: p θ ( y , x ) = e f → θ ( x ) [ y ] Z ( θ ) , {\displaystyle p_{\theta }(y,x)={\frac {e^{{\vec {f}}_{\theta }(x)[y]}}{Z(\theta )}},} with unknown partition function Z ( θ ) {\displaystyle Z(\theta )} and energy E θ ( x , y ) = − f θ ( x ) [ y ] {\displaystyle E_{\theta }(x,y)=-f_{\theta }(x)[y]} . By marginalization, we obtain the unnormalized density p θ ( x ) = ∑ y p θ ( y , x ) = ∑ y e f → θ ( x ) [ y ] Z ( θ ) =: e − E θ ( x ) , {\displaystyle p_{\theta }(x)=\sum _{y}p_{\theta }(y,x)=\sum _{y}{\frac {e^{{\vec {f}}_{\theta }(x)[y]}}{Z(\theta )}}=:e^{-E_{\theta }(x)},} therefore, E θ ( x ) = − log ⁡ ( ∑ y e f → θ ( x ) [ y ] Z ( θ ) ) , {\displaystyle E_{\theta }(x)=-\log \left(\sum _{y}{\frac {e^{{\vec {f}}_{\theta }(x)[y]}}{Z(\theta )}}\right),} so that any classifier can be used to define an energy function E θ ( x ) {\displaystyle E_{\theta }(x)} .