End-to-end encryption (E2EE) is a method of implementing a secure communication system where only the sender and intended recipient can read the messages. No one else, including the system provider, telecom providers, Internet providers or malicious actors, can access the cryptographic keys needed to read or send messages. End-to-end encryption prevents data from being read or secretly modified, except by the sender and intended recipients. In many applications, messages are relayed from a sender to some recipients by a service provider. In an E2EE-enabled service, messages are encrypted on the sender's device such that no third party, including the service provider, has the means to decrypt them. The recipients retrieve encrypted messages and decrypt them independently on their own devices. Since third parties cannot decrypt the data being communicated or stored, services with E2EE are better at protecting user data from data breaches and espionage. Computer security experts, digital freedom organizations, and human rights activists advocate for the use of E2EE due to its security and privacy benefits, including its ability to resist mass surveillance. Popular messaging apps like WhatsApp, iMessage, Facebook Messenger, and Signal use end-to-end encryption for chat messages, with some also supporting E2EE of voice and video calls. As of May 2025, WhatsApp is the most widely used E2EE messaging service, with over 3 billion users. Meanwhile, Signal with an estimated 70 million users, is regarded as the current gold standard in secure messaging by cryptographers, protestors, and journalists. Since end-to-end encrypted services cannot offer decrypted messages in response to government requests, the proliferation of E2EE has been met with controversy. Around the world, governments, law enforcement agencies, and child protection groups have expressed concerns over its impact on criminal investigations. As of 2025, some governments have successfully passed legislation targeting E2EE, such as Australia's Telecommunications and Other Legislation Amendment Act (2018) and the Online Safety Act (2023) in the UK. Other attempts at restricting E2EE include the EARN IT Act in the US and the Child Sexual Abuse Regulation in the EU.[1] Nevertheless, some government bodies such as the UK's Information Commissioner's Office and the US's Cybersecurity and Infrastructure Security Agency (CISA) have argued for the use of E2EE, with Jeff Greene of the CISA advising that "encryption is your friend" following the discovery of the Salt Typhoon espionage campaign in 2024. == Definitions == End-to-end encryption is a means of ensuring the security of communications in applications like secure messaging. Under E2EE, messages are encrypted on the sender's device such that they can be decoded only by the final recipient's device. In many non-E2EE messaging systems, including email and many chat platforms, messages pass through intermediaries and are stored by a third party service provider, from which they are retrieved by the recipient. Even if messages are encrypted, they are only encrypted 'in transit', and are thus accessible by the service provider. Server-side disk encryption is also distinct from E2EE because it does not prevent the service provider from viewing the information, as they have the encryption keys and can simply decrypt it. The term "end-to-end encryption" originally only meant that the communication is never decrypted during its transport from the sender to the receiver. For example, around 2003, E2EE was proposed as an additional layer of encryption for GSM or TETRA, in addition to the existing radio encryption protecting the communication between the mobile device and the network infrastructure. This has been standardized by SFPG for TETRA. Note that in TETRA, the keys are generated by a Key Management Centre (KMC) or a Key Management Facility (KMF), not by the communicating users. Later, around 2014, the meaning of "end-to-end encryption" started to evolve when WhatsApp encrypted a portion of its network, requiring that not only the communication stays encrypted during transport, but also that the provider of the communication service is not able to decrypt the communications—maliciously or when requested by law enforcement agencies. Similarly, messages must be undecryptable in transit by attackers through man-in-the-middle attacks. This new meaning is now the widely accepted one. == Motivations == The lack of end-to-end encryption can allow service providers to easily provide search and other features, or to scan for illegal and unacceptable content. However, it also means that content can be read by anyone who has access to the data stored by the service provider, by design or via a backdoor. This can be a concern in many cases where privacy is important, such as in governmental and military communications, financial transactions, and when sensitive information such as health and biometric data are sent. If this content were shared without E2EE, a malicious actor or adversarial government could obtain it through unauthorized access or subpoenas targeted at the service provider. E2EE alone does not guarantee privacy or security. For example, the data may be held unencrypted on the user's own device or accessed through their own app if their credentials are compromised. == Modern implementations == === Messaging === In May 2026, Meta ended support for end-to-end encryption (E2EE) on Instagram, reversing a previous commitment to expand the technology across its messaging services. The company justified the move as a measure to mitigate fraudulent activity and facilitate the detection of harmful content. The decision highlighted a conflict between digital privacy and online safety; while child protection organizations supported the change to better identify predatory behavior, privacy advocates argued that removing E2EE compromises user security. As of 2025, messaging apps like Signal and WhatsApp are designed to exclusively use end-to-end encryption. Both Signal and WhatsApp use the Signal Protocol. Other messaging apps and protocols that support end-to-end encryption include Facebook Messenger, iMessage, Telegram, Matrix, and Keybase. Although Telegram supports end-to-end encryption, it has been criticized for not enabling it by default, instead supporting E2EE through opt-in "secret chats". As of 2020, Telegram did not support E2EE for group chats and no E2EE on its desktop clients. In 2022, after controversy over the use of Facebook Messenger messages in an abortion lawsuit in Nebraska, Facebook added support for end-to-end encryption in the Messenger app. Writing for Wired, technologist Albert Fox Cahn criticized Messenger's approach to end-to-end encryption, which required the user to opt into E2EE for each conversation and split the message thread into two chats which were easy for users to confuse. In December 2023, Facebook announced plans to enable end-to-end encryption by default despite pressure from British law enforcement agencies. As of 2016, many server-based communications systems did not include end-to-end encryption. These systems can only guarantee the protection of communications between clients and servers, meaning that users have to trust the third parties who are running the servers with the sensitive content. End-to-end encryption is regarded as safer because it reduces the number of parties who might be able to interfere or break the encryption. In the case of instant messaging, users may use a third-party client or plugin to implement an end-to-end encryption scheme over an otherwise non-E2EE protocol. === Audio and video conferencing === Signal and WhatsApp use end-to-end encryption for audio and video calls. Since 2020, Signal has also supported end-to-encrypted video calls. In 2024, Discord added end-to-end encryption for audio and video calls, voice channels, and certain live streams. However, they had no plans to implement E2EE for messages. In 2020, after acquiring Keybase, Zoom announced end-to-end encryption would be limited to paid accounts. Following criticism from human rights advocates, Zoom extended the feature to all users with accounts. In 2021, Zoom settled an $85M class action lawsuit over past misrepresentation about end-to-end encryption. The FTC confirmed Zoom previously retained access to meeting keys. === Other uses === Some encrypted backup and file sharing services provide client-side encryption. Nextcloud and MEGA, offer end-to-end encryption of shared files. The term "end-to-end encryption" is sometimes incorrectly used to describe client-side encryption. Some non-E2EE systems, such as Lavabit and Hushmail, have described themselves as offering "end-to-end" encryption when they did not. == Law enforcement and regulation == In 2022, Facebook Messenger came under scrutiny because the messages between a mother and daughter in Nebraska were used to seek criminal charges in an abortion-rel
Vujak
VuJak is an early video sampler, a VJ remix and mashup tool created in 1992 by Brian Kane, Lisa Eisenpresser, and Jay Haynes. The original name of the project was Mideo, but it was later changed to VuJak. VuJak was based on MIDI control of video in real-time. It was created with MAX from Opcode Systems, and utilized the newly released QuickTime 1.0 movie object. The first working version of the program was built on a Mac IIfx with 8 megs of ram, and could jump in real-time across a 160 x 120 pixel QuickTime movie via a midi keyboard. Later versions could manipulate full screen video, included the first real-time video scratch feature, had looping, vari-speed, and random play features, and allowed for recording and editing of video sequences within the application. VuJak also had networking capabilities which allowed artists to "jam" in real time across standard phone lines. The first public exhibition of VuJak was at the Digital Hollywood conference in Beverly Hills in 1993, where it was promoted by Timothy Leary. VuJak was featured in Mondo 2000, CBS Evening News, Wired Magazine, Electronic Musician, Billboard Magazine, The Hollywood Reporter, and it was used to create promotional videos for MTV. In 1994, VuJak was a featured interactive exhibition at the Exploratorium in San Francisco. Development of VuJak ceased in 1995.
Soft independent modelling of class analogies
Soft independent modelling by class analogy (SIMCA) is a statistical method for supervised classification of data. The method requires a training data set consisting of samples (or objects) with a set of attributes and their class membership. The term soft refers to the fact the classifier can identify samples as belonging to multiple classes and not necessarily producing a classification of samples into non-overlapping classes. == Method == In order to build the classification models, the samples belonging to each class need to be analysed using principal component analysis (PCA); only the significant components are retained. For a given class, the resulting model then describes either a line (for one Principal Component or PC), plane (for two PCs) or hyper-plane (for more than two PCs). For each modelled class, the mean orthogonal distance of training data samples from the line, plane, or hyper-plane (calculated as the residual standard deviation) is used to determine a critical distance for classification. This critical distance is based on the F-distribution and is usually calculated using 95% or 99% confidence intervals. New observations are projected into each PC model and the residual distances calculated. An observation is assigned to the model class when its residual distance from the model is below the statistical limit for the class. The observation may be found to belong to multiple classes and a measure of goodness of the model can be found from the number of cases where the observations are classified into multiple classes. The classification efficiency is usually indicated by Receiver operating characteristics. In the original SIMCA method, the ends of the hyper-plane of each class are closed off by setting statistical control limits along the retained principal components axes (i.e., score value between plus and minus 0.5 times score standard deviation). More recent adaptations of the SIMCA method close off the hyper-plane by construction of ellipsoids (e.g. Hotelling's T2 or Mahalanobis distance). With such modified SIMCA methods, classification of an object requires both that its orthogonal distance from the model and its projection within the model (i.e. score value within the region defined by the ellipsoid) are not significant. == Application == SIMCA as a method of classification has gained widespread use especially in applied statistical fields such as chemometrics and spectroscopic data analysis.
Multilinear principal component analysis
Multilinear principal component analysis (MPCA) is a multilinear extension of principal component analysis (PCA) that is used to analyze M-way arrays, also informally referred to as "data tensors". M-way arrays may be modeled by linear tensor models, such as CANDECOMP/Parafac, or by multilinear tensor models, such as multilinear principal component analysis (MPCA) or multilinear (tensor) independent component analysis (MICA). In 2005, Vasilescu and Terzopoulos introduced the Multilinear PCA terminology as a way to better differentiate between multilinear data models that employed 2nd order statistics versus higher order statistics to compute a set of independent components for each mode, such as Multilinear ICA Multilinear PCA may be applied to compute the causal factors of data formation, or as signal processing tool on data tensors whose individual observation have either been vectorized, or whose observations are treated as a collection of column/row observations, an "observation as a matrix", and concatenated into a data tensor. The latter approach is suitable for compression and reducing redundancy in the rows, columns and fibers that are unrelated to the causal factors of data formation. Vasilescu and Terzopoulos in their paper "TensorFaces" introduced the M-mode SVD algorithm which are algorithms misidentified in the literature as the HOSVD or the Tucker which employ the power method or gradient descent, respectively. Vasilescu and Terzopoulos framed the data analysis, recognition and synthesis problems as multilinear tensor problems. Data is viewed as the compositional consequence of several causal factors, that are well suited for multi-modal tensor factor analysis. The power of the tensor framework was showcased by analyzing human motion joint angles, facial images or textures in the following papers: Human Motion Signatures (CVPR 2001, ICPR 2002), face recognition – TensorFaces, (ECCV 2002, CVPR 2003, etc.) and computer graphics – TensorTextures (Siggraph 2004). == The algorithm == The MPCA solution follows the alternating least square (ALS) approach. It is iterative in nature. As in PCA, MPCA works on centered data. Centering is a little more complicated for tensors, and it is problem dependent. == Feature selection == MPCA features: Supervised MPCA is employed in causal factor analysis that facilitates object recognition while a semi-supervised MPCA feature selection is employed in visualization tasks. == Extensions == Various extension of MPCA: Robust MPCA (RMPCA) Multi-Tensor Factorization, that also finds the number of components automatically (MTF)
Optical neural network
An optical neural network is a physical implementation of an artificial neural network with optical components. Early optical neural networks used a photorefractive Volume hologram to interconnect arrays of input neurons to arrays of output with synaptic weights in proportion to the multiplexed hologram's strength. Volume holograms were further multiplexed using spectral hole burning to add one dimension of wavelength to space to achieve four dimensional interconnects of two dimensional arrays of neural inputs and outputs. This research led to extensive research on alternative methods using the strength of the optical interconnect for implementing neuronal communications. Some artificial neural networks that have been implemented as optical neural networks include the Hopfield neural network and the Kohonen self-organizing map with liquid crystal spatial light modulators Optical neural networks can also be based on the principles of neuromorphic engineering, creating neuromorphic photonic systems. Typically, these systems encode information in the networks using spikes, mimicking the functionality of spiking neural networks in optical and photonic hardware. Photonic devices that have demonstrated neuromorphic functionalities include (among others) vertical-cavity surface-emitting lasers, integrated photonic modulators, optoelectronic systems based on superconducting Josephson junctions or systems based on resonant tunnelling diodes. == Electrochemical vs. optical neural networks == Biological neural networks function on an electrochemical basis, while optical neural networks use electromagnetic waves. Optical interfaces to biological neural networks can be created with optogenetics, but is not the same as an optical neural networks. In biological neural networks there exist a lot of different mechanisms for dynamically changing the state of the neurons, these include short-term and long-term synaptic plasticity. Synaptic plasticity is among the electrophysiological phenomena used to control the efficiency of synaptic transmission, long-term for learning and memory, and short-term for short transient changes in synaptic transmission efficiency. Implementing this with optical components is difficult, and ideally requires advanced photonic materials. Properties that might be desirable in photonic materials for optical neural networks include the ability to change their efficiency of transmitting light, based on the intensity of incoming light. == Rising Era of Optical Neural Networks == With the increasing significance of computer vision in various domains, the computational cost of these tasks has increased, making it more important to develop the new approaches of the processing acceleration. Optical computing has emerged as a potential alternative to GPU acceleration for modern neural networks, particularly considering the looming obsolescence of Moore's Law. Consequently, optical neural networks have garnered increased attention in the research community. Presently, two primary methods of optical neural computing are under research: silicon photonics-based and free-space optics. Each approach has its benefits and drawbacks; while silicon photonics may offer superior speed, it lacks the massive parallelism that free-space optics can deliver. Given the substantial parallelism capabilities of free-space optics, researchers have focused on taking advantage of it. One implementation, proposed by Lin et al., involves the training and fabrication of phase masks for a handwritten digit classifier. By stacking 3D-printed phase masks, light passing through the fabricated network can be read by a photodetector array of ten detectors, each representing a digit class ranging from 1 to 10. Although this network can achieve terahertz-range classification, it lacks flexibility, as the phase masks are fabricated for a specific task and cannot be retrained. An alternative method for classification in free-space optics, introduced by Cahng et al., employs a 4F system that is based on the convolution theorem to perform convolution operations. This system uses two lenses to execute the Fourier transforms of the convolution operation, enabling passive conversion into the Fourier domain without power consumption or latency. However, the convolution operation kernels in this implementation are also fabricated phase masks, limiting the device's functionality to specific convolutional layers of the network only. In contrast, Li et al. proposed a technique involving kernel tiling to use the parallelism of the 4F system while using a Digital Micromirror Device (DMD) instead of a phase mask. This approach allows users to upload various kernels into the 4F system and execute the entire network's inference on a single device. Unfortunately, modern neural networks are not designed for the 4F systems, as they were primarily developed during the CPU/GPU era. Mostly because they tend to use a lower resolution and a high number of channels in their feature maps. == Other Implementations == In 2007 there was one model of Optical Neural Network: the Programmable Optical Array/Analogic Computer (POAC). It had been implemented in the year 2000 and reported based on modified Joint Fourier Transform Correlator (JTC) and Bacteriorhodopsin (BR) as a holographic optical memory. Full parallelism, large array size and the speed of light are three promises offered by POAC to implement an optical CNN. They had been investigated during the last years with their practical limitations and considerations yielding the design of the first portable POAC version. The practical details – hardware (optical setups) and software (optical templates) – were published. However, POAC is a general purpose and programmable array computer that has a wide range of applications including: image processing pattern recognition target tracking real-time video processing document security optical switching == Progress in the 2020s == Taichi from Tsinghua University in Beijing is a hybrid ONN that combines the power efficiency and parallelism of optical diffraction and the configurability of optical interference. Taichi offers 13.96 million parameters. Taichi avoids the high error rates that afflict deep (multi-layer) networks by combining clusters of fewer-layer diffractive units with arrays of interferometers for reconfigurable computation. Its encoding protocol divides large network models into sub-models that can be distributed across multiple chiplets in parallel. Taichi achieved 91.89% accuracy in tests with the Omniglot database. It was also used to generate music Bach and generate images the styles of Van Gogh and Munch. The developers claimed energy efficiency of up to 160 trillion operations second−1 watt−1 and an area efficiency of 880 trillion multiply-accumulate operations mm−2 or 103 more energy efficient than the NVIDIA H100, and 102 times more energy efficient and 10 times more area efficient than previous ONNs. Time dimension has recently been introduced into diffractive neural network by fs laser lithography of perovskite hydration. The temporal behaviour of the neuron can be modulated by the fs laser at the nanoscale, enabling a programmable holographic neural network with temporal evolution functionality, i.e., the functionality can change with time under the hydration stimuli. An in-memory temporal inference functionality was demonstrated to mimic the function evolution of the human brain, i.e., the functionality can change from simple digit image classification to more complicated digit and clothing product image classification with time. This is the first time of introducing time dimension into the optical neural network, laying a foundation for future brain-like photonic chip development.
Empowerment (artificial intelligence)
Empowerment in the field of artificial intelligence formalises and quantifies (via information theory) the potential an agent perceives that it has to influence its environment. An agent which follows an empowerment maximising policy, acts to maximise future options (typically up to some limited horizon). Empowerment can be used as a (pseudo) utility function that depends only on information gathered from the local environment to guide action, rather than seeking an externally imposed goal, thus is a form of intrinsic motivation. The empowerment formalism depends on a probabilistic model commonly used in artificial intelligence. An autonomous agent operates in the world by taking in sensory information and acting to change its state, or that of the environment, in a cycle of perceiving and acting known as the perception-action loop. Agent state and actions are modelled by random variables ( S : s ∈ S , A : a ∈ A {\displaystyle S:s\in {\mathcal {S}},A:a\in {\mathcal {A}}} ) and time ( t {\displaystyle t} ). The choice of action depends on the current state, and the future state depends on the choice of action, thus the perception-action loop unrolled in time forms a causal bayesian network. == Definition == Empowerment ( E {\displaystyle {\mathfrak {E}}} ) is defined as the channel capacity ( C {\displaystyle C} ) of the actuation channel of the agent, and is formalised as the maximal possible information flow between the actions of the agent and the effect of those actions some time later. Empowerment can be thought of as the future potential of the agent to affect its environment, as measured by its sensors. E := C ( A t ⟶ S t + 1 ) ≡ max p ( a t ) I ( A t ; S t + 1 ) {\displaystyle {\mathfrak {E}}:=C(A_{t}\longrightarrow S_{t+1})\equiv \max _{p(a_{t})}I(A_{t};S_{t+1})} In a discrete time model, Empowerment can be computed for a given number of cycles into the future, which is referred to in the literature as 'n-step' empowerment. E ( A t n ⟶ S t + n ) = max p ( a t , . . . , a t + n − 1 ) I ( A t , . . . , A t + n − 1 ; S t + n ) {\displaystyle {\mathfrak {E}}(A_{t}^{n}\longrightarrow S_{t+n})=\max _{p(a_{t},...,a_{t+n-1})}I(A_{t},...,A_{t+n-1};S_{t+n})} The unit of empowerment depends on the logarithm base. Base 2 is commonly used in which case the unit is bits. === Contextual Empowerment === In general the choice of action (action distribution) that maximises empowerment varies from state to state. Knowing the empowerment of an agent in a specific state is useful, for example to construct an empowerment maximising policy. State-specific empowerment can be found using the more general formalism for 'contextual empowerment'. C {\displaystyle C} is a random variable describing the context (e.g. state). E ( A t n ⟶ S t + n ∣ C ) = ∑ c ∈ C p ( c ) E ( A t n ⟶ S t + n ∣ C = c ) {\displaystyle {\mathfrak {E}}(A_{t}^{n}\longrightarrow S_{t+n}{\mid }C)=\sum _{c{\in }C}p(c){\mathfrak {E}}(A_{t}^{n}\longrightarrow S_{t+n}{\mid }C=c)} == Application == Empowerment maximisation can be used as a pseudo-utility function to enable agents to exhibit intelligent behaviour without requiring the definition of external goals, for example balancing a pole in a cart-pole balancing scenario where no indication of the task is provided to the agent. Empowerment has been applied in studies of collective behaviour and in continuous domains. As is the case with Bayesian methods in general, computation of empowerment becomes computationally expensive as the number of actions and time horizon extends, but approaches to improve efficiency have led to usage in real-time control. Empowerment has been used for intrinsically motivated reinforcement learning agents playing video games, and in the control of underwater vehicles.
Density-based clustering validation
Density-Based Clustering Validation (DBCV) is a metric designed to assess the quality of clustering solutions, particularly for density-based clustering algorithms like DBSCAN, Mean shift, and OPTICS. This metric is particularly suited for identifying concave and nested clusters, where traditional metrics such as the Silhouette coefficient, Davies–Bouldin index, or Calinski–Harabasz index often struggle to provide meaningful evaluations. Unlike traditional validation measures, which often rely on compact and well-separated clusters, DBCV index evaluates how well clusters are defined in terms of local density variations and structural coherence. This metric was introduced in 2014 by David Moulavi and colleagues in their work. It utilizes density connectivity principles to quantify clustering structures, making it especially effective at detecting arbitrarily shaped clusters in concave datasets, where traditional metrics may be less reliable. The DBCV index has been employed for clustering analysis in bioinformatics, ecology, techno-economy, and health informatics , as well as in numerous other fields. == Definition == DBCV index evaluates clustering structures by analyzing the relationships between data points within and across clusters. Given a dataset X = x 1 , x 2 , . . . , x n {\displaystyle X={x_{1},x_{2},...,x_{n}}} , a density-based algorithm partitions it into K clusters C 1 , C 2 , . . . , C K {\displaystyle {C_{1},C_{2},...,C_{K}}} . Each point x i {\displaystyle x_{i}} belongs to a specific cluster, denoted as C c l u s t e r ( x i ) {\displaystyle C_{cluster(x_{i})}} A key concept in DBCV index is the notion of density-connected paths. Two points within the same cluster are considered density-connected if there exists a sequence of intermediate points linking them, where each consecutive pair meets a predefined density criterion. The density-based distance between two points is determined by identifying the optimal path that minimizes the maximum local reachability distance along its trajectory. DBCV index extends the Silhouette coefficient by redefining cluster cohesion and separation using density-based distances: Within-cluster density distance measures how closely a point is related to other members of its cluster: a i = 1 | C c l u s t e r ( x i ) | − 1 ∑ x j ∈ C c l u s t e r ( x i ) , y ≠ x d d e n s i t y ( x j , x i ) {\displaystyle a_{i}={\frac {1}{|C_{cluster(x_{i})}|-1}}\sum _{x_{j}\in C_{cluster(x_{i})},y\neq x}d_{density}(x_{j},x_{i})} Nearest-cluster density distance quantifies how far a point is from the closest external cluster: b i = min C ≠ C cluster ( x i ) C ∈ { C 1 , … , C K } ( 1 | C | ∑ x j ∈ C d density ( x i , x j ) ) . {\displaystyle b_{i}=\min _{C\neq C_{{\text{cluster}}(x_{i})} \atop C\in \{C_{1},\dots ,C_{K}\}}\left({\frac {1}{|C|}}\sum _{x_{j}\in C}d_{\text{density}}(x_{i},x_{j})\right).} Using these measures, the DBCV index is computed as: D B C V = 1 n ∑ i = 1 n b i − a i max ( a i , b i ) {\displaystyle DBCV={\frac {1}{n}}\sum _{i=1}^{n}{\frac {b_{i}-a_{i}}{\max(a_{i},b_{i})}}} == Explanation == DBCV index values range between −1 and +1: +1: Strongly cohesive and well-separated clusters. 0: Ambiguous clustering structure. −1: Poorly formed clusters or incorrect assignments. By leveraging density-based distances instead of traditional Euclidean measures, DBCV index provides a more robust evaluation of clustering performance in datasets with irregular or non-spherical distributions.