In statistics, Markov chain Monte Carlo (MCMC) is a class of algorithms used to draw samples from a probability distribution. Given a probability distribution, one can construct a Markov chain whose elements' distribution approximates it, i.e. the Markov chain's equilibrium distribution matches the target distribution. The more steps that are included, the more closely the distribution of the sample matches the actual desired distribution. Markov chain Monte Carlo methods are used to study probability distributions that are too complex or too high dimensional to study with analytic techniques alone. Various algorithms exist for constructing such Markov chains, including the Metropolis–Hastings algorithm. == General explanation == Markov chain Monte Carlo methods create samples from a continuous random variable, with probability density proportional to a known function. These samples can be used to evaluate an integral over that variable, as its expected value or variance. Practically, an ensemble of chains is generally developed, starting from a set of points arbitrarily chosen and sufficiently distant from each other. These chains are stochastic processes of "walkers" which move around randomly according to an algorithm that looks for places with a reasonably high contribution to the integral to move into next, assigning them higher probabilities. Random walk Monte Carlo methods are a kind of random simulation or Monte Carlo method. However, whereas the random samples of the integrand used in a conventional Monte Carlo integration are statistically independent, those used in MCMC are autocorrelated. Correlations of samples introduces the need to use the Markov chain central limit theorem when estimating the error of mean values. These algorithms create Markov chains such that they have an equilibrium distribution which is proportional to the function given. == History == The development of MCMC methods is deeply rooted in the early exploration of Monte Carlo (MC) techniques in the mid-20th century, particularly in physics. These developments were marked by the Metropolis algorithm proposed by Nicholas Metropolis, Arianna W. Rosenbluth, Marshall Rosenbluth, Augusta H. Teller, and Edward Teller in 1953, which was designed to tackle high-dimensional integration problems using early computers. Then in 1970, W. K. Hastings generalized this algorithm and inadvertently introduced the component-wise updating idea, later known as Gibbs sampling. Simultaneously, the theoretical foundations for Gibbs sampling were being developed, such as the Hammersley–Clifford theorem from Julian Besag's 1974 paper. Although the seeds of MCMC were sown earlier, including the formal naming of Gibbs sampling in image processing by Stuart Geman and Donald Geman (1984) and the data augmentation method by Martin A. Tanner and Wing Hung Wong (1987), its "revolution" in mainstream statistics largely followed demonstrations of the universality and ease of implementation of sampling methods (especially Gibbs sampling) for complex statistical (particularly Bayesian) problems, spurred by increasing computational power and software like BUGS. This transformation was accompanied by significant theoretical advancements, such as Luke Tierney's (1994) rigorous treatment of MCMC convergence, and Jun S. Liu, Wong, and Augustine Kong's (1994, 1995) analysis of Gibbs sampler structure. Subsequent developments further expanded the MCMC toolkit, including particle filters (Sequential Monte Carlo) for sequential problems, Perfect sampling aiming for exact simulation (Jim Propp and David B. Wilson, 1996), RJMCMC (Peter J. Green, 1995) for handling variable-dimension models, and deeper investigations into convergence diagnostics and the central limit theorem. Overall, the evolution of MCMC represents a paradigm shift in statistical computation, enabling the analysis of numerous previously intractable complex models and continually expanding the scope and impact of statistics. == Mathematical setting == Suppose (Xn) is a Markov Chain in the general state space X {\displaystyle {\mathcal {X}}} with specific properties. We are interested in the limiting behavior of the partial sums: S n ( h ) = 1 n ∑ i = 1 n h ( X i ) {\displaystyle S_{n}(h)={\dfrac {1}{n}}\sum _{i=1}^{n}h(X_{i})} as n goes to infinity. Particularly, we hope to establish the Law of Large Numbers and the Central Limit Theorem for MCMC. In the following, we state some definitions and theorems necessary for the important convergence results. In short, we need the existence of invariant measure and Harris recurrent to establish the Law of Large Numbers of MCMC (Ergodic Theorem). And we need aperiodicity, irreducibility and extra conditions such as reversibility to ensure the Central Limit Theorem holds in MCMC. === Irreducibility and aperiodicity === Recall that in the discrete setting, a Markov chain is said to be irreducible if it is possible to reach any state from any other state in a finite number of steps with positive probability. However, in the continuous setting, point-to-point transitions have zero probability. In this case, φ-irreducibility generalizes irreducibility by using a reference measure φ on the measurable space ( X , B ( X ) ) {\displaystyle ({\mathcal {X}},{\mathcal {B}}({\mathcal {X}}))} . Definition (φ-irreducibility) Given a measure φ {\displaystyle \varphi } defined on ( X , B ( X ) ) {\displaystyle ({\mathcal {X}},{\mathcal {B}}({\mathcal {X}}))} , the Markov chain ( X n ) {\displaystyle (X_{n})} with transition kernel K ( x , y ) {\displaystyle K(x,y)} is φ-irreducible if, for every A ∈ B ( X ) {\displaystyle A\in {\mathcal {B}}({\mathcal {X}})} with φ ( A ) > 0 {\displaystyle \varphi (A)>0} , there exists n {\displaystyle n} such that K n ( x , A ) > 0 {\displaystyle K^{n}(x,A)>0} for all x ∈ X {\displaystyle x\in {\mathcal {X}}} (Equivalently, P x ( τ A < ∞ ) > 0 {\displaystyle P_{x}(\tau _{A}<\infty )>0} , here τ A = inf { n ≥ 1 ; X n ∈ A } {\displaystyle \tau _{A}=\inf\{n\geq 1;X_{n}\in A\}} is the first n {\displaystyle n} for which the chain enters the set A {\displaystyle A} ). This is a more general definition for irreducibility of a Markov chain in non-discrete state space. In the discrete case, an irreducible Markov chain is said to be aperiodic if it has period 1. Formally, the period of a state ω ∈ X {\displaystyle \omega \in {\mathcal {X}}} is defined as: d ( ω ) := g c d { m ≥ 1 ; K m ( ω , ω ) > 0 } {\displaystyle d(\omega ):=\mathrm {gcd} \{m\geq 1\,;\,K^{m}(\omega ,\omega )>0\}} For the general (non-discrete) case, we define aperiodicity in terms of small sets: Definition (Cycle length and small sets) A φ-irreducible Markov chain ( X n ) {\displaystyle (X_{n})} has a cycle of length d if there exists a small set C {\displaystyle C} , an associated integer M {\displaystyle M} , and a probability distribution ν M {\displaystyle \nu _{M}} such that d is the greatest common divisor of: { m ≥ 1 ; ∃ δ m > 0 such that C is small for ν m ≥ δ m ν M } . {\displaystyle \{m\geq 1\,;\,\exists \,\delta _{m}>0{\text{ such that }}C{\text{ is small for }}\nu _{m}\geq \delta _{m}\nu _{M}\}.} A set C {\displaystyle C} is called small if there exists m ∈ N ∗ {\displaystyle m\in \mathbb {N} ^{}} and a nonzero measure ν m {\displaystyle \nu _{m}} such that: K m ( x , A ) ≥ ν m ( A ) , ∀ x ∈ C , ∀ A ∈ B ( X ) . {\displaystyle K^{m}(x,A)\geq \nu _{m}(A),\quad \forall x\in C,\,\forall A\in {\mathcal {B}}({\mathcal {X}}).} === Harris recurrent === Definition (Harris recurrence) A set A {\displaystyle A} is Harris recurrent if P x ( η A = ∞ ) = 1 {\displaystyle P_{x}(\eta _{A}=\infty )=1} for all x ∈ A {\displaystyle x\in A} , where η A = ∑ n = 1 ∞ I A ( X n ) {\displaystyle \eta _{A}=\sum _{n=1}^{\infty }\mathbb {I} _{A}(X_{n})} is the number of visits of the chain ( X n ) {\displaystyle (X_{n})} to the set A {\displaystyle A} . The chain ( X n ) {\displaystyle (X_{n})} is said to be Harris recurrent if there exists a measure ψ {\displaystyle \psi } such that the chain is ψ {\displaystyle \psi } -irreducible and every measurable set A {\displaystyle A} with ψ ( A ) > 0 {\displaystyle \psi (A)>0} is Harris recurrent. A useful criterion for verifying Harris recurrence is the following: Proposition If for every A ∈ B ( X ) {\displaystyle A\in {\mathcal {B}}({\mathcal {X}})} , we have P x ( τ A < ∞ ) = 1 {\displaystyle P_{x}(\tau _{A}<\infty )=1} for every x ∈ A {\displaystyle x\in A} , then P x ( η A = ∞ ) = 1 {\displaystyle P_{x}(\eta _{A}=\infty )=1} for all x ∈ X {\displaystyle x\in {\mathcal {X}}} , and the chain ( X n ) {\displaystyle (X_{n})} is Harris recurrent. This definition is only needed when the state space X {\displaystyle {\mathcal {X}}} is uncountable. In the countable case, recurrence corresponds to E x [ η x ] = ∞ {\displaystyle \mathbb {E} _{x}[\eta _{x}]=\infty } , which is equivalent to P x ( τ x < ∞ ) = 1 {\displaystyle P_{x}(\tau _{x}<\infty )=1} for all x ∈ X {\displaystyle x\i
Cryptographic module
A cryptographic module is a component of a computer system that securely implements cryptographic algorithms, typically with some element of tamper resistance. NIST defines a cryptographic module as "The set of hardware, software, and/or firmware that implements security functions (including cryptographic algorithms), holds plaintext keys and uses them for performing cryptographic operations, and is contained within a cryptographic module boundary." Hardware security modules, including secure cryptoprocessors, are one way of implementing cryptographic modules. Standards for cryptographic modules include FIPS 140-3 and ISO/IEC 19790.
Catastrophic interference
Catastrophic interference, also known as catastrophic forgetting, is the tendency of an artificial neural network to abruptly and drastically forget previously learned information upon learning new information. Neural networks are an important part of the connectionist approach to cognitive science. The issue of catastrophic interference when modeling human memory with connectionist models was originally brought to the attention of the scientific community by research from McCloskey and Cohen (1989), and Ratcliff (1990). It is a radical manifestation of the 'sensitivity-stability' dilemma or the 'stability-plasticity' dilemma. Specifically, these problems refer to the challenge of making an artificial neural network that is sensitive to, but not disrupted by, new information. Lookup tables and connectionist networks lie on the opposite sides of the stability plasticity spectrum. The former remains completely stable in the presence of new information but lacks the ability to generalize, i.e. infer general principles, from new inputs. On the other hand, connectionist networks like the standard backpropagation network can generalize to unseen inputs, but they are sensitive to new information. Backpropagation models can be analogized to human memory insofar as they have a similar ability to generalize, but these networks often exhibit less stability than human memory. Notably, these backpropagation networks are susceptible to catastrophic interference. This is an issue when modelling human memory, because unlike these networks, humans typically do not show catastrophic forgetting. == Discovery == The term catastrophic interference was originally coined by McCloskey and Cohen (1989) but was also brought to the attention of the scientific community by research from Ratcliff (1990). === The Sequential Learning Problem: McCloskey and Cohen (1989) === McCloskey and Cohen (1989) noted the problem of catastrophic interference during two different experiments with backpropagation neural network modelling. Experiment 1: Learning the ones and twos addition facts In their first experiment they trained a standard backpropagation neural network on a single training set consisting of 17 single-digit ones problems (i.e., 1 + 1 through 9 + 1, and 1 + 2 through 1 + 9) until the network could represent and respond properly to all of them. The error between the actual output and the desired output steadily declined across training sessions, which reflected that the network learned to represent the target outputs better across trials. Next, they trained the network on a single training set consisting of 17 single-digit twos problems (i.e., 2 + 1 through 2 + 9, and 1 + 2 through 9 + 2) until the network could represent, respond properly to all of them. They noted that their procedure was similar to how a child would learn their addition facts. Following each learning trial on the twos facts, the network was tested for its knowledge on both the ones and twos addition facts. Like the ones facts, the twos facts were readily learned by the network. However, McCloskey and Cohen noted the network was no longer able to properly answer the ones addition problems even after one learning trial of the twos addition problems. The output pattern produced in response to the ones facts often resembled an output pattern for an incorrect number more closely than the output pattern for a correct number. This is considered to be a drastic amount of error. Furthermore, the problems 2+1 and 1+2, which were included in both training sets, even showed dramatic disruption during the first learning trials of the twos facts. Experiment 2: Replication of Barnes and Underwood (1959) study In their second connectionist model, McCloskey and Cohen attempted to replicate the study on retroactive interference in humans by Barnes and Underwood (1959). They trained the model on A-B and A-C lists and used a context pattern in the input vector (input pattern), to differentiate between the lists. Specifically the network was trained to respond with the right B response when shown the A stimulus and A-B context pattern and to respond with the correct C response when shown the A stimulus and the A-C context pattern. When the model was trained concurrently on the A-B and A-C items then the network readily learned all of the associations correctly. In sequential training the A-B list was trained first, followed by the A-C list. After each presentation of the A-C list, performance was measured for both the A-B and A-C lists. They found that the amount of training on the A-C list in Barnes and Underwood study that lead to 50% correct responses, lead to nearly 0% correct responses by the backpropagation network. Furthermore, they found that the network tended to show responses that looked like the C response pattern when the network was prompted to give the B response pattern. This indicated that the A-C list apparently had overwritten the A-B list. This could be likened to learning the word dog, followed by learning the word stool and then finding that you think of the word stool when presented with the word dog. McCloskey and Cohen tried to reduce interference through a number of manipulations including changing the number of hidden units, changing the value of the learning rate parameter, overtraining on the A-B list, freezing certain connection weights, changing target values 0 and 1 instead 0.1 and 0.9. However, none of these manipulations satisfactorily reduced the catastrophic interference exhibited by the networks. Overall, McCloskey and Cohen (1989) concluded that: at least some interference will occur whenever new learning alters the weights involved in representing old learning the greater the amount of new learning, the greater the disruption in old knowledge interference was catastrophic in the backpropagation networks when learning was sequential but not concurrent === Constraints Imposed by Learning and Forgetting Functions: Ratcliff (1990) === Ratcliff (1990) used multiple sets of backpropagation models applied to standard recognition memory procedures, in which the items were sequentially learned. After inspecting the recognition performance models he found two major problems: Well-learned information was catastrophically forgotten as new information was learned in both small and large backpropagation networks. Even one learning trial with new information resulted in a significant loss of the old information, paralleling the findings of McCloskey and Cohen (1989). Ratcliff also found that the resulting outputs were often a blend of the previous input and the new input. In larger networks, items learned in groups (e.g. AB then CD) were more resistant to forgetting than were items learned singly (e.g. A then B then C...). However, the forgetting for items learned in groups was still large. Adding new hidden units to the network did not reduce interference. Discrimination between the studied items and previously unseen items decreased as the network learned more. This finding contradicts studies on human memory, which indicated that discrimination increases with learning. Ratcliff attempted to alleviate this problem by adding 'response nodes' that would selectively respond to old and new inputs. However, this method did not work as these response nodes would become active for all inputs. A model which used a context pattern also failed to increase discrimination between new and old items. == Proposed solutions == The main cause of catastrophic interference seems to be overlap in the representations at the hidden layer of distributed neural networks. In a distributed representation, each input tends to create changes in the weights of many of the nodes. Catastrophic forgetting occurs because when many of the weights where "knowledge is stored" are changed, it is unlikely for prior knowledge to be kept intact. During sequential learning, the inputs become mixed, with the new inputs being superimposed on top of the old ones. Another way to conceptualize this is by visualizing learning as a movement through a weight space. This weight space can be likened to a spatial representation of all of the possible combinations of weights that the network could possess. When a network first learns to represent a set of patterns, it finds a point in the weight space that allows it to recognize all of those patterns. However, when the network then learns a new set of patterns, it will move to a place in the weight space for which the only concern is the recognition of the new patterns. To recognize both sets of patterns, the network must find a place in the weight space suitable for recognizing both the new and the old patterns. Below are a number of techniques which have empirical support in successfully reducing catastrophic interference in backpropagation neural networks: === Orthogonality === Many of the early techniques in reducing representational overlap involved making either the input vecto
Region connection calculus
The region connection calculus (RCC) is intended to serve for qualitative spatial representation and reasoning. RCC abstractly describes regions (in Euclidean space, or in a topological space) by their possible relations to each other. RCC8 consists of 8 basic relations that are possible between two regions: disconnected (DC) externally connected (EC) equal (EQ) partially overlapping (PO) tangential proper part (TPP) tangential proper part inverse (TPPi) non-tangential proper part (NTPP) non-tangential proper part inverse (NTPPi) From these basic relations, combinations can be built. For example, proper part (PP) is the union of TPP and NTPP. == Axioms == RCC is governed by two axioms. for any region x, x connects with itself for any region x, y, if x connects with y, y connects with x == Remark on the axioms == The two axioms describe two features of the connection relation, but not the characteristic feature of the connect relation. For example, we can say that an object is less than 10 meters away from itself and that if object A is less than 10 meters away from object B, object B will be less than 10 meters away from object A. So, the relation 'less-than-10-meters' also satisfies the above two axioms, but does not talk about the connection relation in the intended sense of RCC. == Composition table == The composition table of RCC8 are as follows: "" denotes the universal relation, no relation can be discarded. Usage example: if a TPP b and b EC c, (row 4, column 2) of the table says that a DC c or a EC c. == Examples == The RCC8 calculus is intended for reasoning about spatial configurations. Consider the following example: two houses are connected via a road. Each house is located on an own property. The first house possibly touches the boundary of the property; the second one surely does not. What can we infer about the relation of the second property to the road? The spatial configuration can be formalized in RCC8 as the following constraint network: house1 DC house2 house1 {TPP, NTPP} property1 house1 {DC, EC} property2 house1 EC road house2 { DC, EC } property1 house2 NTPP property2 house2 EC road property1 { DC, EC } property2 road { DC, EC, TPP, TPPi, PO, EQ, NTPP, NTPPi } property1 road { DC, EC, TPP, TPPi, PO, EQ, NTPP, NTPPi } property2 Using the RCC8 composition table and the path-consistency algorithm, we can refine the network in the following way: road { PO, EC } property1 road { PO, TPP } property2 That is, the road either overlaps (PO) property2, or is a tangential proper part of it. But, if the road is a tangential proper part of property2, then the road can only be externally connected (EC) to property1. That is, road PO property1 is not possible when road TPP property2. This fact is not obvious, but can be deduced once we examine the consistent "singleton-labelings" of the constraint network. The following paragraph briefly describes singleton-labelings. First, we note that the path-consistency algorithm will also reduce the possible properties between house2 and property1 from { DC, EC } to just DC. So, the path-consistency algorithm leaves multiple possible constraints on 5 of the edges in the constraint network. Since each of the multiple constraints involves 2 constraints, we can reduce the network to 32 (25) possible unique constraint networks, each containing only single labels on each edge ("singleton labelings"). However, of the 32 possible singleton labelings, only 9 are consistent. (See qualreas for details.) Only one of the consistent singleton labelings has the edge road TPP property2 and the same labeling includes road EC property1. Other versions of the region connection calculus include RCC5 (with only five basic relations - the distinction whether two regions touch each other are ignored) and RCC23 (which allows reasoning about convexity). == RCC8 use in GeoSPARQL == RCC8 has been partially implemented in GeoSPARQL as described below: == Implementations == GQR is a reasoner for RCC-5, RCC-8, and RCC-23 (as well as other calculi for spatial and temporal reasoning) qualreas is a Python framework for qualitative reasoning over networks of relation algebras, such as RCC-8, Allen's interval algebra and more.
Botler AI
Botler AI is a Montreal-based Canadian Artificial Intelligence company that helps users navigate the legal system. Launched in 2017 by Amir Morv and Ritika Dutt, Botler offers a free online tool which provides users who are unaware of their legal rights with information and guidance. Botler is known for its role in unveiling misconduct in the Government of Canada's procurement practices. Botler's findings have prompted numerous investigations, including by the Royal Canadian Mounted Police. == History == Botler's first AI was trained on over 300,000 U.S. and Canadian legal documents to help individuals identify and enforce their legal rights, without fear of judgment. Launched during the height of the #MeToo movement, the tool initially focused on sexual harassment with a goal of creating "a general artificial intelligence that would help the average person with any legal issue." === Department of Justice Canada === In 2020, Botler launched an expanded misconduct detection system in the form of an anonymous chatbot which provided users with an explanation of the law and relevant resources. In March 2021, the Minister of Justice and Attorney General of Canada announced the Government of Canada's support for Botler AI to assist complainants of sexual harassment in the workplace. The initiative, entitled Botler for Citizens and implemented with the support of the Department of Justice Canada, established an Artificial Intelligence-powered hybrid legal service delivery model. == Notable cases == On October 4, 2023, the RCMP confirmed to The Globe and Mail that they "are investigating a file referred from the CBSA (Canada Border Services Agency) that is based on allegations brought to their attention by Botler". In 2019, GCStrategies's managing partner, Kristian Firth, reached out to Botler on behalf of his client, the CBSA, to solicit their misconduct detection chatbot. After interactions with GCStrategies, Dalian Enterprises and Coradix Technology Consulting, the three main contractors involved in developing the controversial ArriveCAN app, Dutt and Morv alerted the CBSA to questionable contracting practices in federal government procurement in September, 2021, and again in November, 2022. In response to Botler's November 2022 report, the CBSA launched an internal review and referred the matter to the RCMP. During testimony before a parliamentary committee, the CBSA's President stated that the CBSA investigation to date has raised some concerns and shows "that there was a pattern of persistent collaboration between certain officials and GCStrategies... to circumvent or ignore certain established processes and roles and responsibilities". The Auditor General of Canada, which extended its study into ArriveCAN following the Botler revelations, found that GCStrategies was directly involved in setting narrow terms for a request for proposal for a $25-million government contract it ultimately won. The firm, which has just two employees, charges the government a commission of between 15 per cent and 30 per cent of each contract's value. The Office of the Procurement Ombudsman of Canada found "numerous examples" where GCStrategies "had simply copied and pasted" the required work experience to meet contracting requirements. To date, more than a dozen probes have been launched into the matter, including by the government, parliamentary committees, independent watchdogs and law-enforcement agencies. On April 17, 2024, GCStrategies' Firth was the first person summoned in over a century to answer questions before Members of Parliament in the House of Commons. During his appearance, Firth testified that the RCMP had raided "my property to obtain electronic goods surrounding the Botler allegations". === Government of Canada Reforms === One day after The Globe reported that the RCMP is investigating allegations of misconduct, the federal government responded by announcing new guidelines from the Treasury Board of Canada aimed at cutting back on the use of private consultants and that outsourcing contracts were under examination. Public Services and Procurement Canada (PSPC) invalidated and replaced all master level user agreements with government client departments in November 2023. The agreements set out the conditions for access to select Professional Services methods of supply which are used for outsourcing. In March 2024, PSPC announced its suspension of the respective security statuses of GCStrategies, Dalian and Coradix, barring them from participating in all federal procurements. Records show that the total value of contracts awarded to the three companies amounts to more than $1 Billion.
Software engineering demographics
Software engineers make up a significant portion of the global workforce. As of 2022, there are an estimated 26.9 million professional software engineers worldwide, up from 21 million in 2016. == By country == === United States === In 2023, there were an estimated 1.6 million professional software developers in North America. There are 166 million people employed in the US workforce, making software developers 0.96% of the total workforce. ==== Summary ==== ==== Software engineers vs. traditional engineers ==== The following two tables compare the number of software engineers (611,900 in 2002) versus the number of traditional engineers (1,157,020 in 2002). There are another 1,500,000 people in system analysis, system administration, and computer support, many of whom might be called software engineers. Many systems analysts manage software development teams, and as analysis is an important software engineering role, many of them may be considered software engineers in the near future. This means that the number of software engineers may actually be much higher. It is important to note that the number of software engineers declined by 5 to 10 percent from 2000 to 2002. ==== Computer managers vs. construction and engineering managers ==== Computer and information system managers (264,790) manage software projects, as well as computer operations. Similarly, Construction and engineering managers (413,750) oversee engineering projects, manufacturing plants, and construction sites. Computer management is 64% the size of construction and engineering management. ==== Software engineering educators vs. engineering educators ==== Most people working in the field of computer science, whether making software systems (software engineering) or studying the theoretical and mathematical facts of software systems (computer science), acquire degrees in computer science. According to the U.S. Bureau of Labor Statistics (May 2023 data), there were approximately 44,800 postsecondary computer science teachers and 50,300 engineering teachers, indicating that the computer science educator workforce is nearly 89% as large as that of engineering educators. The combined number of postsecondary chemistry (25,400) and physics (17,100) teachers totaled 42,500, slightly less than the number of computer science educators. ==== Other software and engineering roles ==== ==== Relation to IT demographics ==== Software engineers are part of the much larger software, hardware, application, and operations community. In 2000 in the U.S., there were about 680,000 software engineers and about 10,000,000 IT workers. As of early 2025, there are an estimated 47.2 million software developers worldwide, representing a 50% increase from 31 million in Q1 2022. There are no numbers on testers in the BLS data. === India === There has been a healthy growth in the number of India's IT professionals over the past few years. From a base of 6,800 knowledge workers in 1985–86, the number increased to 522,000 software and services professionals by the end of 2001–02. It is estimated that out of these 528,000 knowledge workers, almost 170,000 are working in the IT software and services export industry; nearly 106,000 are working in the IT enabled services and over 230,000 in user organizations. === Australia === In May 2024, the Australian government reported that 169,300 Australians are employed as software and applications programmers, 17% of who are women. The role grew annually by 8,300 workers. === Russia === According to the Russian government, the number of IT specialists in the country increased by 13% in 2023, reaching approximately 857,000. During the initial phase of the 2022 invasion of Ukraine, an estimated 100,000 IT specialists left Russia.
Thinking Machines Lab
Thinking Machines Lab Inc. is an American artificial intelligence (AI) startup founded by Mira Murati, the former chief technology officer of OpenAI. The company was founded in February 2025, and by July had completed an early-stage funding round led by Andreessen Horowitz, raising $2 billion at a valuation of $12 billion overall from investors such as Nvidia, AMD, Cisco, and Jane Street. The company is based in San Francisco and structured as a public benefit corporation. == History == By its launch in February 2025, Thinking Machines Lab was reported to have hired about 30 researchers and engineers from competitors including OpenAI, Meta AI, and Mistral AI. Its founding team members include Barret Zoph, former OpenAI VP of Research (Post-Training), Lilian Weng, former OpenAI VP, and OpenAI cofounder John Schulman, who joined after a brief stint at the lab's competitor Anthropic. In January 2026, it was reported that Barret Zoph and Luke Metz, departed the startup to return to OpenAI. Other former OpenAI employees who have been hired include Jonathan Lachman and Andrew Tulloch (although Tulloch departed after getting recruited for Meta Superintelligence Labs). Thinking Machines Lab's advisers include Bob McGrew, previously OpenAI's chief research officer, and Alec Radford, who was a lead researcher for OpenAI. On October 1, 2025, it announced Tinker, an API for fine-tuning language models. Users would submit jobs through the API for fine-tuning one of the various open-weight models supported. The Lab would run the jobs on its internal clusters and training infrastructure. == Business structure == Thinking Machines Lab grants Mira Murati a deciding vote on board matters, weighted to provide her with a majority decision-making capability. Additionally, founding shareholders possess votes weighted 100 times greater than those of regular shareholders. In July 2025, Andreessen Horowitz was reported to have led the company's initial funding round, raising "about $2 billion at a valuation of $12 billion". The government of Albania (Murati's country of origin) was also included in this round, making a $10 million investment which required an amendment to the country's 2025 budget. == Partnership == In March 2026, Thinking Machines Lab announced a strategic partnership with NVIDIA involving an undisclosed investment and a multi-year agreement to deploy one gigawatt of Vera Rubin computing capacity.