Consensus clustering is a method of aggregating (potentially conflicting) results from multiple clustering algorithms. Also called cluster ensembles or aggregation of clustering (or partitions), it refers to the situation in which a number of different (input) clusterings have been obtained for a particular dataset and it is desired to find a single (consensus) clustering which is a better fit in some sense than the existing clusterings. Consensus clustering is thus the problem of reconciling clustering information about the same data set coming from different sources or from different runs of the same algorithm. When cast as an optimization problem, consensus clustering is known as median partition, and has been shown to be NP-complete, even when the number of input clusterings is three. Consensus clustering for unsupervised learning is analogous to ensemble learning in supervised learning. == Issues with existing clustering techniques == Current clustering techniques do not address all the requirements adequately. Dealing with large number of dimensions and large number of data items can be problematic because of time complexity; Effectiveness of the method depends on the definition of "distance" (for distance-based clustering) If an obvious distance measure doesn't exist, we must "define" it, which is not always easy, especially in multidimensional spaces. The result of the clustering algorithm (that, in many cases, can be arbitrary itself) can be interpreted in different ways. == Justification for using consensus clustering == There are potential shortcomings for all existing clustering techniques. This may cause interpretation of results to become difficult, especially when there is no knowledge about the number of clusters. Clustering methods are also very sensitive to the initial clustering settings, which can cause non-significant data to be amplified in non-reiterative methods. An extremely important issue in cluster analysis is the validation of the clustering results, that is, how to gain confidence about the significance of the clusters provided by the clustering technique (cluster numbers and cluster assignments). Lacking an external objective criterion (the equivalent of a known class label in supervised analysis), this validation becomes somewhat elusive. Iterative descent clustering methods, such as the SOM and k-means clustering circumvent some of the shortcomings of hierarchical clustering by providing for univocally defined clusters and cluster boundaries. Consensus clustering provides a method that represents the consensus across multiple runs of a clustering algorithm, to determine the number of clusters in the data, and to assess the stability of the discovered clusters. The method can also be used to represent the consensus over multiple runs of a clustering algorithm with random restart (such as K-means, model-based Bayesian clustering, SOM, etc.), so as to account for its sensitivity to the initial conditions. It can provide data for a visualization tool to inspect cluster number, membership, and boundaries. However, they lack the intuitive and visual appeal of hierarchical clustering dendrograms, and the number of clusters must be chosen a priori. == The Monti consensus clustering algorithm == The Monti consensus clustering algorithm is one of the most popular consensus clustering algorithms and is used to determine the number of clusters, K {\displaystyle K} . Given a dataset of N {\displaystyle N} total number of points to cluster, this algorithm works by resampling and clustering the data, for each K {\displaystyle K} and a N × N {\displaystyle N\times N} consensus matrix is calculated, where each element represents the fraction of times two samples clustered together. A perfectly stable matrix would consist entirely of zeros and ones, representing all sample pairs always clustering together or not together over all resampling iterations. The relative stability of the consensus matrices can be used to infer the optimal K {\displaystyle K} . More specifically, given a set of points to cluster, D = { e 1 , e 2 , . . . e N } {\displaystyle D=\{e_{1},e_{2},...e_{N}\}} , let D 1 , D 2 , . . . , D H {\displaystyle D^{1},D^{2},...,D^{H}} be the list of H {\displaystyle H} perturbed (resampled) datasets of the original dataset D {\displaystyle D} , and let M h {\displaystyle M^{h}} denote the N × N {\displaystyle N\times N} connectivity matrix resulting from applying a clustering algorithm to the dataset D h {\displaystyle D^{h}} . The entries of M h {\displaystyle M^{h}} are defined as follows: M h ( i , j ) = { 1 , if points i and j belong to the same cluster 0 , otherwise {\displaystyle M^{h}(i,j)={\begin{cases}1,&{\text{if}}{\text{ points i and j belong to the same cluster}}\\0,&{\text{otherwise}}\end{cases}}} Let I h {\displaystyle I^{h}} be the N × N {\displaystyle N\times N} identicator matrix where the ( i , j ) {\displaystyle (i,j)} -th entry is equal to 1 if points i {\displaystyle i} and j {\displaystyle j} are in the same perturbed dataset D h {\displaystyle D^{h}} , and 0 otherwise. The indicator matrix is used to keep track of which samples were selected during each resampling iteration for the normalisation step. The consensus matrix C {\displaystyle C} is defined as the normalised sum of all connectivity matrices of all the perturbed datasets and a different one is calculated for every K {\displaystyle K} . C ( i , j ) = ( ∑ h = 1 H M h ( i , j ) ∑ h = 1 H I h ( i , j ) ) {\displaystyle C(i,j)=\left({\frac {\textstyle \sum _{h=1}^{H}M^{h}(i,j)\displaystyle }{\sum _{h=1}^{H}I^{h}(i,j)}}\right)} That is the entry ( i , j ) {\displaystyle (i,j)} in the consensus matrix is the number of times points i {\displaystyle i} and j {\displaystyle j} were clustered together divided by the total number of times they were selected together. The matrix is symmetric and each element is defined within the range [ 0 , 1 ] {\displaystyle [0,1]} . A consensus matrix is calculated for each K {\displaystyle K} to be tested, and the stability of each matrix, that is how far the matrix is towards a matrix of perfect stability (just zeros and ones) is used to determine the optimal K {\displaystyle K} . One way of quantifying the stability of the K {\displaystyle K} th consensus matrix is examining its CDF curve (see below). == Over-interpretation potential of the Monti consensus clustering algorithm == Monti consensus clustering can be a powerful tool for identifying clusters, but it needs to be applied with caution as shown by Şenbabaoğlu et al. It has been shown that the Monti consensus clustering algorithm is able to claim apparent stability of chance partitioning of null datasets drawn from a unimodal distribution, and thus has the potential to lead to over-interpretation of cluster stability in a real study. If clusters are not well separated, consensus clustering could lead one to conclude apparent structure when there is none, or declare cluster stability when it is subtle. Identifying false positive clusters is a common problem throughout cluster research, and has been addressed by methods such as SigClust and the GAP-statistic. However, these methods rely on certain assumptions for the null model that may not always be appropriate. Şenbabaoğlu et al demonstrated the original delta K metric to decide K {\displaystyle K} in the Monti algorithm performed poorly, and proposed a new superior metric for measuring the stability of consensus matrices using their CDF curves. In the CDF curve of a consensus matrix, the lower left portion represents sample pairs rarely clustered together, the upper right portion represents those almost always clustered together, whereas the middle segment represent those with ambiguous assignments in different clustering runs. The proportion of ambiguous clustering (PAC) score measure quantifies this middle segment; and is defined as the fraction of sample pairs with consensus indices falling in the interval (u1, u2) ∈ [0, 1] where u1 is a value close to 0 and u2 is a value close to 1 (for instance u1=0.1 and u2=0.9). A low value of PAC indicates a flat middle segment, and a low rate of discordant assignments across permuted clustering runs. One can therefore infer the optimal number of clusters by the K {\displaystyle K} value having the lowest PAC. == Related work == Clustering ensemble (Strehl and Ghosh): They considered various formulations for the problem, most of which reduce the problem to a hyper-graph partitioning problem. In one of their formulations they considered the same graph as in the correlation clustering problem. The solution they proposed is to compute the best k-partition of the graph, which does not take into account the penalty for merging two nodes that are far apart. Clustering aggregation (Fern and Brodley): They applied the clustering aggregation idea to a collection of soft clusterings they obtained by random projections. They used an agglomerative algorithm
Supertoroid
In geometry and computer graphics, a supertoroid or supertorus is usually understood to be a family of doughnut-like surfaces (technically, a topological torus) whose shape is defined by mathematical formulas similar to those that define the superellipsoids. The plural of "supertorus" is either supertori or supertoruses. The family was described and named by Alan Barr in 1994. Barr's supertoroids have been fairly popular in computer graphics as a convenient model for many objects, such as smooth frames for rectangular things. One quarter of a supertoroid can provide a smooth and seamless 90-degree joint between two superquadric cylinders. However, they are not algebraic surfaces (except in special cases). == Formulas == Alan Barr's supertoroids are defined by parametric equations similar to the trigonometric equations of the torus, except that the sine and cosine terms are raised to arbitrary powers. Namely, the generic point P(u, v) of the surface is given by P ( u , v ) = ( X ( u , v ) Y ( u , v ) Z ( u , v ) ) = ( ( a + C u s ) C v t ( b + C u s ) S v t S u s ) {\displaystyle P(u,v)=\left({\begin{array}{c}X(u,v)\\Y(u,v)\\Z(u,v)\end{array}}\right)=\left({\begin{array}{c}(a+C_{u}^{s})C_{v}^{t}\\(b+C_{u}^{s})S_{v}^{t}\\S_{u}^{s}\end{array}}\right)} where C θ ε = sgn ( cos θ ) | cos θ | ε , S θ ε = sgn ( sin θ ) | sin θ | ε , {\displaystyle {\begin{aligned}C_{\theta }^{\varepsilon }&=\operatorname {sgn} (\cos \theta )\,\left|\,\cos \theta \,\right|^{\varepsilon },\\S_{\theta }^{\varepsilon }&=\operatorname {sgn} (\sin \theta )\ \left|\,\sin \theta \ \right|^{\varepsilon },\end{aligned}}} sgn is the sign function, and the parameters u, v range from 0 to 360 degrees (0 to 2π radians). In these formulas, the parameter s > 0 controls the "squareness" of the vertical sections, t > 0 controls the squareness of the horizontal sections, and a, b ≥ 1 are the major radii in the x and y directions. With s = t = 1 and a = b = R one obtains the ordinary torus with major radius R and minor radius 1, with the center at the origin and rotational symmetry about the z-axis. In general, the supertorus defined as above spans the intervals: − ( a + 1 ) ≤ x ≤ + ( a + 1 ) − ( b + 1 ) ≤ y ≤ + ( b + 1 ) − 1 ≤ z ≤ + 1 {\displaystyle {\begin{array}{rcccl}-(a+1)&\leq &x&\leq &+(a+1)\\[4pt]-(b+1)&\leq &y&\leq &+(b+1)\\[4pt]-1&\leq &z&\leq &+1\end{array}}} The whole shape is symmetric about the planes x = 0, y = 0, and z = 0. The hole runs in the z direction and spans the intervals − ( a − 1 ) ≤ x ≤ + ( a − 1 ) − ( b − 1 ) ≤ y ≤ + ( b − 1 ) − ∞ ≤ z ≤ + ∞ {\displaystyle {\begin{array}{rcccl}-(a-1)&\leq &x&\leq &+(a-1)\\[4pt]-(b-1)&\leq &y&\leq &+(b-1)\\[4pt]-\infty &\leq &z&\leq &+\infty \end{array}}} A curve of constant u on this surface is a horizontal Lamé curve with exponent 2 t , {\displaystyle {\tfrac {2}{t}},} scaled in x and y and displaced in z. A curve of constant v, projected on the plane x = 0 or y = 0, is a Lamé curve with exponent 2 s , {\displaystyle {\tfrac {2}{s}},} scaled and horizontally shifted. If v = 0, the curve is planar and spans the intervals: a − 1 ≤ x ≤ a + 1 − 1 ≤ z ≤ + 1 {\displaystyle {\begin{array}{rcccl}a-1&\leq &x&\leq &a+1\\[4pt]-1&\leq &z&\leq &+1\end{array}}} and similarly if v = 90°, 180°, 270°. The curve is also planar if a = b. In general, if a ≠ b and v is not a multiple of 90 degrees, the curve of constant v will not be planar; and, conversely, a vertical plane section of the supertorus will not be a Lamé curve. The basic supertoroid shape defined above is often modified by non-uniform scaling to yield supertoroids of specific width, length, and vertical thickness. == Plotting code == The following GNU Octave code generates plots of a supertorus:
Juergen Pirner
Juergen Pirner (born 1956) is the German creator of Jabberwock, a chatterbot that won the 2003 Loebner prize. Pirner created Jabberwock modelling the Jabberwocky from Lewis Carroll's poem of the same name. Initially, Jabberwock would just give rude or fantasy-related answers; but over the years, Pirner has programmed better responses into it. As of 2007 he has taught it 2.7 million responses. Pirner lives in Hamburg, Germany.
Harvey (software)
Harvey is a generative artificial intelligence (AI) product developed by the Counsel AI Corporation for the legal industry. The product has been described as a provider of customised large language models (LLMs) for law firms and in-house legal teams. It is named after the lead character of the legal drama Suits, Harvey Specter. == History == Harvey was founded in the summer of 2022 by Winston Weinberg, who was a securities and antitrust litigator at O'Melveny & Myers, and Gabriel Pereyra, who was a research scientist at Google DeepMind and Meta. Pereyra and Weinberg were roommates in Los Angeles. Pereyra was brainstorming startup ideas with his research colleagues. He showed Weinberg OpenAI's GPT-3 text-generating system, and Weinberg realized that it could be used to improve legal workflows. They developed an early chain-of-thought prompt based on GPT-3, focused on California tenant law. They ran the model on 100 legal questions from a public forum and hired three attorneys to evaluate the answers and determine whether they could be sent to clients unchanged. Out of those 100 questions, 86 were approved. After that, Pereyra and Weinberg contacted Sam Altman and Jason Kwon, General Counsel at OpenAI, about their results. Shortly after, on July 4, 2022, they met with OpenAI's C-suite, and OpenAI became their seed investor. OpenAI also gave Pereyra and Weinberg early access to GPT-4. Gordon Moodie, a corporate partner at Wachtell, Lipton, Rosen & Katz, also joined Harvey in July 2023 as the company's chief product officer. In March 2024, Harvey had 82 employees and stated that it intended to double that figure by the end of 2024. The company has reportedly hired a large number of lawyers, including from White & Case, Latham & Watkins, Skadden, Gunderson Dettmer, Katten Muchin Rosenman, and Paul Weiss. Harvey CEO Weinberg explained that many members of the company's sales team were formerly attorneys at 'Big Law', i.e. large US law firms, and that the sales team's experience was useful in convincing attorneys to trial the company's software. The integration of former 'Big Law' attorneys into product and sales teams has been attributed as a major factor in Harvey's success. In February 2026, Harvey announced its first brand partnership with actor Gabriel Macht, who portrayed the character Harvey Specter in Suits, to launch the company's Instagram page. In May 2026, it was announced the company is sponsoring the Golden State Valkyries and the New York Liberty. == Funding == In November 2022, it was reported that Harvey raised US$5 million in funding led by the OpenAI Startup Fund, together with other investors such as Jeff Dean, the head of Google AI, Elad Gil, the founder of Mixer Labs, Sarah Guo, the founder of Conviction, and other angel investors. Harvey raised another $23 million in April 2023 in a funding round led by Sequoia Capital. Harvey announced in December 2023 that it had raised $80 million in a Series B funding round led by Elad Gil and Kleiner Perkins which valued the company at $715 million. Other investors in the round included Sequoia Capital and the OpenAI Startup Fund. In July 2024, Harvey announced that it had raised $100 million in a Series C funding round that valued the company at $1.5 billion. The round was led by venture capital firm GV, and other participants included OpenAI, Kleiner Perkins, Sequoia Capital, Elad Gil, and SV Angel. In February 2025, Harvey announced it had raised $300 million in a Series D funding round that valued the company at $3 billion. Just months later, in June 2025, Harvey closed a $300 million Series E co-led by Kleiner Perkins and Coatue, again with participation from Conviction, Elad Gil, OpenAI, and Sequoia, boosting its valuation to about $5 billion and supporting international growth and expanded legal product offerings. In December 2025, Harvey secured a $160 million Series F round led by Andreessen Horowitz, with continued participation from investors including EQT, WndrCo, Sequoia, Kleiner Perkins, Conviction, and Elad Gil, valuing the legal AI company at roughly $8 billion. In March 2026, Harvey raised $200 million at a valuation of $11 billion, in a round co-led by GIC and Sequoia Capital. == Features == In May 2024, Harvey launched its products on Microsoft Azure and stated that it would offer a Harvey on Azure version of its product going forward. It was also reported that Harvey would begin offering general commercial access to some of its products, such as its case law models, as well as product bundles that included its AI assistant, specialised models, and its Vault feature for running prompts on large document collections. == Applications == Various law firms around the world are customers of Harvey. US law firm Paul Weiss began testing Harvey within the firm in January 2023, and became a client of the company later that year. Gina Lynch, the firm's chief knowledge and innovation officer, explained that the firm was not using hard metrics, such as time saved, to assess productivity gains because the time and effort needed to carefully review the output made efficiency gains difficult to measure. In February 2023, the UK law firm, Allen & Overy (now A&O Shearman), announced that it had been trialing Harvey since November 2022 within its Markets Innovation Group. This was reported to be the first known use of a generative AI product within the UK magic circle law firms. According to Allen & Overy, during the trial, 3,500 lawyers had used Harvey for around 40,000 queries in the course of their day to day work. The firm's press release stated that "Whilst the output needs careful review by an A&O lawyer, Harvey can help generate insights, recommendations and predictions based on large volumes of data". David Wakeling, head of the Markets Innovation Group, also cautioned that "You must validate everything coming out of the system. You have to check everything". The Irish law firm, A&L Goodbody, announced in February 2024 that it would be working with Harvey to enhance its services in relation to document analysis, due diligence, litigation, and regulatory compliance. In June 2024, UK law firm Ashurst announced that it would partner with Harvey and roll out its services to its branches worldwide. In September 2024, PwC announced that it would be adopting Harvey to empower its lawyers in Singapore. Singapore law firm WongPartnership also announced that month that it had become the first Southeast Asian law firm to test Harvey's generative AI solutions.
Frame (artificial intelligence)
Frames are an artificial intelligence data structure used to divide knowledge into substructures by representing "stereotyped situations". They were proposed by Marvin Minsky in his 1974 article "A Framework for Representing Knowledge". Frames are the primary data structure used in artificial intelligence frame languages; they are stored as ontologies of sets. Frames are also an extensive part of knowledge representation and reasoning schemes. They were originally derived from semantic networks and are therefore part of structure-based knowledge representations. According to Russell and Norvig's Artificial Intelligence: A Modern Approach, structural representations assemble "facts about particular object and event types and [arrange] the types into a large taxonomic hierarchy analogous to a biological taxonomy". == Frame structure == The frame contains information on how to use the frame, what to expect next, and what to do when these expectations are not met. Some information in the frame is generally unchanged while other information, stored in "terminals", usually change. Terminals can be considered as variables. Top-level frames carry information, that is always true about the problem in hand, however, terminals do not have to be true. Their value might change with the new information encountered. Different frames may share the same terminals. Each piece of information about a particular frame is held in a slot. The information can contain: Facts or Data Values (called facets) Procedures (also called procedural attachments) IF-NEEDED: deferred evaluation IF-ADDED: updates linked information Default Values For Data For Procedures Other Frames or Subframes == Features and advantages == A frame's terminals are already filled with default values, which is based on how the human mind works. For example, when a person is told "a boy kicks a ball", most people will visualize a particular ball (such as a familiar soccer ball) rather than imagining some abstract ball with no attributes. One particular strength of frame-based knowledge representations is that, unlike semantic networks, they allow for exceptions in particular instances. This gives frames a degree of flexibility that allows representations to reflect real-world phenomena more accurately. Like semantic networks, frames can be queried using spreading activation. Following the rules of inheritance, any value given to a slot that is inherited by subframes will be updated (IF-ADDED) to the corresponding slots in the subframes and any new instances of a particular frame will feature that new value as the default. Because frames are based on structures, it is possible to generate a semantic network given a set of frames even though it lacks explicit arcs. References to Noam Chomsky and his generative grammar of 1950 are generally missing from Minsky's work. The simplified structures of frames allow for easy analogical reasoning, a much prized feature in any intelligent agent. The procedural attachments provided by frames also allow a degree of flexibility that makes for a more realistic representation and gives a natural affordance for programming applications. == Example == Worth noticing here is the easy analogical reasoning (comparison) that can be done between a boy and a monkey just by having similarly named slots. Also notice that Alex, an instance of a boy, inherits default values like "Sex" from the more general parent object Boy, but the boy may also have different instance values in the form of exceptions such as the number of legs. == Frame language == A frame language is a technology used for knowledge representation in artificial intelligence. They are similar to class hierarchies in object-oriented languages although their fundamental design goals are different. Frames are focused on explicit and intuitive representation of knowledge whereas objects focus on encapsulation and information hiding. Frames originated in AI research and objects primarily in software engineering. However, in practice, the techniques and capabilities of frame and object-oriented languages overlap significantly. === Example === A simple example of concepts modeled in a frame language is the Friend of A Friend (FOAF) ontology defined as part of the Semantic Web as a foundation for social networking and calendar systems. The primary frame in this simple example is a Person. Example slots are the person's email, home page, phone, etc. The interests of each person can be represented by additional frames describing the space of business and entertainment domains. The slot knows links each person with other persons. Default values for a person's interests can be inferred by the web of people they are friends of. === Implementations === The earliest frame-based languages were custom developed for specific research projects and were not packaged as tools to be re-used by other researchers. Just as with expert system inference engines, researchers soon realized the benefits of extracting part of the core infrastructure and developing general-purpose frame languages that were not coupled to specific applications. One of the first general-purpose frame languages was KRL. One of the most influential early frame languages was KL-ONE. KL-ONE spawned several subsequent Frame languages. One of the most widely used successors to KL-ONE was the Loom language developed by Robert MacGregor at the Information Sciences Institute. In the 1980s, Artificial Intelligence generated a great deal of interest in the business world fueled by expert systems. This led to the development of many commercial products for the development of knowledge-based systems. These early products were usually developed in Lisp and integrated constructs such as IF-THEN rules for logical reasoning with Frame hierarchies for representing data. One of the most well known of these early Lisp knowledge-base tools was the Knowledge Engineering Environment (KEE) from Intellicorp. KEE provided a full Frame language with multiple inheritance, slots, triggers, default values, and a rule engine that supported backward and forward chaining. As with most early commercial versions of AI software KEE was originally deployed in Lisp on Lisp machine platforms but was eventually ported to PCs and Unix workstations. The research agenda of the Semantic Web spawned a renewed interest in automatic classification and frame languages. An example is the Web Ontology Language (OWL) standard for describing information on the Internet. OWL is a standard to provide a semantic layer on top of the Internet. The goal is that rather than searching the web using keywords as most search engines (e.g. Google) do today, the web can be organized by concepts organized in an ontology, like a directory structure. The name of the OWL language itself provides a good example of the value of a Semantic Web. If one were to search for "OWL" using the Internet today most of the pages retrieved would be on the bird Owl rather than the standard OWL. With a Semantic Web it would be possible to specify the concept "Web Ontology Language" and the user would not need to worry about the various possible acronyms or synonyms as part of the search. Likewise, the user would not need to worry about homonyms crowding the search results with irrelevant data such as information about birds of prey as in this simple example. In addition to OWL, various standards and technologies that are relevant to the Semantic Web and were influenced by Frame languages include OIL and DAML. The Protege Open Source software tool from Stanford University provides an ontology editing capability that is built on OWL and has the full capabilities of a classifier. However it ceased to explicitly support frames as of version 3.5 (which is maintained for those preferring frame orientation), with the current version being 5.6.8 as of 2025. The justification for moving from explicit frames being that OWL DL is more expressive and "industry standard". === Comparison of frames and objects === Frame languages have a significant overlap with object-oriented languages. The terminologies and goals of the two communities were different but as they moved from the academic world and labs to the commercial world developers tended to not care about philosophical issues and focused primarily on specific capabilities, taking the best from either camp regardless of where the idea began. What both paradigms have in common is a desire to reduce the distance between concepts in the real world and their implementation in software. As such both paradigms arrived at the idea of representing the primary software objects in taxonomies starting with very general types and progressing to more specific types. The following table illustrates the correlation between standard terminology from the object-oriented and frame language communities: The primary difference between the two paradigms was in the degree that encapsulation was considered a majo
Foodsi
Foodsi is a Polish mobile application that connects customers with restaurants, convenience stores, bakeries and cafes that have a surplus of food, allowing its users to buy the surplus at a reduced price. The service launched in 2019 in Warsaw and has expanded to other major cities in Poland. In 2023, a new feature was introduced in the app, allowing users to buy packages not only with self-pickup but also with delivery. The products range has also been expanded to include unsold magazines, cosmetics or plants. == History == The company was created in 2019 in Poland by Mateusz Kowalczyk and Jakub Fryszczyn. During studies in their home country and abroad, when they made a living working in restaurants and bakeries, they recognized the problem and the scale of food waste. They launched the application by themselves, having previously raised PLN 100,000 on their own for the purpose. Initially, Foodsi was an Android-only app, but over time, an IOS version was developed. In 2022, the startup raised PLN 6 million in a seed round from VC companies including CofounderZone and Status Starter, as well as private investors such as founders of Pyszne.pl. As of December 2023, it claimed more than 5000 businesses, serving over 1,5 million users, have saved nearly 3 million bags of food. == Purpose == Foodsi aims to significantly reduce food waste, which contributes to the Sustainable Development Goals. The application bridges the gap between the customers who are looking for shopping deals and the companies that want to reduce surplus products but are unable to sell them at a normal price. This allows the customers to buy unsold products for as little as 30% of the normal price. The company claims that every 4 out of 5 packages are sold on average. As of 2019 Foodsi employed more than 30 people. By 2024 it was more than 50. For now, Foodsi operates in major Polish cities such as Warsaw, Kraków, Trójmiasto, Wrocław, Poznań etc. However, in the upcoming years, Foodsi plans to expand to other countries. == Use == To start selling surplus, a company must leave Foodsi its contact information to register in the system. Registration in the app is completely free of charge. Then, companies offer available packages anticipating what won’t be sold and post them in the app along with the price so that users can buy them and pick them up. Companies can put their packages in the app at any time during the day. Users can pick up packages from bakeries, grocery stores, restaurants, but also florists and beauty stores. Foodsi charges a small commission on each package from the cooperating companies. If a user wants to start ordering packages from Foodsi, he or she needs to install the app on their mobile phone (Android or IOS) and register an account. The app displays a list of restaurants and other venues available in a specific region set by the user's location. Customers can see the price, address, distance and time range for package pickup. Packages are usually in the form of so-called 'surprise-packages', meaning that customers do not know specifically what kind of food/product will be inside. Some restaurants offer a choice of different package sizes. Prices are up to 70% lower than those of the original products. Customers have to show up at the restaurant to pick up the package using their phone at a time specified in the app. == Awards == Auler All-Stars 2025 - 3rd place Deloitte Technology Fast 50 - 2025 Central Europe Executive Club - Innowacja Roku: Żywność i Rolnictwo - Wyróżnienie (2025) Stena Circular Economy Award - Lider Gospodarki Obiegu Zamkniętego (2025) - wyróżnienie w kategorii start-up wdrażający GOZ na rynku polskim 255th place in the international poll FoodTech 500 2025 Finalist for the EY Entrepreneur Of The Year™ 2025 Wpływowi 2024 - Laureat w kategorii “Zrównoważony rozwój” Supplier of the Year 2024 - XXII Food & Business Forum Supplier of the Year 2024 - VII Sweets & Coffee Forum Innovative Leader 2024 - Leader in Food / Food-Tech Category - Executive Summit “Orzeł Innowacji - Start-up z potencjałem Polska-Świat” (Rzeczpospolita, 2024) 102nd place in the international poll FoodTech 500 2024 Auler 2023 Startup of the Year 2023 according to money.pl Start(up) w zrównoważoną przyszłość Kongresu Kompas ESG 2023 Marka Godna Zaufania according to My Company Polska 2023 184th place in the international poll FoodTech 500 2023 In 2023, Foodsi co-founder Mateusz Kowalczyk was recognized by Forbes magazine and included in its "30 before 30" list.
Instantaneously trained neural networks
Instantaneously trained neural networks are feedforward artificial neural networks that create a new hidden neuron node for each novel training sample. The weights to this hidden neuron separate out not only this training sample but others that are near it, thus providing generalization. This separation is done using the nearest hyperplane that can be written down instantaneously. In the two most important implementations the neighborhood of generalization either varies with the training sample (CC1 network) or remains constant (CC4 network). These networks use unary coding for an effective representation of the data sets. This type of network was first proposed in a 1993 paper of Subhash Kak. Since then, instantaneously trained neural networks have been proposed as models of short term learning and used in web search, and financial time series prediction applications. They have also been used in instant classification of documents and for deep learning and data mining. As in other neural networks, their normal use is as software, but they have also been implemented in hardware using FPGAs and by optical implementation. == CC4 network == In the CC4 network, which is a three-stage network, the number of input nodes is one more than the size of the training vector, with the extra node serving as the biasing node whose input is always 1. For binary input vectors, the weights from the input nodes to the hidden neuron (say of index j) corresponding to the trained vector is given by the following formula: w i j = { − 1 , for x i = 0 + 1 , for x i = 1 r − s + 1 , for i = n + 1 {\displaystyle w_{ij}={\begin{cases}-1,&{\mbox{for }}x_{i}=0\\+1,&{\mbox{for }}x_{i}=1\\r-s+1,&{\mbox{for }}i=n+1\end{cases}}} where r {\displaystyle r} is the radius of generalization and s {\displaystyle s} is the Hamming weight (the number of 1s) of the binary sequence. From the hidden layer to the output layer the weights are 1 or -1 depending on whether the vector belongs to a given output class or not. The neurons in the hidden and output layers output 1 if the weighted sum to the input is 0 or positive and 0, if the weighted sum to the input is negative: y = { 1 if ∑ x i ≥ 0 0 if ∑ x i < 0 {\displaystyle y=\left\{{\begin{matrix}1&{\mbox{if }}\sum x_{i}\geq 0\\0&{\mbox{if }}\sum x_{i}<0\end{matrix}}\right.} == Other networks == The CC4 network has also been modified to include non-binary input with varying radii of generalization so that it effectively provides a CC1 implementation. In feedback networks the Willshaw network as well as the Hopfield network are able to learn instantaneously.