In theoretical computer science and formal language theory, a weighted automaton or weighted finite-state machine is a generalization of a finite-state machine in which the edges have weights, for example real numbers or integers. Finite-state machines are only capable of answering decision problems; they take as input a string and produce a Boolean output, i.e. either "accept" or "reject". In contrast, weighted automata produce a quantitative output, for example a count of how many answers are possible on a given input string, or a probability of how likely the input string is according to a probability distribution. They are one of the simplest studied models of quantitative automata. The definition of a weighted automaton is generally given over an arbitrary semiring R {\displaystyle R} , an abstract set with an addition operation + {\displaystyle +} and a multiplication operation × {\displaystyle \times } . The automaton consists of a finite set of states, a finite input alphabet of characters Σ {\displaystyle \Sigma } and edges which are labeled with both a character in Σ {\displaystyle \Sigma } and a weight in R {\displaystyle R} . The weight of any path in the automaton is defined to be the product of weights along the path, and the weight of a string is the sum of the weights of all paths which are labeled with that string. The weighted automaton thus defines a function from Σ ∗ {\displaystyle \Sigma ^{}} to R {\displaystyle R} . Weighted automata generalize deterministic finite automata (DFAs) and nondeterministic finite automata (NFAs), which correspond to weighted automata over the Boolean semiring, where addition is logical disjunction and multiplication is logical conjunction. In the DFA case, there is only one accepting path for any input string, so disjunction is not applied. When the weights are real numbers and the outgoing weights for each state add to one, weighted automata can be considered a probabilistic model and are also known as probabilistic automata. These machines define a probability distribution over all strings, and are related to other probabilistic models such as Markov decision processes and Markov chains. Weighted automata have applications in natural language processing where they are used to assign weights to words and sentences, as well as in image compression. They were first introduced by Marcel-Paul Schützenberger in his 1961 paper On the definition of a family of automata. Since their introduction, many extensions have been proposed, for example nested weighted automata, cost register automata, and weighted finite-state transducers. Researchers have studied weighted automata from the perspective of learning a machine from its input-output behavior (see computational learning theory) and studying decidability questions. == Definition == A commutative semiring (or rig) is a set R equipped with two distinguished elements 0 ≠ 1 {\displaystyle 0\neq 1} and addition and multiplication operations ⊕ {\displaystyle \oplus } and ⊗ {\displaystyle \otimes } such that ⊕ {\displaystyle \oplus } is commutative and associative with identity 0 {\displaystyle 0} , ⊗ {\displaystyle \otimes } is commutative and associative with identity 1 {\displaystyle 1} , ⊗ {\displaystyle \otimes } distributes over ⊕ {\displaystyle \oplus } , and 0 is an absorbing element for ⊗ {\displaystyle \otimes } . A weighted automaton over R {\displaystyle R} is a tuple A = ( Q , Σ , Δ , I , F ) {\displaystyle {\mathcal {A}}=(Q,\Sigma ,\Delta ,I,F)} where: Q {\displaystyle Q} is a finite set of states. Σ {\displaystyle \Sigma } is a finite alphabet. Δ ⊆ Q × Σ × R × Q {\displaystyle \Delta \subseteq Q\times \Sigma \times R\times Q} is a finite set of transitions ( q , σ , w , q ′ ) {\displaystyle (q,\sigma ,w,q')} , where σ {\displaystyle \sigma } is called a character and w {\displaystyle w} is called a weight. I : Q → R {\displaystyle I:Q\to R} is an initial weight function. F : Q → R {\displaystyle F:Q\to R} is a final weight function. A path on input w ∈ Σ ∗ {\displaystyle w\in \Sigma ^{}} is a finite path in the graph, where the concatenation of the character labels equals w {\displaystyle w} . The weight of the path q 0 , q 1 , … , q n {\displaystyle q_{0},q_{1},\ldots ,q_{n}} is the product ( ⊗ {\displaystyle \otimes } ) of the weights along the path, additionally multiplied by the initial and final weights I ( q 0 ) ⊗ F ( q n ) {\displaystyle I(q_{0})\otimes F(q_{n})} . The weight of the word w {\displaystyle w} is the sum ( ⊕ {\displaystyle \oplus } ) of the weights of all paths on input w {\displaystyle w} (or 0 if there are no accepting paths). In this way the machine defines a function [ [ A ] ] : Σ ∗ → R {\displaystyle [\![{\mathcal {A}}]\!]:\Sigma ^{}\to R} . == Ambiguity and determinism == Since Δ {\displaystyle \Delta } is a set of transitions, weighted automata allow multiple transitions (or paths) on a single input string. Therefore a weighted automaton can be considered analogous to a nondeterministic finite automaton (NFA). As is the case with NFAs, restrictions of weighted automata are considered that correspond to the concepts of deterministic finite automaton and unambiguous finite automaton (deterministic weighted automata and unambiguous weighted automata, respectively). First, a preliminary definition: the underlying NFA of A {\displaystyle {\mathcal {A}}} is an NFA formed by removing all transitions with weight 0 {\displaystyle 0} and then erasing all of the weights on the transitions Δ {\displaystyle \Delta } , so that the new transition set lies in Q × Σ × Q {\displaystyle Q\times \Sigma \times Q} . The initial states and final states are the set of states q {\displaystyle q} such that I ( q ) ≠ 0 {\displaystyle I(q)\neq 0} and F ( q ) ≠ 0 {\displaystyle F(q)\neq 0} , respectively. A weighted automaton is deterministic if the underlying NFA is deterministic and unambiguous if the underlying NFA is unambiguous. Every deterministic weighted automaton is unambiguous. In both the deterministic and unambiguous cases, there is always at most one accepting path, so the ⊕ {\displaystyle \oplus } operation is never applied and can be omitted from the definition. == Variations == The requirement that there is a zero element for ⊕ {\displaystyle \oplus } is sometimes omitted; in this case the machine defines a partial function from Σ ∗ {\displaystyle \Sigma ^{}} to R {\displaystyle R} rather than a total function. It is possible to extend the definition to allow epsilon transitions ( q , ϵ , w , q ′ ) {\displaystyle (q,\epsilon ,w,q')} , where ϵ {\displaystyle \epsilon } is the empty string. In this case, one must then require that there are no cycles of epsilon transitions. This does not increase the expressiveness of weighted automata. If epsilon transitions are allowed, the initial weights and final weights can be replaced by initial and final sets of states without loss of expressiveness. Some authors omit the initial and final weight functions I {\displaystyle I} and F {\displaystyle F} . Instead, I {\displaystyle I} and F {\displaystyle F} are replaced by a set of initial and final states. If epsilon transitions are not present, this technically decreases expressiveness as it forces [ [ A ] ] ( ε ) {\displaystyle [\![{\mathcal {A}}]\!](\varepsilon )} to depend only on the number of states that are both initial and final. The transition function can be given as a matrix Δ σ ∈ R Q × Q {\displaystyle \Delta _{\sigma }\in R^{Q\times Q}} with entries in R {\displaystyle R} for each σ {\displaystyle \sigma } , rather than a set of transitions. The entry of the matrix at ( q , q ′ ) {\displaystyle (q,q')} is the sum of all transitions labeled ( q , σ , q ′ ) {\displaystyle (q,\sigma ,q')} . Some authors restrict to specific semirings, such as N {\displaystyle \mathbb {N} } or Z {\displaystyle \mathbb {Z} } , particularly when studying decidability results.
LemonStand
LemonStand was a Canadian e-commerce company headquartered in Vancouver, British Columbia, that developed cloud-based computer software for online retailers. LemonStand was shut down on June 5, 2019. == History == LemonStand Version 1 was launched on July 28, 2001. It is written in the PHP programming language. Version 1 was released as an on-premises proprietary licensed software, and the commercial license was not free. However, there was a free trial license available. June 2012, LemonStand raised seed funding from the BDC Venture Capital, and a group of angel investors. December 20, 2013, a cloud-based SaaS version of the LemonStand eCommerce platform was released publicly. May 9, 2014, LemonStand and Payfirma, a payments processing company, partnered to provide integrated services for online retailers. May 3, 2016, LemonStand raised funding from BDC Venture Capital and Silicon Valley–based angel investors. March 5, 2019, LemonStand announced their intention to shut down on June 5, 2019. LemonStand was quietly acquired by Mailchimp at the end of February. == Pricing == LemonStand offered three levels of service plans. LemonStand did not charge any transaction fees.
MobileNet
MobileNet is a family of convolutional neural network (CNN) architectures designed for image classification, object detection, and other computer vision tasks. They are designed for small size, low latency, and low power consumption, making them suitable for on-device inference and edge computing on resource-constrained devices like mobile phones and embedded systems. They were originally designed to be run efficiently on mobile devices with TensorFlow Lite. The need for efficient deep learning models on mobile devices led researchers at Google to develop MobileNet. As of June 2025, the family has five versions, each improving upon the previous one in terms of performance and efficiency. == Features == === V1 === MobileNetV1 was published in April 2017. Its main architectural innovation was incorporation of depthwise separable convolutions. It was first developed by Laurent Sifre during an internship at Google Brain in 2013 as an architectural variation on AlexNet to improve convergence speed and model size. The depthwise separable convolution decomposes a single standard convolution into two convolutions: a depthwise convolution that filters each input channel independently and a pointwise convolution ( 1 × 1 {\displaystyle 1\times 1} convolution) that combines the outputs of the depthwise convolution. This factorization significantly reduces computational cost. The MobileNetV1 has two hyperparameters: a width multiplier α {\displaystyle \alpha } that controls the number of channels in each layer. Smaller values of α {\displaystyle \alpha } lead to smaller and faster models, but at the cost of reduced accuracy, and a resolution multiplier ρ {\displaystyle \rho } , which controls the input resolution of the images. Lower resolutions result in faster processing but potentially lower accuracy. === V2 === MobileNetV2 was published in March 2019. It uses inverted residual layers and linear bottlenecks. Inverted residuals modify the traditional residual block structure. Instead of compressing the input channels before the depthwise convolution, they expand them. This expansion is followed by a 1 × 1 {\displaystyle 1\times 1} depthwise convolution and then a 1 × 1 {\displaystyle 1\times 1} projection layer that reduces the number of channels back down. This inverted structure helps to maintain representational capacity by allowing the depthwise convolution to operate on a higher-dimensional feature space, thus preserving more information flow during the convolutional process. Linear bottlenecks removes the typical ReLU activation function in the projection layers. This was rationalized by arguing that that nonlinear activation loses information in lower-dimensional spaces, which is problematic when the number of channels is already small. === V3 === MobileNetV3 was published in 2019. The publication included MobileNetV3-Small, MobileNetV3-Large, and MobileNetEdgeTPU (optimized for Pixel 4). They were found by a form of neural architecture search (NAS) that takes mobile latency into account, to achieve good trade-off between accuracy and latency. It used piecewise-linear approximations of swish and sigmoid activation functions (which they called "h-swish" and "h-sigmoid"), squeeze-and-excitation modules, and the inverted bottlenecks of MobileNetV2. === V4 === MobileNetV4 was published in September 2024. The publication included a large number of architectures found by NAS. Inspired by Vision Transformers, the V4 series included multi-query attention. It also unified both inverted residual and inverted bottleneck from the V3 series with the "universal inverted bottleneck", which includes these two as special cases. === V5 === MobileNetV5's architecture was published shortly after the release of Gemma 3n in June 2025. While the announcement stated a technical report on MobileNetV5 would be available soon, this has not yet materialised. The network is 10 times larger than the largest V4 variant.
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.
Artificial intimacy
Artificial intimacy is a form of human-AI interaction in which an individual will form social connections, emotional bonds, or intimate relationships with various forms of artificial intelligence, including chatbots, virtual assistants, and other artificial entities. Artificially intimate relationships include not only romances, but parasocial relationships with virtual AI characters and the use of griefbots trained on a dead or otherwise lost individual. Artificial intimacy can arise because humans are prone to anthropomorphism. Responses from these AI models are often designed to simulate human interaction. Individuals experiencing artificial intimacy may exhibit attachment, love and commitment to certain AI models, akin to the bonds typically shared between humans. == Causes == === Perceived responsiveness === Robin Dunbar famously proposed that due to emergence of larger groups of humans, vocal communication and language in humans evolved to replace grooming as a means of bonding, arguing that language was a more efficient way to maintain and strengthen social bonds across wider social settings and networks. Further research in this field leads many psychologists to agree that social cognition, affiliative bonding and language in humans are deeply connected. The interpersonal model of intimacy considers communication to be key in affiliative bonding, suggesting that intimacy develops and deepens through open communication between partners in relationship. Specifically, when individuals communicate emotions and perceive their partner as responsive and caring, feelings of closeness and connection are enhanced, building intimacy. Social penetration theory also aligns with the idea of communication being central to intimacy, by explaining how interpersonal relationships develop through gradual increases in self-disclosure. When the benefits of emotional bonding outweigh the costs of vulnerability, individuals will partake in self-disclosure, opening up to one another. Thereby, the literature can be used to provide a proximate explanation for the emergence of artificial intimacy to understand how the phenomenon occurs. Artificial entities are able to mimic interpersonal communication between humans, which in turn can simulate sensations of intimacy within human users though a perceived sense of responsiveness. The relationship between human and AI does not come with the cost of vulnerability or social rejection, which may make self-disclosure easier than with other humans. Altogether, these factors may lead to the experience of anthropomorphism and formation of affiliative relationships. Skjuve et al's interview study on Replika chatbot users further aligns with this explanation, finding that users' perception of chatbots as "accepting, understanding and non-judgmental" facilitated relationship development between the AI and users, and the act of self-disclosure possibly strengthened relationships. Another study on Replika users' reviews and survey results found users perceived chatbots as emotional supportive companions. This evidence further suggests that the perception of artificial entities as capable of empathy and responsiveness in communication facilitate the development of intimate relationships between users and AI. === Loneliness and coping with negative emotions === Research has suggested that humans evolved social bonds as a result of evolutionary pressures that favored cooperation, information exchange and transmission, and group living. Many studies stress the presence of social bonds to be important for human living: research by Baumeister and Leary suggests that humans have a basic psychological need to form and maintain "strong, stable interpersonal relationships", and that a lack of social bonds or sense of belonging leads to negative psychological and physical outcomes. Eisenberger et al's study on the neuroimaging of brain activity suggests that human brains process social rejection and exclusion similarly to physical pain. Furthermore, Song et al's study found that lonely individuals tend to seek more connections in mediated environments, such as online platforms like Facebook. This was suggested to be as a means to reduce their offline loneliness from a lack of in-person interaction, while also fulfilling a need to communicate. Leading on from this, an ultimate explanation for why humans seek the perceived sense of connection from artificial intimacy is to fulfil an evolutionary need for bonding and belonging. Xie et al's study found loneliness to be a driving factor in chatbot interaction. Herbener and Damholdt's study on Danish high school students found that students who sought emotional support or engaged in reciprocal conversations with chatbots were significantly more lonely than their peers, perceived themselves as having less social support, and used the chatbots to cope with negative emotions. The aforementioned notion that chatbots were perceived to have a positive effect on users' negative emotions is also further supported by other studies. Skjuve et al's study found that chatbot relationships may have a positive effect on users' wellbeing. De Freitas et al ran several studies on the effect of chatbots on loneliness, consistently finding evidence suggesting that interaction with chatbots reduces loneliness in users: It was found that existing chatbot users used AI to alleviate loneliness, having an AI companion consistently reduced loneliness over the course of a week, and reductions in loneliness could be explained by chatbot performance—and specifically whether it was able to make users feel heard. Overall the evidence suggests an innate need for bonding evokes feelings of loneliness in users, who turn to artificial intimacy as a low-cost method alleviate these emotions. While many users report positive experiences, some researchers caution that pursuing artificial intimacy may lead to reduced social motivation, social substitution effects, withdrawal from real-life relationships and difficulty discerning reality from fantasy, which may increase longer-term loneliness and isolation. The long-term psychological and societal impacts remain under active investigation.
Mix automation
In music recording, mix automation allows the mixing console to remember the mixing engineer's dynamic adjustment of faders during a musical piece in the post-production editing process. A timecode is necessary for the synchronization of automation. Modern mixing consoles and digital audio workstations use comprehensive mix automation. The need for automated mixing originated from the late 1970s transition form 8-track to 16-track and then 24-track multitrack recording, as mixing could be laborious and require multiple people and hands, and the results could be almost impossible to reproduce. With 48-track recording - synchronized twin 24-track recorders (for a net 46 audio tracks, with one on each machine for SMPTE timecode) - came larger recording and mixing consoles with even more channel faders to manage during mixdown. Manufacturers, such as Neve Electronics (now AMS Neve) and Solid State Logic (SSL), both English companies, developed systems that enabled one engineer to oversee every detail of a complex mix, although the computers required to power these desks remained a rarity into the late 1970s. According to record producer Roy Thomas Baker, Queen's 1975 single "Bohemian Rhapsody" was one of the first mixes to be done with automation. == Types == Voltage Controlled Automation fader levels are regulated by voltage-controlled amplifiers (VCA). VCAs control the audio level and not the actual fader. Moving Fader Automation a motor is attached to the fader, which then can be controlled by the console, digital audio workstation (DAW), or user. Software Controlled Automation the software can be internal to the console, or external as part of a DAW. The virtual fader can be adjusted in the software by the user. MIDI Automation the communications protocol MIDI can be used to send messages to the console to control automation. == Modes == Auto Write used the first time automation is created or when writing over existing automation Auto Touch writes automation data only while a fader is touched/faders return to any previously automated position after release Auto Latch starts writing automation data when a fader is touched/stays in position after release Auto Read digital Audio Workstation performs the written automation Auto Off automation is temporarily disabled All of these include the mute button. If mute is pressed during writing of automation, the audio track will be muted during playback of that automation. Depending on software, other parameters such as panning, sends, and plug-in controls can be automated as well. In some cases, automation can be written using a digital potentiometer instead of a fader.
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-