Hebbian theory

Hebbian theory is a neuropsychological theory claiming that an increase in synaptic efficacy arises from a presynaptic cell's repeated and persistent stimulation of a postsynaptic cell. It is an attempt to explain synaptic plasticity, the adaptation of neurons during the learning process. Hebbian theory was introduced by Donald Hebb in his 1949 book The Organization of Behavior. The theory is also called Hebb's rule, Hebb's law, Hebb's postulate, and cell assembly theory. Hebb states it as follows: Let us assume that the persistence or repetition of a reverberatory activity (or "trace") tends to induce lasting cellular changes that add to its stability. ... When an axon of cell A is near enough to excite a cell B and repeatedly or persistently takes part in firing it, some growth process or metabolic change takes place in one or both cells such that A's efficiency, as one of the cells firing B, is increased. The theory is often summarized as "Neurons that fire together, wire together." However, Hebb emphasized that cell A needs to "take part in firing" cell B, and such causality can occur only if cell A fires just before, not at the same time as, cell B. This aspect of causation in Hebb's work foreshadowed what is now known about spike-timing-dependent plasticity, which requires temporal precedence. Hebbian theory attempts to explain associative or Hebbian learning, in which simultaneous activation of cells leads to pronounced increases in synaptic strength between those cells. It also provides a biological basis for errorless learning methods for education and memory rehabilitation. In the study of neural networks in cognitive function, it is often regarded as the neuronal basis of unsupervised learning. == Engrams, cell assembly theory, and learning == Hebbian theory provides an explanation for how neurons might connect to become engrams, which may be stored in overlapping cell assemblies, or groups of neurons that encode specific information. Initially created as a way to explain recurrent activity in specific groups of cortical neurons, Hebb's theories on the form and function of cell assemblies can be understood from the following: The general idea is an old one, that any two cells or systems of cells that are repeatedly active at the same time will tend to become 'associated' so that activity in one facilitates activity in the other. Hebb also wrote: When one cell repeatedly assists in firing another, the axon of the first cell develops synaptic knobs (or enlarges them if they already exist) in contact with the soma of the second cell. D. Alan Allport posits additional ideas regarding cell assembly theory and its role in forming engrams using the concept of auto-association, or the brain's ability to retrieve information based on a partial cue, described as follows: If the inputs to a system cause the same pattern of activity to occur repeatedly, the set of active elements constituting that pattern will become increasingly strongly inter-associated. That is, each element will tend to turn on every other element and (with negative weights) to turn off the elements that do not form part of the pattern. To put it another way, the pattern as a whole will become 'auto-associated'. We may call a learned (auto-associated) pattern an engram. Research conducted in the laboratory of Nobel laureate Eric Kandel has provided evidence supporting the role of Hebbian learning mechanisms at synapses in the marine gastropod Aplysia californica. Because synapses in the peripheral nervous system of marine invertebrates are much easier to control in experiments, Kandel's research found that Hebbian long-term potentiation along with activity-dependent presynaptic facilitation are both necessary for synaptic plasticity and classical conditioning in Aplysia californica. While research on invertebrates has established fundamental mechanisms of learning and memory, much of the work on long-lasting synaptic changes between vertebrate neurons involves the use of non-physiological experimental stimulation of brain cells. However, some of the physiologically relevant synapse modification mechanisms that have been studied in vertebrate brains do seem to be examples of Hebbian processes. One such review indicates that long-lasting changes in synaptic strengths can be induced by physiologically relevant synaptic activity using both Hebbian and non-Hebbian mechanisms. == Principles == In artificial neurons and artificial neural networks, Hebb's principle can be described as a method of determining how to alter the weights between model neurons. The weight between two neurons increases if the two neurons activate simultaneously, and reduces if they activate separately. Nodes that tend to be either both positive or both negative at the same time have strong positive weights, while those that tend to be opposite have strong negative weights. The following is a formulaic description of Hebbian learning (many other descriptions are possible): w i j = x i x j , {\displaystyle \,w_{ij}=x_{i}x_{j},} where w i j {\displaystyle w_{ij}} is the weight of the connection from neuron j {\displaystyle j} to neuron i {\displaystyle i} , and x i {\displaystyle x_{i}} is the input for neuron i {\displaystyle i} . This is an example of pattern learning, where weights are updated after every training example. In a Hopfield network, connections w i j {\displaystyle w_{ij}} are set to zero if i = j {\displaystyle i=j} (no reflexive connections allowed). With binary neurons (activations either 0 or 1), connections would be set to 1 if the connected neurons have the same activation for a pattern. When several training patterns are used, the expression becomes an average of the individuals: w i j = 1 p ∑ k = 1 p x i k x j k , {\displaystyle w_{ij}={\frac {1}{p}}\sum _{k=1}^{p}x_{i}^{k}x_{j}^{k},} where w i j {\displaystyle w_{ij}} is the weight of the connection from neuron j {\displaystyle j} to neuron i {\displaystyle i} , p {\displaystyle p} is the number of training patterns and x i k {\displaystyle x_{i}^{k}} the k {\displaystyle k} -th input for neuron i {\displaystyle i} . This is learning by epoch, with weights updated after all the training examples are presented and is last term applicable to both discrete and continuous training sets. Again, in a Hopfield network, connections w i j {\displaystyle w_{ij}} are set to zero if i = j {\displaystyle i=j} (no reflexive connections). A variation of Hebbian learning that takes into account phenomena such as blocking and other neural learning phenomena is the mathematical model of Harry Klopf. Klopf's model assumes that parts of a system with simple adaptive mechanisms can underlie more complex systems with more advanced adaptive behavior, such as neural networks. == Relationship to unsupervised learning, stability, and generalization == Because of the simple nature of Hebbian learning, based only on the coincidence of pre- and post-synaptic activity, it may not be intuitively clear why this form of plasticity leads to meaningful learning. However, it can be shown that Hebbian plasticity does pick up the statistical properties of the input in a way that can be categorized as unsupervised learning. This can be mathematically shown in a simplified example. Let us work under the simplifying assumption of a single rate-based neuron of rate y ( t ) {\displaystyle y(t)} , whose inputs have rates x 1 ( t ) . . . x N ( t ) {\displaystyle x_{1}(t)...x_{N}(t)} . The response of the neuron y ( t ) {\displaystyle y(t)} is usually described as a linear combination of its input, ∑ i w i x i {\displaystyle \sum _{i}w_{i}x_{i}} , followed by a response function f {\displaystyle f} : y = f ( ∑ i = 1 N w i x i ) . {\displaystyle y=f\left(\sum _{i=1}^{N}w_{i}x_{i}\right).} As defined in the previous sections, Hebbian plasticity describes the evolution in time of the synaptic weight w {\displaystyle w} : d w i d t = η x i y . {\displaystyle {\frac {dw_{i}}{dt}}=\eta x_{i}y.} Assuming, for simplicity, an identity response function f ( a ) = a {\displaystyle f(a)=a} , we can write d w i d t = η x i ∑ j = 1 N w j x j {\displaystyle {\frac {dw_{i}}{dt}}=\eta x_{i}\sum _{j=1}^{N}w_{j}x_{j}} or in matrix form: d w d t = η x x T w . {\displaystyle {\frac {d\mathbf {w} }{dt}}=\eta \mathbf {x} \mathbf {x} ^{T}\mathbf {w} .} As in the previous chapter, if training by epoch is done an average ⟨ … ⟩ {\displaystyle \langle \dots \rangle } over discrete or continuous (time) training set of x {\displaystyle \mathbf {x} } can be done: d w d t = ⟨ η x x T w ⟩ = η ⟨ x x T ⟩ w = η C w . {\displaystyle {\frac {d\mathbf {w} }{dt}}=\langle \eta \mathbf {x} \mathbf {x} ^{T}\mathbf {w} \rangle =\eta \langle \mathbf {x} \mathbf {x} ^{T}\rangle \mathbf {w} =\eta C\mathbf {w} .} where C = ⟨ x x T ⟩ {\displaystyle C=\langle \,\mathbf {x} \mathbf {x} ^{T}\rangle } is the correlation matrix of the input under the additional assumption that ⟨ x ⟩ = 0 {\displaystyle \langle \mathbf

Instance-based learning

In machine learning, instance-based learning (sometimes called memory-based learning) is a family of learning algorithms that, instead of performing explicit generalization, compare new problem instances with instances seen in training, which have been stored in memory. Because computation is postponed until a new instance is observed, these algorithms are sometimes referred to as "lazy." It is called instance-based because it constructs hypotheses directly from the training instances themselves. This means that the hypothesis complexity can grow with the data: in the worst case, a hypothesis is a list of n training items and the computational complexity of classifying a single new instance is O(n). One advantage that instance-based learning has over other methods of machine learning is its ability to adapt its model to previously unseen data. Instance-based learners may simply store a new instance or throw an old instance away. Examples of instance-based learning algorithms are the k-nearest neighbors algorithm, kernel machines and RBF networks. These store (a subset of) their training set; when predicting a value/class for a new instance, they compute distances or similarities between this instance and the training instances to make a decision. To battle the memory complexity of storing all training instances, as well as the risk of overfitting to noise in the training set, instance reduction algorithms have been proposed.

Leabra

Leabra stands for local, error-driven and associative, biologically realistic algorithm. It is a model of learning which is a balance between Hebbian and error-driven learning with other network-derived characteristics. This model is used to mathematically predict outcomes based on inputs and previous learning influences. Leabra is heavily influenced by and contributes to neural network designs and models, including emergent. == Background == It is the default algorithm in emergent (successor of PDP++) when making a new project, and is extensively used in various simulations. Hebbian learning is performed using conditional principal components analysis (CPCA) algorithm with correction factor for sparse expected activity levels. Error-driven learning is performed using GeneRec, which is a generalization of the recirculation algorithm, and approximates Almeida–Pineda recurrent backpropagation. The symmetric, midpoint version of GeneRec is used, which is equivalent to the contrastive Hebbian learning algorithm (CHL). See O'Reilly (1996; Neural Computation) for more details. The activation function is a point-neuron approximation with both discrete spiking and continuous rate-code output. Layer or unit-group level inhibition can be computed directly using a k-winners-take-all (KWTA) function, producing sparse distributed representations. A feedforward and feedback (FFFB) form of inhibition has now replaced the KWTA form of inhibition. FFFB inhibition can be efficiently implemented by using the average excitatory input and activity levels in a given layer. The net input is computed as an average, not a sum, over connections, based on normalized, sigmoidally transformed weight values, which are subject to scaling on a connection-group level to alter relative contributions. Automatic scaling is performed to compensate for differences in expected activity level in the different projections. Documentation about this algorithm can be found in the book "Computational Explorations in Cognitive Neuroscience: Understanding the Mind by Simulating the Brain" published by MIT press. and in the Emergent Documentation Archived 2009-04-16 at the Wayback Machine == Overview of the leabra algorithm == The pseudocode for Leabra is given here, showing exactly how the pieces of the algorithm described in more detail in the subsequent sections fit together. Iterate over minus and plus phases of settling for each event. o At start of settling, for all units: - Initialize all state variables (activation, v_m, etc.). - Apply external patterns (clamp input in minus, input & output in plus). - Compute net input scaling terms (constants, computed here so network can be dynamically altered). - Optimization: compute net input once from all static activations (e.g., hard-clamped external inputs). o During each cycle of settling, for all non-clamped units: - Compute excitatory netinput (g_e(t), aka eta_j or net) -- sender-based optimization by ignoring inactives. - Compute kWTA inhibition for each layer, based on g_i^Q: Sort units into two groups based on g_i^Q: top k and remaining k+1 -> n. If basic, find k and k+1th highest If avg-based, compute avg of 1 -> k & k+1 -> n. Set inhibitory conductance g_i from g^Q_k and g^Q_k+1 - Compute point-neuron activation combining excitatory input and inhibition o After settling, for all units, record final settling activations as either minus or plus phase (y^-_j or y^+_j). After both phases update the weights (based on linear current weight values), for all connections: o Compute error-driven weight changes with CHL with soft weight bounding o Compute Hebbian weight changes with CPCA from plus-phase activations o Compute net weight change as weighted sum of error-driven and Hebbian o Increment the weights according to net weight change. == Implementations == Emergent Archived 2015-10-03 at the Wayback Machine is the original implementation of Leabra; its most recent implementation is written in Go. It was written chiefly by Dr. O'Reilly, but professional software engineers were recently hired to improve the existing codebase. This is the fastest implementation, suitable for constructing large networks. Although emergent has a graphical user interface, it is very complex and has a steep learning curve. If you want to understand the algorithm in detail, it will be easier to read non-optimized code. For this purpose, check out the MATLAB version. There is also an R version available, that can be easily installed via install.packages("leabRa") in R and has a short introduction to how the package is used. The MATLAB and R versions are not suited for constructing very large networks, but they can be installed quickly and (with some programming background) are easy to use. Furthermore, they can also be adapted easily. == Special algorithms == Temporal differences and general dopamine modulation. Temporal differences (TD) is widely used as a model of midbrain dopaminergic firing. Primary value learned value (PVLV). PVLV simulates behavioral and neural data on Pavlovian conditioning and the midbrain dopaminergic neurons that fire in proportion to unexpected rewards (an alternative to TD). Prefrontal cortex basal ganglia working memory (PBWM). PBWM uses PVLV to train prefrontal cortex working memory updating system, based on the biology of the prefrontal cortex and basal ganglia.

Mittens (chess)

Mittens is a chess engine developed by Chess.com. It was released on January 1, 2023, alongside four other engines, all of them given cat-related names. The engine became a viral sensation in the chess community due to exposure through content made by chess streamers and a social media marketing campaign, later contributing to record levels of traffic to the Chess.com website and causing issues with database scalability. Mittens was given a rating of one point by Chess.com, although it was evidently stronger than that. Various chess masters played matches against the engine, with players such as Hikaru Nakamura and Levy Rozman drawing and losing their games respectively. A month after its release, Mittens was removed from the website on February 1, as expected through Chess.com's monthly bot cycles. In December 2023, Mittens was brought back in a group of Chess.com's most popular bots of 2023. In January 2024, Mittens was removed again. == Release == Mittens was released on January 1, 2023, as part of a New Year event on Chess.com. It was one of five engines released, all with names related to cats. The other engines released were named Scaredy Cat, rated 800; Angry Cat, rated 1000; Mr. Grumpers, rated 1200 and Catspurrov (a pun on Garry Kasparov), rated 1400. As part of the announcement, a picture of each engine was accompanied by a short description of its character. The description given for Mittens suggested that the engine was hiding something, reading: Mittens likes chess… But how good is she? Of the five engines released, Mittens was by far the most popular. In December 2023, Chess.com re-released Mittens as part of a "best of 2023" group of chess bots made to showcase their most popular bots of the year. == Design == Mittens was conceptualized by Chess.com employee Will Whalen. Appearing as a kitten, Mittens trash talked its opponents with a selection of voice lines: these lines included quotes from J. Robert Oppenheimer, Vincent van Gogh and Friedrich Nietzsche, as well as the 1967 film Le Samouraï. The engine's "personality" was devised by a writing team headed by Sean Becker, and Marija Casic provided the engine's graphics. Chess.com did not disclose any information about the software running the engine. It may be based on Chess.com's Komodo Dragon 3 engine. Mittens' strategy was to slowly grind down an opponent, a tactic likened to the playing style of Anatoly Karpov. Becker stated that the design team believed it would be "way more demoralizing and funny" for the engine to play this way. According to Hikaru Nakamura, Mittens sometimes missed the best move (or winning positions). == Rating == On Chess.com, Mittens had a rating of one point. However, the engine's playing style and tactics showed that it was stronger than that; Mittens was able to beat or draw against many top human players. In an interview with CNN Business, Whalen stated that the idea behind giving Mittens a rating of one was to surprise its opponents, giving it the upper hand psychologically. Estimates of Mittens' true rating range from an Elo of 3200 to 3500, because of its ability to beat other engines of around that level. An upper bound of the engine's rating was found after Levy Rozman made Mittens play against Stockfish 15, a 3700 rated engine. Mittens lost the two games that the engines played. The range of Mittens' possible ratings was summarized by Dot Esports, who stated: It seems like she’s around the 3200–3500 rating range (in Chess.com terms, where the best human players, like Magnus Carlsen and Hikaru Nakamura, sport a 3000–3100 rating in the faster formats), as evidenced by her victories over the site’s otherwise strongest, 3200-rated bots, and her defeat to Stockfish 15, which is currently rated around 3700. == Games == Against human players, Mittens won over 99 percent of the millions of games it played. Chess players such as Hikaru Nakamura, Benjamin Bok, Levy Rozman and Eric Rosen struggled against Mittens; while Rozman and Rosen both lost against the engine, Nakamura and Bok were both able to make a draw. In particular, Nakamura's game against the engine lasted 166 moves; he was playing as White. Bok, Benjamin Finegold and Rozman later went on to win against Mittens, the latter with engine assistance from Stockfish. Magnus Carlsen publicly refused to play the engine, calling it a "transparent marketing trick" and "a soulless computer". Against other chess engines, Mittens participated in the Chess.com Computer Chess Championship as a side act. In the competition, Mittens played 150 games against an engine named after the film M3GAN and won overall with a score of 81.5 to 68.5. This equated to 54 percent of the games played. During the event, an estimate of Mittens' rating was made at 3515 points. == Impact == Mittens went viral in the chess community due to its concept and design: according to an announcement by Chess.com, a combined total of 120 million games were played against the cat engines over the course of January, with around 40 million played against Mittens. The popularity of the engine was helped by the social media exposure created by Chess.com. This included creating an official Twitter account to promote the engine. Chess streamers like Rozman and Nakamura helped cultivate this by creating content around the engine. A video by Nakamura entitled "Mittens the chess bot will make you quit chess" gained over 3.5 million views on YouTube. On January 11, Chess.com reported issues with database scalability due to record levels of traffic: 40 percent more games had been played on Chess.com in January 2023 than any other month since the website's release. According to The Wall Street Journal, the popularity spike was more than the similar surge following the release of Netflix's The Queen's Gambit. The popularity of Mittens was cited by Chess.com as a reason for this instability. The problems continued throughout January; Chess.com stated that they would have to upgrade their servers and invest more in cloud computing to solve the problems caused by the website's popularity surge. On February 1, 2023, Mittens and the other cat engines were removed from the computer section of Chess.com. They were replaced with five new engines themed around artificial intelligence. A tweet was posted on the Mittens's Twitter account after the engine's removal, reading "This is just the beginning. Goodbye for now."

Richard S. Sutton

Richard Stuart Sutton (born 1957 or 1958) is a Canadian computer scientist. He is a professor of computing science at the University of Alberta, fellow & Chief Scientific Advisor at the Alberta Machine Intelligence Institute, and a research scientist at Keen Technologies. Sutton is considered one of the founders of modern computational reinforcement learning. In particular, he contributed to temporal difference learning and policy gradient methods. He received the 2024 Turing Award with Andrew Barto. == Education and early life == Richard Sutton was born in either 1957 or 1958 in Toledo, Ohio, and grew up in Oak Brook, Illinois, a suburb of Chicago, United States. Sutton received his Bachelor of Arts (BA) degree in psychology from Stanford University in 1978 before taking a Master of Science (1980) and PhD (1984) in computer science from the University of Massachusetts Amherst supervised by Andrew Barto. His doctoral dissertation introduced actor-critic architectures and temporal credit assignment. He was influenced by Harry Klopf's work in the 1970s, which proposed that supervised learning is insufficient for AI or explaining intelligent behavior, and trial-and-error learning, driven by "hedonic aspects of behavior", is necessary. This focused his interest to reinforcement learning. == Career and research == Sutton held a postdoctoral research position at the University of Massachusetts Amherst in 1984. He worked at GTE Laboratories in Waltham, Massachusetts as principal member of technical staff from 1985 to 1994, then returned to the University of Massachusetts Amherst as a senior research scientist. He joined AT&T Labs Shannon Laboratory in Florham Park, New Jersey as principal technical staff member from 1998 to 2002. He has been a professor of computing science at the University of Alberta since 2003, where he helped establish the Reinforcement Learning and Artificial Intelligence Laboratory. In 2017 he became a distinguished research scientist with Google DeepMind and helped launch DeepMind Alberta in Edmonton, a research office operated in close collaboration with the University of Alberta. 1984: Postdoctoral researcher, University of Massachusetts Amherst (Amherst, Massachusetts) 1985–1994: Principal member of technical staff, Computer and Intelligent Systems Laboratory, GTE Laboratories (Waltham, Massachusetts) 1995–1998: Senior research scientist, University of Massachusetts Amherst (Amherst, Massachusetts) 1998–2002: Principal technical staff member, Artificial Intelligence Department, AT&T Labs Shannon Laboratory (Florham Park, New Jersey) 2003–present: Professor of computing science, University of Alberta (Edmonton, Alberta) 2017–2023: Distinguished research scientist, DeepMind Alberta, Google DeepMind (Edmonton, Alberta) 2024–Present: Research scientist, Keen Technologies === Reinforcement learning === Sutton joined Andrew Barto in the early 1980s at UMass, trying to explore the behavior of neurons in the human brain as the basis for human intelligence, a concept that had been advanced by computer scientist A. Harry Klopf. Sutton and Barto used mathematics toward furthering the concept and using it as the basis for artificial intelligence. This concept became known as reinforcement learning and went on to becoming a key part of artificial intelligence techniques. Barto and Sutton used Markov decision processes (MDP) as the mathematical foundation to explain how agents (algorithmic entities) made decisions when in a stochastic or random environment, receiving rewards at the end of every action. Traditional MDP theory assumed the agents knew all information about the MDPs in their attempt toward maximizing their cumulative rewards. Barto and Sutton's reinforcement learning techniques allowed for both the environment and the rewards to be unknown, and thus allowed for these category of algorithms to be applied to a wide array of problems. Sutton returned to Canada in the 2000s and continued working on the topic which continued to develop in academic circles until one of its first major real world applications saw Google's AlphaGo program built on this concept defeating the then prevailing human champion. Barto and Sutton have widely been credited and accepted as pioneers of modern reinforcement learning, with the technique itself being foundational to the AI boom. In a 2019 essay, Sutton proposed the "bitter lesson", which criticized the field of AI research for failing to learn that "building in how we think we think does not work in the long run", arguing that "70 years of AI research [had shown] that general methods that leverage computation are ultimately the most effective, and by a large margin", beating efforts building on human knowledge about specific fields like computer vision, speech recognition, chess or Go. Sutton argues that large language models aren’t capable of learning on-the-job, and so new model architectures are required to enable continual learning. Sutton further argues that a special training phase will be unnecessary — the agent will learn on-the-fly, rendering large language models obsolete. In 2023, Sutton and John Carmack announced a partnership for the development of artificial general intelligence (AGI). === Awards and honors === Sutton has been a Fellow of the Association for the Advancement of Artificial Intelligence (AAAI) since 2001; his nomination read: "For significant contributions to many topics in machine learning, including reinforcement learning, temporal difference techniques, and neural networks." In 2003, he received the President's Award from the International Neural Network Society and in 2013, the Outstanding Achievement in Research award from the University of Massachusetts Amherst. He received the 2024 Turing Award from the Association for Computing Machinery together with Andrew Barto; the citation of the award read: "For developing the conceptual and algorithmic foundations of reinforcement learning." In 2016, Sutton was elected Fellow of the Royal Society of Canada. In 2021, he was elected Fellow of the Royal Society (FRS) of London. === Research === Sutton introduced temporal-difference methods for prediction and control, establishing convergence properties and practical algorithms. He proposed integrated learning and planning through the Dyna architecture. He co-developed the options framework for temporal abstraction in reinforcement learning. He co-authored the first modern policy gradient formulation with function approximation. Sutton's essay The Bitter Lesson argued that general methods that scale with computation dominate domain-specific approaches in the long run. His former doctoral students include David Silver and Doina Precup. === Selected publications === His publications include: == Personal life == Sutton became a Canadian citizen in 2015, and his renunciation of US citizenship was reported in 2017.

Quantum image processing

Quantum image processing (QIMP) is using quantum computing or quantum information processing to create and work with quantum images. Due to some of the properties inherent to quantum computation, notably entanglement and parallelism, it is hoped that QIMP technologies will offer capabilities and performances that surpass their traditional equivalents, in terms of computing speed, security, and minimum storage requirements. == Background == A. Y. Vlasov's work in 1997 focused on using a quantum system to recognize orthogonal images. This was followed by efforts using quantum algorithms to search specific patterns in binary images and detect the posture of certain targets. Notably, more optics-based interpretations for quantum imaging were initially experimentally demonstrated in and formalized in after seven years. In 2003, Salvador Venegas-Andraca and S. Bose presented Qubit Lattice, the first published general model for storing, processing and retrieving images using quantum systems. Later on, in 2005, Latorre proposed another kind of representation, called the Real Ket, whose purpose was to encode quantum images as a basis for further applications in QIMP. Furthermore, in 2010 Venegas-Andraca and Ball presented a method for storing and retrieving binary geometrical shapes in quantum mechanical systems in which it is shown that maximally entangled qubits can be used to reconstruct images without using any additional information. Technically, these pioneering efforts with the subsequent studies related to them can be classified into three main groups: Quantum-assisted digital image processing (QDIP): These applications aim at improving digital or classical image processing tasks and applications. Optics-based quantum imaging (OQI) Classically inspired quantum image processing (QIMP) A survey of quantum image representation has been published in. Furthermore, the recently published book Quantum Image Processing provides a comprehensive introduction to quantum image processing, which focuses on extending conventional image processing tasks to the quantum computing frameworks. It summarizes the available quantum image representations and their operations, reviews the possible quantum image applications and their implementation, and discusses the open questions and future development trends. == Quantum image representations == There are various approaches for quantum image representation, that are usually based on the encoding of color information. A common representation is FRQI (Flexible Representation for Quantum Images), that captures the color and position at every pixel of the image, and defined as: | I ⟩ = 1 2 n ∑ i = 0 2 2 n − 1 | c i ⟩ ⊗ | i ⟩ {\displaystyle \vert I\rangle ={\frac {1}{2^{n}}}\sum _{i=0}^{2^{2n-1}}\vert c_{i}\rangle \otimes \vert i\rangle } where | i ⟩ {\textstyle |i\rangle } is the position and | c i ⟩ = c o s θ i | 0 ⟩ + s i n θ i | 1 ⟩ {\textstyle \vert c_{i}\rangle =cos\theta _{i}\vert 0\rangle +sin\theta _{i}\vert 1\rangle } the color with a vector of angles θ i ∈ [ 0 , π / 2 ] {\textstyle \theta _{i}\in \left[0,\pi /2\right]} . As it can be seen, | c i ⟩ {\textstyle \vert c_{i}\rangle } is a regular qubit state of the form | ψ ⟩ = α | 0 ⟩ + β | 1 ⟩ {\displaystyle \vert \psi \rangle =\alpha \vert 0\rangle +\beta \vert 1\rangle } , with basis states | 0 ⟩ = ( 1 0 ) {\textstyle \vert 0\rangle ={\begin{pmatrix}1\\0\end{pmatrix}}} and | 1 ⟩ = ( 0 1 ) {\textstyle \vert 1\rangle ={\begin{pmatrix}0\\1\end{pmatrix}}} , as well as amplitudes α {\textstyle \alpha } and β {\textstyle \beta } that satisfy | α | 2 + | β | 2 = 1 {\textstyle \left|\alpha \right|^{2}+\left|\beta \right|^{2}=1} . Another common representation is MCQI (Multi-Channel Representation for Quantum Images), that uses the RGB channels with quantum states and following FRQI definition: | I ⟩ = 1 2 n + 1 ∑ i = 0 2 2 n − 1 | C R G B i ⟩ ⊗ | i ⟩ {\displaystyle \vert I\rangle ={\frac {1}{2^{n+1}}}\sum _{i=0}^{2^{2n-1}}\vert C_{RGB}^{i}\rangle \otimes \vert i\rangle } | C R G B i ⟩ = cos ⁡ θ R i | 000 ⟩ + cos ⁡ θ G i | 001 ⟩ + cos ⁡ θ B i | 010 ⟩ + sin ⁡ θ R i | 100 ⟩ + sin ⁡ θ G i | 101 ⟩ + sin ⁡ θ B i | 110 ⟩ + cos ⁡ θ α | 011 ⟩ + sin ⁡ θ α | 111 ⟩ {\displaystyle {\begin{aligned}{\begin{aligned}\vert C_{RGB}^{i}\rangle &={\cos \theta _{R}^{i}\vert 000\rangle }+{\cos \theta _{G}^{i}\vert 001\rangle }+{\cos \theta _{B}^{i}\vert 010\rangle }\\&\quad +{\sin \theta _{R}^{i}\vert 100\rangle }+{\sin \theta _{G}^{i}\vert 101\rangle }+{\sin \theta _{B}^{i}\vert 110\rangle }\\&\quad +{\cos {\theta _{\alpha }}\vert 011\rangle }+{\sin \theta _{\alpha }\vert 111\rangle }\end{aligned}}\end{aligned}}} Departing from the angle-based approach of FRQI and MCQI, and using a qubit sequence, NEQR (Novel Enhanced Representation for Quantum Images) is another representation approach, that uses a function f ( y , x ) = C y x q − 1 C y x q − 2 … C y x 1 C y x 0 {\textstyle f\left(y,x\right)=C_{yx}^{q-1}C_{yx}^{q-2}\ldots C_{yx}^{1}C_{yx}^{0}} to encode color values for a 2 n × 2 n {\displaystyle 2^{n}\times 2^{n}} image: | I ⟩ = 1 2 n ∑ y = 0 2 n − 1 ∑ x = 0 2 n − 1 | f ( y , x ) ⟩ | y x ⟩ {\displaystyle \vert I\rangle ={\frac {1}{2^{n}}}\sum _{y=0}^{2^{n}-1}\sum _{x=0}^{2^{n}-1}\vert f\left(y,x\right)\rangle \vert yx\rangle } == Quantum image manipulations == A lot of the effort in QIMP has been focused on designing algorithms to manipulate the position and color information encoded using flexible representation of quantum images (FRQI) and its many variants. For instance, FRQI-based fast geometric transformations including (two-point) swapping, flip, (orthogonal) rotations and restricted geometric transformations to constrain these operations to a specified area of an image were initially proposed. Recently, NEQR-based quantum image translation to map the position of each picture element in an input image into a new position in an output image and quantum image scaling to resize a quantum image were discussed. While FRQI-based general form of color transformations were first proposed by means of the single qubit gates such as X, Z, and H gates. Later, Multi-Channel Quantum Image-based channel of interest (CoI) operator to entail shifting the grayscale value of the preselected color channel and the channel swapping (CS) operator to swap the grayscale values between two channels have been fully discussed. To illustrate the feasibility and capability of QIMP algorithms and application, researchers always prefer to simulate the digital image processing tasks on the basis of the QIRs that we already have. By using the basic quantum gates and the aforementioned operations, so far, researchers have contributed to quantum image feature extraction, quantum image segmentation, quantum image morphology, quantum image comparison, quantum image filtering, quantum image classification, quantum image stabilization, among others. In particular, QIMP-based security technologies have attracted extensive interest of researchers as presented in the ensuing discussions. Similarly, these advancements have led to many applications in the areas of watermarking, encryption, and steganography etc., which form the core security technologies highlighted in this area. In general, the work pursued by the researchers in this area are focused on expanding the applicability of QIMP to realize more classical-like digital image processing algorithms; propose technologies to physically realize the QIMP hardware; or simply to note the likely challenges that could impede the realization of some QIMP protocols. == Quantum image transform == By encoding and processing the image information in quantum-mechanical systems, a framework of quantum image processing is presented, where a pure quantum state encodes the image information: to encode the pixel values in the probability amplitudes and the pixel positions in the computational basis states. Given an image F = ( F i , j ) M × L {\displaystyle F=(F_{i,j})_{M\times L}} , where F i , j {\displaystyle F_{i,j}} represents the pixel value at position ( i , j ) {\displaystyle (i,j)} with i = 1 , … , M {\displaystyle i=1,\dots ,M} and j = 1 , … , L {\displaystyle j=1,\dots ,L} , a vector f → {\displaystyle {\vec {f}}} with M L {\displaystyle ML} elements can be formed by letting the first M {\displaystyle M} elements of f → {\displaystyle {\vec {f}}} be the first column of F {\displaystyle F} , the next M {\displaystyle M} elements the second column, etc. A large class of image operations is linear, e.g., unitary transformations, convolutions, and linear filtering. In the quantum computing, the linear transformation can be represented as | g ⟩ = U ^ | f ⟩ {\displaystyle |g\rangle ={\hat {U}}|f\rangle } with the input image state | f ⟩ {\displaystyle |f\rangle } and the output image state | g ⟩ {\displaystyle |g\rangle } . A unitary transformation can be implemented as a unitary evolution. Some basic and commonly used image transforms (e.g., the Fourier, Hadamard, an

Copyright and artificial intelligence in the United Kingdom

The interaction of artificial intelligence and copyright law has become one of the most contentious tech policy debates in the United Kingdom, centering on whether AI developers should be permitted to train their models on copyrighted material without explicit consent or remuneration. This debate has exposed a deep fracture between the creative industries, which seek to protect their intellectual property from unauthorised commercial exploitation, and tech companies. The academic and library sectors are also impacted, and argue that overly restrictive copyright laws hinder scientific research and the UK's sovereign AI capabilities. In 2024, the UK government proposed a broad text and data mining (TDM) exception to copyright that would have allowed AI companies to use publicly available copyrighted material for training, offering creators only an "opt-out" mechanism, similar to the exception introduced in Europe. This proposal faced intense opposition from across the creative sector. Trade unions representing writers, musicians, performers, and journalists argued that such an exception would effectively expropriate their members' work for the commercial benefit of tech giants. A report from the House of Lords Communications and Digital Committee, warned that generative AI posed a "clear and present danger" to the £124 billion creative economy. The government abandoned the opt-out model in March 2026, opting instead to build a stronger evidence base before pursuing any copyright reform. Conversely, the academic and library sectors have raised significant concerns that the UK's current TDM exception, which is strictly limited to non-commercial research, is too narrow. Universities and research libraries occupy a dual role as both creators of vast datasets and beneficiaries of TDM exceptions. They argue that the current legal framework restricts their ability to computationally analyse the very research they produce, thereby hobbling the UK's "AI for Science" strategy. Advocacy groups have highlighted a "triple payment" problem, wherein publicly funded research is handed over to publishers, who then charge universities substantial subscription fees and demand additional payments for specific TDM licences. This tension is further complicated by the commercial practices of major academic publishers. While publishers often restrict universities from using subscribed databases for AI training, they have simultaneously entered into lucrative, multi-million-dollar licensing agreements to sell access to this academic content to commercial AI developers. Furthermore, academics have accused publishers of actively steering authors away from permissive open-access licences towards more restrictive variants. By doing so, publishers retain the exclusive commercial rights necessary to strike these AI training deals, often without consulting the original authors or offering them any additional remuneration. This dynamic has not only reopened debates within the Open Access movement but has also created complex legal scenarios where publishers, rather than authors, control the terms of copyright litigation against major tech companies. == Training on copyrighted material == The question of whether AI developers should be permitted to train their models on copyrighted material without payment or consent has been one of the most contentious policy debates in the UK AI landscape. In 2024, the then-Conservative government proposed a broad text and data mining (TDM) exception that would have allowed AI companies to use any publicly available copyrighted material for training purposes, with creators able only to "opt out" of having their work used. This proposal provoked intense opposition from writers, musicians, visual artists, publishers, and broadcasters, who argued it would effectively expropriate their intellectual property for the commercial benefit of AI companies. The debate over text and data mining exceptions extends significantly beyond generative AI and the creative industries, implicating a wide range of scientific, industrial, and academic research applications. TDM is a foundational process for analysing large datasets to identify patterns, trends, and correlations, which is heavily utilised in fields such as medical research, climate modelling, and financial services. In the scientific and academic sectors, researchers rely on TDM to process vast amounts of published literature. For example, in biomedical research, TDM is used to accelerate drug discovery, identify new uses for existing medicines, and extract insights from clinical notes and genomic datasets. However, the application of traditional copyright frameworks to scientific literature has been criticised by academics. Researchers argue that scientific writing is intended to convey factual, verifiable information rather than creative originality, and that copyright restrictions on TDM hinder reproducibility, validation, and the advancement of science. The current UK copyright exception for TDM (Section 29A of the Copyright, Designs and Patents Act 1988) is limited strictly to non-commercial research, which creates barriers for public-private research partnerships and commercial scientific development. Beyond academia, non-generative AI and TDM are critical to various industrial and commercial operations. In the financial services sector, TDM is employed to monitor transactions, detect fraud, and analyse market feeds. Other non-generative applications include search engine indexing, plagiarism detection software, and media monitoring. A 2026 report by Public First estimated that 19% of UK businesses use specialised TDM tools, and that a restrictive copyright regime requiring licenses for all copyrighted content could cost the UK economy £220 billion in lost AI-driven GDP growth by 2035 compared to a broad commercial TDM exemption. Industry advocates argue that the lack of a commercial TDM exception in the UK creates legal uncertainty that stifles innovation across these broader, non-generative applications of data analysis. === Tech and AI industry positions === The technology and artificial intelligence industries lobbied for a broad text and data mining (TDM) exception to UK copyright law, arguing that such an exception is essential for the UK to remain globally competitive in AI development. Industry bodies such as techUK have argued that without a TDM exception, the UK risks becoming an "AI taker rather than an AI maker," as developers will relocate training operations to jurisdictions with more permissive copyright regimes, such as the United States, Japan, Singapore, and the European Union. During the UK government's 2024–2025 consultation on copyright and AI, major AI developers and trade associations strongly supported "Option 2" (a broad TDM exception) or "Option 3" (a TDM exception with an opt-out mechanism). OpenAI stated in its consultation response that a broad TDM exception is "necessary to drive AI innovation and investment in the UK," arguing that developers should be permitted to train models on lawfully accessed copies without further distribution. The Computer and Communications Industry Association (CCIA) similarly argued that restricting TDM to non-commercial development would undermine the government's ambitions for the UK tech sector and frustrate partnerships between commercial entities and research institutions. Tech industry advocates have also highlighted the economic implications of copyright policy. According to analysis by the think tank UK Day One, adopting an overly restrictive licensing-only approach could result in the UK economy losing up to £182 billion over 20 years, whereas a broad TDM exception could generate a positive impact of £131.61 billion over the same period. Following the government's March 2026 decision to drop plans for a TDM exception in favour of a market-led licensing approach, techUK's Deputy CEO Antony Walker criticised the move, stating that "copyright material cannot be used for AI development and training without permission" under the current framework, which he argued would push AI model training to the US. === Creative sector and political opposition to text and data mining === In March 2026, the House of Lords Communications and Digital Committee published a report, AI, Copyright and the Creative Industries, which concluded that the creative industries face "a clear and present danger from generative AI" and that it would be "a very poor bet" for the government to weaken copyright protections to attract AI investment. The Committee noted that the creative industries contributed £124 billion to the UK economy in 2023 and employed 2.4 million people, compared to the AI sector's £12 billion GVA and 86,000 employees in 2024. The Committee called on the government to develop a "licensing-first" regime underpinned by mandatory transparency requirements, and to rule out any new commercial TDM exception with an opt-out model. Tra