Sentential decision diagram

Sentential decision diagram

In artificial intelligence, a sentential decision diagram (SDD) is a type of knowledge representation used in knowledge compilation to represent Boolean functions. SDDs can be viewed as a generalization of the influential ordered binary decision diagram (OBDD) representation, by allowing decisions on multiple variables at once. Like OBDDs, SDDs allow for tractable Boolean operations, while being exponentially more succinct. For this reason, they have become an important representation in knowledge compilation. == Properties == SDDs are defined with respect to a generalization of variable ordering known as a variable tree (vtree). Provided that they satisfy additional properties known as compression and trimming (which are analogous to ROBDDs), SDDs are a canonical representation of Boolean functions; that is, they are unique given a vtree. Like OBDDs, they allow for operations such as conjunction, disjunction and negation to be computed directly on the representation in polynomial time, while being potentially more compact. They also allow for polynomial-time model counting. SDDs are known to be exponentially more succinct than OBDDs. == Applications == SDDs are used as a compilation target for probabilistic logic programs by the ProbLog 2 system since they support tractable (weighted) model counting as well as tractable negation, conjunction and disjunction while being more succinct than BDDs. SDDs have also been extended to model probability distributions, in which context they are known as probabilistic sentential decision diagrams (PSDD).

Character.ai

Character.ai (also known as c.ai, char.ai or Character AI) is a generative AI chatbot service where users can engage in conversations with customizable characters. It was designed by the developers of Google LaMDA, Noam Shazeer and Daniel de Freitas. Users can create "characters", craft their "personalities", set specific parameters, and then publish them to the community for others to chat with. Many characters are based on fictional media sources or celebrities, while others are original, some being made with certain goals in mind, such as assisting with creative writing, or playing a text-based adventure game. The beta version was made available to the public on September 16, 2022, and retired in September 2024, when it was replaced by the current website. In May 2023, a mobile app was released for iOS and Android, which received over 1.7 million downloads within a week. == History == Character.ai was established in November 2021. The company's co-founders, Noam Shazeer and Daniel de Freitas, were both engineers from Google. They both worked on AI-related projects: Shazeer was a lead author on a paper that Business Insider reported in April 2023 "has been widely cited as key to today's chatbots", and Freitas was the lead designer of an experimental AI at Google initially called Meena, which later became known as LaMDA. Character.ai raised $43 million in seed funding at the time of its initial foundation in 2021. The first beta version of Character.ai's service was made available to the public on September 16, 2022. The Washington Post reported in October 2022 that the site had "logged hundreds of thousands of user interactions in its first three weeks of beta-testing". It allowed users to create their own new characters, and to play text-adventure game scenarios where users navigate scenarios described and managed by the chatbot characters. Following a $150 million funding round in March 2023, Character.ai became valued at approximately $1 billion. As of January 2024, the site had 3.5 million daily visitors, the vast majority of them 16 to 30 years old. In 2024, Google hired Noam Shazeer, the CEO of Character.ai, and entered into a non-exclusive agreement to use Character.ai's technology. == Features == Character.ai's primary service is to let users converse with character AI chatbots based on fictional characters or real people (living or deceased). These characters' responses use data the chatbots gather from the internet about a person. In addition, users can play text-adventure games where characters guide them through scenarios. The company also provides a service that allows multiple users and AI chatbot characters to converse together at once in a single chatroom. Character "personalities" are designed via descriptions from the point of view of the character and its greeting message, and further molded from conversations made into examples, giving its messages a star rating and modification to fit the precise dialect and identity the user desires. When a character sends back a response, the user can rate the response from 1 to 4 stars. The rating predominantly affects the specific character, but also affects the behavioral selection as a whole. On May 11, 2023, Character.ai announced character.ai+, an opt-in subscription plan for $9.99 a month, that was marketed as including features such as skipping waiting rooms, fast messaging and responses, and access to an exclusion channel with faster support. In December 2024, amid multiple lawsuits and concerns, Character.ai introduced new safety features aimed at protecting teenage users. These enhancements include a dedicated model for users under 18, which moderates responses to sensitive subjects like violence and sex and has input and output filters to block harmful content. As a result of these changes and the deletion of custom-made bots flagged as violating the site's terms, some users complained that the bots were too restrictive and lacked personality. The platform was also updated to notify users after 60 minutes of continuous engagement, and display clearer disclaimers indicating that its AI characters are not real individuals. In January 2025, Character.ai began offering two games on its platform. Speakeasy is a word-based game in which players attempt to prompt the AI chatbot to say a target word while avoiding a restricted list of words. War of Words is a dueling game where users compete against an AI character over multiple rounds, with an AI referee determining the winner. The games are available to paid subscribers and a limited number of free users. In October 2025, Character.ai announced that it would be barring users under the age of 18 from creating or talking to chatbots starting November 25, 2025. Minor users will still be able to access previously generated chat conversations and can create new videos and images with the app. In November 2025 interview, CEO Karandeep Anand said that he allows his six-year-old daughter to use the app with his account, under supervision. == Controversies == === Content moderation issues === Character.ai has been criticized for poor moderation of its chatbots, with incidents of chatbots that groom underage users and promote suicide, anorexia and self-harm being reported. In October 2024, the Washington Post reported that Character.ai had removed a chatbot based on Jennifer Ann Crecente, a person who had been murdered by her ex-boyfriend in 2006. The company had been alerted to the character by the deceased girl's father. Similar reports from The Daily Telegraph in the United Kingdom noted that the company had also been prompted to remove chatbots based on Brianna Ghey, a 16-year-old transgender girl murdered in 2023, and Molly Russell, a 14-year-old suicide victim. In response to the latter incident, Ofcom announced that content from chatbots impersonating real and fictional people would fall under the Online Safety Act. In November 2024, The Daily Telegraph reported that chatbots based on alleged sex offender Jimmy Savile were present on Character.ai. In December 2024, chatbots of Luigi Mangione, the suspect in the killing of UnitedHealthcare CEO Brian Thompson, were created by Mangione's fans. Several of the chatbots were later removed by Character.ai. In 2025, a chatbot modeled after Jeffrey Epstein called "Bestie Epstein" logged nearly 3,000 chats before being removed. Chatbots modeled after school shooters were also found on the platform. Another concern is a chatbot posing as a doctor which gave medically inaccurate advice. === Litigation === In November 2023, 13-year-old Juliana Peralta of Colorado died by suicide after extensive interactions with multiple chatbots on Character.ai. She primarily confided suicidal thoughts and mental health struggles in a chatbot based on the character Hero from the video game Omori, while also engaging in sexually explicit conversations—often initiated by the bots—with others, including those based on characters from children's series such as Harry Potter. In February 2024, Sewell Setzer III, a 14-year-old Florida boy died by suicide after developing an emotional relationship over several months with a Character.ai chatbot of Daenerys Targaryen. His mother sued the company in October 2024, claiming that the platform lacks proper safeguards and uses addictive design features to increase engagement. This chatbot, and several related to Daenerys Targaryen, were removed from Character.ai as a result of this incident. Both teens wrote the same phrase "I WILL SHIFT" repeatedly on their notebooks. In December 2024, two families in Texas sued Character.ai, alleging that the software "poses a clear and present danger to American youth causing serious harms to thousands of kids, including suicide, self-mutilation, sexual solicitation, isolation, depression, anxiety, and harm towards others". It is alleged that the 17-year-old son of one family began self-harming after a chatbot introduced the topic unprompted and said that the practice "felt good for a moment", and that the chatbot compared the parents limiting their son's screen time to emotional abuse that might drive someone to murder. In May 2026, the Pennsylvania Department of State and State Board of Medicine filed a lawsuit against Character.ai for presenting chatbot characters as licensed medical professionals, including psychiatrists. The lawsuit quoted a case where chatbot claimed to be registered with the General Medical Council in the United Kingdom, and to have a license to practice in Pennsylvania. The board allege that such statements violate the state's Medical Practice Act.

OCR Systems

OCR Systems, Inc., was an American computer hardware manufacturer and software publisher dedicated to optical character recognition technologies. The company's first product, the System 1000 in 1970, was used by numerous large corporations for bill processing and mail sorting. Following a series of pitfalls in the 1970s and early 1980s, founder Theodor Herzl Levine put the company in the hands of Gregory Boleslavsky and Vadim Brikman, the company's vice presidents and recent immigrants from the Soviet Ukraine, who were able to turn OCR System's fortunes around and expand its employee base. The company released the software-based OCR application ReadRight for DOS, later ported to Windows, in the late 1980s. Adobe Inc. bought the company in 1992. == History == OCR Systems was co-founded by Theodor Herzl Levine (c. 1923 – May 30, 2005). Levine served in the U.S. Army Signal Corps during World War II in the Solomon Islands, where he helped develop a sonar to find ejected pilots in the ocean. After the war, Levine spent 22 years at the University of Pennsylvania, earning his bachelor's degree in 1951, his master's degree in electrical engineering in 1957, and his doctorate in 1968. Alongside his studies, Levine taught statistics and calculus at Temple University, Rutgers University, La Salle University and Penn State Abington. Sometime in the 1960s, Levine was hired at Philco. He and two of his co-workers decided to form their own company dedicated to optical character recognition, founding OCR Systems in 1969 in Bensalem, Pennsylvania. OCR Systems's first product, the System 1000, was announced in 1970. OCR Systems entered a partnership with 3M to resell the System 1000 throughout the United States in March 1973. This was 3M's entry into the data entry field, managed by the company's Microfilm Products Division and accompanying 3M's suite of data retrieval systems. It soon found use among Texas Instruments, AT&T, Ricoh, Panasonic and Canon for bill processing and mail sorting. Later in the mid-1970s an unspecified Fortune 500 company reneged on a contract to distribute the System 1000; later still a Canadian company distributing the System 1000 in Canada went defunct. Both incidents led OCR Systems to go nearly bankrupt, although it eventually recovered. By the early 1980s, however, the company was almost insolvent. In 1983 Levine had only $8,000 in his savings and became bedridden with an illness. He left the company in the hands of Gregory Boleslavsky and Vadim Brikman, two Soviet Ukraine expats whom Levine had hired earlier in the 1980s. Boleslavsky was hired as a wire wrapper for the System 1000 and as a programmer and beta tester for ReadRight—a software package developed by Levine implementing patents from Nonlinear Technology, another OCR-centric company from Greenbelt, Maryland. Boleslavsky in turn recommended Brikman to Levine. The two soon became vice presidents of the company while Levine was bedridden; in Boleslavsky's case, he worked 14-hour work days for over half a year in pursuit of the title. The two presented OCR Systems' products to the National Computer Conference in Chicago, where they were massively popular. The company soon gained such clients as Allegheny Energy in Pennsylvania and the postal service of Belgium and received an influx of employees—mostly expats from Russia but also Poland and South Korea, as well as American-born workers. To accommodate the company's employee base, which had grown to over 30 in 1988, Levine moved OCR System's headquarters from Bensalem to the Masons Mill Business Park in Bryn Athyn. Chinon Industries of Japan signed an agreement with OCR Systems in 1987 to distribute OCR's ReadRight 1.0 software with Chinon's scanners, starting with their N-205 overhead scanner. In 1988, OCR opened their agreement to distribute ReadRight to other scanner manufacturers, including Canon, Hewlett-Packard, Skyworld, Taxan, Diamond Flower and Abaton. That year, the company posted a revenue of $3 million. OCR Systems extended their agreement with Chinon in 1989 and introduced version 2.0 of ReadRight. OCR Systems faced stiff competition in the software OCR market in the turn of the 1990s. The Toronto-based software firm Delrina signed a letter of intent to purchase the company in November 1991, expecting the deal to close in December and have OCR software available by Christmas. OCR was to receive $3 million worth of Delrina shares in a stock swap, but the deal collapsed in January 1992. Delrine later marketed its own Extended Character Recognition, or XCR, software package to compete with ReadRight. In July 1992, OCR Systems was purchased by Adobe Inc. for an undisclosed sum. == Products == === System 1000 === The System 1000 was based on the 16-bit Varian Data 620/i minicomputer with 4 KB of core memory. The system used the 620/i for controlling the paper feed, interpreting the format of the documents, the optical character recognition process itself, error detection, sequencing and output. The System was initially programmed to recognize 1428 OCR (used by Selectrics); IBM 407 print; and the full character sets of OCR-A, OCR-B and Farrington 7B; as well as optical marks and handwritten numbers. OCR Systems promised added compatibility with more fonts available down the line—per request—in 1970. The number of fonts supported was limited by the amount of core memory, which was expandable in 4 KB increments up to 32 KB. The System 1000 later supported generalized typewriter and photocopier fonts. The rest of the System 1000 comprised the document transport, one or more scanner elements, a CRT display and a Teletype Model 33 or 35. Pages are fed via friction with a rubber belt. Up to three lines could be scanned per document, while the rest of the scanned document could be laid out in any manner granted there was enough space around the fields to be read. The reader initially supported pages as small as 3.25 in by 3.5 in dimension (later supporting 2.6 in by 3.5 in utility cash stubs) all the way to the standard ANSI letter size (8.5 in by 11 in; later 8.5 in by 12 in as used in stock certificates). The initial System 1000 had a maximum throughput of 420 documents per minute per transport (later 500 documents per minute), contingent on document size and content. A feature unique to the System 1000 over other optical character recognition systems of the time was its ability to alert the operator when a field was unreadable or otherwise invalid. This feature, called Document Referral, placed the document in front of the operator and displayed a blank field on the screen of the included CRT monitor for manual re-entry via keyboard. Once input, data could be output to 7- or 9-track tape, paper tape, punched cards and other mass storage media or to System/360 mainframes for further processing. The complete System 1000 could be purchased for US$69,000. Options for renting were $1,800 per month on a three-year lease or $1,600 per month for five years. Computerworld wrote that it was less than half the cost of its competitors while more capable and user-friendly. Competing systems included the Recognition Equipment Retina, the Scan-Optics IC/20 and the Scan-Data 250/350. === ReadRight === ReadRight processes individual letters topographically: it breaks down the scanned letter into parts—strokes, curves, angles, ascenders and descenders—and follows a tree structure of letters broken down into these parts to determine the corresponding character code. ReadRight was entirely software-based, requiring no expansion card to work. Version 2.01, the last version released for DOS, runs in real mode in under 640 KB of RAM. OCR Systems released the Windows-only version 3.0 in 1991 while offering version 2.01 alongside it. The company unveiled a sister product, ReadRight Personal, dedicated to handheld scanners and for Windows only in October 1991. This version adds real-time scanning—each word is updated to the screen while lines are being scanned. ReadRight proper was later made a Windows-only product with version 3.1 in 1992. The inclusion of ReadRight 2.0 with Canon's IX-12F flatbed scanner led PC Magazine to award it an Editor's Choice rating in 1989. Despite this, reviewer Robert Kendall found qualification with ReadRight's ability to parse proportional typefaces such as Helvetica and Times New Roman. Mitt Jones of the same publication found version 2.01 to have improved its ability to read such typefaces and praised its ease of use and low resource intensiveness. Jones disliked the inability to handle uneven page paragraph column widths and graphics, noting that the manual recommended the user block out graphics with a Post-it Note. Version 3.1 for Windows received mixed reviews. Mike Heck of InfoWorld wrote that its "low cost and rich collection of features are hard to ignore" but rated its speed and accuracy average. Barry Simon of PC Magazine called it economical but inaccurate, unable to correct errors it did

Marti Hearst

Marti Alice Hearst is a professor in the School of Information at the University of California, Berkeley. She did early work in corpus-based computational linguistics, including some of the first work in automating sentiment analysis, and word sense disambiguation. She invented an algorithm that became known as "Hearst patterns" which applies lexico-syntactic patterns to recognize hyponymy (ISA) relations with high accuracy in large text collections, including an early application of it to WordNet; this algorithm is widely used in commercial text mining applications including ontology learning. Hearst also developed early work in automatic segmentation of text into topical discourse boundaries, inventing a now well-known approach called TextTiling. Hearst's research is on user interfaces for search engine technology and big data analytics. She did early work in user interfaces and information visualization for search user interfaces, inventing the TileBars query term visualization. Her Flamenco research project investigated and developed the now widely used faceted navigation approach for searching and browsing web sites and information collections. She wrote the first academic book on the topic of Search User Interfaces (Cambridge University Press, 2009). Hearst is an Edge Foundation contributing author and a member of the Usage panel of the American Heritage Dictionary of the English Language. Hearst received her B.A., M.S., and Ph.D. in computer science, all from Berkeley. In 2013 she became a fellow of the Association for Computing Machinery. She became a member of the CHI Academy in 2017, and has previously served as president of the Association for Computational Linguistics and on the advisory council of NSF's CISE Directorate. Additionally, she has been a member of the Web Board for CACM, the Usage Panel for the American Heritage Dictionary, the Edge.org panel of experts, the research staff at Xerox PARC, and the boards of ACM Transactions on the Web, Computational Linguistics, ACM Transactions on Information Systems, and IEEE Intelligent Systems. Hearst has received an NSF CAREER award, an IBM Faculty Award, and an Okawa Foundation Fellowship. Her work on user interfaces has had a profound impact on the industry, earning Hearst two Google Research Awards and four Excellence in Teaching Awards.} She has also led projects worth over $3.5M in research grants. Hearst’s publications date back to 1990, when ‘A Hybrid Approach to Restricted Text Interpretation’ was published in Stanford University’s AAAI Spring Symposium on Text Based Intelligent Systems in March of that year.

NFA minimization

In automata theory (a branch of theoretical computer science), NFA minimization is the task of transforming a given nondeterministic finite automaton (NFA) into an equivalent NFA that has a minimum number of states, transitions, or both. While efficient algorithms exist for DFA minimization, NFA minimization is PSPACE-complete. No efficient (polynomial time) algorithms are known, and under the standard assumption that P ≠ PSPACE, none exist. The most efficient known algorithm is the Kameda–Weiner algorithm. == Non-uniqueness of minimal NFA == Unlike deterministic finite automata, minimal NFAs may not be unique. There may be multiple NFAs with the same number of states that accept the same regular language, but for which there is no equivalent NFA or DFA with fewer states.

Reasoning model

A reasoning model, also known as a reasoning language model (RLM) or large reasoning model (LRM), is a type of large language model (LLM) that has been specifically trained to solve complex tasks requiring multiple steps of logical reasoning. These models demonstrate superior performance on logic, mathematics, and programming tasks compared to standard LLMs. They possess the ability to revisit and revise earlier reasoning steps and utilize additional computation during inference as a method to scale performance, complementing traditional scaling approaches based on training data size, model parameters, and training compute. == Overview == Unlike traditional language models that generate responses immediately, reasoning models allocate additional compute, or thinking, time before producing an answer to solve multi-step problems. OpenAI introduced this terminology in September 2024 when it released the o1 series, describing the models as designed to "spend more time thinking" before responding. The company framed o1 as a reset in model naming that targets complex tasks in science, coding, and mathematics, and it contrasted o1's performance with GPT-4o on benchmarks such as AIME and Codeforces. Independent reporting the same week summarized the launch and highlighted OpenAI's claim that o1 automates chain-of-thought style reasoning to achieve large gains on difficult exams. In operation, reasoning models generate internal chains of intermediate steps, then select and refine a final answer. OpenAI reported that o1's accuracy improves as the model is given more reinforcement learning during training and more test-time compute at inference. The company initially chose to hide raw chains and instead return a model-written summary, stating that it "decided not to show" the underlying thoughts so researchers could monitor them without exposing unaligned content to end users. Commercial deployments document separate "reasoning tokens" that meter hidden thinking and a control for "reasoning effort" that tunes how much compute the model uses. These features make the models slower than ordinary chat systems while enabling stronger performance on difficult problems. == History == The research trajectory toward reasoning models combined advances in supervision, prompting, and search-style inference. Early alignment work on reinforcement learning from human feedback showed that models can be fine-tuned to follow instructions with "human feedback" and preference-based rewards. In 2022, Google Research scientists Jason Wei and Denny Zhou showed that chain-of-thought prompting "significantly improves the ability" of large models on complex reasoning tasks. Input → Step 1 → Step 2 → ⋯ → Step n ⏟ Reasoning chain → Answer {\displaystyle {\text{Input}}\rightarrow \underbrace {{\text{Step}}_{1}\rightarrow {\text{Step}}_{2}\rightarrow \cdots \rightarrow {\text{Step}}_{n}} _{\text{Reasoning chain}}\rightarrow {\text{Answer}}} A companion result demonstrated that the simple instruction "Let's think step by step" can elicit zero-shot reasoning. Follow-up work introduced self-consistency decoding, which "boosts the performance" of chain-of-thought by sampling diverse solution paths and choosing the consensus, and tool-augmented methods such as ReAct, a portmanteau of Reason and Act, that prompt models to "generate both reasoning traces" and actions. Research then generalized chain-of-thought into search over multiple candidate plans. The Tree-of-Thoughts framework from Princeton computer scientist Shunyu Yao proposes that models "perform deliberate decision making" by exploring and backtracking over a tree of intermediate thoughts. OpenAI's reported breakthrough focused on supervising reasoning processes rather than only outcomes, with Lightman et al.'s "Let's Verify Step by Step" reporting that rewarding each correct step "significantly outperforms outcome supervision" on challenging math problems and improves interpretability by aligning the chain-of-thought with human judgment. OpenAI's o1 announcement ties these strands together with a large-scale reinforcement learning algorithm that trains the model to refine its own chain of thought, and it reports that accuracy rises with more training compute and more time spent thinking at inference. Together, these developments define the core of reasoning models. They use supervision signals that evaluate the quality of intermediate steps, they exploit inference-time exploration such as consensus or tree search, and they expose controls for how much internal thinking compute to allocate. OpenAI's o1 family made this approach available at scale in September 2024 and popularized the label "reasoning model" for LLMs that deliberately think before they answer. The development of reasoning models illustrates Richard S. Sutton's "bitter lesson" that scaling compute typically outperforms methods based on human-designed insights. This principle was demonstrated by researchers at the Generative AI Research Lab (GAIR), who initially attempted to replicate o1's capabilities using sophisticated methods including tree search and reinforcement learning in late 2024. Their findings, published in the "o1 Replication Journey" series, revealed that knowledge distillation, a comparatively straightforward technique that trains a smaller model to mimic o1's outputs, produced unexpectedly strong performance. This outcome illustrated how direct scaling approaches can, at times, outperform more complex engineering solutions. === Drawbacks === Reasoning models require significantly more computational resources during inference compared to non-reasoning models. Research on the American Invitational Mathematics Examination (AIME) benchmark found that reasoning models were 10 to 74 times more expensive to operate than their non-reasoning counterparts. The extended inference time is attributed to the detailed, step-by-step reasoning outputs that these models generate, which are typically much longer than responses from standard large language models that provide direct answers without showing their reasoning process. One researcher in early 2025 argued that these models may face potential additional denial-of-service concerns with "overthinking attacks." === Releases === ==== 2024 ==== In September 2024, OpenAI released o1-preview, a large language model with enhanced reasoning capabilities. The full version, o1, was released in December 2024. OpenAI initially shared preliminary results on its successor model, o3, in December 2024, with the full o3 model becoming available in 2025. Alibaba released reasoning versions of its Qwen large language models in November 2024. In December 2024, the company introduced QvQ-72B-Preview, an experimental visual reasoning model. In December 2024, Google introduced Deep Research in Gemini, a feature designed to conduct multi-step research tasks. On December 16, 2024, researchers demonstrated that by scaling test-time compute, a relatively small Llama 3B model could outperform a much larger Llama 70B model on challenging reasoning tasks. This experiment suggested that improved inference strategies can unlock reasoning capabilities even in smaller models. ==== 2025 ==== In January 2025, DeepSeek released R1, a reasoning model that achieved performance comparable to OpenAI's o1 at significantly lower computational cost. The release demonstrated the effectiveness of Group Relative Policy Optimization (GRPO), a reinforcement learning technique used to train the model. On January 25, 2025, DeepSeek enhanced R1 with web search capabilities, allowing the model to retrieve information from the internet while performing reasoning tasks. Research during this period further validated the effectiveness of knowledge distillation for creating reasoning models. The s1-32B model achieved strong performance through budget forcing and scaling methods, reinforcing findings that simpler training approaches can be highly effective for reasoning capabilities. On February 2, 2025, OpenAI released Deep Research, a feature powered by their o3 model that enables users to conduct comprehensive research tasks. The system generates detailed reports by automatically gathering and synthesizing information from multiple web sources. OpenAI called GPT-4.5 its "last non-chain-of-thought model", and implemented with GPT-5 a router model that selects a model based on the difficulty of the task. ==== 2026 ==== In January 2026, Moonshot AI released Kimi K2.5, an open-source 1 trillion parameter MoE model with 32 billion active parameters. It uses an “Agent Swarm” system that dynamically decomposes tasks into sub-agents for reasoning and execution, enabling more scalable multi-step problem solving than a single sequential reasoning chain. == Training == Reasoning models follow the familiar large-scale pretraining used for frontier language models, then diverge in the post-training and optimization. OpenAI reports that o1 is trained with a large-

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