Jared Daniel Kaplan is a theoretical physicist and artificial intelligence researcher. He is an associate professor in the Johns Hopkins University Department of Physics & Astronomy, and a co-founder and chief science officer of Anthropic. == Education == Kaplan attended the Illinois Mathematics and Science Academy during high school. He received a bachelor's degree in physics and mathematics from Stanford University and a PhD in physics from Harvard University. His doctoral thesis is titled Aspects of holography, advised by Nima Arkani-Hamed. == Academic career and physics research == Kaplan’s research interests include quantum gravity, holography (AdS/CFT), conformal field theory, and related topics in particle physics and cosmology. He worked as a postdoctoral fellow at SLAC and Stanford University and has been a professor at Johns Hopkins University since 2012. == Machine learning research == Kaplan joined OpenAI in 2019 as a researcher, where he co-authored Scaling Laws for Neural Language Models (2020), which reported that empirically, the performance of language models steadily improves with their size and the amount of data and compute used for training. He is also a co-author of Language Models are Few-Shot Learners (2020), which introduced GPT-3. At the company, he was also involved in the development of Codex. == Anthropic == Kaplan co-founded Anthropic and serves as its chief science officer. In October 2024, Anthropic announced that Kaplan would serve as the company's "Responsible Scaling Officer", overseeing its responsible scaling policy (RSP). In this role, Kaplan determines the safety assessments and precautions to adopt before model release. In December 2025, The Guardian published an interview with Kaplan about AI autonomy and recursive self-improvement timelines. == Honors and recognition == Kaplan was a Hertz Fellow (2005). He has also received a Sloan Research Fellowship and an NSF CAREER award (PHY-1454083). == Selected works == Scaling Laws for Neural Language Models (2020). Language Models are Few-Shot Learners (2020). A Natural Language for AdS/CFT Correlators (2011). == Personal life == As of 2026, Forbes estimated Kaplan's net worth at $3.7 billion. He lives in Pacifica, California, and has a son.
Toy problem
In scientific disciplines, a toy problem or a puzzlelike problem is a problem that is not of immediate scientific interest, yet is used as an expository device to illustrate a trait that may be shared by other, more complicated, instances of the problem, or as a way to explain a particular, more general, problem solving technique. A toy problem is useful to test and demonstrate methodologies. Researchers can use toy problems to compare the performance of different algorithms. They are also good for game designing. For instance, while engineering a large system, the large problem is often broken down into many smaller toy problems which have been well understood in detail. Often these problems distill a few important aspects of complicated problems so that they can be studied in isolation. Toy problems are thus often very useful in providing intuition about specific phenomena in more complicated problems. As an example, in the field of artificial intelligence, classical puzzles, games and problems are often used as toy problems. These include sliding-block puzzles, N-Queens problem, missionaries and cannibals problem, tic-tac-toe, chess, Tower of Hanoi and others.
HOCR
hOCR is an open standard of data representation for formatted text obtained from optical character recognition (OCR). The definition encodes text, style, layout information, recognition confidence metrics and other information using Extensible Markup Language (XML) in the form of Hypertext Markup Language (HTML) or XHTML. == Software == The following OCR software can output the recognition result as hOCR file: OCRopus Tesseract Cuneiform ghostscript HebOCR gcv2hocr gImageReader == Example == The following example is an extract of an hOCR file: The recognized text is stored in normal text nodes of the HTML file. The distribution into separate lines and words is here given by the surrounding span tags. Moreover, the usual HTML entities are used, for example the p tag for a paragraph. Additional information is given in the properties such as: different layout elements such as "ocr_par", "ocr_line", "ocrx_word" geometric information for each element with a bounding box "bbox" language information "lang" some confidence values "x_wconf" == bbox == === General === The Layout of the Bounding Box Object or bbox Object is Grammar. property-name = "bbox" property-value = uint uint uint uint ==== Example ==== bbox 0 0 100 200 The bbox - short for "bounding box" - of an element is a rectangular box around this element, which is defined by the upper-left corner (x0, y0) and the lower-right corner (x1, y1). the values are with reference to the top-left corner of the document image and measured in pixels the order of the values are x0 y0 x1 y1 = "left top right bottom" ===== Usage ===== Use x_bboxes below for character bounding boxes. Do not use bbox unless the bounding box of the layout component is, in fact, rectangular, some non-rectangular layout components may have rectangular bounding boxes if the non-rectangularity is caused by floating elements around which text flows. The bounding box bbox of this line is shown in blue and it is span by the upper-left corner (10, 20) and the lower-right corner (160, 30). All coordinates are measured with reference to the top-left corner of the document image which border is drawn in black. == Searchable PDF files == The hOCR format is most commonly used in order to make searchable PDF files or as an extracted metadata of the PDF file. In order to create searchable PDF files we can use a scanned document image and a .hocr file of the particular image. We can use the following open source tools in order to achieve that. === hocr-tools === Source: hocr-tools is an open source library written in Python. It has a command-line utility attached in the scripts called hocr-pdf that enables us to convert standard hocr files to a searchable PDF file. It is also worth noting that the version for dealing with hocr files in RTL or non-Latin scripts like Arabic, we need to use the GitHub repository at the moment. hocr-pdf We can use the hocr-pdf utility using the following basic syntax. hocr-pdf—savefile final.pdf folder_images_and_hocr The folder_images_and_hocr must contain the respective .jpg and .hocr format files with their file extensions changed. ==== Known issues ==== Some of the known issues of hocr-pdf script in PyPI installation are the following. Not up to date with GitHub repository. hocr-pdf is broken on line 134 due to decodebytes() depreciated after Python 3.1 ==== Known fixes ==== Compile hocr-tools using latest GitHub repository. === hocr2pdf === hocr2pdf is another library that supports the conversion of hocr files. It is written in C++ and is cross-compatible with other libraries. It also has support for UTF-8 languages but that may require some additional debugging and browsing through some google conversation records to achieve that. According to Ubuntu Manpages,ExactImage is a fast C++ image processing library. Unlike many other library frameworks it allows operation in several color spaces and bit depths natively, resulting in low memory and computational requirements. hocr2pdf creates well layouted, searchable PDF files from hOCR (annotated HTML) input obtained from an OCR system. == hOCR to PDF attempts == In addition to the following discussed and stable libraries there have been many contributions to the hOCR format over the years with support from many of the early adopters of this format. You can get access to inlaying text on an Image with hOCR and converting that in a PDF file using Python 2 with this 12-year-old script as of 2021. This script can also be updated and made functional by converting that Python 2 Source code to Python 3 Supported Context. - HOCRConverter by jbrinley (Documentation) === HOCRConverter === The HOCRConverter is a script written in Python 2.x that can used in order to convert a hOCR file with a specified image file in order to convert it to a searchable PDF file. You can see the documentation using the link above. ==== Known issues ==== Has not been tested. Does not natively support Python 3.x
Self-verifying finite automaton
In automata theory, a self-verifying finite automaton (SVFA) is a special kind of a nondeterministic finite automaton (NFA) with a symmetric kind of nondeterminism introduced by Hromkovič and Schnitger. Generally, in self-verifying nondeterminism, each computation path is concluded with any of the three possible answers: yes, no, and I do not know. For each input string, no two paths may give contradictory answers, namely both answers yes and no on the same input are not possible. At least one path must give answer yes or no, and if it is yes then the string is considered accepted. SVFA accept the same class of languages as deterministic finite automata (DFA) and NFA but have different state complexity. == Formal definition == An SVFA is represented formally by a 6-tuple, A=(Q, Σ, Δ, q0, Fa, Fr) such that (Q, Σ, Δ, q0, Fa) is an NFA, and Fa, Fr are disjoint subsets of Q. For each word w = a1a2 … an, a computation is a sequence of states r0,r1, …, rn, in Q with the following conditions: r0 = q0 ri+1 ∈ Δ(ri, ai+1), for i = 0, …, n−1. If rn ∈ Fa then the computation is accepting, and if rn ∈ Fr then the computation is rejecting. There is a requirement that for each w there is at least one accepting computation or at least one rejecting computation but not both. == Results == Each DFA is a SVFA, but not vice versa. Jirásková and Pighizzini proved that for every SVFA of n states, there exists an equivalent DFA of g ( n ) = Θ ( 3 n / 3 ) {\displaystyle g(n)=\Theta (3^{n/3})} states. Furthermore, for each positive integer n, there exists an n-state SVFA such that the minimal equivalent DFA has exactly g ( n ) {\displaystyle g(n)} states. Other results on the state complexity of SVFA were obtained by Jirásková and her colleagues.
Dialogflow
Dialogflow is a natural language understanding platform used to design and integrate a conversational user interface into mobile apps, web applications, devices, bots, interactive voice response systems and related uses. == History == In May 2012, Speaktoit received a venture round (funding terms undisclosed) from Intel Capital. In July 2014, Speaktoit closed their Series B funding led by Motorola Solutions Venture Capital with participation from new investor Plug and Play Ventures and existing backers Intel Capital and Alpine Technology Fund. In September 2014, Speaktoit released api.ai (the voice-enabling engine that powers Assistant) to third-party developers, allowing the addition of voice interfaces to apps based on Android, iOS, HTML5, and Cordova. The SDK's contain voice recognition, natural language understanding, and text-to-speech. api.ai offers a web interface to build and test conversation scenarios. The platform is based on the natural language processing engine built by Speaktoit for its Assistant application. Api.ai allows Internet of Things developers to include natural language voice interfaces in their products. Assistant and Speaktoit's websites now redirect to api.ai's website Archived 2017-10-10 at the Wayback Machine, which redirects to the Dialogflow website. Google bought the company in September 2016 and was initially known as API.AI; it provides tools to developers building apps ("Actions") for the Google Assistant virtual assistant. The organization discontinued the Assistant app on December 15, 2016. In October 2017, it was renamed as Dialogflow. In November 2017, Dialogflow became part of Google Cloud Platform.
Reflection lines
Engineers use reflection lines to judge a surface's quality. Reflection lines reveal surface flaws, particularly discontinuities in normals indicating that the surface is not C 2 {\displaystyle C^{2}} . Reflection lines may be created and examined on physical surfaces or virtual surfaces with the help of computer graphics. For example, the shiny surface of an automobile body is illuminated with reflection lines by surrounding the car with parallel light sources. Virtually, a surface can be rendered with reflection lines by modulating the surfaces point-wise color according to a simple calculation involving the surface normal, viewing direction and a square wave environment map. == Mathematical definition == Consider a point p {\displaystyle p} on a surface M {\displaystyle M} with (normalized) normal n {\displaystyle n} . If an observer views this point from infinity at view direction v {\displaystyle v} then the reflected view direction r {\displaystyle r} is: r = v − 2 ( n ⋅ v ) n . {\displaystyle r=v-2(n\cdot v)n.} (The vector v {\displaystyle v} is decomposed into its normal part v n = ( n ⋅ v ) v {\displaystyle v_{n}=(n\cdot v)v} and tangential part v t = v − v n {\displaystyle v_{t}=v-v_{n}} . Upon reflection, the tangential part is kept and the normal part is negated.) For reflection lines we consider the surface M {\displaystyle M} surrounded by parallel lines with direction a {\displaystyle a} , representing infinite, non-dispersive light sources. For each point p {\displaystyle p} on M {\displaystyle M} we determine which line is seen from direction v {\displaystyle v} . The position on each line is of no interest. Define the vector r p {\displaystyle r_{p}} to be the reflection direction r {\displaystyle r} projected onto a plane P {\displaystyle P} that is orthogonal to a {\displaystyle a} : r p = r − ( r ⋅ a ) a {\displaystyle r_{p}=r-(r\cdot a)a} and similarly let v p {\displaystyle v_{p}} be the viewing direction projected onto P {\displaystyle P} : v p = v − ( v ⋅ a ) a {\displaystyle v_{p}=v-(v\cdot a)a} Finally, define v o {\displaystyle v_{o}} to be the direction lying in P {\displaystyle P} perpendicular to a {\displaystyle a} and v p {\displaystyle v_{p}} : v o = a × v p {\displaystyle v_{o}=a\times v_{p}} Using these vectors, the reflection line function θ ( p ) : M → ( − π , π ] {\displaystyle \theta (p):M\rightarrow (-\pi ,\pi ]} is a scalar function mapping points p {\displaystyle p} on the surface to angles between v p {\displaystyle v_{p}} and r p {\displaystyle r_{p}} : θ = arctan ( r p ⋅ v o , r p ⋅ v p ) {\displaystyle \theta =\arctan {(r_{p}\cdot v_{o},r_{p}\cdot v_{p})}} where a r c t a n ( y , x ) {\displaystyle arctan(y,x)} is the atan2 function producing a number in the range ( − π , π ] {\displaystyle (-\pi ,\pi ]} . ( v p {\displaystyle v_{p}} and v o {\displaystyle v_{o}} can be viewed as a local coordinate system in P {\displaystyle P} with x {\displaystyle x} -axis in direction v p {\displaystyle v_{p}} and y {\displaystyle y} -axis in direction v o {\displaystyle v_{o}} .) Finally, to render the reflection lines positive values θ > 0 {\displaystyle \theta >0} are mapped to a light color and non-positive values to a dark color. == Highlight lines == Highlight lines are a view-independent alternative to reflection lines. Here the projected normal is directly compared against some arbitrary vector x {\displaystyle x} perpendicular to the light source: θ = arctan ( n a ⋅ a ⊥ , n a ⋅ x ) {\displaystyle \theta =\arctan {(n_{a}\cdot a^{\perp },n_{a}\cdot x)}} where n a {\displaystyle n_{a}} is the surface normal projected on the light source plane P {\displaystyle P} : n a ^ / | n a ^ | , n a ^ = n − ( n ⋅ a ) a {\displaystyle {\hat {n_{a}}}/|{\hat {n_{a}}}|,{\hat {n_{a}}}=n-(n\cdot a)a} The relationship between reflection lines and highlight lines is likened to that between specular and diffuse shading.
Laws of Form
Laws of Form (hereinafter LoF) is a book by G. Spencer-Brown, written by August 1967 and published in 1969. The book straddles the boundary between mathematics and philosophy. LoF describes three distinct logical systems: The primary arithmetic (described in Chapter 4 of LoF), whose models include Boolean arithmetic; The primary algebra (Chapter 6 of LoF), whose models include the two-element Boolean algebra (hereinafter abbreviated 2), Boolean logic, and the classical propositional calculus; Equations of the second degree (Chapter 11), whose interpretations include finite automata and Alonzo Church's Restricted Recursive Arithmetic (RRA). "Boundary algebra" is a Meguire (2011) term for the union of the primary algebra and the primary arithmetic. Laws of Form sometimes loosely refers to the "primary algebra" as well as to LoF. == Contents == The preface states that the work was first explored in 1959, and Spencer Brown cites Bertrand Russell as being supportive of his endeavour. He also thanks J. C. P. Miller of University College London for helping with the proofreading and offering other guidance. In 1963 Spencer Brown was invited by Harry Frost, staff lecturer in the physical sciences at the department of Extra-Mural Studies of the University of London, to deliver a course on the mathematics of logic. LoF emerged from work in electronic engineering its author did around 1960. Key ideas of the LOF were first outlined in his 1961 manuscript Design with the Nor, which remained unpublished until 2021, and further refined during subsequent lectures on mathematical logic he gave under the auspices of the University of London's extension program. LoF has appeared in several editions. The second series of editions appeared in 1972 with the "Preface to the First American Edition", which emphasised the use of self-referential paradoxes, and the most recent being a 1997 German translation. LoF has never gone out of print. LoF's mystical and declamatory prose and its love of paradox make it a challenging read for all. Spencer-Brown was influenced by Ludwig Wittgenstein and R. D. Laing. LoF also echoes a number of themes from the writings of Charles Sanders Peirce, Bertrand Russell, and Alfred North Whitehead. The work has had curious effects on some classes of its readership; for example, on obscure grounds, it has been claimed that the entire book is written in an operational way, giving instructions to the reader instead of telling them what "is", and that in accordance with G. Spencer-Brown's interest in paradoxes, the only sentence that makes a statement that something is, is the statement which says no such statements are used in this book. Furthermore, the claim asserts that except for this one sentence the book can be seen as an example of E-Prime. What prompted such a claim, is obscure, either in terms of incentive, logical merit, or as a matter of fact, because the book routinely and naturally uses the verb to be throughout, and in all its grammatical forms, as may be seen both in the original and in quotes shown below. == Reception == Ostensibly a work of formal mathematics and philosophy, LoF became something of a cult classic: it was praised by Heinz von Foerster when he reviewed it for the Whole Earth Catalog. Those who agree point to LoF as embodying an enigmatic "mathematics of consciousness", its algebraic symbolism capturing an (perhaps even "the") implicit root of cognition: the ability to "distinguish". LoF argues that primary algebra reveals striking connections among logic, Boolean algebra, and arithmetic, and the philosophy of language and mind. Stafford Beer wrote in a review for Nature in 1969, "When one thinks of all that Russell went through sixty years ago, to write the Principia, and all we his readers underwent in wrestling with those three vast volumes, it is almost sad". Banaschewski (1977) argues that the primary algebra is nothing but new notation for Boolean algebra. Indeed, the two-element Boolean algebra 2 can be seen as the intended interpretation of the primary algebra. Yet the notation of the primary algebra: Fully exploits the duality characterizing not just Boolean algebras but all lattices; Highlights how syntactically distinct statements in logic and 2 can have identical semantics; Dramatically simplifies Boolean algebra calculations, and proofs in sentential and syllogistic logic. Moreover, the syntax of the primary algebra can be extended to formal systems other than 2 and sentential logic, resulting in boundary mathematics. LoF has influenced, among others, Heinz von Foerster, Louis Kauffman, Niklas Luhmann, Humberto Maturana, Francisco Varela and William Bricken. Some of these authors have modified the primary algebra in a variety of interesting ways. LoF claimed that certain well-known mathematical conjectures of very long standing, such as the four color theorem, Fermat's Last Theorem, and the Goldbach conjecture, are provable using extensions of the primary algebra. Spencer-Brown eventually circulated a purported proof of the four color theorem, but it was met with skepticism. == The form (Chapter 1) == The symbol: Also called the "mark" or "cross", is the essential feature of the Laws of Form. In Spencer-Brown's inimitable and enigmatic fashion, the Mark symbolizes the root of cognition, i.e., the dualistic Mark indicates the capability of differentiating a "this" from "everything else but this". In LoF, a Cross denotes the drawing of a "distinction", and can be thought of as signifying the following, all at once: The act of drawing a boundary around something, thus separating it from everything else; That which becomes distinct from everything by drawing the boundary; Crossing from one side of the boundary to the other. All three ways imply an action on the part of the cognitive entity (e.g., person) making the distinction. As LoF puts it: "The first command: Draw a distinction can well be expressed in such ways as: Let there be a distinction, Find a distinction, See a distinction, Describe a distinction, Define a distinction, Or: Let a distinction be drawn". (LoF, Notes to chapter 2) The counterpoint to the Marked state is the Unmarked state, which is simply nothing, the void, or the un-expressable infinite represented by a blank space. It is simply the absence of a Cross. No distinction has been made and nothing has been crossed. The Marked state and the void are the two primitive values of the Laws of Form. The Cross can be seen as denoting the distinction between two states, one "considered as a symbol" and another not so considered. From this fact arises a curious resonance with some theories of consciousness and language. Paradoxically, the Form is at once Observer and Observed, and is also the creative act of making an observation. LoF (excluding back matter) closes with the words: ...the first distinction, the Mark and the observer are not only interchangeable, but, in the form, identical. C. S. Peirce came to a related insight in the 1890s; see § Related work. == The primary arithmetic (Chapter 4) == The syntax of the primary arithmetic goes as follows. There are just two atomic expressions: The empty Cross ; All or part of the blank page (the "void"). There are two inductive rules: A Cross may be written over any expression; Any two expressions may be concatenated. The semantics of the primary arithmetic are perhaps nothing more than the sole explicit definition in LoF: "Distinction is perfect continence". Let the "unmarked state" be a synonym for the void. Let an empty Cross denote the "marked state". To cross is to move from one value, the unmarked or marked state, to the other. We can now state the "arithmetical" axioms A1 and A2, which ground the primary arithmetic (and hence all of the Laws of Form): "A1. The law of Calling". Calling twice from a state is indistinguishable from calling once. To make a distinction twice has the same effect as making it once. For example, saying "Let there be light" and then saying "Let there be light" again, is the same as saying it once. Formally: = {\displaystyle \ =} "A2. The law of Crossing". After crossing from the unmarked to the marked state, crossing again ("recrossing") starting from the marked state returns one to the unmarked state. Hence recrossing annuls crossing. Formally: = {\displaystyle \ =} In both A1 and A2, the expression to the right of '=' has fewer symbols than the expression to the left of '='. This suggests that every primary arithmetic expression can, by repeated application of A1 and A2, be simplified to one of two states: the marked or the unmarked state. This is indeed the case, and the result is the expression's "simplification". The two fundamental metatheorems of the primary arithmetic state that: Every finite expression has a unique simplification. (T3 in LoF); Starting from an initial marked or unmarked state, "complicating" an expression by a finite number of repeated application of A1 and A2 cannot yield