AI Email Builder

AI Email Builder — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

Immuni

Immuni was an open-source COVID-19 contact tracing app used for digital contact tracing in Italy, dismissed on 31 December 2022, after a long and debated criticism for having been a failure due to the lack of trust placed by citizens. Immuni COVID-19 contact-tracing app had in fact been downloaded only by 12% of Italians between 14 and 75 years old (the government had previously stated that, in order for the app to work properly, it should have been downloaded by at least 60% of Italians). It makes use of the Apple/Google Exposure Notification system. == Development == It was developed by Bending Spoons and released by the Italian Ministry of Health on 1 June 2020. After a testing phase in 4 Italian regions (Abruzzo, Apulia, Liguria, Marche), the app started being active in the whole country on 15 June 2020. The app was initially released on App Store and Google Play, and since 1 February 2021 it is available on the Huawei AppGallery as well. === Source code === The source code was published on GitHub on the 25 May. The app only works in Italy, but compatibility with other European contact tracing apps was a goal. Since 19 October 2020 the app supports key-exchanges with the EU Interoperability Gateway and is therefore able to communicate with contact tracing apps of other EU countries. == Shutdown == As of 16 December 2020, the app was downloaded more than 10 million times, a number which increased to 21.882.502 downloads the day before the app's shutdown. On 27 December 2022 the Italian Ministry of Health announced that the app and its infrastructures will be dismissed on the 31 December of the same year.
Read more →
Radford M. Neal

Radford M. Neal (born September 12, 1956) is a professor emeritus at the Department of Statistics and Department of Computer Science at the University of Toronto, where he held a Canada research chair in statistics and machine learning. == Education and career == Neal studied computer science at the University of Calgary, where he received his B.Sc. in 1977 and M.Sc. in 1980, with thesis work supervised by David Hill. He worked for several years as a sessional instructor at the University of Calgary and as a statistical consultant in the industry before coming back to the academia. Neal continued his study at the University of Toronto, where he received his Ph.D. in 1995 under the supervision of Geoffrey Hinton. Neal became an assistant professor at the University of Toronto in 1995, an associated professor in 1999 and a full professor since 2001. He was the Canada Research Chair in Statistics and Machine Learning from 2003 to 2016 and retired in 2017. Neal has made great contributions in the area of machine learning and statistics, where he is particularly well known for his work on Markov chain Monte Carlo, error correcting codes and Bayesian learning for neural networks. He is also known for his blog and as the developer of pqR: a new version of the R interpreter.
Read more →
Devi Parikh

Devi Parikh is an American computer scientist. == Career == Parikh earned her PhD in Electrical and Computer Engineering at Carnegie Mellon University. She has served as a professor at Virginia Tech and Georgia Tech, and as of 2022 she is a research director at Meta. == Research == Parikh's research focuses on computer vision and natural language processing. In 2015, Parikh and her students at Virginia Tech worked on AI for Visual Question Answering (VQA). This technology allows users to ask questions about pictures, e.g. "Is this a vegetarian pizza?" Parikh's VQA dataset has been used to evaluate over 30 AI models. In 2017, Parikh published a conversational agent called ParlAI. In 2020, she developed an AI system that generates dance moves in sync with songs. In 2022, Parikh and a team at Meta developed Make-a-Video, a text-to-video AI model that is based on the diffusion algorithm. == Awards == 2017 IJCAI Computers and Thought Award 2011 ICCV Best-Paper Award ("Marr Prize")
Read more →
Is an AI Blog Writer Worth It in 2026?

Trying to pick the best AI blog writer? An AI blog writer is software that uses machine learning to help you get more done — it scales effortlessly from a single task to thousands. The best picks balance beginner-friendly simplicity with the depth power users need, and they ship updates often. Whether you are a beginner or a pro, the right AI blog writer slots into your workflow and pays for itself fast. This guide breaks down the top picks, their pros and cons, and who each one is best for.
Read more →
Comparison of video editing software

This is a comparison of non-linear video editing software applications. See also a more complete list of video editing software. == General information == This table gives basic general information about the different editors: === Active === === Discontinued / Inactive === ==== Definition ==== professional: used for full length Hollywood movies; professional (small): mainly used for paid commercials, short films or podcasts/YouTube channels; prosumer: Mainly targeting private use, anything that can do more than just trimming a film; basic: trimming a film; == System requirements == This table lists the operating systems that different editors can run on without emulation, as well as other system requirements. Note that minimum system requirements are listed; some features (like High Definition support) may be unavailable with these specifications. "Unix" includes the similar Linux, BSD and Unix-like operating systems. == High definition/High resolution import == The table below indicates the ability of each program to import various High Definition video or High resolution video formats for editing. == Feature set == == Output options == Please note that recording to Blu-ray does not imply 1080@50p/60p . Most only support up to 1080i 25/30 frames per second recording. Also not all formats can be output.
Read more →
Claire Cardie

Claire Cardie is an American computer scientist specializing in natural language processing. Since 2006, she has been a professor of computer science and information science at Cornell University, and from 2010 to 2011 she was the first Charles and Barbara Weiss Chair of Information Science at Cornell. Her research interests include coreference resolution and sentiment analysis. == Education and career == Cardie is a 1982 graduate of Yale University, majoring in computer science. After working for several companies as a computer programmer, she returned to graduate study in the late 1980s and completed her Ph.D. at the University of Massachusetts Amherst in 1994. Her dissertation, Domain-Specific Knowledge Acquisition for Conceptual Sentence Analysis, was supervised by Wendy Lehnert. She has been on the Cornell University faculty since 1994, initially in computer science and since 2005 also in information science. She was an assistant professor (1994–2000) and associate professor (2000–06), before being promoted to a full professorship in 2006. In 2007 she founded a start-up company, Appinions, and she was its chief scientist until 2015. Her doctoral students at Cornell have included Amit Singhal and Kiri Wagstaff. == Recognition == Cardie became a Fellow of the Association for Computational Linguistics in 2016. She was elected as an ACM Fellow in 2019 "for contributions to natural language processing, including coreference resolution, information and opinion extraction". She was named to the 2021 class of Fellows of the American Association for the Advancement of Science.
Read more →
AI Clip Makers Reviews: What Actually Works in 2026

In search of the best AI clip maker? An AI clip maker is software that uses machine learning to help you get more done — it turns a rough idea into a polished result in seconds. When choosing one, weigh output quality, pricing, export formats, and how well it fits the tools you already use. Whether you are a beginner or a pro, the right AI clip maker slots into your workflow and pays for itself fast. We tested the leading options and ranked them by quality, value, and ease of use.
Read more →
Cheng Xiang Zhai

ChengXiang Zhai is a computer scientist. He is a Donald Biggar Willett Professor in Engineering in the Department of Computer Science at the University of Illinois at Urbana-Champaign. == Biography == Zhai received the BS (1984), MS (1987, under Guoliang Zheng), and PhD (1990, under Jiafu Xu) in Computer Science from Nanjing University. He spent 1990 to 1993 working at Nanjing University's State Key Laboratory for Novel Software Technology. In 1993, he left for America to pursue a second PhD, this time at Carnegie Mellon University (CMU) with David A. Evans. Evans then left to spend more time with the company ClariTech. Zhai obtained from CMU a MS (1997) in computational linguistics and then started working with John Lafferty. He finally received from CMU a PhD in Language and Information Technologies in 2002. Since then, he has been an Assistant Professor (2002–2008), Associate Professor (2008–2013), Professor (2013–2018), and Donald Biggar Willett Professor (2018–) at the UIUC Department of Computer Science. He also holds joint appointments with the Carl R. Woese Institute for Genomic Biology, Department of Statistics, and School of Information Sciences at UIUC. == Awards == ACM SIGIR Gerard Salton Award, 2021, "for significant and sustained contributions to information retrieval and data science. His work has defined many of the theoretical foundations of the language modeling approach, yielding major insights into areas such as smoothing methods, relevance feedback, topic diversification, and text representations that incorporate positional information. He and his collaborators have also pioneered the axiomatic approach to information retrieval, which continues to provide inspiration for retrieval model and evaluation research." ACM SIGIR Academy inductee, 2021 ACM Fellow, 2017, "for contributions to information retrieval and text data mining." ACM SIGIR Test of Time Award, 2016, for paper A study of smoothing methods for language models applied to Ad Hoc information retrieval ACM SIGIR Test of Time Award, 2016, for paper Document language models, query models, and risk minimization for information retrieval ACM SIGIR Test of Time Award, 2014, for paper Beyond independent relevance: methods and evaluation metrics for subtopic retrieval ACM Distinguished Member, 2009 Presidential Early Career Award for Scientists and Engineers (PECASE), 2004, "for his work on user-centered, adaptive intelligent information access. His techniques expect to improve search-engine performance, support better information organization and enable understanding of large volumes of information. Zhai's work in information retrieval is expected to enhance curricula and provide new educational tools for the growing information technology workforce." ACM SIGIR Best Paper Award, 2004, for paper A formal study of information retrieval heuristics == Personal == Zhai's son Alex has earned three medals at the International Mathematical Olympiad.
Read more →
AI effect

The AI effect is a phenomenon in which advances in artificial intelligence lead to a redefinition of what is considered intelligence, such that capabilities achieved by AI systems are no longer regarded as examples of "real" intelligence. The concept has been used to describe both a cognitive tendency and a sociotechnical pattern, in which successful AI techniques are reclassified as routine computation or absorbed into other domains. Historian Pamela McCorduck described this as a recurring feature of AI research, noting in her 2004 book Machines Who Think that once a problem is solved, it is no longer considered evidence of intelligence. Researcher Rodney Brooks similarly observed in 2002 that once systems are understood, they are often regarded as "just computation". == Definition == The AI effect refers to a shift in how intelligence is defined as machines acquire new capabilities. Tasks such as playing chess, recognizing speech, or interpreting images were historically considered indicators of intelligence, but after successful automation they are often reclassified as routine computation. McCorduck described this as an "odd paradox", in which successful AI systems are assimilated into other domains, leaving AI researchers to focus on unsolved problems. The phenomenon is often interpreted as an instance of moving the goalposts. A commonly cited formulation is Tesler's theorem, often expressed as "AI is whatever hasn't been done yet". When problems are not fully formalised, they may be described using models involving human computation, such as human-assisted Turing machines. == Historical examples == === Game playing === Early AI systems capable of playing games such as checkers and chess were initially regarded as demonstrations of machine intelligence. As these systems improved and became better understood, their achievements were often reinterpreted as examples of computation rather than intelligence. The victory of IBM's Deep Blue over Garry Kasparov in 1997 is a frequently cited example. Critics argued that the system relied on brute-force methods rather than genuine understanding. === Pattern recognition === Technologies such as optical character recognition and speech recognition were once considered core problems in artificial intelligence. As these systems became reliable and widely deployed, they were increasingly treated as standard engineering solutions. === Integration into applications === Many techniques originally developed within AI research have been incorporated into broader technological systems, including marketing, automation, and software applications. Michael Swaine reported in 2007 that AI advances are often presented as developments in other fields. Marvin Minsky observed that successful AI innovations often evolve into separate disciplines. Nick Bostrom noted in 2006 that widely adopted technologies are often no longer labeled as AI. == Contemporary discussion == The AI effect continues to be discussed in the context of recent advances in machine learning, particularly large language models and other generative AI systems. As these systems have become more widely used, some researchers and commentators have noted that their capabilities are frequently described as statistical or mechanical once understood, rather than as intelligence. A 2016 survey of artificial intelligence also noted that AI systems are increasingly embedded in everyday applications, reinforcing earlier observations that successful AI technologies tend to become normalized and no longer identified as AI. At the same time, the widespread commercial use of artificial intelligence has led to greater visibility of the field, contrasting with earlier periods in which AI techniques were often present but unacknowledged. == Interpretations == === Cognitive bias === Some authors describe the AI effect as a cognitive bias in which expectations of intelligence shift as machines achieve new capabilities. === Sociotechnical perspective === Another interpretation emphasizes how technologies are reclassified over time as they become widespread and commercially successful. === Philosophical debate === Some philosophers argue that reclassification reflects genuine conceptual distinctions rather than bias. == Historical context == During periods such as the AI winter, researchers sometimes avoided the term "artificial intelligence" due to negative perceptions. In the 21st century, however, the term "AI" has become widely used in public discourse and marketing. == Broader implications == The AI effect has been linked to broader questions about human uniqueness and the nature of intelligence. Michael Kearns suggested that people may seek to preserve a special role for humans. Similar patterns have been observed in studies of animal cognition. Herbert A. Simon noted that artificial intelligence can provoke strong emotional reactions.
Read more →
Deepset

deepset is an enterprise software vendor that provides developers with the tools to build production-ready Artificial Intelligence (AI) and natural language processing (NLP) systems, using architectures such as agents, retrieval augmented generation (RAG) and multimodal AI. It was founded in 2018 in Berlin by Milos Rusic, Malte Pietsch, and Timo Möller. deepset authored and maintains the open source software Haystack and its commercial SaaS and self-hosted (VPC, on-prem, air gapped) offering, Haystack Enterprise Platform. (formerly known as deepset Cloud and deepset AI Platform) == History == In June 2018, Milos Rusic, Malte Pietsch, and Timo Möller co-founded deepset in Berlin, Germany. In the same year, the company served first customers who wanted to implement NLP services by tailoring BERT language models to their domain. In July 2019, the company released the initial version of the open source software FARM. In November 2019, the company released the initial version of the open source software Haystack. Throughout 2020 and 2021 deepset published several applied research papers at EMNLP, COLING and ACL, the leading conferences in the area of NLP. In 2020, the research contributions comprised German language models named GBERT and GELECTRA, and a question answering dataset addressing the COVID-19 pandemic called COVID-QA, which was created in collaboration with Intel and has been annotated by biomedical experts. In 2021, the research contributions comprised German models and datasets for question answering and passage retrieval named GermanQuAD and GermanDPR, a semantic answer similarity metric, and an approach for multimodal retrieval of texts and tables to enable question answering on tabular data. Haystack contains implementations of all three contributions, enabling the use of the research through the open source framework. In November 2021, the development of the FARM framework was discontinued and its main features were integrated into the Haystack framework. In April 2022, the company announced its commercial SaaS offering deepset Cloud, which was rebranded in 2025 as Haystack Enterprise Platform supporting SaaS and on-premise deployment options. As of August 2023, the most popular finetuned language model created by deepset was downloaded more than 52 million times. In 2024, deepset was named a Gartner Cool Vendor in AI Engineering. In 2025, deepset was recognized for its growth by WirtschaftsWoche and Sifted and shared partnership integrations and announcements with Meta Llama Stack, MongoDB, NVIDIA, Amazon Web Services (AWS), and PwC. As of September 2025, the Haystack open source AI orchestration framework has more than 24,000 GitHub stars. == Products and applications == Haystack is an open source Python AI Orchestration framework for building custom AI agents and applications with large language models. With its modular building block components, software developers and AI engineers can implement pipelines to build and customize various AI architectures over large document and multimodal data collections, such as agents, retrieval augmented generation (RAG), intelligent document processing (IDP), text-to-SQL as well as document retrieval, semantic search, text generation, question answering, or summarization. Haystack emphasizes context engineering, an approach to AI system design that focuses on explicit control over how contextual information is retrieved, structured, routed to language models, and evaluated after generation. This allows developers to build AI systems with transparent data flow, tool usage, and configurable reasoning processes. Haystack integrates with 90+ model and technology providers including Hugging Face Transformers, Elasticsearch, OpenSearch, OpenAI, Cohere, Anthropic, Mistral and others. Developers can extend these integrations with their own custom components. The framework has an active community on Discord with more than 4k members and GitHub, where so far more than 300 people have contributed to its continuous development, and engage on Meetup. Thousands of organizations use the framework, including public sector leaders like the European Commission and Global 500 enterprises like Airbus, Intel, NVIDIA, Lufthansa, Netflix, Apple, Infineon, Alcatel-Lucent Enterprise, BetterUp, Etalab, Sooth.ai, and Lego. On top of the Haystack open source framework, deepset offers two enterprise offerings to organizations. Haystack Enterprise Starter provides enterprise support on the open source framework from the Haystack engineering team as well as a private GitHub repository with production use case templates and Kubernetes deployment guides. The Haystack Enterprise Platform supports customers at building scalable AI applications by covering the entire process of prototyping, experimentation, deployment, monitoring, and governance. It is built on the Haystack open source framework and is available for hosting in the cloud and self-hosted via VPC, on-premise, or air gapped environments. deepset's enterprise tools are used by organizations including The European Commission, The Economist, Oxford University Press, the German Federal Ministry of Research, Technology, and Space (BMFTR), Manz Verlag, and the German Armed Forces. FARM was an earlier framework for adapting representation models. One of its core concepts was the implementation of adaptive models, which comprised language models and an arbitrary number of prediction heads. FARM supported domain-adaptation and finetuning of these models with advanced options, for example gradient accumulation, cross-validation or automatic mixed-precision training. Its main features were integrated into Haystack in November 2021, and its development was discontinued at that time. == Funding == On August 9, 2023, deepset announced a Series B investment round of $30 million led by Balderton Capital and including participation from existing investors GV, System.One, Lunar Ventures and Harpoon Ventures. On April 28, 2022, deepset announced a Series A investment round of $14 million led by GV, with the participation of Harpoon Ventures, Acequia Capital and a team of experienced commercial open source software and machine learning founders, such as Alex Ratner (Snorkel AI), Mustafa Suleyman (Deepmind), Spencer Kimball (Cockroach Labs), Jeff Hammerbacher (Cloudera) and Emil Eifrem (Neo4j). A previous pre-seed investment round of $1.6 million on March 8, 2021, was led by System.One and Lunar Ventures, who also participated in the subsequent Series A round.
Read more →
Top 10 Conversational AI Platforms Compared (2026)

In search of the best conversational AI platform? An conversational AI platform is software that uses machine learning to help you get more done — it turns a rough idea into a polished result in seconds. When choosing one, weigh output quality, pricing, export formats, and how well it fits the tools you already use. Whether you are a beginner or a pro, the right conversational AI platform slots into your workflow and pays for itself fast. We tested the leading options and ranked them by quality, value, and ease of use.
Read more →
Klaus-Robert Müller

Klaus-Robert Müller (born 1964 in Karlsruhe, West Germany) is a German computer scientist and physicist, most noted for his work in machine learning and brain–computer interfaces. == Career == Klaus-Robert Müller received his Diplom in mathematical physics and PhD in theoretical computer science from the University of Karlsruhe. Following his Ph.D. he went to Berlin as a postdoctoral fellow at GMD (German National Research Center for Computer Science) Berlin (now part of Fraunhofer Institute for Open Communication Systems), where he started building up the Intelligent Data Analysis (IDA) group. From 1994 to 1995 he was a research fellow at Shun'ichi Amari's lab at the University of Tokyo. 1999 Müller became an associate professor for neuroinformatics at the University of Potsdam, transitioning to the full professorship for Neural Networks and Time Series Analysis in 2003. Since 2006 he holds the chair for Machine Learning at Technische Universität Berlin. Since 2012 he holds a distinguished professorship at Korea University in Seoul. He co-founded and is co-director of the Berlin Big Data Center (BBDC) of TU Berlin. As of 2017, 29 former doctoral or postdoctoral researchers of Klaus-Robert Müller have become full professors themselves. Bernhard Schölkopf and Alexander J. Smola were supervised by him as members of his research group. Since 2020 he is director of the Berlin Institute for the Foundations of Learning and Data (BIFOLD), a German National AI Competence Center, and director of the European Laboratory for Learning and Intelligent Systems (ELLIS) unit Berlin. In 2020/2021 he spent his sabbatical at Google Brain as a principal scientist. == Research == Müller has contributed extensively to several major interests of machine learning, including support vector machines (SVMs) and kernel methods, and artificial neural networks. He pioneered applying new methods of pattern recognition in domains like brain–computer interfaces, using them for patients with Locked-in syndrome. He is one of the leading computer scientists affiliated with Germany. His current research interests include: Statistical learning theory (Support Vector Machines, Deep Neural Networks, Boosting) Learning of non-stationarity data Fusion of structured heterogeneous multi-modal data, co-adaptation Applications: MEG, EEG, NIRS, ECoG, EMG, Brain Computer Interfaces, computational neuroscience, computer vision, genomic data analysis, computational chemistry and atomistic simulations, digital pathology == Honours and awards == Klaus-Robert Müller was elected a fellow of the German National Academy of Sciences Leopoldina in 2012. In 2017 he was elected member of the Berlin-Brandenburg Academy of Sciences and Humanities and also external scientific member of the Max Planck Society. In 2021 he was elected member of the German Academy of Science and Engineering. His work was honoured with several awards, including: 2026 Gottfried Wilhelm Leibniz Prize 2025 IEEE Neural Network Pioneer Award 2024 Feynman Prize in Nanotechnology 2023 Hector Fellow 2025, 2024, 2023, 2022, 2021, 2020, and 2019 Clarivate Highly Cited Researcher 2017 Vodafone Innovations Award 2017 2014 Science Prize of Berlin 2014 by the Governing Mayor of Berlin 2014 European Research Council Panel Consolidator Grants 2009 Best Paper award by IEEE Engineering in Medicine and Biology Society EMBS 2006 SEL-ALCATEL Research Prize for Technical Communication 1999 Olympus Award for Pattern Recognition == Books == with Holzinger, Andreas; et al., eds. (2022). xxAI – Beyond Explainable Artificial Intelligence. Lecture Notes in Computer Science. Vol. 13200. Springer Cham. doi:10.1007/978-3-031-04083-2. ISBN 978-3-031-04082-5. with Schütt, Kristof T.; et al., eds. (2020). Machine Learning Meets Quantum Physics. Lecture Notes in Physics. Vol. 968. Springer Cham. doi:10.1007/978-3-030-40245-7. ISBN 978-3-030-40244-0. S2CID 242406994. with Samek, Wojciech; et al., eds. (2019). Explainable AI: Interpreting, Explaining and Visualizing Deep Learning. Lecture Notes in Computer Science. Vol. 11700. Springer Cham. doi:10.1007/978-3-030-28954-6. ISBN 978-3-030-28953-9. with Montavon, Grégoire; et al., eds. (2012). Neural Networks: Tricks of the Trade. Lecture Notes in Computer Science. Vol. 7700 (2nd ed.). Springer Berlin, Heidelberg. doi:10.1007/978-3-642-35289-8. ISBN 978-3-642-35288-1. S2CID 39578794.
Read more →
Gödel machine

A Gödel machine is a hypothetical self-improving computer program that solves problems in an optimal way. It uses a recursive self-improvement protocol in which it rewrites its own code when it can prove the new code provides a better strategy. The machine was invented by Jürgen Schmidhuber (first proposed in 2003), but is named after Kurt Gödel who inspired the mathematical theories. The Gödel machine is often discussed when dealing with issues of meta-learning, also known as "learning to learn." Applications include automating human design decisions and transfer of knowledge between multiple related tasks, and may lead to design of more robust and general learning architectures. Though theoretically possible, no full implementation has been created. The Gödel machine is often compared with Marcus Hutter's AIXI, another formal specification for an artificial general intelligence. Schmidhuber points out that the Gödel machine could start out by implementing AIXItl as its initial sub-program, and self-modify after it finds proof that another algorithm for its search code will be better. == Limitations == Traditional problems solved by a computer only require one input and provide some output. Computers of this sort had their initial algorithm hardwired. This does not take into account the dynamic natural environment, and thus was a goal for the Gödel machine to overcome. The Gödel machine has limitations of its own, however. According to Gödel's First Incompleteness Theorem, any formal system that encompasses arithmetic is either flawed or allows for statements that cannot be proved in the system. Hence even a Gödel machine with unlimited computational resources must ignore those self-improvements whose effectiveness it cannot prove. == Variables of interest == There are three variables that are particularly useful in the run time of the Gödel machine. At some time t {\displaystyle t} , the variable time {\displaystyle {\text{time}}} will have the binary equivalent of t {\displaystyle t} . This is incremented steadily throughout the run time of the machine. Any input meant for the Gödel machine from the natural environment is stored in variable x {\displaystyle x} . It is likely the case that x {\displaystyle x} will hold different values for different values of variable time {\displaystyle {\text{time}}} . The outputs of the Gödel machine are stored in variable y {\displaystyle y} , where y ( t ) {\displaystyle y(t)} would be the output bit-string at some time t {\displaystyle t} . At any given time t {\displaystyle t} , where ( 1 ≤ t ≤ T ) {\displaystyle (1\leq t\leq T)} , the goal is to maximize future success or utility. A typical utility function follows the pattern u ( s , E n v ) : S × E → R {\displaystyle u(s,\mathrm {Env} ):S\times E\rightarrow \mathbb {R} } : u ( s , E n v ) = E μ [ ∑ τ = time T r ( τ ) ∣ s , E n v ] {\displaystyle u(s,\mathrm {Env} )=E_{\mu }{\Bigg [}\sum _{\tau ={\text{time}}}^{T}r(\tau )\mid s,\mathrm {Env} {\Bigg ]}} where r ( t ) {\displaystyle r(t)} is a real-valued reward input (encoded within s ( t ) {\displaystyle s(t)} ) at time t {\displaystyle t} , E μ [ ⋅ ∣ ⋅ ] {\displaystyle E_{\mu }[\cdot \mid \cdot ]} denotes the conditional expectation operator with respect to some possibly unknown distribution μ {\displaystyle \mu } from a set M {\displaystyle M} of possible distributions ( M {\displaystyle M} reflects whatever is known about the possibly probabilistic reactions of the environment), and the above-mentioned time = time ⁡ ( s ) {\displaystyle {\text{time}}=\operatorname {time} (s)} is a function of state s {\displaystyle s} which uniquely identifies the current cycle. Note that we take into account the possibility of extending the expected lifespan through appropriate actions. == Instructions used by proof techniques == The nature of the six proof-modifying instructions below makes it impossible to insert an incorrect theorem into proof, thus trivializing proof verification. === get-axiom(n) === Appends the n-th axiom as a theorem to the current theorem sequence. Below is the initial axiom scheme: Hardware Axioms formally specify how components of the machine could change from one cycle to the next. Reward Axioms define the computational cost of hardware instruction and the physical cost of output actions. Related Axioms also define the lifetime of the Gödel machine as scalar quantities representing all rewards/costs. Environment Axioms restrict the way new inputs x are produced from the environment, based on previous sequences of inputs y. Uncertainty Axioms/String Manipulation Axioms are standard axioms for arithmetic, calculus, probability theory, and string manipulation that allow for the construction of proofs related to future variable values within the Gödel machine. Initial State Axioms contain information about how to reconstruct parts or all of the initial state. Utility Axioms describe the overall goal in the form of utility function u. === apply-rule(k, m, n) === Takes in the index k of an inference rule (such as Modus tollens, Modus ponens), and attempts to apply it to the two previously proved theorems m and n. The resulting theorem is then added to the proof. === delete-theorem(m) === Deletes the theorem stored at index m in the current proof. This helps to mitigate storage constraints caused by redundant and unnecessary theorems. Deleted theorems can no longer be referenced by the above apply-rule function. === set-switchprog(m, n) === Replaces switchprog S pm:n, provided it is a non-empty substring of S p. === check() === Verifies whether the goal of the proof search has been reached. A target theorem states that given the current axiomatized utility function u (Item 1f), the utility of a switch from p to the current switchprog would be higher than the utility of continuing the execution of p (which would keep searching for alternative switchprogs). === state2theorem(m, n) === Takes in two arguments, m and n, and attempts to convert the contents of Sm:n into a theorem. == Example applications == === Time-limited NP-hard optimization === The initial input to the Gödel machine is the representation of a connected graph with a large number of nodes linked by edges of various lengths. Within given time T it should find a cyclic path connecting all nodes. The only real-valued reward will occur at time T. It equals 1 divided by the length of the best path found so far (0 if none was found). There are no other inputs. The by-product of maximizing expected reward is to find the shortest path findable within the limited time, given the initial bias. === Fast theorem proving === Prove or disprove as quickly as possible that all even integers > 2 are the sum of two primes (Goldbach’s conjecture). The reward is 1/t, where t is the time required to produce and verify the first such proof. === Maximizing expected reward with bounded resources === A cognitive robot that needs at least 1 liter of gasoline per hour interacts with a partially unknown environment, trying to find hidden, limited gasoline depots to occasionally refuel its tank. It is rewarded in proportion to its lifetime, and dies after at most 100 years or as soon as its tank is empty or it falls off a cliff, and so on. The probabilistic environmental reactions are initially unknown but assumed to be sampled from the axiomatized Speed Prior, according to which hard-to-compute environmental reactions are unlikely. This permits a computable strategy for making near-optimal predictions. One by-product of maximizing expected reward is to maximize expected lifetime.
Read more →
Best AI Subtitle Generators in 2026

Comparing the best AI subtitle generator? An AI subtitle generator is software that uses machine learning to help you get more done — it lowers the barrier so anyone can produce professional output. Privacy matters too: check whether your data trains the model and whether a no-log or enterprise tier is available. Whether you are a beginner or a pro, the right AI subtitle generator slots into your workflow and pays for itself fast. Below we compare features, pricing, and real output so you can choose with confidence.
Read more →
Top 10 AI Video Editors Compared (2026)

Looking for the best AI video editor? An AI video editor is software that uses machine learning to help you get more done — it can save you hours every week by automating repetitive work. Most options offer a generous free tier, with paid plans unlocking higher limits, faster processing, and team features. Whether you are a beginner or a pro, the right AI video editor slots into your workflow and pays for itself fast. Read on for hands-on impressions, pricing tiers, and the standout features that matter.
Read more →