Lion algorithm (LA) is one among the bio-inspired (or) nature-inspired optimization algorithms (or) that are mainly based on meta-heuristic principles. It was first introduced by B. R. Rajakumar in 2012 in the name, Lion’s Algorithm. It was further extended in 2014 to solve the system identification problem. This version was referred as LA, which has been applied by many researchers for their optimization problems. == Inspiration from lion’s social behaviour == Lions form a social system called a "pride", which consists of 1–3 pair of lions. A pride of lions shares a common area known as territory in which a dominant lion is called as territorial lion. The territorial lion safeguards its territory from outside attackers, especially nomadic lions. This process is called territorial defense. It protects the cubs till they become sexually matured. The maturity period is about 2–4 years. The pride undergoes survival fights to protect its territory and the cubs from nomadic lions. Upon getting defeated by the nomadic lions, the dominating nomadic lion takes the role of territorial lion by killing or driving out the cubs of the pride. The lioness of the pride give birth to cubs though the new territorial lion. When the cubs of the pride mature and considered to be stronger than the territorial lion, they take over the pride. This process is called territorial take-over. If territorial take-over happens, either the old territorial lion, which is considered to be laggard, is driven out or it leaves the pride. The stronger lions and lioness form the new pride and give birth to their own cubs == Terminology == In the LA, the terms that are associated with lion’s social system are mapped to the terminology of optimization problems. Few of such notable terms are related here. Lion: A potential solution to be generated or determined as optimal (or) near-optimal solution of the problem. The lion can be a territorial lion and lioness, cubs and nomadic lions that represent the solution based on the processing steps of the LA. Territorial lion: The strongest solution of the pride that tends to meet the objective function. Nomadic lion: A random solution, sometimes termed as nomad, to facilitate the exploration principle Laggard lion: Poor solutions that are failed in the survival fight. Pride: A pool of potential solutions i.e. a lion, lioness and their cubs, that are potential solutions of the search problem. Fertility evaluation: A process of evaluating whether the territorial lion and lioness are able to provide potential solutions in the future generations i.e. It ensures that the lion or lioness converge at every generation. Survival fight: It is a greedy selection process, which is often carried out between the pride and nomadic lion. == Algorithm == The steps involved in LA are given below: Pride Generation: Generate X m a l e {\displaystyle X^{male}} , X f e m a l e {\displaystyle X^{female}} and X 1 n o m a d {\displaystyle X_{1}^{nomad}} Determine f ( X m a l e ) {\displaystyle f(X^{male})} , f ( X f e m a l e ) {\displaystyle f(X^{female})} , f ( X 1 n o m a d ) {\displaystyle f(X_{1}^{nomad})} Initialize f r e f {\displaystyle f^{ref}} as f ( X m a l e ) {\displaystyle f(X^{male})} and N g {\displaystyle N_{g}} as 0 Memorize X m a l e {\displaystyle X^{male}} and X f e m a l e {\displaystyle X^{female}} Apply Fertility evaluation Process Generation of cubpool by mating Gender clustering: Define X c u b m a l e {\displaystyle X_{cub}^{male}} and X c u b f e m a l e {\displaystyle X_{cub}^{female}} Initialize a g e c u b {\displaystyle age_{cub}} as zero Apply Cub growth function Territorial defense: If X m a l e {\displaystyle X^{male}} (or pride) fails in the survival fight i.e. X 1 n o m a d {\displaystyle X_{1}^{nomad}} defeats the pride, go to step 4, else continue Increase a g e c u b {\displaystyle age_{cub}} by 1 and check whether cub attains maturity i.e., if a g e c u b > a g e m a x {\displaystyle age_{cub}>age_{max}} , go to Step 9, else continue Territorial takeover: If X c u b m a l e {\displaystyle X_{cub}^{male}} and X c u b f e m a l e {\displaystyle X_{cub}^{female}} are found to be closer to optimal solution, update X m a l e {\displaystyle X^{male}} and X f e m a l e {\displaystyle X^{female}} Increment N g {\displaystyle N_{g}} by 1 Repeat from Step 5, if termination criterion is not violated, else return X m a l e {\displaystyle X^{male}} as the near-optimal solution == Variants == The LA has been further taken forward to adopt in different problem areas. According to the characteristics of the problem area, significant amendment has been done in the processes and the models used in the LA. Accordingly, diverse variants have been developed by the researchers. They can be broadly grouped as hybrid LAs and non-hybrid LAs. Hybrid LAs are the LAs that are amended by the principle of other meta-heuristics, whereas the Non-hybrid LAs take any scientific amendment inside its operation that are felt to be essential to attend the respective problem area. == Applications == LA is applied in diverse engineering applications that range from network security, text mining, image processing, electrical systems, data mining and many more. Few of the notable applications are discussed here. Networking applications: In WSN, LA is used to solve the cluster head selection problem by determining optimal cluster head. Route discovery problem in both the VANET and MANET are also addressed by the LA in the literature. It is also used to detect attacks in advanced networking scenarios such as Software-Defined Networks (SDN) Power Systems: LA has attended generation rescheduling problem in a deregulated environment, optimal localization and sizing of FACTS devices for power quality enhancement and load-frequency controlling problem Cloud computing: LA is used in optimal container-resource allocation problem in cloud environment and cloud security
Multisample anti-aliasing
Multisample anti-aliasing (MSAA) is a type of spatial anti-aliasing, a technique used in computer graphics to remove jaggies. It is an optimization of supersampling, where only the necessary parts are sampled more. Jaggies are only noticed in a small area, so the area is quickly found, and only that is anti-aliased. == Definition == The term generally refers to a special case of supersampling. Initial implementations of full-scene anti-aliasing (FSAA) worked conceptually by simply rendering a scene at a higher resolution, and then downsampling to a lower-resolution output. Most modern GPUs are capable of this form of anti-aliasing, but it greatly taxes resources such as texture, bandwidth, and fillrate. (If a program is highly TCL-bound or CPU-bound, supersampling can be used without much performance hit.) According to the OpenGL GL_ARB_multisample specification, "multisampling" refers to a specific optimization of supersampling. The specification dictates that the renderer evaluate the fragment program once per pixel, and only "truly" supersample the depth and stencil values. (This is not the same as supersampling but, by the OpenGL 1.5 specification, the definition had been updated to include fully supersampling implementations as well.) In graphics literature in general, "multisampling" refers to any special case of supersampling where some components of the final image are not fully supersampled. The lists below refer specifically to the ARB_multisample definition. == Description == In supersample anti-aliasing, multiple locations are sampled within every pixel, and each of those samples is fully rendered and combined with the others to produce the pixel that is ultimately displayed. This is computationally expensive, because the entire rendering process must be repeated for each sample location. It is also inefficient, as aliasing is typically only noticed in some parts of the image, such as the edges, whereas supersampling is performed for every single pixel. In multisample anti-aliasing, if any of the multi sample locations in a pixel is covered by the triangle being rendered, a shading computation must be performed for that triangle. However this calculation only needs to be performed once for the whole pixel regardless of how many sample positions are covered; the result of the shading calculation is simply applied to all of the relevant multi sample locations. In the case where only one triangle covers every multi sample location within the pixel, only one shading computation is performed, and these pixels are little more expensive than (and the result is no different from) the non-anti-aliased image. This is true of the middle of triangles, where aliasing is not an issue. (Edge detection can reduce this further by explicitly limiting the MSAA calculation to pixels whose samples involve multiple triangles, or triangles at multiple depths.) In the extreme case where each of the multi sample locations is covered by a different triangle, a different shading computation will be performed for each location and the results then combined to give the final pixel, and the result and computational expense are the same as in the equivalent supersampled image. The shading calculation is not the only operation that must be performed on a given pixel; multisampling implementations may variously sample other operations such as visibility at different sampling levels. == Advantages == The pixel shader usually only needs to be evaluated once per pixel for every triangle covering at least one sample point. The edges of polygons (the most obvious source of aliasing in 3D graphics) are anti-aliased. Since multiple subpixels per pixel are sampled, polygonal details smaller than one pixel that might have been missed without MSAA can be captured and made a part of the final rendered image if enough samples are taken. == Disadvantages == === Alpha testing === Alpha testing is a technique common to older video games used to render translucent objects by rejecting pixels from being written to the framebuffer. If the alpha value of a translucent fragment (pixel) is below a specified threshold, it will be discarded. Because this is performed on a pixel by pixel basis, the image does not receive the benefits of multi-sampling (all of the multisamples in a pixel are discarded based on the alpha test) for these pixels. The resulting image may contain aliasing along the edges of transparent objects or edges within textures, although the image quality will be no worse than it would be without any anti-aliasing. Translucent objects that are modelled using alpha-test textures will also be aliased due to alpha testing. This effect can be minimized by rendering objects with transparent textures multiple times, although this would result in a high performance reduction for scenes containing many transparent objects. === Aliasing === Because multi-sampling calculates interior polygon fragments only once per pixel, aliasing and other artifacts will still be visible inside rendered polygons where fragment shader output contains high frequency components. === Performance === While less performance-intensive than SSAA (supersampling), it is possible in certain scenarios (scenes heavy in complex fragments) for MSAA to be multiple times more intensive for a given frame than post processing anti-aliasing techniques such as FXAA, SMAA and MLAA. Early techniques in this category tend towards a lower performance impact, but suffer from accuracy problems. More recent post-processing based anti-aliasing techniques such as temporal anti-aliasing (TAA), which reduces aliasing by combining data from previously rendered frames, have seen the reversal of this trend, as post-processing AA becomes both more versatile and more expensive than MSAA, which cannot antialias an entire frame alone. == Sampling methods == === Point sampling === In a point-sampled mask, the coverage bit for each multisample is only set if the multisample is located inside the rendered primitive. Samples are never taken from outside a rendered primitive, so images produced using point-sampling will be geometrically correct, but filtering quality may be low because the proportion of bits set in the pixel's coverage mask may not be equal to the proportion of the pixel that is actually covered by the fragment in question. === Area sampling === Filtering quality can be improved by using area sampled masks. In this method, the number of bits set in a coverage mask for a pixel should be proportionate to the actual area coverage of the fragment. This will result in some coverage bits being set for multisamples that are not actually located within the rendered primitive, and can cause aliasing and other artifacts. == Sample patterns == === Regular grid === A regular grid sample pattern, where multisample locations form an evenly spaced grid throughout the pixel, is easy to implement and simplifies attribute evaluation (i.e. setting subpixel masks, sampling color and depth). This method is computationally expensive due to the large number of samples. Edge optimization is poor for screen-aligned edges, but image quality is good when the number of multisamples is large. === Sparse regular grid === A sparse regular grid sample pattern is a subset of samples that are chosen from the regular grid sample pattern. As with the regular grid, attribute evaluation is simplified due to regular spacing. The method is less computationally expensive due to having a fewer samples. Edge optimization is good for screen aligned edges, and image quality is good for a moderate number of multisamples. === Stochastic sample patterns === A stochastic sample pattern is a random distribution of multisamples throughout the pixel. The irregular spacing of samples makes attribute evaluation complicated. The method is cost efficient due to low sample count (compared to regular grid patterns). Edge optimization with this method, although sub-optimal for screen aligned edges. Image quality is excellent for a moderate number of samples. == Quality == Compared to supersampling, multisample anti-aliasing can provide similar quality at higher performance, or better quality for the same performance. Further improved results can be achieved by using rotated grid subpixel masks. The additional bandwidth required by multi-sampling is reasonably low if Z and colour compression are available. Most modern GPUs support 2×, 4×, and 8× MSAA samples. Higher values result in better quality, but are slower.
Prompt engineering
Prompt engineering is the process of structuring natural language inputs (known as prompts) to produce specified outputs from a generative artificial intelligence (GenAI) model. Context engineering is the related area of software engineering that focuses on the management of non-prompt contexts supplied to the GenAI model, such as metadata, API tools, and tokens. It can also be defined as the practice of designing and refining input instructions given to a generative AI model to produce more accurate, relevant, or useful outputs. Effective prompt engineering involves understanding how a model interprets language, and may include techniques such as few-shot prompting, chain-of-thought prompting, and role assignment. It is increasingly considered a skill for working with large language models (LLMs) in both research and professional contexts. During the 2020s AI boom, prompt engineering became regarded as a business capability across corporations and industries. Employees with the title prompt engineer were hired to create prompts that would increase productivity and efficacy, although the individual title has since lost traction amid AI models that produce better prompts than humans and corporate training in prompting for general employees. Common prompting techniques include multi-shot, chain-of-thought, and tree-of-thought prompting, as well as the use of assigning roles to the model. Automated prompt generation methods, such as retrieval-augmented generation (RAG), provide for greater accuracy and a wider scope of functions for prompt engineers. Prompt injection is a type of cybersecurity attack that targets machine learning models through malicious prompts. == Terminology == The Oxford English Dictionary defines prompt engineering as "The action or process of formulating and refining prompts for an artificial intelligence program, algorithm, etc., in order to optimize its output or to achieve a desired outcome; the discipline or profession concerned with this." In 2023, prompt ("an instruction given to an artificial intelligence program, algorithm, etc., which determines or influences the content it generates") was the runner-up to Oxford's word of the year. === Prompt === A prompt is some natural language text that describes and prescribes the task that an artificial intelligence (AI) should perform. A prompt for a text-to-text language model can be a query, a command, or a longer statement referencing context, instructions, and conversation history. The process of prompt engineering may involve designing clear queries, refining wording, providing relevant context, specifying the style of output, and assigning a character for the AI to mimic in order to guide the model toward more accurate, useful, and consistent responses. When communicating with a text-to-image or a text-to-audio model, a typical prompt contains a description of a desired output such as "a high-quality photo of an astronaut riding a horse" or "Lo-fi slow BPM electro chill with organic samples". Prompt engineering may be applied to text-to-image models to achieve a desired subject, style, layout, lighting, and aesthetic. === Techniques === Common terms used to describe various specific prompt engineering techniques include chain-of-thought, tree-of-thought, and retrieval-augmented generation (RAG). A 2024 survey of the field identified over 50 distinct text-based prompting techniques, 40 multimodal variants, and a vocabulary of 33 terms used across prompting research, highlighting a present lack of standardised terminology for prompt engineering. Vibe coding is an AI-assisted software development method where a user prompts an LLM with a description of what they want and lets it generate or edit the code. In 2025, "vibe coding" was the Collins Dictionary word of the year. === Context engineering === Context engineering is a related process that focuses on the context elements that accompany user prompts, which include system instructions, retrieved knowledge, tool definitions, conversation summaries, and task metadata. Context engineering is performed to improve reliability, provenance and token efficiency in production LLM systems. The concept emphasises operational practices such as token budgeting, provenance tags, versioning of context artifacts, observability (logging which context was supplied), and context regression tests to ensure that changes to supplied context do not silently alter system behaviour. == Rationale == Research has found that the performance of large language models (LLMs) is highly sensitive to choices such as the ordering of examples, the quality of demonstration labels, and even small variations in phrasing. In some cases, reordering examples in a prompt produced accuracy shifts of more than 40 percent. === In-context learning === A model's ability to temporarily learn from prompts is known as in-context learning. In-context learning is an emergent ability of large language models. It is an emergent property of model scale, meaning that breaks in scaling laws occur, leading to its efficacy increasing at a different rate in larger models than in smaller models. Unlike training and fine-tuning, which produce lasting changes, in-context learning is temporary. Training models to perform in-context learning can be viewed as a form of meta-learning, or "learning to learn". === Prompting to estimate model sensitivity === Research consistently demonstrates that LLMs are highly sensitive to subtle variations in prompt formatting, structure, and linguistic properties. Some studies have shown up to 76 accuracy points across formatting changes in few-shot settings. Linguistic features significantly influence prompt effectiveness—such as morphology, syntax, and lexico-semantic changes—which meaningfully enhance task performance across a variety of tasks. Clausal syntax, for example, improves consistency and reduces uncertainty in knowledge retrieval. This sensitivity persists even with larger model sizes, additional few-shot examples, or instruction tuning. To address sensitivity of models and make them more robust, several evaluative methods have been proposed. FormatSpread facilitates systematic analysis by evaluating a range of plausible prompt formats, offering a more comprehensive performance interval. Similarly, PromptEval estimates performance distributions across diverse prompts, enabling robust metrics such as performance quantiles and accurate evaluations under constrained budgets. == Prompting techniques == === Multi-shot === A prompt may include a few examples for a model to learn from in context, an approach called few-shot learning. For example, the prompt may ask the model to complete "maison → house, chat → cat, chien →", with the expected response being dog. === Chain-of-thought === Chain-of-thought (CoT) prompting is a technique that allows large language models (LLMs) to solve a problem as a series of intermediate steps before giving a final answer. In 2022, Google Brain reported that chain-of-thought prompting improves reasoning ability by inducing the model to answer a multi-step problem with steps of reasoning that mimic a train of thought. Chain-of-thought techniques were developed to help LLMs handle multi-step reasoning tasks, such as arithmetic or commonsense reasoning questions. When applied to PaLM, a 540 billion parameter language model, according to Google, CoT prompting significantly aided the model, allowing it to perform comparably with task-specific fine-tuned models on several tasks, achieving state-of-the-art results at the time on the GSM8K mathematical reasoning benchmark. It is possible to fine-tune models on CoT reasoning datasets to enhance this capability further and stimulate better interpretability. As originally proposed by Google, each CoT prompt is accompanied by a set of input/output examples—called exemplars—to demonstrate the desired model output, making it a few-shot prompting technique. However, according to a later paper from researchers at Google and the University of Tokyo, simply appending the words "Let's think step-by-step" was also effective, which allowed for CoT to be employed as a zero-shot technique. ==== Self-consistency ==== Self-consistency performs several chain-of-thought rollouts, then selects the most commonly reached conclusion out of all the rollouts. === Tree-of-thought === Tree-of-thought prompting generalizes chain-of-thought by generating multiple lines of reasoning in parallel, with the ability to backtrack or explore other paths. It can use tree search algorithms like breadth-first, depth-first, or beam. === Text-to-image prompting === In 2022, text-to-image models like DALL-E 2, Stable Diffusion, and Midjourney were released to the public. These models take text prompts as input and use them to generate images. Early text-to-image models typically do not understand negation, grammar and sentence structure in the same way as large language models, and may thus requi
AI data center
An AI data center is a specialized data center facility designed for the computationally intensive tasks of training and running inference for artificial intelligence (AI) and machine learning models. Unlike general-purpose data centers, they are optimized for the parallel processing demands of AI workloads, typically using hardware such as AI accelerators (e.g., GPUs, TPUs) and high-speed interconnects. The global push to construct these specialized facilities accelerated dramatically during the AI boom of the 2020s. Memory manufacturers prioritized production of High Bandwidth Memory (HBM) essential for AI servers, which led to a global memory supply shortage amid a broader competition for advanced chips, power, and infrastructure. Major tech companies are estimated to spend $650 billion on AI data centers in 2026. == Architecture == Data centers for building and running large machine learning models contain specialized computer chips, GPUs, that use 2 to 4 times as much energy as their regular CPU counterparts (250-500 watts). AI data centers use 60 or more kilowatts per server rack, whereas more standard data centers typically use 5 to 10 kilowatts per rack. == Operators == As of August 2025, The Information tracked 18 planned or existing AI data centers in the United States, operated by Amazon Web Services, CoreWeave, Crusoe, Meta, Microsoft/OpenAI, Oracle, Tesla, and xAI. Other AI data center operators include Digital Realty and Alibaba. Data centers are also being built in China, India, Europe, Saudi Arabia, and Canada. The New Yorker described CoreWeave as the most prominent AI data center operator in the United States. Two types of data center providers for machine learning have been noted: hyperscalers and neoclouds. The Verge listed large technology companies such as Google, Meta, Microsoft, Oracle and Amazon as hyperscalers. The New York Times described neoclouds as "a new generation of data center providers". CoreWeave, Nebius, Nscale, and Lambda have been described as examples of neoclouds. In January 2025, OpenAI, in partnership with Oracle and Softbank, announced the Stargate project, which as of September 2025 is composed of six built or proposed AI data centers in the United States. In response to the Stargate project, Amazon launched in October 2025 an AI data center on 1,200 acres of farmland in Indiana. This data center, known as Project Rainier, is one of the largest AI data centers in the world, with Amazon spending $11 billion on the project. Rainier is specifically intended for training and running machine learning models from Anthropic. As of that time, this facility contains seven data centers (out of an estimated 30 planned) and will use 2.2 gigawatts of electricity (equivalent to 1 million households) and millions of gallons of water per year. Computer chips from Annapurna Labs and Anthropic, Trainium 2, were designed for use in such facilities. Amazon pumped millions of gallons of water out of the ground to construct the data center, and as of June 2025, Indiana state officials are investigating whether this dewatering process led to dry wells for local residents. In November 2025, Anthropic announced a plan in partnership with Fluidstack to develop artificial intelligence infrastructure in the United States, including data centers in New York and Texas, worth $50 billion. Other AI data center projects include the Colossus supercomputer from xAI, a Louisiana-based project from Meta, Hyperion, expected to use 5 GW of power, and a second Ohio-based Meta project, Prometheus, with a capacity of 1 GW. A 3,200-acre AI data center, capable of 4.4-4.5 GW of power and located on the decommissioned Homer City Generating Station, is under construction as of 2025, and will use seven 30-acre gas generating stations supplied by EQT. As of December 2025, CRH is working on over 100 data centers in the United States. In 2025, ExxonMobil and NextEra announced plans to build a data center powered by natural gas and using carbon capture technology, with 1.2 GW of power capacity. They previously purchased 2,500 acres of land in the Southeastern United States and plan to market the data center to an artificial intelligence company. The increased interest in AI data centers has led to several executives from companies in that space becoming billionaires, including CoreWeave, QTS, Nebius, Astera Labs, Groq, Fermi (which is connected to former United States Secretary of Energy Rick Perry), Snowflake and Cipher Mining. Several companies involved in cryptocurrency mining, such as Bitdeer, CoreWeave, Cipher Mining, TeraWulf, IREN, Core Scientific, and CleanSpark have also been involved with AI data centers. == Finances == Between January and August 2024, Microsoft, Meta, Google and Amazon collectively spent $125 billion on AI data centers. Citigroup forecasted that $2.8 trillion would be spent on AI data centers by 2030, while McKinsey and Company estimated that almost $7 trillion would be spent globally by that time. According to S&P Global, $61 billion has been spent on the data center market as a whole in 2025, while debt issuance for data centers was $182 billion during the same year. Large technology companies have offloaded the financial risks of building AI data centers by setting up special purpose vehicles or by contracting with neoclouds. For example, Meta's Hyperion was mostly funded by Blue Owl Capital, which did so using a bond offering from PIMCO. Those bonds were sold to a number of clients, including BlackRock. Meta did not borrow money itself and instead established a special purpose vehicle from which it would rent the data center. This deal was structured by Morgan Stanley for $30 billion, the largest known private capital transaction as of 2025. Neoclouds such as CoreWeave have gone into debt to buy computer chips from Nvidia for their data centers, and the chips themselves have been used for loan collateral. As of December 2025, CoreWeave took out three GPU-backed loans, collectively worth $12.4 billion, from private credit firms (Blackstone, Coatue, BlackRock, PIMCO) and from banks (Goldman Sachs, JPMorgan Chase, Wells Fargo). Thus, these companies provide an indirect connection between private credit and established banks. Data centers have also established asset-backed securities, and debt for data centers has its own derivative financial products. The real estate industry, including asset managers, public companies and private investors, has also invested in data centers. == Energy sourcing == == Environmental footprint == Average AI data centers have an electricity footprint equivalent to 100,000 households, and use billions of gallons of water for cooling their hardware. In 2025, the International Energy Agency estimated that the larger AI data centers currently under construction could consume as much electricity as 2 million households. A 2024 report from the United States Department of Energy stated that data centers overall used 17 billion gallons of water per year in the United States, primarily due to "rapid proliferation of AI servers", and that this usage was forecasted to grow to nearly 80 billion gallons by 2028. Researchers estimated that AI data centers in the United States would emit 24-44 million metric tons of carbon dioxide and use 731–1,125 million cubic meters of water per year between 2024 and 2030. Peaking power plants, which have been proposed as a power source for AI data centers, emit sulfur dioxide and have historically been located disproportionately near communities of color in the United States. Reciprocating internal combustion engines, proposed as another power source for a data center, emit PM 2.5, nitrogen oxides, and volatile organic compounds. == AI data centers in the United States == In the United States, both the Biden administration and second Trump administration supported the construction of AI data centers. In January 2025, then-president Joe Biden signed an executive order for federal government agencies to support AI data centers on federal sites built by private companies, study their effect on energy prices, and encourage their use of renewable energy. In April 2025, the United States Department of Energy suggested 16 possible sites, including Los Alamos National Laboratory, Sandia National Laboratories and Oak Ridge National Laboratory. In its July 2025 AI Action Plan, the second Trump administration supported increased production of AI data centers. Several US states have incentivized local data center construction. For example, in 2024, lawmakers in Michigan approved tax breaks for data center equipment and construction material. Some data center companies have also invested or promised to invest in the infrastructure of local communities. In December 2025, Democratic senators Elizabeth Warren, Chris Van Hollen, and Richard Blumenthal wrote to seven technology companies (Google, Microsoft, Amazon, Meta, CoreWeave, Digital Realty, and Equinix) that they w
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-
Cloud computing
Cloud computing is defined by the International Organization for Standardization (ISO) as "a paradigm for enabling network access to a scalable and elastic pool of shareable physical or virtual resources with self-service provisioning and administration on demand". It is commonly referred to as "the cloud". == Characteristics == In 2011, the National Institute of Standards and Technology (NIST) identified five "essential characteristics" for cloud systems. Below are the exact definitions according to NIST: On-demand self-service: "A consumer can unilaterally provision computing capabilities, such as server time and network storage, as needed automatically without requiring human interaction with each service provider." Broad network access: "Capabilities are available over the network and accessed through standard mechanisms that promote use by heterogeneous thin or thick client platforms (e.g., mobile phones, tablets, laptops, and workstations)." Resource pooling: " The provider's computing resources are pooled to serve multiple consumers using a multi-tenant model, with different physical and virtual resources dynamically assigned and reassigned according to consumer demand." Rapid elasticity: "Capabilities can be elastically provisioned and released, in some cases automatically, to scale rapidly outward and inward commensurate with demand. To the consumer, the capabilities available for provisioning often appear unlimited and can be appropriated in any quantity at any time." Measured service: "Cloud systems automatically control and optimize resource use by leveraging a metering capability at some level of abstraction appropriate to the type of service (e.g., storage, processing, bandwidth, and active user accounts). Resource usage can be monitored, controlled, and reported, providing transparency for both the provider and consumer of the utilized service. By 2023, the International Organization for Standardization (ISO) had expanded and refined the list. == History == The history of cloud computing extends to the 1960s, with the initial concepts of time-sharing becoming popularized via remote job entry (RJE). The "data center" model, where users submitted jobs to operators to run on mainframes, was predominantly used during this era. This period saw broad experimentation with making large-scale computing power more accessible through time-sharing, while optimizing infrastructure, platforms, and applications to improve efficiency for end users. The "cloud" metaphor for virtualized services dates to 1994, when it was used by General Magic for the universe of "places" that mobile agents in the Telescript environment could "go". The metaphor is credited to David Hoffman, a General Magic communications specialist, based on its long-standing use in networking and telecom. The expression cloud computing became more widely known in 1996 when Compaq Computer Corporation drew up a business plan for future computing and the Internet. The company's ambition was to supercharge sales with "cloud computing-enabled applications". The business plan foresaw that online consumer file storage would likely be commercially successful. As a result, Compaq decided to sell server hardware to internet service providers. In the 2000s, the application of cloud computing began to take shape with the establishment of Amazon Web Services (AWS) in 2002, which allowed developers to build applications independently. In 2006 Amazon Simple Storage Service, known as Amazon S3, and the Amazon Elastic Compute Cloud (EC2) were released. In 2008 NASA's development of the first open-source software for deploying private and hybrid clouds. The following decade saw the launch of various cloud services. In 2010, Microsoft launched Microsoft Azure, and Rackspace Hosting and NASA initiated an open-source cloud-software project, OpenStack. IBM introduced the IBM SmartCloud framework in 2011, and Oracle announced the Oracle Cloud in 2012. In December 2019, Amazon launched AWS Outposts, a service that extends AWS infrastructure, services, APIs, and tools to customer data centers, co-location spaces, or on-premises facilities. == Value proposition == Cloud computing can shorten time to market by offering pre-configured tools, scalable resources, and managed services, allowing users to focus on core business value rather than maintaining infrastructure. Cloud platforms can enable organizations and individuals to reduce upfront capital expenditures on physical infrastructure by shifting to an operational expenditure model, where costs scale with usage. Cloud platforms also offer managed services and tools, such as artificial intelligence, data analytics, and machine learning, which might otherwise require significant in-house expertise and infrastructure investment. While cloud computing can offer cost advantages through effective resource optimization, organizations often face challenges such as unused resources, inefficient configurations, and hidden costs without proper oversight and governance. Many cloud platforms provide cost management tools, such as AWS Cost Explorer and Azure Cost Management, and frameworks like FinOps have emerged to standardize financial operations in the cloud. Cloud computing also facilitates collaboration, remote work, and global service delivery by enabling secure access to data and applications from any location with an internet connection. Cloud providers offer various redundancy options for core services, such as managed storage and managed databases, though redundancy configurations often vary by service tier. Advanced redundancy strategies, such as cross-region replication or failover systems, typically require explicit configuration and may incur additional costs or licensing fees. Cloud environments operate under a shared responsibility model, where providers are typically responsible for infrastructure security, physical hardware, and software updates, while customers are accountable for data encryption, identity and access management (IAM), and application-level security. These responsibilities vary depending on the cloud service model—Infrastructure as a Service (IaaS), Platform as a Service (PaaS), or Software as a Service (SaaS)—with customers typically having more control and responsibility in IaaS environments and progressively less in PaaS and SaaS models, often trading control for convenience and managed services. == Adoption and suitability == The decision to adopt cloud computing or maintain on-premises infrastructure depends on factors such as scalability, cost structure, latency requirements, regulatory constraints, and infrastructure customization. Organizations with variable or unpredictable workloads, limited capital for upfront investments, or a focus on rapid scalability benefit from cloud adoption. Startups, SaaS companies, and e-commerce platforms often prefer the pay-as-you-go operational expenditure (OpEx) model of cloud infrastructure. Additionally, companies prioritizing global accessibility, remote workforce enablement, disaster recovery, and leveraging advanced services such as AI/ML and analytics are well-suited for the cloud. In recent years, some cloud providers have started offering specialized services for high-performance computing and low-latency applications, addressing some use cases previously exclusive to on-premises setups. On the other hand, organizations with strict regulatory requirements, highly predictable workloads, or reliance on deeply integrated legacy systems may find cloud infrastructure less suitable. Businesses in industries like defense, government, or those handling highly sensitive data often favor on-premises setups for greater control and data sovereignty. Additionally, companies with ultra-low latency requirements, such as high-frequency trading (HFT) firms, rely on custom hardware (e.g., FPGAs) and physical proximity to exchanges, which most cloud providers cannot fully replicate despite recent advancements. Similarly, tech giants like Google, Meta, and Amazon build their own data centers due to economies of scale, predictable workloads, and the ability to customize hardware and network infrastructure for optimal efficiency. However, these companies also use cloud services selectively for certain workloads and applications where it aligns with their operational needs. In practice, many organizations are increasingly adopting hybrid cloud architectures, combining on-premises infrastructure with cloud services. This approach allows businesses to balance scalability, cost-effectiveness, and control, offering the benefits of both deployment models while mitigating their respective limitations. == Challenges and limitations == One of the primary challenges of cloud computing, compared with traditional on-premises systems, is maintaining data security and privacy. Cloud users entrust their sensitive data to third-party providers, who may not have adequate measures to protect it from unau
Coupled pattern learner
Coupled Pattern Learner (CPL) is a machine learning algorithm which couples the semi-supervised learning of categories and relations to forestall the problem of semantic drift associated with boot-strap learning methods. == Coupled Pattern Learner == Semi-supervised learning approaches using a small number of labeled examples with many unlabeled examples are usually unreliable as they produce an internally consistent, but incorrect set of extractions. CPL solves this problem by simultaneously learning classifiers for many different categories and relations in the presence of an ontology defining constraints that couple the training of these classifiers. It was introduced by Andrew Carlson, Justin Betteridge, Estevam R. Hruschka Jr. and Tom M. Mitchell in 2009. == CPL overview == CPL is an approach to semi-supervised learning that yields more accurate results by coupling the training of many information extractors. Basic idea behind CPL is that semi-supervised training of a single type of extractor such as ‘coach’ is much more difficult than simultaneously training many extractors that cover a variety of inter-related entity and relation types. Using prior knowledge about the relationships between these different entities and relations CPL makes unlabeled data as a useful constraint during training. For e.g., ‘coach(x)’ implies ‘person(x)’ and ‘not sport(x)’. == CPL description == === Coupling of predicates === CPL primarily relies on the notion of coupling the learning of multiple functions so as to constrain the semi-supervised learning problem. CPL constrains the learned function in two ways. Sharing among same-arity predicates according to logical relations Relation argument type-checking === Sharing among same-arity predicates === Each predicate P in the ontology has a list of other same-arity predicates with which P is mutually exclusive. If A is mutually exclusive with predicate B, A’s positive instances and patterns become negative instances and negative patterns for B. For example, if ‘city’, having an instance ‘Boston’ and a pattern ‘mayor of arg1’, is mutually exclusive with ‘scientist’, then ‘Boston’ and ‘mayor of arg1’ will become a negative instance and a negative pattern respectively for ‘scientist.’ Further, Some categories are declared to be a subset of another category. For e.g., ‘athlete’ is a subset of ‘person’. === Relation argument type-checking === This is a type checking information used to couple the learning of relations and categories. For example, the arguments of the ‘ceoOf’ relation are declared to be of the categories ‘person’ and ‘company’. CPL does not promote a pair of noun phrases as an instance of a relation unless the two noun phrases are classified as belonging to the correct argument types. === Algorithm description === Following is a quick summary of the CPL algorithm. Input: An ontology O, and a text corpus C Output: Trusted instances/patterns for each predicate for i=1,2,...,∞ do foreach predicate p in O do EXTRACT candidate instances/contextual patterns using recently promoted patterns/instances; FILTER candidates that violate coupling; RANK candidate instances/patterns; PROMOTE top candidates; end end ==== Inputs ==== A large corpus of Part-Of-Speech tagged sentences and an initial ontology with predefined categories, relations, mutually exclusive relationships between same-arity predicates, subset relationships between some categories, seed instances for all predicates, and seed patterns for the categories. ==== Candidate extraction ==== CPL finds new candidate instances by using newly promoted patterns to extract the noun phrases that co-occur with those patterns in the text corpus. CPL extracts, Category Instances Category Patterns Relation Instances Relation Patterns ==== Candidate filtering ==== Candidate instances and patterns are filtered to maintain high precision, and to avoid extremely specific patterns. An instance is only considered for assessment if it co-occurs with at least two promoted patterns in the text corpus, and if its co-occurrence count with all promoted patterns is at least three times greater than its co-occurrence count with negative patterns. ==== Candidate ranking ==== CPL ranks candidate instances using the number of promoted patterns that they co-occur with so that candidates that occur with more patterns are ranked higher. Patterns are ranked using an estimate of the precision of each pattern. ==== Candidate promotion ==== CPL ranks the candidates according to their assessment scores and promotes at most 100 instances and 5 patterns for each predicate. Instances and patterns are only promoted if they co-occur with at least two promoted patterns or instances, respectively. == Meta-Bootstrap Learner == Meta-Bootstrap Learner (MBL) was also proposed by the authors of CPL. Meta-Bootstrap learner couples the training of multiple extraction techniques with a multi-view constraint, which requires the extractors to agree. It makes addition of coupling constraints on top of existing extraction algorithms, while treating them as black boxes, feasible. MBL assumes that the errors made by different extraction techniques are independent. Following is a quick summary of MBL. Input: An ontology O, a set of extractors ε Output: Trusted instances for each predicate for i=1,2,...,∞ do foreach predicate p in O do foreach extractor e in ε do Extract new candidates for p using e with recently promoted instances; end FILTER candidates that violate mutual-exclusion or type-checking constraints; PROMOTE candidates that were extracted by all extractors; end end Subordinate algorithms used with MBL do not promote any instance on their own, they report the evidence about each candidate to MBL and MBL is responsible for promoting instances. == Applications == In their paper authors have presented results showing the potential of CPL to contribute new facts to existing repository of semantic knowledge, Freebase