Vibe coding

Vibe coding is a software development practice assisted by artificial intelligence (AI) where the software developer describes a project or task in a prompt to a large language model (LLM), which generates source code automatically. Vibe coding may involve accepting AI-generated code without thorough review of the output, instead relying on results and follow-up prompts to guide changes. The term was coined in February 2025 by computer scientist Andrej Karpathy, a co-founder of OpenAI and former AI leader at Tesla. Merriam-Webster listed the term in March 2025 as a "slang & trending" expression. It was named the Collins English Dictionary Word of the Year for 2025. Advocates of vibe coding say that it allows even amateur programmers to produce software without the extensive training and skills required for software engineering. Critics point out a lack of accountability, maintainability, and the increased risk of introducing security vulnerabilities in the resulting software. == Definition == The concept refers to a coding approach that relies on LLMs, allowing programmers to generate working code by providing natural language descriptions rather than manually writing in a formal programming language. Karpathy described it as a form of coding where you "fully give in to the vibes, embrace exponentials, and forget that the code even exists". When vibe coding, the programmer guides, tests, and gives feedback about the AI-generated source code, rather than manually writing code. The concept of vibe coding elaborates on Karpathy's claim from 2023 that "the hottest new programming language is English", meaning that the capabilities of LLMs were such that humans would no longer need to learn specific programming languages to command computers. Some commentators argue that a key to the definition is a lack of knowledge about the code, and that thorough review and testing is incompatible with the definition of vibe coding. Programmer Simon Willison said: "If an LLM wrote every line of your code, but you've reviewed, tested, and understood it all, that's not vibe coding in my book—that's using an LLM as a typing assistant." == Reception and use == In February 2025, New York Times journalist Kevin Roose, who is not a professional coder, experimented with vibe coding to create several small-scale applications. He described these as "software for one" due to the ability to personalize the software. However, Roose also stated that the results are often limited and prone to errors. In one case, the AI-generated code fabricated fake reviews for an e-commerce site. In response to Roose, cognitive scientist Gary Marcus said that the algorithm that generated Roose's LunchBox Buddy app had presumably been trained on existing code for similar tasks. Marcus said that Roose's enthusiasm stemmed from reproduction, not originality. In March 2025, Y Combinator reported that 25% of startup companies in its Winter 2025 batch had codebases that were 95% AI-generated, reflecting a shift toward AI-assisted development within newer startups. The question asked was about AI-generated code in general, and not specifically about vibed code. Inspired by "vibe coding", The Economist suggested the term "vibe valuation" to describe the very large valuations of AI startups by venture capital firms that ignore accepted metrics such as annual recurring revenue. In June 2025, Andrew Ng took issue with the term, saying that it misleads people into assuming that software engineers just "go with the vibes" when using AI tools to create applications. In July 2025, The Wall Street Journal reported that vibe coding was being adopted by professional software engineers for commercial use cases. In July 2025, SaaStr founder documented his negative experiences with vibe coding: Replit's AI agent deleted a database despite explicit instructions not to make any changes. In September 2025, Fast Company reported that the "vibe coding hangover" is upon us, with senior software engineers citing "development hell" when working with AI-generated code. It was reported in January 2026 that Linus Torvalds had made use of Google Antigravity to vibe code a tool component of his AudioNoise random digital audio effects generator. Torvalds explained in the project's README file that "the Python visualizer tool has been basically written by vibe-coding". == Criticism == === Quality of code and security issues === Vibe coding has raised concerns about understanding and accountability. Developers may use AI-generated code without comprehending its functionality, leading to undetected bugs, errors, or security vulnerabilities. While this approach may be suitable for prototyping or "throwaway weekend projects" as Karpathy originally envisioned, it is considered by some experts to pose risks in professional settings, where a deep understanding of the code is crucial for debugging, maintenance, and security. Ars Technica cites Simon Willison, who stated: "Vibe coding your way to a production codebase is clearly risky. Most of the work we do as software engineers involves evolving existing systems, where the quality and understandability of the underlying code is crucial." In May 2025, Lovable, a Swedish vibe coding app, was reported to have security vulnerabilities in the code it generated, with 170 out of 1,645 Lovable-created web applications having an issue that would allow personal information to be accessed by anyone. In October 2025 Veracode released a study that showed that over the last 3 years LLMs had become dramatically better at generating functional code, but that the security of generated code had generally not improved. Moreover, larger models were not better than small ones at generating secure code. There was a small increase in security from the OpenAI reasoning models, but not in other reasoning models, and this increase was nothing like the improvement in generated functionality. In December 2025, computer security researcher Etizaz Mohsin discovered a security flaw in the Orchids vibe coding platform, which he demonstrated to a BBC News reporter in February 2026. A December 2025 analysis by CodeRabbit of 470 open-source GitHub pull requests found that code that was co-authored by generative AI contained approximately 1.7 times more "major" issues compared to human-written code. The study revealed that AI co-authored code showed elevated rates of logic errors, including incorrect dependencies, flawed control flow, misconfigurations (75% more common), and security vulnerabilities (2.74x higher). Additionally, they also reported high code readability issues, including formatting errors and naming inconsistencies. === Code maintainability and technical debt === Vibe coding has the potential of making code harder to maintain in the longer term, leading to technical debt. In early 2025, GitClear published the results of a longitudinal analysis of 211 million lines of code changes from 2020 to 2024. They found that the volume of code refactoring dropped from 25% of changed lines in 2021 to under 10% by 2024, code duplication increased approximately four times in volume, copy-pasted code exceeded moved code for the first time in two decades, and code churn (prematurely merged code getting rewritten shortly after merging) nearly doubled. === Task complexity and developer productivity === Generative AI is highly capable of handling simple tasks like basic algorithms. However, such systems struggle with more novel, complex coding problems like projects involving multiple files, poorly documented libraries, or safety-critical code. In July 2025, METR, an organization that evaluates frontier models, ran a randomized controlled trial to understand developer productivity involving generative AI programming tools available in early 2025. They found that experienced open-source developers were 19% slower when using AI coding tools, despite predicting they would be 24% faster and still believing afterward they had been 20% faster. === Challenges with debugging === LLMs generate code dynamically, and the structure of such code may be subject to variation. In addition, since the developer did not write the code, the developer may struggle to understand its syntax and concepts. === Impact on open-source software === In January 2026, a paper authored by experts from several universities titled "Vibe Coding Kills Open Source" argued that vibe coding has negative impact on the open-source software ecosystem. The authors say that increased vibe coding reduces user engagement with open-source maintainers, which has hidden costs for said maintainers. Speaking with The Register about their paper, the authors argued:"Vibe coding raises productivity by lowering the cost of using and building on existing code, but it also weakens the user engagement through which many maintainers earn returns," the authors argue. "When OSS is monetized only through direct user engagement, greater adoption of vibe coding lowers e

Quickly (software)

Quickly is a framework for creating software programs for a Linux distribution using Python, PyGTK, Glade Interface Designer and Desktop Couch. It then allows for easy publishing using bzr and Launchpad. Quickly is designed to speed up the start of new projects with the use of templates, not only for programs but for any type of project. These templates are used to automate project configuration and maintenance. Delegating into templates and not into a specific library allows projects created using Quickly not to require dependencies on any particular library or runtime of Quickly itself. The project was started by Rick Spencer after his frustration as a beginner Ubuntu developer. == Updates == Last available software update is on 2013-01-31 for Ubuntu 11.04.

Myhill–Nerode theorem

In the theory of formal languages, the Myhill–Nerode theorem provides a necessary and sufficient condition for a language to be regular. The theorem is named for John Myhill and Anil Nerode, who proved it at the University of Chicago in 1957 (Nerode & Sauer 1957, p. ii). == Statement == Given a language L {\displaystyle L} , and a pair of strings x {\displaystyle x} and y {\displaystyle y} , define a distinguishing extension to be a string z {\displaystyle z} such that exactly one of the two strings x z {\displaystyle xz} and y z {\displaystyle yz} belongs to L {\displaystyle L} . Define a relation ∼ L {\displaystyle \sim _{L}} on strings as x ∼ L y {\displaystyle x\;\sim _{L}\ y} if there is no distinguishing extension for x {\displaystyle x} and y {\displaystyle y} . It is easy to show that ∼ L {\displaystyle \sim _{L}} is an equivalence relation on strings, and thus it divides the set of all strings into equivalence classes. The Myhill–Nerode theorem states that a language L {\displaystyle L} is regular if and only if ∼ L {\displaystyle \sim _{L}} has a finite number of equivalence classes, and moreover, that this number is equal to the number of states in the minimal deterministic finite automaton (DFA) accepting L {\displaystyle L} . Furthermore, every minimal DFA for the language is isomorphic to the canonical one (Hopcroft & Ullman 1979). Generally, for any language, the constructed automaton is a state automaton acceptor. However, it does not necessarily have finitely many states. The Myhill–Nerode theorem shows that finiteness is necessary and sufficient for language regularity. Some authors refer to the ∼ L {\displaystyle \sim _{L}} relation as Nerode congruence, in honor of Anil Nerode. == Use and consequences == The Myhill–Nerode theorem may be used to show that a language L {\displaystyle L} is regular by proving that the number of equivalence classes of ∼ L {\displaystyle \sim _{L}} is finite. This may be done by an exhaustive case analysis in which, beginning from the empty string, distinguishing extensions are used to find additional equivalence classes until no more can be found. For example, the language consisting of binary representations of numbers that can be divided by 3 is regular. Given two binary strings x , y {\displaystyle x,y} , extending them by one digit gives 2 x + b , 2 y + b {\displaystyle 2x+b,2y+b} , so 2 x + b ≡ 2 y + b mod 3 {\displaystyle 2x+b\equiv 2y+b\mod 3} iff x ≡ y mod 3 {\displaystyle x\equiv y\mod 3} . Thus, 00 {\displaystyle 00} (or 11 {\displaystyle 11} ), 01 {\displaystyle 01} , and 10 {\displaystyle 10} are the only distinguishing extensions, resulting in the 3 classes. The minimal automaton accepting our language would have three states corresponding to these three equivalence classes. Another immediate corollary of the theorem is that if for a language L {\displaystyle L} the relation ∼ L {\displaystyle \sim _{L}} has infinitely many equivalence classes, it is not regular. It is this corollary that is frequently used to prove that a language is not regular. == Generalizations == The Myhill–Nerode theorem can be generalized to tree automata.

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In search of the best AI headshot generator? An AI headshot generator is software that uses machine learning to help you get more done — it turns a rough idea into a polished result in seconds. When choosing one, weigh output quality, pricing, export formats, and how well it fits the tools you already use. Whether you are a beginner or a pro, the right AI headshot generator slots into your workflow and pays for itself fast. Below we compare features, pricing, and real output so you can choose with confidence.

Structured sparsity regularization

Structured sparsity regularization is a class of methods, and an area of research in statistical learning theory, that extend and generalize sparsity regularization learning methods. Both sparsity and structured sparsity regularization methods seek to exploit the assumption that the output variable Y {\displaystyle Y} (i.e., response, or dependent variable) to be learned can be described by a reduced number of variables in the input space X {\displaystyle X} (i.e., the domain, space of features or explanatory variables). Sparsity regularization methods focus on selecting the input variables that best describe the output. Structured sparsity regularization methods generalize and extend sparsity regularization methods, by allowing for optimal selection over structures like groups or networks of input variables in X {\displaystyle X} . Common motivation for the use of structured sparsity methods are model interpretability, high-dimensional learning (where dimensionality of X {\displaystyle X} may be higher than the number of observations n {\displaystyle n} ), and reduction of computational complexity. Moreover, structured sparsity methods allow to incorporate prior assumptions on the structure of the input variables, such as overlapping groups, non-overlapping groups, and acyclic graphs. Examples of uses of structured sparsity methods include face recognition, magnetic resonance image (MRI) processing, socio-linguistic analysis in natural language processing, and analysis of genetic expression in breast cancer. == Definition and related concepts == === Sparsity regularization === Consider the linear kernel regularized empirical risk minimization problem with a loss function V ( y i , f ( x ) ) {\displaystyle V(y_{i},f(x))} and the ℓ 0 {\displaystyle \ell _{0}} "norm" as the regularization penalty: min w ∈ R d 1 n ∑ i = 1 n V ( y i , ⟨ w , x i ⟩ ) + λ ‖ w ‖ 0 , {\displaystyle \min _{w\in \mathbb {R} ^{d}}{\frac {1}{n}}\sum _{i=1}^{n}V(y_{i},\langle w,x_{i}\rangle )+\lambda \|w\|_{0},} where x , w ∈ R d {\displaystyle x,w\in \mathbb {R^{d}} } , and ‖ w ‖ 0 {\displaystyle \|w\|_{0}} denotes the ℓ 0 {\displaystyle \ell _{0}} "norm", defined as the number of nonzero entries of the vector w {\displaystyle w} . f ( x ) = ⟨ w , x i ⟩ {\displaystyle f(x)=\langle w,x_{i}\rangle } is said to be sparse if ‖ w ‖ 0 = s < d {\displaystyle \|w\|_{0}=s 0 {\displaystyle w_{j}>0} . However, as in this case groups may overlap, we take the intersection of the complements of those groups that are not set to zero. This intersection of complements selection criteria implies the modeling choice that we allow some coefficients within a particular group g {\displaystyle g} to be set to zero, while others within the same group g {\displaystyle g} may remain positive. In other words, coefficients within a group may differ depending on the several group memberships that each variable within the group may have. ==== Union of groups: latent group Lasso ==== A different approach is to consider union of groups for variable selection. This approach captures the modeling situation where variables can be selected as long as they belong at least to one group with positive coefficients. This modeling perspective implies that we want to preserve group structure. The formulation of the union of groups approach is also referred to as latent group Lasso, and requires to modify the group ℓ 2 {\displaystyle \ell _{2}} norm considered above and introduce the following regularizer R ( w ) = i n f { ∑ g ‖ w g ‖ g : w = ∑ g = 1 G w ¯ g } {\displaystyle R(w)=inf\left\{\sum _{g}\|w_{g}\|_{g}:w=\sum _{g=1}^{G}{\bar {w}}_{g}\right\}} where w ∈ R d {\displaystyle w\in {\mathbb {R^{d}} }} , w g ∈ G g {\displaystyle w_{g}\in G_{g}} is the vector of coefficients of group g, and w ¯ g ∈ R d {\displaystyle {\bar {w}}_{g}\in {\mathbb {R^{d}} }} is a vector with coefficients w g j {\displaystyle w_{g}^{j}} for all variables j {

Markov partition

A Markov partition in mathematics is a tool used in dynamical systems theory, allowing the methods of symbolic dynamics to be applied to the study of hyperbolic dynamics. By using a Markov partition, the system can be made to resemble a discrete-time Markov process, with the long-term dynamical characteristics of the system represented as a Markov shift. The appellation 'Markov' is appropriate because the resulting dynamics of the system obeys the Markov property. The Markov partition thus allows standard techniques from symbolic dynamics to be applied, including the computation of expectation values, correlations, topological entropy, topological zeta functions, Fredholm determinants and the like. == Motivation == Let ( M , φ ) {\displaystyle (M,\varphi )} be a discrete dynamical system. A basic method of studying its dynamics is to find a symbolic representation: a faithful encoding of the points of M {\displaystyle M} by sequences of symbols such that the map φ {\displaystyle \varphi } becomes the shift map. Suppose that M {\displaystyle M} has been divided into a number of pieces E 1 , E 2 , … , E r {\displaystyle E_{1},E_{2},\ldots ,E_{r}} which are thought to be as small and localized, with virtually no overlaps. The behavior of a point x {\displaystyle x} under the iterates of φ {\displaystyle \varphi } can be tracked by recording, for each n {\displaystyle n} , the part E i {\displaystyle E_{i}} which contains φ n ( x ) {\displaystyle \varphi ^{n}(x)} . This results in an infinite sequence on the alphabet { 1 , 2 , … , r } {\displaystyle \{1,2,\ldots ,r\}} which encodes the point. In general, this encoding may be imprecise (the same sequence may represent many different points) and the set of sequences which arise in this way may be difficult to describe. Under certain conditions, which are made explicit in the rigorous definition of a Markov partition, the assignment of the sequence to a point of M {\displaystyle M} becomes an almost one-to-one map whose image is a symbolic dynamical system of a special kind called a shift of finite type. In this case, the symbolic representation is a powerful tool for investigating the properties of the dynamical system ( M , φ ) {\displaystyle (M,\varphi )} . == Formal definition == A Markov partition is a finite cover of the invariant set of the manifold by a set of curvilinear rectangles { E 1 , E 2 , … , E r } {\displaystyle \{E_{1},E_{2},\ldots ,E_{r}\}} such that For any pair of points x , y ∈ E i {\displaystyle x,y\in E_{i}} , that W s ( x ) ∩ W u ( y ) ∈ E i {\displaystyle W_{s}(x)\cap W_{u}(y)\in E_{i}} Int ⁡ E i ∩ Int ⁡ E j = ∅ {\displaystyle \operatorname {Int} E_{i}\cap \operatorname {Int} E_{j}=\emptyset } for i ≠ j {\displaystyle i\neq j} If x ∈ Int ⁡ E i {\displaystyle x\in \operatorname {Int} E_{i}} and φ ( x ) ∈ Int ⁡ E j {\displaystyle \varphi (x)\in \operatorname {Int} E_{j}} , then φ [ W u ( x ) ∩ E i ] ⊃ W u ( φ x ) ∩ E j {\displaystyle \varphi \left[W_{u}(x)\cap E_{i}\right]\supset W_{u}(\varphi x)\cap E_{j}} φ [ W s ( x ) ∩ E i ] ⊂ W s ( φ x ) ∩ E j {\displaystyle \varphi \left[W_{s}(x)\cap E_{i}\right]\subset W_{s}(\varphi x)\cap E_{j}} Here, W u ( x ) {\displaystyle W_{u}(x)} and W s ( x ) {\displaystyle W_{s}(x)} are the unstable and stable manifolds of x, respectively, and Int ⁡ E i {\displaystyle \operatorname {Int} E_{i}} simply denotes the interior of E i {\displaystyle E_{i}} . These last two conditions can be understood as a statement of the Markov property for the symbolic dynamics; that is, the movement of a trajectory from one open cover to the next is determined only by the most recent cover, and not the history of the system. It is this property of the covering that merits the 'Markov' appellation. The resulting dynamics is that of a Markov shift; that this is indeed the case is due to theorems by Yakov Sinai (1968) and Rufus Bowen (1975), thus putting symbolic dynamics on a firm footing. Variants of the definition are found, corresponding to conditions on the geometry of the pieces E i {\displaystyle E_{i}} . == Examples == Markov partitions have been constructed in several situations. Anosov diffeomorphisms of the torus. Dynamical billiards, in which case the covering is countable. Markov partitions make homoclinic and heteroclinic orbits particularly easy to describe. The system ( [ 0 , 1 ) , x ↦ 2 x m o d 1 ) {\displaystyle ([0,1),x\mapsto 2x\ mod\ 1)} has the Markov partition E 0 = ( 0 , 1 / 2 ) , E 1 = ( 1 / 2 , 1 ) {\displaystyle E_{0}=(0,1/2),E_{1}=(1/2,1)} , and in this case the symbolic representation of a real number in [ 0 , 1 ) {\displaystyle [0,1)} is its binary expansion. For example: x ∈ E 0 , T x ∈ E 1 , T 2 x ∈ E 1 , T 3 x ∈ E 1 , T 4 x ∈ E 0 ⇒ x = ( 0.01110... ) 2 {\displaystyle x\in E_{0},Tx\in E_{1},T^{2}x\in E_{1},T^{3}x\in E_{1},T^{4}x\in E_{0}\Rightarrow x=(0.01110...)_{2}} . The assignment of points of [ 0 , 1 ) {\displaystyle [0,1)} to their sequences in the Markov partition is well defined except on the dyadic rationals - morally speaking, this is because ( 0.01111 … ) 2 = ( 0.10000 … ) 2 {\displaystyle (0.01111\dots )_{2}=(0.10000\dots )_{2}} , in the same way as 1 = 0.999 … {\displaystyle 1=0.999\dots } in decimal expansions.

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