Mehryar Mohri is a professor and theoretical computer scientist at the Courant Institute of Mathematical Sciences. He is also heading the Machine Learning Theory (ML Theory) team at Google Research. == Career == Prior to joining the Courant Institute, Mohri was a research department head and later technology leader at AT&T Bell Labs, where he was a member of the technical staff for about ten years. Mohri has also taught as an assistant professor at the University of Paris 7 (1992-1993) and Ecole Polytechnique (1992-1994). == Research == Mohri's main area of research is machine learning, in particular learning theory. He is also an expert in automata theory and algorithms. He is the author of several core algorithms that have served as the foundation for the design of many deployed speech recognition and natural language processing systems. == Publications == Mohri is the author of the reference book Foundations of Machine Learning used as a textbook in many graduate-level machine learning courses. Mohri is also a member of the Lothaire group of mathematicians with the pseudonym M. Lothaire and contributed to the book on Applied Combinatorics on Words. He is the author of more than 250 conference and journal publications. == Organizational affiliations == Mohri is currently the President of the Association for Algorithmic Learning Theory (AALT) and the Steering Committee Chair for the ALT conference. He is also Editorial Board member of Machine Learning and TheoretiCS, Action Editor of the Journal of Machine Learning Research (JMLR) and a member of the advisory board for the Journal of Automata, Languages and Combinatorics.
AppValley
AppValley is an independent American digital distribution service operated and trademarked by AppValley LLC. It serves as an alternative app store for the iOS mobile operating system, which allows users to download applications that are not available on the App Store, most commonly tweaked "++" apps, jailbreak apps, and apps including paid apps on the app store. == Legality == AppValley is among several services that violate enterprise developer certificates from Apple. The terms under which these are granted make clear that they are for companies who wish to distribute apps to their employees. AppValley uses these certificates to distribute software directly to non-employees, thereby bypassing the AppStore. AppValley's conduct had implications in U.S. sanctioned markets like Iran, Iraq, North Korea, Cuba, and Venezuela, which have all been subject to commercial sanctions. Among the software offered by AppValley and other services is pirated software, including paid apps on the app store and premium versions of Instagram, Spotify, Pokémon Go, and others. For instance, AppValley distributes an ad-free version of the music streaming app Spotify even on the free tier. == History == The website was founded in May 2017, releasing late that month with a very basic version of the app. There were less than 100 apps available for download at this time. On Jan 19, 2018, a new version dubbed AppValley 2.0 was released bringing dark mode, more categories, a search, and a much faster interface. On February 14, 2019, a Chinese partner "Jason Wu" allegedly took control of the main Twitter account and domain, causing the original AppValley developers to migrate to the domain app-valley.vip and the Twitter account handle @App_Valley_vip. As of September 2024, the app-valley.vip domain now redirects to appvalley.signulous.com. Today, AppValley continues to offer an alternative to Apple's App Store where app developers can publish their applications. == Features == AppValley is a mobile app installer which can also support iOS version that can be installed and downloaded on the mobile or the devices of the people who wish to get access to many different applications available. AppValley also contains apps that have been modified or tweaked for user preferences, and allows the user to by pass national restrictions on the use of apps, without having to resort to jailbreaking. As of June 2, 2020, there are over 1300 apps available for download.
Evaluation of binary classifiers
Evaluation of a binary classifier typically assigns a numerical value, or values, to a classifier that represent its accuracy. An example is error rate, which measures how frequently the classifier makes a mistake. There are many metrics that can be used; different fields have different preferences. For example, in medicine sensitivity and specificity are often used, while in computer science precision and recall are preferred. An important distinction is between metrics that are independent of the prevalence or skew (how often each class occurs in the population), and metrics that depend on the prevalence – both types are useful, but they have very different properties. Often, evaluation is used to compare two methods of classification, so that one can be adopted and the other discarded. Such comparisons are more directly achieved by a form of evaluation that results in a single unitary metric rather than a pair of metrics. == Contingency table == Given a data set, a classification (the output of a classifier on that set) gives two numbers: the number of positives and the number of negatives, which add up to the total size of the set. To evaluate a classifier, one compares its output to another reference classification – ideally a perfect classification, but in practice the output of another gold standard test – and cross tabulates the data into a 2×2 contingency table, comparing the two classifications. One then evaluates the classifier relative to the gold standard by computing summary statistics of these 4 numbers. Generally these statistics will be scale invariant (scaling all the numbers by the same factor does not change the output), to make them independent of population size, which is achieved by using ratios of homogeneous functions, most simply homogeneous linear or homogeneous quadratic functions. Say we test some people for the presence of a disease. Some of these people have the disease, and our test correctly says they are positive. They are called true positives (TP). Some have the disease, but the test incorrectly claims they don't. They are called false negatives (FN). Some don't have the disease, and the test says they don't – true negatives (TN). Finally, there might be healthy people who have a positive test result – false positives (FP). These can be arranged into a 2×2 contingency table (confusion matrix), conventionally with the test result on the vertical axis and the actual condition on the horizontal axis. These numbers can then be totaled, yielding both a grand total and marginal totals. Totaling the entire table, the number of true positives, false negatives, true negatives, and false positives add up to 100% of the set. Totaling the columns (adding vertically) the number of true positives and false positives add up to 100% of the test positives, and likewise for negatives. Totaling the rows (adding horizontally), the number of true positives and false negatives add up to 100% of the condition positives (conversely for negatives). The basic marginal ratio statistics are obtained by dividing the 2×2=4 values in the table by the marginal totals (either rows or columns), yielding 2 auxiliary 2×2 tables, for a total of 8 ratios. These ratios come in 4 complementary pairs, each pair summing to 1, and so each of these derived 2×2 tables can be summarized as a pair of 2 numbers, together with their complements. Further statistics can be obtained by taking ratios of these ratios, ratios of ratios, or more complicated functions. The contingency table and the most common derived ratios are summarized below; see sequel for details. Note that the rows correspond to the condition actually being positive or negative (or classified as such by the gold standard), as indicated by the color-coding, and the associated statistics are prevalence-independent, while the columns correspond to the test being positive or negative, and the associated statistics are prevalence-dependent. There are analogous likelihood ratios for prediction values, but these are less commonly used, and not depicted above. == Pairs of metrics == Often accuracy is evaluated with a pair of metrics composed in a standard pattern. === Sensitivity and specificity === The fundamental prevalence-independent statistics are sensitivity and specificity. Sensitivity or True Positive Rate (TPR), also known as recall, is the proportion of people that tested positive and are positive (True Positive, TP) of all the people that actually are positive (Condition Positive, CP = TP + FN). It can be seen as the probability that the test is positive given that the patient is sick. With higher sensitivity, fewer actual cases of disease go undetected (or, in the case of the factory quality control, fewer faulty products go to the market). Specificity (SPC) or True Negative Rate (TNR) is the proportion of people that tested negative and are negative (True Negative, TN) of all the people that actually are negative (Condition Negative, CN = TN + FP). As with sensitivity, it can be looked at as the probability that the test result is negative given that the patient is not sick. With higher specificity, fewer healthy people are labeled as sick (or, in the factory case, fewer good products are discarded). The relationship between sensitivity and specificity, as well as the performance of the classifier, can be visualized and studied using the Receiver Operating Characteristic (ROC) curve. In theory, sensitivity and specificity are independent in the sense that it is possible to achieve 100% in both (such as in the red/blue ball example given above). In more practical, less contrived instances, however, there is usually a trade-off, such that they are inversely proportional to one another to some extent. This is because we rarely measure the actual thing we would like to classify; rather, we generally measure an indicator of the thing we would like to classify, referred to as a surrogate marker. The reason why 100% is achievable in the ball example is because redness and blueness is determined by directly detecting redness and blueness. However, indicators are sometimes compromised, such as when non-indicators mimic indicators or when indicators are time-dependent, only becoming evident after a certain lag time. The following example of a pregnancy test will make use of such an indicator. Modern pregnancy tests do not use the pregnancy itself to determine pregnancy status; rather, human chorionic gonadotropin is used, or hCG, present in the urine of gravid females, as a surrogate marker to indicate that a woman is pregnant. Because hCG can also be produced by a tumor, the specificity of modern pregnancy tests cannot be 100% (because false positives are possible). Also, because hCG is present in the urine in such small concentrations after fertilization and early embryogenesis, the sensitivity of modern pregnancy tests cannot be 100% (because false negatives are possible). === Positive and negative predictive values === In addition to sensitivity and specificity, the performance of a binary classification test can be measured with positive predictive value (PPV), also known as precision, and negative predictive value (NPV). The positive prediction value answers the question "If the test result is positive, how well does that predict an actual presence of disease?". It is calculated as TP/(TP + FP); that is, it is the proportion of true positives out of all positive results. The negative prediction value is the same, but for negatives, naturally. ==== Impact of prevalence on predictive values ==== Prevalence has a significant impact on prediction values. As an example, suppose there is a test for a disease with 99% sensitivity and 99% specificity. If 2000 people are tested and the prevalence (in the sample) is 50%, 1000 of them are sick and 1000 of them are healthy. Thus about 990 true positives and 990 true negatives are likely, with 10 false positives and 10 false negatives. The positive and negative prediction values would be 99%, so there can be high confidence in the result. However, if the prevalence is only 5%, so of the 2000 people only 100 are really sick, then the prediction values change significantly. The likely result is 99 true positives, 1 false negative, 1881 true negatives and 19 false positives. Of the 19+99 people tested positive, only 99 really have the disease – that means, intuitively, that given that a patient's test result is positive, there is only 84% chance that they really have the disease. On the other hand, given that the patient's test result is negative, there is only 1 chance in 1882, or 0.05% probability, that the patient has the disease despite the test result. === Precision and recall === Precision and recall can be interpreted as (estimated) conditional probabilities: Precision is given by P ( C = P | C ^ = P ) {\displaystyle P(C=P|{\hat {C}}=P)} while recall is given by P ( C ^ = P | C = P ) {\displaystyle P({\hat {C}}=P|C=P)} , where C ^ {\
Deep Learning Anti-Aliasing
Deep Learning Anti-Aliasing (DLAA) is a form of spatial anti-aliasing developed by Nvidia. DLAA depends on and requires Tensor Cores available in Nvidia RTX cards. DLAA is similar to Deep Learning Super Sampling (DLSS) in its anti-aliasing method, with one important differentiation being that the goal of DLSS is to increase performance at the cost of image quality, whereas the main priority of DLAA is improving image quality at the cost of performance (irrelevant of resolution upscaling or downscaling). DLAA is similar to temporal anti-aliasing (TAA) in that they are both spatial anti-aliasing solutions relying on past frame data. Compared to TAA, DLAA is substantially better when it comes to shimmering, flickering, and handling small meshes like wires. == Technical overview == DLAA collects game rendering data including raw low-resolution input, motion vectors, depth buffers, and exposure information. This information feeds into a convolutional neural network that processes the image to reduce aliasing while preserving fine detail. The neural network architecture employs an auto-encoder design trained on high-quality reference images. The training dataset includes diverse scenarios focusing on challenging cases like sub-pixel details, high-contrast edges, and transparent surfaces. The network then processes frames in real-time. Unlike traditional anti-aliasing solutions that rely on manually written heuristics, such as TAA, DLAA uses its neural network to preserve fine details while eliminating unwanted visual artifacts. == History == DLAA was initially called and marketed by Nvidia as DLSS 2x. The first game that added support for DLAA was The Elder Scrolls Online, which implemented the feature in 2021. By June 2022, DLAA was only available in six games. This number rose to 17 by February 2023. In June 2023, TechPowerUp reported that "DLAA is seeing sluggish adoption among game developers", and that Nvidia was working on adding DLAA to the quality presets of DLSS to boost adoption. By December 2023, DLAA was supported in 41 games. In early 2025, an update for the Nvidia App added a driver-based DLSS override feature that enables users to activate DLAA even in games that do not support it natively. == Differences between TAA and DLAA == TAA is used in many modern video games and game engines; however, all previous implementations have used some form of manually written heuristics to prevent temporal artifacts such as ghosting and flickering. One example of this is neighborhood clamping which forcefully prevents samples collected in previous frames from deviating too much compared to nearby pixels in newer frames. This helps to identify and fix many temporal artifacts, but deliberately removing fine details in this way is analogous to applying a blur filter, and thus the final image can appear blurry when using this method. DLAA uses an auto-encoder convolutional neural network trained to identify and fix temporal artifacts, instead of manually programmed heuristics as mentioned above. Because of this, DLAA can generally resolve detail better than other TAA and TAAU implementations, while also removing most temporal artifacts. == Differences between DLSS and DLAA == While DLSS handles upscaling with a focus on performance, DLAA handles anti-aliasing with a focus on visual quality. DLAA runs at the given screen resolution with no upscaling or downscaling functionality provided by DLAA. DLSS and DLAA share the same AI-driven anti-aliasing method. As such, DLAA functions like DLSS without the upscaling part. Both are made by Nvidia and require Tensor Cores. However, DLSS and DLAA cannot be enabled at the same time, only one can be selected depending on whether performance or image quality is prioritized. == Reception == TechPowerUp found that "[c]ompared to TAA and DLSS, DLAA is clearly producing the best image quality, especially at lower resolutions", arguing that, while "DLSS was already doing a better job than TAA at reconstructing small objects", "DLAA does an even better job". In a Cyberpunk 2077 performance test, IGN stated that "DLAA provided somewhat similar results [FPS wise] to the normal raster mode in most cases but got significant performance boost with the help of frame generation", a feature not available when using native resolution. Rock Paper Shotgun noted that, while DLAA is "not a completely perfect form of anti-aliasing, as the occasional jaggies are present", it "looks a lot sharper overall [than TAA], and especially in motion." According to PC World, "DLAA offers very good anti-aliasing without losing visual information — alternatives like TAA tend to struggle during motion-filled scenes, where DLAA doesn’t. Furthermore, DLAA’s loss of performance is lower than with conventional anti-aliasing methods."
Something Big Is Happening
"Something Big Is Happening" is an essay by Matt Shumer, an AI entrepreneur, about the impact of artificial intelligence, published in February 2026, that has since been reportedly viewed more than 80 million times and widely discussed. Shumer noted that the technology has crossed an important threshold, where AI has become capable of creating self-improving systems. Referring to one the most recent AI models, he wrote: "It was making intelligent decisions. It had something that felt, for the first time, like judgment. Like taste." Speaking to CNBC's Power Lunch, Shumer said that his "core message" is "people in the workforce should start to use and experiment with AI tools so they can understand what’s coming". Even as the essay was widely shared and discussed, the essay also elicited criticism. Paulo Carvao, in an essay published by the Forbes Magazine stated that some of his advice is sound, but added: "It reads at times like a sales pitch. He urges readers to subscribe to the most advanced AI tools. He implies that those with access to premium models will outpace those without. He frames paid AI subscriptions as a form of insurance against obsolescence." Writing in The Guardian, Dan Milmo and Aisha Down mentioned Shumer as having a history of AI hype and stated, "He previously excited the internet by announcing the release of the world's "top open-source model", which it was not". Many workers in the technology sector criticized the article in blog posts shared on Hacker News; Edward Zitron commented that "while coding LLMs can test products, or scan/fix some bugs, this suggests they A) do this autonomously without human input, B) they do this correctly every time (or ever!)." In an article alluding to Shumer's original post, Ari Colaprete wrote "the LLM is fundamentally a writing machine, it does everything via text, and if you make it produce writing that exists purely to serve some sort of mechanical function, and you train it to succeed in that task, then it will tend to do so, even with vast intricacy."
Evntlive
Evntlive was an interactive digital concert venue that allowed music fans worldwide to stream concerts to their computer, tablet, or phone. Based in Redwood City, CA, EVNTLIVE Beta launched on April 15, 2013. EVNTLIVE provided users with the ability to switch camera angles, view All Access interviews and clips from artists, buy music, and chat with other online concert-goers in the in-app feature. Users could watch live and on-demand concerts with both free and pay-per-view concerts offered. In its first two months, EVNTLIVE streamed live performances of popular artists ranging from Bon Jovi to Wale, as well as music festivals such as Taste of Country and Mountain Jam; including performances by The Lumineers, Gary Clark Jr., Phil Lesh & Friends, Primus, and more. On December 6, 2013, Evntlive was acquired and absorbed by Yahoo!. The site ceased operations and redirected viewers to Yahoo! Music and Yahoo! Screen promptly afterwards. == About the Platform == EvntLive is an HTML5, web-based platform available on laptops, iPads, and mobile devices. Users must register for a free account on Evntlive’s website in order to reserve tickets and access live and on-demand content. Once they reserve tickets, they can view All Access features from their favorite artists or bands, purchase music, and interact with other online audience members using Buzz. Users can also switch between alternate camera angles as though they are on the concert floor - sharing the experience with their friends online in real-time. EvntLive was acquired by Yahoo in December 2013 == Artists == Bon Jovi Wale Escape the Fate The Parlotones === Taste of Country Music Festival === Trace Adkins Willie Nelson Justin Moore Montgomery Gentry Craig Campbell Blackberry Smoke Gloriana Dustin Lynch LoCash Cowboys Rachel Farley Parmalee Joe Nichols === Mountain Jam Music Festival === Source: The Lumineers Primus Widespread Panic Gov't Mule Phil Lesh The Avett Brothers Dispatch Rubblebucket Michael Franti Jackie Greene Deer Tick Gary Clark Jr. ALO The London Souls Nicki Bluhm Amy Helm The Lone Bellow The Revivalists Swear and Shake Roadkill Ghost Choir Michael Bernard Fitzgerald Michele Clark 's Sunset Sessions Semi Precious Weapons Dale Earnhardt Jr. Jr. DigiTour Media Pentatonix Allstar Weekend Tyler Ward === Launch Music Festival ===
Multimodal representation learning
Multimodal representation learning is a subfield of representation learning focused on integrating and interpreting information from different modalities, such as text, images, audio, or video, by projecting them into a shared latent space. This allows for semantically similar content across modalities to be mapped to nearby points within that space, facilitating a unified understanding of diverse data types. By automatically learning meaningful features from each modality and capturing their inter-modal relationships, multimodal representation learning enables a unified representation that enhances performance in cross-media analysis tasks such as video classification, event detection, and sentiment analysis. It also supports cross-modal retrieval and translation, including image captioning, video description, and text-to-image synthesis. == Motivation == The primary motivations for multimodal representation learning arise from the inherent nature of real-world data and the limitations of unimodal approaches. Since multimodal data offers complementary and supplementary information about an object or event from different perspectives, it is more informative than relying on a single modality. A key motivation is to narrow the heterogeneity gap that exists between different modalities by projecting their features into a shared semantic subspace. This allows semantically similar content across modalities to be represented by similar vectors, facilitating the understanding of relationships and correlations between them. Multimodal representation learning aims to leverage the unique information provided by each modality to achieve a more comprehensive and accurate understanding of concepts. These unified representations are crucial for improving performance in various cross-media analysis tasks such as video classification, event detection, and sentiment analysis. They also enable cross-modal retrieval, allowing users to search and retrieve content across different modalities. Additionally, it facilitates cross-modal translation, where information can be converted from one modality to another, as seen in applications like image captioning and text-to-image synthesis. The abundance of ubiquitous multimodal data in real-world applications, including understudied areas like healthcare, finance, and human-computer interaction (HCI), further motivates the development of effective multimodal representation learning techniques. == Approaches and methods == === Canonical-correlation analysis based methods === Canonical-correlation analysis (CCA) was first introduced in 1936 by Harold Hotelling and is a fundamental approach for multimodal learning. CCA aims to find linear relationships between two sets of variables. Given two data matrices X ∈ R n × p {\displaystyle X\in \mathbb {R} ^{n\times p}} and Y ∈ R n × q {\displaystyle Y\in \mathbb {R} ^{n\times q}} representing different modalities, CCA finds projection vectors w x ∈ R p {\displaystyle w_{x}\in \mathbb {R} ^{p}} and w y ∈ R q {\displaystyle w_{y}\in \mathbb {R} ^{q}} that maximizes the correlation between the projected variables: ρ = max w x , w y w x ⊤ Σ x y w y w x ⊤ Σ x x w x w y ⊤ Σ y y w y {\displaystyle \rho =\max _{w_{x},w_{y}}{\frac {w_{x}^{\top }\Sigma _{xy}w_{y}}{{\sqrt {w_{x}^{\top }\Sigma _{xx}w_{x}}}{\sqrt {w_{y}^{\top }\Sigma _{yy}w_{y}}}}}} such that Σ x x {\displaystyle \Sigma _{xx}} and Σ y y {\displaystyle \Sigma _{yy}} are the within-modality covariance matrices, and Σ x y {\displaystyle \Sigma _{xy}} is the between-modality covariance matrix. However, standard CCA is limited by its linearity, which led to the development of nonlinear extensions, such as kernel CCA and deep CCA. ==== Kernel CCA ==== Kernel canonical correlation analysis (KCCA) extends traditional CCA to capture nonlinear relationships between modalities by implicitly mapping the data into high dimensional feature spaces using kernel functions. Given kernel functions K x {\displaystyle K_{x}} and K y {\displaystyle K_{y}} with corresponding Gram matrices K x ∈ R n × n {\displaystyle K_{x}\in \mathbb {R} ^{n\times n}} and K y ∈ R n × n {\displaystyle K_{y}\in \mathbb {R} ^{n\times n}} , KCCA seeks coefficients α {\displaystyle \alpha } and β {\displaystyle \beta } that maximize: ρ = max α , β α ⊤ K x K y β α ⊤ K x 2 α β ⊤ K y 2 β {\displaystyle \rho =\max _{\alpha ,\beta }{\frac {\alpha ^{\top }K_{x}Ky\beta }{{\sqrt {\alpha ^{\top }K_{x}^{2}\alpha }}{\sqrt {\beta ^{\top }K_{y}^{2}\beta }}}}} To prevent overfitting, regularization terms are typically added, resulting in: ρ = max α , β α T K x K y β α T ( K x 2 + λ x K x ) α β T ( K y 2 + λ y K y ) β {\displaystyle \rho =\max _{\alpha ,\beta }{\frac {\alpha ^{T}K_{x}K_{y}\beta }{{\sqrt {\alpha ^{T}\left(K_{x}^{2}+\lambda _{x}K_{x}\right)\alpha }}{\sqrt {\;\beta ^{T}\left(K_{y}^{2}+\lambda _{y}K_{y}\right)\beta }}}}} where λ x {\displaystyle \lambda _{x}} and λ y {\displaystyle \lambda _{y}} are regularization parameters. KCCA has proven effective for tasks such as cross-modal retrieval and semantic analysis, though it faces computational challenges with large datasets due to its O ( n 2 ) {\displaystyle O(n^{2})} memory requirement for sorting kernel matrices. KCCA was proposed independently by several researchers. ==== Deep CCA ==== Deep canonical correlation analysis (DCCA), introduced in 2013, employs neural networks to learn nonlinear transformations for maximizing the correlation between modalities. DCCA uses separate neural networks f x {\displaystyle f_{x}} and f y {\displaystyle f_{y}} for each modality to transform the original data before applying CCA: max W x , W y , θ x , θ y corr ( f x ( X ; θ x ) , f y ( Y ; θ y ) ) {\displaystyle \max _{W_{x},W_{y},\theta _{x},\theta _{y}}\operatorname {corr} \left(f_{x}(X;\theta _{x}),f_{y}(Y;\theta _{y})\right)} where θ x {\displaystyle \theta _{x}} and θ y {\displaystyle \theta _{y}} represent the parameters of the neural networks, and W x {\displaystyle W_{x}} and W y {\displaystyle W_{y}} are the CCA projection matrices. The correlation objective is computed as: corr ( H x , H y ) = tr ( T − 1 / 2 H x T H y S − 1 / 2 ) {\displaystyle \operatorname {corr} (H_{x},H_{y})=\operatorname {tr} \left(T^{-1/2}H_{x}^{T}H_{y}S^{-1/2}\right)} where H x = f x ( X ) {\displaystyle H_{x}=f_{x}(X)} and H y = f y ( Y ) {\displaystyle H_{y}=f_{y}(Y)} are the network outputs, T = H x T H x + r x I {\displaystyle T=H_{x}^{T}H_{x}+r_{x}I} , S = H y T H y + r y I {\displaystyle S=H_{y}^{T}H_{y}+r_{y}I} and r x , r y {\displaystyle r_{x},r_{y}} are the regularization parameters. DCCA overcomes the limitations of linear CCA and kernel CCA by learning complex nonlinear relationships while maintaining computational efficiency for large datasets through mini-batch optimization. === Graph-based methods === Graph-based approaches for multimodal representation learning leverage graph structure to model relationships between entities across different modalities. These methods typically represent each modality as a graph and then learn embedding that preserve cross-modal similarities, enabling more effective joint representation of heterogeneous data. One such method is cross-modal graph neural networks (CMGNNs) that extend traditional graph neural networks (GNNs) to handle data from multiple modalities by constructing graphs that capture both intra-modal and inter-modal relationships. These networks model interactions across modalities by representing them as nodes and their relationships as edges. Other graph-based methods include Probabilistic Graphical Models (PGMs) such as deep belief networks (DBN) and deep Boltzmann machines (DBM). These models can learn a joint representation across modalities, for instance, a multimodal DBN achieves this by adding a shared restricted Boltzmann Machine (RBM) hidden layer on top of modality-specific DBNs. Additionally, the structure of data in some domains like Human-Computer Interaction (HCI), such as the view hierarchy of app screens, can potentially be modeled using graph-like structures. The field of graph representation learning is also relevant, with ongoing progress in developing evaluation benchmarks. === Diffusion maps === Another set of methods relevant to multimodal representation learning are based on diffusion maps and their extensions to handle multiple modalities. ==== Multi-view diffusion maps ==== Multi-view diffusion maps address the challenge of achieving multi-view dimensionality reduction by effectively utilizing the availability of multiple views to extract a coherent low-dimensional representation of the data. The core idea is to exploit both the intrinsic relations within each view and the mutual relations between the different views, defining a cross-view model where a random walk process implicitly hops between objects in different views. A multi-view kernel matrix is constructed by combining these relations, defining a cross-view diffusion process and associ