The r-to-1 collision problem is an important theoretical problem in complexity theory, quantum computing, and computational mathematics. The collision problem most often refers to the 2-to-1 version: given n {\displaystyle n} even and a function f : { 1 , … , n } → { 1 , … , n } {\displaystyle f:\,\{1,\ldots ,n\}\rightarrow \{1,\ldots ,n\}} , we are promised that f is either 1-to-1 or 2-to-1. We are only allowed to make queries about the value of f ( i ) {\displaystyle f(i)} for any i ∈ { 1 , … , n } {\displaystyle i\in \{1,\ldots ,n\}} . The problem then asks how many such queries we need to make to determine with certainty whether f is 1-to-1 or 2-to-1. == Classical solutions == === Deterministic === Solving the 2-to-1 version deterministically requires n 2 + 1 {\textstyle {\frac {n}{2}}+1} queries, and in general distinguishing r-to-1 functions from 1-to-1 functions requires n r + 1 {\textstyle {\frac {n}{r}}+1} queries. This is a straightforward application of the pigeonhole principle: if a function is r-to-1, then after n r + 1 {\textstyle {\frac {n}{r}}+1} queries we are guaranteed to have found a collision. If a function is 1-to-1, then no collision exists. Thus, n r + 1 {\textstyle {\frac {n}{r}}+1} queries suffice. If we are unlucky, then the first n / r {\displaystyle n/r} queries could return distinct answers, so n r + 1 {\textstyle {\frac {n}{r}}+1} queries is also necessary. === Randomized === If we allow randomness, the problem is easier. By the birthday paradox, if we choose (distinct) queries at random, then with high probability we find a collision in any fixed 2-to-1 function after Θ ( n ) {\displaystyle \Theta ({\sqrt {n}})} queries. == Quantum solution == The BHT algorithm, which uses Grover's algorithm, solves this problem optimally by only making O ( n 1 / 3 ) {\displaystyle O(n^{1/3})} queries to f. The matching lower bound of Ω ( n 1 / 3 ) {\displaystyle \Omega (n^{1/3})} was proved by Aaronson and Shi using the polynomial method.
Structural risk minimization
Structural risk minimization (SRM) is an inductive principle of use in machine learning. Commonly in machine learning, a generalized model must be selected from a finite data set, with the consequent problem of overfitting – the model becoming too strongly tailored to the particularities of the training set and generalizing poorly to new data. The SRM principle addresses this problem by balancing the model's complexity against its success at fitting the training data. This principle was first set out in a 1974 book by Vladimir Vapnik and Alexey Chervonenkis and uses the VC dimension. In practical terms, Structural Risk Minimization is implemented by minimizing E t r a i n + β H ( W ) {\displaystyle E_{train}+\beta H(W)} , where E t r a i n {\displaystyle E_{train}} is the train error, the function H ( W ) {\displaystyle H(W)} is called a regularization function, and β {\displaystyle \beta } is a constant. H ( W ) {\displaystyle H(W)} is chosen such that it takes large values on parameters W {\displaystyle W} that belong to high-capacity subsets of the parameter space. Minimizing H ( W ) {\displaystyle H(W)} in effect limits the capacity of the accessible subsets of the parameter space, thereby controlling the trade-off between minimizing the training error and minimizing the expected gap between the training error and test error. The SRM problem can be formulated in terms of data. Given n data points consisting of data x and labels y, the objective J ( θ ) {\displaystyle J(\theta )} is often expressed in the following manner: J ( θ ) = 1 2 n ∑ i = 1 n ( h θ ( x i ) − y i ) 2 + λ 2 ∑ j = 1 d θ j 2 {\displaystyle J(\theta )={\frac {1}{2n}}\sum _{i=1}^{n}(h_{\theta }(x^{i})-y^{i})^{2}+{\frac {\lambda }{2}}\sum _{j=1}^{d}\theta _{j}^{2}} The first term is the mean squared error (MSE) term between the value of the learned model, h θ {\displaystyle h_{\theta }} , and the given labels y {\displaystyle y} . This term is the training error, E t r a i n {\displaystyle E_{train}} , that was discussed earlier. The second term, places a prior over the weights, to favor sparsity and penalize larger weights. The trade-off coefficient, λ {\displaystyle \lambda } , is a hyperparameter that places more or less importance on the regularization term. Larger λ {\displaystyle \lambda } encourages sparser weights at the expense of a more optimal MSE, and smaller λ {\displaystyle \lambda } relaxes regularization allowing the model to fit to data. Note that as λ → ∞ {\displaystyle \lambda \to \infty } the weights become zero, and as λ → 0 {\displaystyle \lambda \to 0} , the model typically suffers from overfitting.
Levenshtein automaton
In computer science, a Levenshtein automaton for a string w and a number n is a finite-state automaton that can recognize the set of all strings whose Levenshtein distance from w is at most n. That is, a string x is in the formal language recognized by the Levenshtein automaton if and only if x can be transformed into w by at most n single-character insertions, deletions, and substitutions. == Applications == Levenshtein automata may be used for spelling correction, by finding words in a given dictionary that are close to a misspelled word. In this application, once a word is identified as being misspelled, its Levenshtein automaton may be constructed, and then applied to all of the words in the dictionary to determine which ones are close to the misspelled word. If the dictionary is stored in compressed form as a trie, the time for this algorithm (after the automaton has been constructed) is proportional to the number of nodes in the trie, significantly faster than using dynamic programming to compute the Levenshtein distance separately for each dictionary word. It is also possible to find words in a regular language, rather than a finite dictionary, that are close to a given target word, by computing the Levenshtein automaton for the word, and then using a Cartesian product construction to combine it with an automaton for the regular language, giving an automaton for the intersection language. Alternatively, rather than using the product construction, both the Levenshtein automaton and the automaton for the given regular language may be traversed simultaneously using a backtracking algorithm. Levenshtein automata are used in Lucene for full-text searches that can return relevant documents even if the query is misspelled. == Construction == For any fixed constant n, the Levenshtein automaton for w and n may be constructed in time O(|w|). Mitankin studies a variant of this construction called the universal Levenshtein automaton, determined only by a numeric parameter n, that can recognize pairs of words (encoded in a certain way by bitvectors) that are within Levenshtein distance n of each other. Touzet proposed an effective algorithm to build this automaton. Yet a third finite automaton construction of Levenshtein (or Damerau–Levenshtein) distance are the Levenshtein transducers of Hassan et al., who show finite state transducers implementing edit distance one, then compose these to implement edit distances up to some constant.
Dilek Hakkani-Tür
Dilek Z. Hakkani-Tür is a Turkish-American computer scientist focusing on speech processing, speech recognition, and dialogue systems. She is a professor of computer science at the University of Illinois Urbana-Champaign. == Education and career == Hakkani-Tür is a 1994 graduate of Middle East Technical University in Ankara, Turkey. She continued her studies at Bilkent University, also in Ankara, where she earned a master's degree in 1996 and completed her Ph.D. in 2000. She worked as a researcher at AT&T Labs from 2001 to 2005, at the International Computer Science Institute from 2006 to 2010, at Microsoft Research from 2010 to 2016, at Google Research from 2016 to 2018, and at Amazon Alexa from 2018 to 2023. At Microsoft, she was in the team of scientists that built the first prototype of the Cortana virtual assistant. While working for Amazon Alexa, she also taught at the University of California, Santa Cruz as a distinguished visiting instructor. She joined the University of Illinois Urbana-Champaign faculty in 2023. She was editor-in-chief of IEEE/ACM Transactions on Audio, Speech and Language Processing from 2019 to 2021, and is president of the Special Interest Group on Discourse and Dialogue of the Association for Computational Linguistics for the 2023–2025 term. She has served as co-editor-in-chief of Transactions of the Association for Computational Linguistics since 2024. == Recognition == In 2014, Hakkani-Tür was elected as an IEEE Fellow "for contributions to spoken language processing", and as a Fellow of the International Speech Communication Association "for contributions to advancing the state-of-the-art in spoken language processing, especially for human/human and human/machine conversational understanding". In 2024, she was elected as a Fellow of the Association for Computational Linguistics for her contributions to spoken dialogue systems.
Frederick Jelinek
Frederick Jelinek (18 November 1932 – 14 September 2010) was a Czech-American researcher in information theory, automatic speech recognition, and natural language processing. He is well known for his oft-quoted statement, "Every time I fire a linguist, the performance of the speech recognizer goes up". Jelinek was born in Czechoslovakia before World War II and emigrated with his family to the United States in the early years of the communist regime. He studied engineering at the Massachusetts Institute of Technology and taught for 10 years at Cornell University before accepting a job at IBM Research. In 1961, he married Czech screenwriter Milena Jelinek. At IBM, his team advanced approaches to computer speech recognition and machine translation. After IBM, he went to head the Center for Language and Speech Processing at Johns Hopkins University for 17 years, where he was still working on the day he died. == Personal life == Jelinek was born on November 18, 1932, as Bedřich Jelínek in Kladno to Vilém and Trude Jelínek. His father was Jewish; his mother was born in Switzerland to Czech Catholic parents and had converted to Judaism. Jelínek senior, a dentist, had planned early to escape Nazi occupation and flee to England; he arranged for a passport, visa, and the shipping of his dentistry materials. The couple planned to send their son to an English private school. However, Vilém decided to stay at the last minute and was eventually sent to the Theresienstadt concentration camp, where he died in 1945. The family was forced to move to Prague in 1941, but Frederick, his sister and mother—thanks to the latter's background—escaped the concentration camps. After the war, Jelinek entered in the gymnasium, despite having missed several years of schooling because education of Jewish children had been forbidden since 1942. His mother, anxious that her son should get a good education, made great efforts for their emigration, especially when it became clear he would not be allowed to even attempt the graduation examination. His mother hoped her son would become a physician, but Jelinek dreamed of being a lawyer. He studied engineering in evening classes at the City College of New York and received stipends from the National Committee for a Free Europe that allowed him to study at the Massachusetts Institute of Technology. About his choice of specialty, he said: "Fortunately, to electrical engineering there belonged a discipline whose aim was not the construction of physical systems: the theory of information". He obtained his Ph.D. in 1962, with Robert Fano as his adviser. In 1957, Jelinek paid an unexpected visit to Prague. He had been in Vienna and applied for a visa, hoping to see his former acquaintances again. He met with his old friend Miloš Forman, who introduced him to film student Milena Tobolová—whose screenplay had been the basis for the movie Easy Life (Snadný život). His flight back to the U.S. had a stopover in Munich, during which he called her to propose. Tobolová was considered a dissident and the authorities were not happy with her film. Jelinek asked for help from Jerome Wiesner and Cyrus Eaton, the latter who lobbied Nikita Khrushchev. Following the inauguration of John F. Kennedy, a group of Czech dissidents were allowed to emigrate in January 1961. Thanks to the lobbying, the future Milena Jelinek was one of them. After completing his graduate studies, Jelinek, who had developed an interest in linguistics, had plans to work with Charles F. Hockett at Cornell University. However these fell through and during the next ten years he continued to study information theory. Having previously worked at IBM during a sabbatical, he began full-time work there in 1972—at first on leave for Cornell, but permanently from 1974. He remained there for over twenty years. Although at first he had been offered a regular research job, upon his arrival he learned that Josef Raviv had recently been promoted to head of the newly opened IBM Haifa Research Laboratory, and became head of the Continuous Speech Recognition group at the Thomas J. Watson Research Center. Despite his team's successes in this area, Jelinek's work remained little known in his home country because Czech scientists were not allowed to participate in key conferences. After the 1989 fall of communism, Jelinek helped establish scientific relationships, regularly visiting to lecture and helping to persuade IBM to establish a computing centre at Charles University. In 1993, he retired from IBM and went to Johns Hopkins University's Center for Language and Speech Processing, where he was director and Julian Sinclair Smith Professor of Electrical and Computer Engineering. He was still working there at the time of his death; Jelinek died of a heart attack at the close of an otherwise normal workday in mid-September 2010. He was survived by his wife, daughter and son, sister, stepsister, and three grandchildren, including Sophie Gold Jelinek. == Research and legacy == Information theory was a fashionable scientific approach in the mid '50s. However, pioneer Claude Shannon wrote in 1956 that this trendiness was dangerous. He said, "Our fellow scientists in many different fields, attracted by the fanfare and by the new avenues opened to scientific analysis, are using these ideas in their own problems ... It will be all too easy for our somewhat artificial prosperity to collapse overnight when it is realized that the use of a few exciting words like information, entropy, redundancy, do not solve all our problems." During the next decade, a combination of factors shut down the application of information theory to natural language processing (NLP) problems—in particular machine translation. One factor was the 1957 publication of Noam Chomsky's Syntactic Structures, which stated, "probabilistic models give no insight into the basic problems of syntactic structure". This accorded well with the philosophy of the artificial intelligence research of the time, which promoted rule-based approaches. The other factor was the 1966 ALPAC report, which recommended that the government should stop funding research into machine translation. ALPAC chairman John Pierce later said that the field was filled with "mad inventors or untrustworthy engineers". He said that the underlying linguistic problems must be solved before attempts at NLP could be reasonably made. These elements essentially halted research in the field. Jelinek had begun to develop an interest in linguistics after the immigration of his wife, who initially enrolled in the MIT linguistics program with the help of Roman Jakobson. Jelinek often accompanied her to Chomsky's lectures, and even discussed the possibility of changing orientation with his adviser. Fano was "really upset", and after the failure of his project with Hockett at Cornell, he did not return to this field of research until starting work at IBM. The scope of research at IBM was considerably different from that of most other teams. According to Mark Liberman, "While [Jelinek] was leading IBM's effort to solve the general dictation problem during the decade or so following 1972, most other U.S. companies and academic researchers were working on very limited problems ... or were staying out of the field entirely". Jelinek regarded speech recognition as an information theory problem—a noisy channel, in this case the acoustic signal—which some observers considered a daring approach. The concept of perplexity was introduced in their first model, New Raleigh Grammar, which was published in 1976 as the paper "Continuous Speech Recognition by Statistical Methods" in the journal Proceedings of the IEEE. According to Young, the basic noisy channel approach "reduced the speech recognition problem to one of producing two statistical models". Whereas New Raleigh Grammar was a hidden Markov model, their next model, called Tangora, was broader and involved n-grams, specifically trigrams. Even though "it was obvious to everyone that this model was hopelessly impoverished", it was not improved upon until Jelinek presented another paper in 1999. The same trigram approach was applied to phones in single words. Although the identification of parts of speech turned out not to be very useful for speech recognition, tagging methods developed during these projects are now used in various NLP applications. The incremental research techniques developed at IBM eventually became dominant in the field after DARPA, in the mid-80s, returned to NLP research and imposed that methodology to participating teams, shared common goals, data, and precise evaluation metrics. The Continuous Speech Recognition Group's research, which required large amounts of data to train the algorithms, eventually led to the creation of the Linguistic Data Consortium. In the 1980s, although the broader problem of speech recognition remained unsolved, they sought to apply the methods developed to other problems; machine translat
Robotic process automation
Robotic process automation (RPA) is a form of business process automation that is based on software robots (bots) or artificial intelligence (AI) agents. RPA should not be confused with artificial intelligence as it is based on automation technology following a predefined workflow. It is sometimes referred to as software robotics (not to be confused with robot software). In traditional workflow automation tools, a software developer produces a list of actions to automate a task and interface to the back end system using internal application programming interfaces (APIs) or dedicated scripting language. In contrast, RPA systems develop the action list by watching the user perform that task in the application's graphical user interface (GUI) and then perform the automation by repeating those tasks directly in the GUI. This can lower the barrier to the use of automation in products that might not otherwise feature APIs for this purpose. RPA tools have strong technical similarities to graphical user interface testing tools. These tools also automate interactions with the GUI, and often do so by repeating a set of demonstration actions performed by a user. RPA tools differ from such systems in that they allow data to be handled in and between multiple applications, for instance, receiving email containing an invoice, extracting the data, and then typing that into a bookkeeping system. == Historic evolution == As a form of automation, the concept has been around for a long time in the form of screen scraping, so long that to early PC users the reminder of it often blurs with the idea of malware infection. Yet compared to screen scraping, RPA is much more extensible, consisting of API integration into other enterprise applications, connectors into ITSM systems, terminal services and even some types of AI (e.g. machine learning) services such as image recognition. It is considered to be a significant technological evolution in the sense that new software platforms are emerging which are sufficiently mature, resilient, scalable and reliable to make this approach viable for use in large enterprises (who would otherwise be reluctant due to perceived risks to quality and reputation). == Use == The hosting of RPA services also aligns with the metaphor of a software robot, with each robotic instance having its own virtual workstation, much like a human worker. The robot uses keyboard and mouse controls to take actions and execute automations. Normally, all of these actions take place in a virtual environment and not on screen; the robot does not need a physical screen to operate, rather it interprets the screen display electronically. The scalability of modern solutions based on architectures such as these owes much to the advent of virtualization technology, without which the scalability of large deployments would be limited by the available capacity to manage physical hardware and by the associated costs. The implementation of RPA in business enterprises has shown dramatic cost savings when compared to traditional non-RPA solutions. === RPA actual use === Banking and finance process automation Mortgage and lending processes Customer care automation eCommerce merchandising operations Social media marketing Optical character recognition applications Data extraction process Fixed automation process Manual and repetitive tasks automation Voice recognition and digital dictation software linked to join up business processes for straight through processing without manual intervention Specialised remote infrastructure management software featuring automated investigation and resolution of problems, using robots for the first line IT support Chatbots used by internet retailers and service providers to service customer requests for information. Also used by companies to service employee requests for information from internal databases Presentation layer automation software, increasingly used by business process outsourcers to displace human labour Interactive voice response (IVR) systems incorporating intelligent interaction with callers == Impact on employment == According to Harvard Business Review, most operations groups adopting RPA have promised their employees that automation would not result in layoffs. Instead, workers have been redeployed to do more interesting work. One academic study highlighted that knowledge workers did not feel threatened by automation: they embraced it and viewed the robots as team-mates. The same study highlighted that, rather than resulting in a lower "headcount", the technology was deployed in such a way as to achieve more work and greater productivity with the same number of people. Conversely, however, some analysts proffer that RPA represents a threat to the business process outsourcing (BPO) industry. The thesis behind this notion is that RPA will enable enterprises to "repatriate" processes from offshore locations into local data centers, with the benefit of this new technology. The effect, if true, will be to create high-value jobs for skilled process designers in onshore locations (and within the associated supply chain of IT hardware, data center management, etc.) but to decrease the available opportunity to low-skilled workers offshore. On the other hand, this discussion appears to be healthy ground for debate as another academic study was at pains to counter the so-called "myth" that RPA will bring back many jobs from offshore. === Impact on society === Academic studies project that RPA, among other technological trends, is expected to drive a new wave of productivity and efficiency gains in the global labour market. Although not directly attributable to RPA alone, Oxford University conjectures that up to 35% of all jobs might be automated by 2035. There are geographic implications to the trend in robotic automation. In the example above where an offshored process is "repatriated" under the control of the client organization (or even displaced by a business process outsourcer) from an offshore location to a data centre, the impact will be a deficit in economic activity to the offshore location and an economic benefit to the originating economy. On this basis, developed economies – with skills and technological infrastructure to develop and support a robotic automation capability – can be expected to achieve a net benefit from the trend. In a TEDx talk hosted by University College London (UCL), entrepreneur David Moss explains that digital labour in the form of RPA is likely to revolutionize the cost model of the services industry by driving the price of products and services down, while simultaneously improving the quality of outcomes and creating increased opportunity for the personalization of services. In a separate TEDx in 2019 talk, Japanese business executive, and former CIO of Barclays bank, Koichi Hasegawa noted that digital robots can be a positive effect on society if we start using a robot with empathy to help every person. He provides a case study of the Japanese insurance companies – Sompo Japan and Aioi – both of whom introduced bots to speed up the process of insurance pay-outs in past massive disaster incidents. Meanwhile, Professor Willcocks, author of the LSE paper cited above, speaks of increased job satisfaction and intellectual stimulation, characterising the technology as having the ability to "take the robot out of the human", a reference to the notion that robots will take over the mundane and repetitive portions of people's daily workload, leaving them to be used in more interpersonal roles or to concentrate on the remaining, more meaningful, portions of their day. It was also found in a 2021 study observing the effects of robotization in Europe that, the gender pay gap increased at a rate of .18% for every 1% increase in robotization of a given industry. == Unassisted RPA == Unassisted RPA, or RPAAI, is the next generation of RPA related technologies. Technological advancements around artificial intelligence allow a process to be run on a computer without needing input from a user. == Hyperautomation == Hyperautomation is the application of advanced technologies like RPA, artificial intelligence, machine learning (ML) and process mining to augment workers and automate processes in ways that are significantly more impactful than traditional automation capabilities. Hyperautomation is the combination of technologies that allow faster application authorship (like low-code and no-code) with automation technologies that coordinate different worker types (i.e. human and artificial) for intelligent and strategic workflow optimization. Gartner's report notes that this trend was kicked off with robotic process automation (RPA). The report notes that, "RPA alone is not hyperautomation. Hyperautomation requires a combination of tools to help support replicating pieces of where the human is involved in a task." == Outsourcing == Back office clerical processes outsourced by large organisations
The Best Free AI Art Generator for Beginners
Trying to pick the best AI art generator? An AI art generator is software that uses machine learning to help you get more done — it scales effortlessly from a single task to thousands. The best picks balance beginner-friendly simplicity with the depth power users need, and they ship updates often. Whether you are a beginner or a pro, the right AI art generator slots into your workflow and pays for itself fast. This guide breaks down the top picks, their pros and cons, and who each one is best for.