Algorithm engineering focuses on the design, analysis, implementation, optimization, profiling and experimental evaluation of computer algorithms, bridging the gap between algorithmics theory and practical applications of algorithms in software engineering. It is a general methodology for algorithmic research. == Origins == In 1995, a report from an NSF-sponsored workshop "with the purpose of assessing the current goals and directions of the Theory of Computing (TOC) community" identified the slow speed of adoption of theoretical insights by practitioners as an important issue and suggested measures to reduce the uncertainty by practitioners whether a certain theoretical breakthrough will translate into practical gains in their field of work, and tackle the lack of ready-to-use algorithm libraries, which provide stable, bug-free and well-tested implementations for algorithmic problems and expose an easy-to-use interface for library consumers. But also, promising algorithmic approaches have been neglected due to difficulties in mathematical analysis. The term "algorithm engineering" was first used with specificity in 1997, with the first Workshop on Algorithm Engineering (WAE97), organized by Giuseppe F. Italiano. == Difference from algorithm theory == Algorithm engineering does not intend to replace or compete with algorithm theory, but tries to enrich, refine and reinforce its formal approaches with experimental algorithmics (also called empirical algorithmics). This way it can provide new insights into the efficiency and performance of algorithms in cases where the algorithm at hand is less amenable to algorithm theoretic analysis, formal analysis pessimistically suggests bounds which are unlikely to appear on inputs of practical interest, the algorithm relies on the intricacies of modern hardware architectures like data locality, branch prediction, instruction stalls, instruction latencies which the machine model used in Algorithm Theory is unable to capture in the required detail, the crossover between competing algorithms with different constant costs and asymptotic behaviors needs to be determined. == Methodology == Some researchers describe algorithm engineering's methodology as a cycle consisting of algorithm design, analysis, implementation and experimental evaluation, joined by further aspects like machine models or realistic inputs. They argue that equating algorithm engineering with experimental algorithmics is too limited, because viewing design and analysis, implementation and experimentation as separate activities ignores the crucial feedback loop between those elements of algorithm engineering. === Realistic models and real inputs === While specific applications are outside the methodology of algorithm engineering, they play an important role in shaping realistic models of the problem and the underlying machine, and supply real inputs and other design parameters for experiments. === Design === Compared to algorithm theory, which usually focuses on the asymptotic behavior of algorithms, algorithm engineers need to keep further requirements in mind: Simplicity of the algorithm, implementability in programming languages on real hardware, and allowing code reuse. Additionally, constant factors of algorithms have such a considerable impact on real-world inputs that sometimes an algorithm with worse asymptotic behavior performs better in practice due to lower constant factors. === Analysis === Some problems can be solved with heuristics and randomized algorithms in a simpler and more efficient fashion than with deterministic algorithms. Unfortunately, this makes even simple randomized algorithms difficult to analyze because there are subtle dependencies to be taken into account. === Implementation === Huge semantic gaps between theoretical insights, formulated algorithms, programming languages and hardware pose a challenge to efficient implementations of even simple algorithms, because small implementation details can have rippling effects on execution behavior. The only reliable way to compare several implementations of an algorithm is to spend an considerable amount of time on tuning and profiling, running those algorithms on multiple architectures, and looking at the generated machine code. === Experiments === See: Experimental algorithmics === Application engineering === Implementations of algorithms used for experiments differ in significant ways from code usable in applications. While the former prioritizes fast prototyping, performance and instrumentation for measurements during experiments, the latter requires thorough testing, maintainability, simplicity, and tuning for particular classes of inputs. === Algorithm libraries === Stable, well-tested algorithm libraries like LEDA play an important role in technology transfer by speeding up the adoption of new algorithms in applications. Such libraries reduce the required investment and risk for practitioners, because it removes the burden of understanding and implementing the results of academic research. == Conferences == Two main conferences on Algorithm Engineering are organized annually, namely: Symposium on Experimental Algorithms (SEA), established in 1997 (formerly known as WEA). SIAM Meeting on Algorithm Engineering and Experiments (ALENEX), established in 1999. The 1997 Workshop on Algorithm Engineering (WAE'97) was held in Venice (Italy) on September 11–13, 1997. The Third International Workshop on Algorithm Engineering (WAE'99) was held in London, UK in July 1999. The first Workshop on Algorithm Engineering and Experimentation (ALENEX99) was held in Baltimore, Maryland on January 15–16, 1999. It was sponsored by DIMACS, the Center for Discrete Mathematics and Theoretical Computer Science (at Rutgers University), with additional support from SIGACT, the ACM Special Interest Group on Algorithms and Computation Theory, and SIAM, the Society for Industrial and Applied Mathematics.
Human–AI interaction
Human–AI interaction is a developing field of research and a sub-field of human–computer interaction (HCI). HCI is a field of research that explores the interactions between humans and computer-based technology, focusing on design implementation, user experience, and psychological factors. With the proliferation of artificial intelligence (AI), there has developed a sub-section of HCI research dedicated specifically to artificial intelligence and how people interact with and are impacted by it. This is human–AI interaction, abbreviated either as HAX or HAII. == Introduction == Artificial intelligence (AI), in general, has fluid definitions and varied research applications, but in brief can be applied to mechanizing tasks that would require human intelligence to complete. AI are tools designed to replicate the human abilities of navigating uncertainty, active learning, and processing information in different contexts. Within the context of HCI and HAX research, artificial intelligence can be broken into two sub-fields, natural language processing (NLP) and computer vision (CV). AI technologies notably include machine-learning, deep-learning and neural networks, and large-language models (LLMs). As a new and rapidly developing technology, AI is changing how computers work and therefore changing how humans interact with computers. Unlike the traditional human-computer interaction, where a human directs a machine, human-AI interaction is characterized by a more collaborative relationship between the computer program (the AI) and the human user, as AI is perceived as an active agent rather than a tool. This changing dynamic creates new questions and necessitates new research methods that are not present in traditional HCI research. According to a scoping review on the state of the discipline, the HAX field comprises research on the "design, development, and evaluation of AI systems" and encompasses the themes of human-AI collaboration, human-AI competition, human-AI conflict, and human-AI symbiosis. == Design == Machine learning and artificial intelligence have been used for decades in targeted advertising and to recommend content in social media. Ethical Guidelines (Framework for ethical AI development) == User Experience (UX) == This section should handle research on how users interact with tools. What techniques do they use, do they develop habits, what types of programs and devices are they using to access these tools, what do they use these tools to do exactly. === Cognitive Frameworks in AI Tool Users === AI has been viewed with various expectations, attributions, and often misconceptions. Many people exclusively understand AI as the LLM chatbots they interact with, like ChatGPT or Claude, or other generative AI programs. [Insert section: discuss how people interact with these specific AI tools as a connection to the following paragraphs] Most fundamentally, humans have a mental model of understanding AI's reasoning and motivation for its decision recommendations, and building a holistic and precise mental model of AI helps people create prompts to receive more valuable responses from AI. However, these mental models are not whole because people can only gain more information about AI through their limited interaction with it; more interaction with AI builds a better mental model that a person may build to produce better prompt outcomes. Research on human-AI interaction has emphasized that users develop mental models of AI systems and revise those models through repeated use, feedback, and explanation, while design research has stressed the importance of communicating capabilities and limitations early and supporting trust calibration through explanation and correction. In a 2025 SSRN working paper, John DeVadoss proposed "Hypothetico-Deductive Interaction" (HDI), a framework that describes human-AI interaction as a mutual process of conjecture and refutation in which users test assumptions about an AI system's capabilities while the system infers and updates assumptions about user goals through its responses and clarifying questions. DeVadoss argued that this framing helps explain prompt iteration, weak capability awareness, and trust miscalibration, and suggested design responses such as clearer communication of uncertainty, easier correction, actionable explanations, and safer failure modes. == Research themes == === Human-AI collaboration === Human-AI collaboration occurs when the human and AI supervise the task on the same level and extent to achieve the same goal. Some collaboration occurs in the form of augmenting human capability. AI may help human ability in analysis and decision-making through providing and weighing a volume of information, and learning to defer to the human decision when it recognizes its unreliability. It is especially beneficial when the human can detect a task that AI can be trusted to make few errors so that there is not a lot of excessive checking process required on the human's end. Some findings show signs of human-AI augmentation, or human–AI symbiosis, in which AI enhances human ability in a way that co-working on a task with AI produces better outcomes than a human working alone. For example: the quality and speed of customer service tasks increase when a human agent collaborates with AI, training on specific models allows AI to improve diagnoses in clinical settings, and AI with human-intervention can improve creativity of artwork while fully AI-generated haikus were rated negatively. Human-AI synergy, a concept in which human-AI collaboration would produce more optimal outcomes than either human or AI working alone could explain why AI does not always help with performance. Some AI features and development may accelerate human-AI synergy, while others may stagnate it. For example, when AI updates for better performance, it sometimes worsens the team performance with human and AI by reducing the compatibility with the new model and the mental model a user has developed on the previous version. Research has found that AI often supports human capabilities in the form of human-AI augmentation and not human-AI synergy, potentially because people rely too much on AI and stop thinking on their own. Prompting people to actively engage in analysis and think when to follow AI recommendations reduces their over-reliance, especially for individuals with higher need for cognition. === Human-AI competition === Robots and computers have substituted routine tasks historically completed by humans, but agentic AI has made it possible to also replace cognitive tasks including taking phone calls for appointments and driving a car. At the point of 2016, research has estimated that 45% of paid activities could be replaced by AI by 2030. Perceived autonomy of robots is known to increase people's negative attitude toward them, and worry about the technology taking over leads people to reject it. There has been a consistent tendency of algorithm aversion in which people prefer human advice over AI advice. However, people are not always able to tell apart tasks completed by AI or other humans. See AI takeover for more information. It is also notable that this sentiment is more prominent in the Western cultures as Westerners tend to show less positive views about AI compared to East Asians. == Research on the psychological impacts of AI == === Perception on others who use AI === As much as people perceive and make judgment about AI itself, they also form impressions of themselves and others who use AI. In the workplace, employees who disclose the use of AI in their tasks are more likely to receive feedback that they are not as hardworking as those who are in the same job who receive non-AI help to complete the same tasks. AI use disclosure diminishes the perceived legitimacy in the employee's task and decision making which ultimately leads observers to distrust people who use AI. Although these negative effects of AI use disclosure are weakened by the observers who use AI frequently themselves, the effect is still not attenuated by the observers' positive attitude towards AI. === Bias, AI, and human === Although AI provides a wide range of information and suggestions to its users, AI itself is not free of biases and stereotypes, and it does not always help people reduce their cognitive errors and biases. People are prone to such errors by failing to see other potential ideas and cases that are not listed by AI responses and committing to a decision suggested by AI that directly contradicts the correct information and directions that they are already aware of. Gender bias is also reflected as the female gendering of AI technologies which conceptualizes females as a helpful assistant. == Emotional connection with AI == Human-AI interaction has been theorized in the context of interpersonal relationships mainly in social psychology, communications and media studies, and as a technology interface through the lens of hu
Greg Brockman
Gregory Brockman (born November 29, 1987) is an American entrepreneur and software engineer. He is co-founder and president of OpenAI. He began his career at Stripe in 2010, upon leaving MIT, and became CTO in 2013. He left Stripe in 2015 to co-found OpenAI, where he also served as CTO. == Early life == Brockman was born in Thompson, North Dakota, and attended Red River High School, where he excelled in mathematics, chemistry, and computer science. He won a silver medal in the 2006 International Chemistry Olympiad and became the first finalist from North Dakota to participate in the Intel science talent search since 1973. In 2003, 2005, and 2007, he attended Canada/USA Mathcamp, a summer program for mathematically talented high-school students. In 2008, Brockman enrolled at Harvard University but left a year later, briefly enrolling at the Massachusetts Institute of Technology. == Career == In 2010, he dropped out of MIT to join Stripe, a company founded by Patrick Collison, his MIT classmate, and John Collison. In 2013, he became Stripe's first CTO, while the company grew from 5 to 205 employees. Brockman left Stripe in May 2015. === OpenAI === Brockman met with Sam Altman and Elon Musk, and led the recruiting of the OpenAI founding team. Many of its members, including Ilya Sutskever, were top AI research talent that left high paying jobs for the opportunity at OpenAI. He co-founded OpenAI in December 2015 alongside Altman, Sutskever and others. The company initially operated from Brockman's living room. He led various projects at OpenAI, including OpenAI Gym and OpenAI Five, a Dota 2 bot. On February 14, 2019, OpenAI announced that they had developed a new large language model called GPT-2, but kept it private due to their concern for its potential misuse. They released the model to a limited group of beta testers in May 2019. On March 14, 2023, in a live video demo, Brockman unveiled GPT-4, the fourth iteration in the GPT series. On November 17, 2023, alongside the firing of Sam Altman, Brockman was told he had been removed from the board. Sutskever supplied the board with a document of alleged bullying by Brockman. Mira Murati said Brockman's relationship with Altman made it impossible for her to do her job, and Altman had already "fielded many requests from OpenAI employees to rein in Brockman". Brockman was to report to Murati, but on November 17, he announced that he had quit the company. On November 20, 2023, Microsoft CEO Satya Nadella announced that Brockman and Altman would join Microsoft to lead a new advanced AI research team. The following day, after a deal was reached to reinstate Altman as CEO, Brockman returned to OpenAI. Brockman took a sabbatical from August to November 2024. === Elon Musk lawsuit === Jury selection for OpenAI cofounder Elon Musk's lawsuit against OpenAI and its current executives, including Brockman, began on April 27, 2026. On April 28, 2026, trial testimony was by now underway, with Elon Musk beginning his testimony against Altman and OpenAI. On April 30, 2026 Musk would enter his third day of testimony. == Personal life == In November 2019 after a year of dating, Brockman married Anna at OpenAI's offices on a workday. Ilya Sutskever officiated. == Political activities == Brockman and his wife were the biggest donors to Donald Trump's Super PAC, MAGA Inc., in 2025 with each of them donating US$12.5 million. Brockman and his wife also donated $50 million to Leading the Future, a super PAC dedicated to AI deregulation that he helped found with Andreessen Horowitz co-founders Marc Andreessen and Ben Horowitz. OpenAI publicly expressed openness to increased regulatory oversight and has a policy against donating to such Super PACs.
Hyper basis function network
In machine learning, a Hyper basis function network, or HyperBF network, is a generalization of radial basis function (RBF) networks concept, where the Mahalanobis-like distance is used instead of the Euclidean distance measure. Hyper basis function networks were first introduced by Poggio and Girosi in the 1990 paper “Networks for Approximation and Learning”. == Network Architecture == The typical HyperBF network structure consists of a real input vector x ∈ R n {\displaystyle x\in \mathbb {R} ^{n}} , a hidden layer of activation functions and a linear output layer. The output of the network is a scalar function of the input vector, ϕ : R n → R {\displaystyle \phi :\mathbb {R} ^{n}\to \mathbb {R} } , is given by where N {\displaystyle N} is a number of neurons in the hidden layer, μ j {\displaystyle \mu _{j}} and a j {\displaystyle a_{j}} are the center and weight of neuron j {\displaystyle j} . The activation function ρ j ( | | x − μ j | | ) {\displaystyle \rho _{j}(||x-\mu _{j}||)} at the HyperBF network takes the following form where R j {\displaystyle R_{j}} is a positive definite d × d {\displaystyle d\times d} matrix. Depending on the application, the following types of matrices R j {\displaystyle R_{j}} are usually considered R j = 1 2 σ 2 I d × d {\displaystyle R_{j}={\frac {1}{2\sigma ^{2}}}\mathbb {I} _{d\times d}} , where σ > 0 {\displaystyle \sigma >0} . This case corresponds to the regular RBF network. R j = 1 2 σ j 2 I d × d {\displaystyle R_{j}={\frac {1}{2\sigma _{j}^{2}}}\mathbb {I} _{d\times d}} , where σ j > 0 {\displaystyle \sigma _{j}>0} . In this case, the basis functions are radially symmetric, but are scaled with different width. R j = d i a g ( 1 2 σ j 1 2 , . . . , 1 2 σ j z 2 ) I d × d {\displaystyle R_{j}=diag\left({\frac {1}{2\sigma _{j1}^{2}}},...,{\frac {1}{2\sigma _{jz}^{2}}}\right)\mathbb {I} _{d\times d}} , where σ j i > 0 {\displaystyle \sigma _{ji}>0} . Every neuron has an elliptic shape with a varying size. Positive definite matrix, but not diagonal. == Training == Training HyperBF networks involves estimation of weights a j {\displaystyle a_{j}} , shape and centers of neurons R j {\displaystyle R_{j}} and μ j {\displaystyle \mu _{j}} . Poggio and Girosi (1990) describe the training method with moving centers and adaptable neuron shapes. The outline of the method is provided below. Consider the quadratic loss of the network H [ ϕ ∗ ] = ∑ i = 1 N ( y i − ϕ ∗ ( x i ) ) 2 {\displaystyle H[\phi ^{}]=\sum _{i=1}^{N}(y_{i}-\phi ^{}(x_{i}))^{2}} . The following conditions must be satisfied at the optimum: where R j = W T W {\displaystyle R_{j}=W^{T}W} . Then in the gradient descent method the values of a j , μ j , W {\displaystyle a_{j},\mu _{j},W} that minimize H [ ϕ ∗ ] {\displaystyle H[\phi ^{}]} can be found as a stable fixed point of the following dynamic system: where ω {\displaystyle \omega } determines the rate of convergence. Overall, training HyperBF networks can be computationally challenging. Moreover, the high degree of freedom of HyperBF leads to overfitting and poor generalization. However, HyperBF networks have an important advantage that a small number of neurons is enough for learning complex functions.
Leading the Future
Leading the Future is an American super PAC network focused on lobbying for policies friendly to the artificial intelligence industry. It was launched in 2025 with over $100 million from industry stakeholders including Andreessen Horowitz, OpenAI President Greg Brockman and Palantir co-founder Joe Lonsdale. The launch was preceded by talks between Collin McCune, head of government affairs at Andreessen Horowitz, and Chris Lehane, chief global affairs officer at OpenAI. Among the members of the network are the American Mission PAC, which supported Chris Gober, and the Think Big PAC, which targeted Alex Bores. Leading the Future is affiliated with the nonprofit Build American AI, which Axios describes as a dark money advocacy "offshoot" operating alongside the super PAC. NBC News states that the network’s efforts are modeled after the pro-cryptocurrency group Fairshake. Leading the Future is led by Zac Moffatt and Josh Vlasto, the latter of whom previously served as an advisor to Fairshake. In response to the creation of Leading the Future, former members of Congress Brad Carson and Chris Stewart co-founded the super PAC network Public First, aiming to counter the group’s influence. In April 2026, an investigation by Model Republic linked Leading the Future to The Wire By Acutus, an automated news website that allegedly used AI agents posing as human journalists to solicit interviews. The site's content was found to closely mirror the PAC's deregulatory policy goals while targeting researchers and advocates skeptical of rapid AI development. In May 2026, Wired revealed that Build American AI used a "dark money" campaign to pay TikTok and Instagram influencers $5,000 per video to promote scripted narratives framing Chinese AI as a "national security threat." According to internal documents and staff at the marketing agency managing the project, the campaign's explicit goal was to "subtly shift public debate" toward the deregulation of AI industries while intentionally avoiding technical discussions regarding AI quality or safety. During the 2026 primary season Leading the Future went on to endorse several candidates in both Democratic and Republican races with several of them going on to win.
Neural style transfer
Neural style transfer (NST) software algorithms are able to manipulate digital images, or videos, in order to adopt the appearance or visual style of another image. NST algorithms are characterized by their use of deep neural networks for the sake of image transformation. Common uses for NST are the creation of artificial artwork from photographs, for example by transferring the appearance of famous paintings to user-supplied photographs. Several notable mobile apps use NST techniques for this purpose, including DeepArt and Prisma. This method has been used by artists and designers around the globe to develop new artwork based on existent style(s). == History == NST is an example of image stylization, a problem studied for over two decades within the field of non-photorealistic rendering. The first two example-based style transfer algorithms were image analogies and image quilting. Both of these methods were based on patch-based texture synthesis algorithms. Given a training pair of images–a photo and an artwork depicting that photo–a transformation could be learned and then applied to create new artwork from a new photo, by analogy. If no training photo was available, it would need to be produced by processing the input artwork; image quilting did not require this processing step, though it was demonstrated on only one style. NST was first published in the paper "A Neural Algorithm of Artistic Style" by Leon Gatys et al., originally released to ArXiv 2015, and subsequently accepted by the peer-reviewed CVPR conference in 2016. The original paper used a VGG-19 architecture that has been pre-trained to perform object recognition using the ImageNet dataset. In 2017, Google AI introduced a method that allows a single deep convolutional style transfer network to learn multiple styles at the same time. This algorithm permits style interpolation in real-time, even when done on video media. == Mathematics == This section closely follows the original paper. === Overview === The idea of Neural Style Transfer (NST) is to take two images—a content image p → {\displaystyle {\vec {p}}} and a style image a → {\displaystyle {\vec {a}}} —and generate a third image x → {\displaystyle {\vec {x}}} that minimizes a weighted combination of two loss functions: a content loss L content ( p → , x → ) {\displaystyle {\mathcal {L}}_{\text{content }}({\vec {p}},{\vec {x}})} and a style loss L style ( a → , x → ) {\displaystyle {\mathcal {L}}_{\text{style }}({\vec {a}},{\vec {x}})} . The total loss is a linear sum of the two: L NST ( p → , a → , x → ) = α L content ( p → , x → ) + β L style ( a → , x → ) {\displaystyle {\mathcal {L}}_{\text{NST}}({\vec {p}},{\vec {a}},{\vec {x}})=\alpha {\mathcal {L}}_{\text{content}}({\vec {p}},{\vec {x}})+\beta {\mathcal {L}}_{\text{style}}({\vec {a}},{\vec {x}})} By jointly minimizing the content and style losses, NST generates an image that blends the content of the content image with the style of the style image. Both the content loss and the style loss measures the similarity of two images. The content similarity is the weighted sum of squared-differences between the neural activations of a single convolutional neural network (CNN) on two images. The style similarity is the weighted sum of Gram matrices within each layer (see below for details). The original paper used a VGG-19 CNN, but the method works for any CNN. === Symbols === Let x → {\textstyle {\vec {x}}} be an image input to a CNN. Let F l ∈ R N l × M l {\textstyle F^{l}\in \mathbb {R} ^{N_{l}\times M_{l}}} be the matrix of filter responses in layer l {\textstyle l} to the image x → {\textstyle {\vec {x}}} , where: N l {\textstyle N_{l}} is the number of filters in layer l {\textstyle l} ; M l {\textstyle M_{l}} is the height times the width (i.e. number of pixels) of each filter in layer l {\textstyle l} ; F i j l ( x → ) {\textstyle F_{ij}^{l}({\vec {x}})} is the activation of the i th {\textstyle i^{\text{th}}} filter at position j {\textstyle j} in layer l {\textstyle l} . A given input image x → {\textstyle {\vec {x}}} is encoded in each layer of the CNN by the filter responses to that image, with higher layers encoding more global features, but losing details on local features. === Content loss === Let p → {\textstyle {\vec {p}}} be an original image. Let x → {\textstyle {\vec {x}}} be an image that is generated to match the content of p → {\textstyle {\vec {p}}} . Let P l {\textstyle P^{l}} be the matrix of filter responses in layer l {\textstyle l} to the image p → {\textstyle {\vec {p}}} . The content loss is defined as the squared-error loss between the feature representations of the generated image and the content image at a chosen layer l {\displaystyle l} of a CNN: L content ( p → , x → , l ) = 1 2 ∑ i , j ( A i j l ( x → ) − A i j l ( p → ) ) 2 {\displaystyle {\mathcal {L}}_{\text{content }}({\vec {p}},{\vec {x}},l)={\frac {1}{2}}\sum _{i,j}\left(A_{ij}^{l}({\vec {x}})-A_{ij}^{l}({\vec {p}})\right)^{2}} where A i j l ( x → ) {\displaystyle A_{ij}^{l}({\vec {x}})} and A i j l ( p → ) {\displaystyle A_{ij}^{l}({\vec {p}})} are the activations of the i th {\displaystyle i^{\text{th}}} filter at position j {\displaystyle j} in layer l {\displaystyle l} for the generated and content images, respectively. Minimizing this loss encourages the generated image to have similar content to the content image, as captured by the feature activations in the chosen layer. The total content loss is a linear sum of the content losses of each layer: L content ( p → , x → ) = ∑ l v l L content ( p → , x → , l ) {\displaystyle {\mathcal {L}}_{\text{content }}({\vec {p}},{\vec {x}})=\sum _{l}v_{l}{\mathcal {L}}_{\text{content }}({\vec {p}},{\vec {x}},l)} , where the v l {\displaystyle v_{l}} are positive real numbers chosen as hyperparameters. === Style loss === The style loss is based on the Gram matrices of the generated and style images, which capture the correlations between different filter responses at different layers of the CNN: L style ( a → , x → ) = ∑ l = 0 L w l E l , {\displaystyle {\mathcal {L}}_{\text{style }}({\vec {a}},{\vec {x}})=\sum _{l=0}^{L}w_{l}E_{l},} where E l = 1 4 N l 2 M l 2 ∑ i , j ( G i j l ( x → ) − G i j l ( a → ) ) 2 . {\displaystyle E_{l}={\frac {1}{4N_{l}^{2}M_{l}^{2}}}\sum _{i,j}\left(G_{ij}^{l}({\vec {x}})-G_{ij}^{l}({\vec {a}})\right)^{2}.} Here, G i j l ( x → ) {\displaystyle G_{ij}^{l}({\vec {x}})} and G i j l ( a → ) {\displaystyle G_{ij}^{l}({\vec {a}})} are the entries of the Gram matrices for the generated and style images at layer l {\displaystyle l} . Explicitly, G i j l ( x → ) = ∑ k F i k l ( x → ) F j k l ( x → ) {\displaystyle G_{ij}^{l}({\vec {x}})=\sum _{k}F_{ik}^{l}({\vec {x}})F_{jk}^{l}({\vec {x}})} Minimizing this loss encourages the generated image to have similar style characteristics to the style image, as captured by the correlations between feature responses in each layer. The idea is that activation pattern correlations between filters in a single layer captures the "style" on the order of the receptive fields at that layer. Similarly to the previous case, the w l {\displaystyle w_{l}} are positive real numbers chosen as hyperparameters. === Hyperparameters === In the original paper, they used a particular choice of hyperparameters. The style loss is computed by w l = 0.2 {\displaystyle w_{l}=0.2} for the outputs of layers conv1_1, conv2_1, conv3_1, conv4_1, conv5_1 in the VGG-19 network, and zero otherwise. The content loss is computed by w l = 1 {\displaystyle w_{l}=1} for conv4_2, and zero otherwise. The ratio α / β ∈ [ 5 , 50 ] × 10 − 4 {\displaystyle \alpha /\beta \in [5,50]\times 10^{-4}} . === Training === Image x → {\displaystyle {\vec {x}}} is initially approximated by adding a small amount of white noise to input image p → {\displaystyle {\vec {p}}} and feeding it through the CNN. Then we successively backpropagate this loss through the network with the CNN weights fixed in order to update the pixels of x → {\displaystyle {\vec {x}}} . After several thousand epochs of training, an x → {\displaystyle {\vec {x}}} (hopefully) emerges that matches the style of a → {\displaystyle {\vec {a}}} and the content of p → {\displaystyle {\vec {p}}} . As of 2017, when implemented on a GPU, it takes a few minutes to converge. == Extensions == In some practical implementations, it is noted that the resulting image has too much high-frequency artifact, which can be suppressed by adding the total variation to the total loss. Compared to VGGNet, AlexNet does not work well for neural style transfer. NST has also been extended to videos. Subsequent work improved the speed of NST for images by using special-purpose normalizations. In a paper by Fei-Fei Li et al. adopted a different regularized loss metric and accelerated method for training to produce results in real-time (three orders of magnitude faster than Gatys). Their idea was to use not the pixel-based loss defined above but rather a 'perceptual loss' measuring t
No Fakes Act
The NO FAKES Act or the Nurture Originals, Foster Art, and Keep Entertainment Safe Act, is proposed United States federal legislation concerning digital replicas. The bill was first introduced in 2023 as a discussion draft, formally introduced in 2024, and reintroduced in 2025. If enacted, the bill would establish a federal right of publicity, giving public figures and private individuals greater control over the creation and use of digital replicas of their likenesses, including artificial intelligence (AI)-generated content. If passed, the NO FAKES Act would create a legal framework for licensing digital replicas, including provisions for liability, safe harbors, and statutory exceptions. The proposal has received broad support from the entertainment and technology industries. However, digital rights organizations have raised concerns that the Act risks chilling protected speech. == Background == === Entertainment industry concerns === Actors’ concerns over studios' use of their digital likeness were one of the primary drivers of the Screen Actors Guild–American Federation of Television and Radio Artists (SAG-AFTRA) strike in 2023. Negotiators for SAG-AFTRA alleged that the Alliance of Motion Picture and Television Producers (AMPTP) sought to use the digital likenesses of actors in perpetuity and would try to replace union members, especially background actors. The AMPTP denied SAG-AFTRA's interpretation of its proposal. In November 2023, AMPTP and SAG-AFTRA reached an agreement on the use of actors’ digital replicas, which included requirements for consent and compensation. Recording labels have also expressed concerns over unauthorized digital replicas of their performers' likeness. In 2023, TikTok user Ghostwriter977 released "Heart on My Sleeve," an AI-produced song in the styles of Drake and the Weeknd. After the song received millions of streams, the Universal Music Group (UMG) initiated takedown requests to TikTok and YouTube, which removed the song from their platforms. The legal arguments attorneys made were not disclosed; however, commentators noted that they likely used the Digital Millennium Copyright Act (DMCA). This presented a novel scenario, since UMG did not have licensing rights to "Heart on My Sleeve." According to The Verge, UMG based its DMCA takedown request on an unauthorized sample used at the start of the song for the producer tag. While legal commentators noted that UMG could have asserted a violation of the artists’ rights of publicity, existing state right of publicity laws do not provide notice-and-takedown mechanisms comparable to those under the DMCA. === Legal landscape === Legal scholars have observed that AI-generated digital replicas raise questions under existing copyright and intellectual property law. U.S. copyright law generally requires that original authorship be attributable to a human; however, the extent of human intervention needed to satisfy this requirement is not clear. Copyright holders have filed lawsuits against AI companies alleging unauthorized usage of copyrighted material to train their models, though many of these cases remain pending. In terms of outputs, record labels often hold rights to artists’ musical works but do not necessarily control the artists’ voice, appearance, or likeness in the same way. As a result, AI-generated recordings such as "Heart on My Sleeve" may fall outside the scope of certain traditional copyright protections. Individuals' likenesses have historically been governed under the Lanham Act, the Federal Trade Commission Act, and right of publicity laws. The right of publicity, recognized in many state-level statutes and common law, allows individuals to bring legal claims against unauthorized commercial use of their identities. It has often, but not exclusively, been applied to celebrities or other recognizable individuals. There is no federal-level right to publicity, and state-level protections vary, especially on issues relating to digital replicas and posthumous rights, which makes it difficult for creators or other individuals to prevent unauthorized use of their likenesses. In July 2024, the U.S. Copyright Office released a report on digital replicas and recommended that Congress create a federal law to protect individuals from unauthorized uses of their digital replicas, noting the inadequacy, narrowness, and inconsistency of existing laws. == Provisions == Under the NO FAKES Act of 2025, a digital replica is defined as "a newly created, computer-generated, highly realistic electronic representation that is readily identifiable as the voice or visual likeness of an individual," living or dead. A digital replica can be embodied in sound recordings, images, or audiovisual works in which the individual did not perform or in which the individual did perform but the "fundamental character of the performance or appearance has been materially altered." The Act specifies that digital replicas do not include reproduced samples of works authorized by the copyright holder. The Act defines a "right holder" as either the individual who is the subject of a digital replica or an entity that has acquired the rights to that individual’s likeness. The Act grants right holders the exclusive right to authorize the use of an individual’s likeness in a digital replica. This right is not assignable during the individual’s lifetime; however, it can be licensed to a living individual for up to 10 years under certain conditions. Postmortem rights The Act provides that the right does not automatically expire upon an individual’s death. It may be transferred to executors, heirs, or other parties designated by the individual. The right is held by the right holder for 10 years following the individual’s death. If the right holder demonstrates active use of the digital replica within the 2 years preceding the end of the 10-year term, the right may be extended for an additional 5-year period. These five-year extensions may be renewed for up to 70 years after the individual’s death. Liability The Act establishes liability for individuals who knowingly distribute a digital replica without authorization from the right holder, as well as for entities that make available a service primarily designed to produce unlawful digital replicas. Safe harbor provisions Similar to the Communications Decency Act and the DMCA, the Act establishes safe harbor provisions for online service providers. Providers are shielded from liability if they adopt and inform users of a policy for terminating accounts that repeatedly violate the Act. The NO FAKES Act does not require online services to proactively monitor content. Instead, it creates a notice-and-takedown mechanism under which providers must promptly respond to notifications seeking the removal of unauthorized digital replicas. These safe harbor protections apply only if the online service provider designates an agent with the U.S. Copyright Office to receive notifications of alleged violations. Remedies The NO FAKES Act provides remedies that are similar to those available under U.S. copyright law. Under the Act, individuals may be held liable for either statutory damages of $5,000 or actual damages for creating or distributing an unauthorized digital replica. The legislation also establishes a tiered liability framework for online service providers. Those that make good faith efforts to comply with the Act may face statutory damages of up to $25,000 per work for violations or actual damages. Providers that do not undertake such compliance efforts may be liable for $5,000 per unauthorized display or transmission of a digital replica, with damages capped at $750,000 per work. Exclusions The Act includes several exceptions to liability that are modeled in part on fair use principles. Digital replicas are excluded from liability when "used in a bona fide news, public affairs, or sports broadcast or account;" in a documentary or historical context; or in a way that is "consistent with the public interest." These exclusions do not apply to de minimis uses or to digital replicas that are sexually explicit in nature. The Act further states that licensing requirements do not apply to licenses established through collective bargaining agreements that contain provisions governing the use of digital replicas. The Act does not impose secondary liability on providers of generative artificial intelligence tools or services whose primary purpose is not the creation of unauthorized digital replicas. Preemption The NO FAKES Act preempts laws that protect "an individual's voice and visual likeness rights in connection with a digital replica, as defined in this Act, in an expressive work." However, the Act preserves state laws governing digital replicas enacted before January 2, 2025, as well as state laws addressing digital replicas that portray sexually explicit conduct. == History == In 2023, Senators Marsha Blackburn, Chris Coons, Amy Klobuchar, and Th