Real-Time UML (RTUML) refers to the application of the Unified Modelling Language (UML) for the analysis, design, and implementation of real-time and embedded systems, where timing constraints, concurrency, and resource management are critical. It extends standard UML with profiles, notations, and semantics to handle hard and soft real-time requirements, such as modelling predictable response times and fault tolerance. RTUML is not a separate language but a methodology leveraging UML diagrams (e.g., statecharts, sequence diagrams) for time-sensitive applications like automotive controls, avionics, and medical devices. The term is closely associated with Bruce Powel Douglass, who popularised it through his books and the Harmony process for embedded software development. As of 2025, RTUML remains relevant in industries requiring certified systems, though its adoption varies with agile methodologies and model-driven engineering tools. == Background == Real-Time UML emerged in the late 1990s as UML was standardized by the Object Management Group (OMG) in 1997, addressing the need for object-oriented modeling in real-time systems previously dominated by procedural languages like C. Traditional real-time development relied on "bare metal" programming or theoretical models, but RTUML introduced visual notations for object structure, behaviour, and timing. Bruce Powel Douglass’s 1999 book, Real-Time UML: Developing Efficient Objects for Embedded Systems, formalised the approach, emphasising statecharts for concurrency and timing constraints. Later editions (2004, 2006) incorporated UML 2.0 features like activity and timing diagrams, aligning with OMG’s Real-Time Profile (now part of MARTE—Modelling and Analysis of Real-Time and Embedded Systems). The Harmony process integrates RTUML with executable models for simulation and code generation. RTUML addresses hard real-time systems (e.g., strict deadlines in avionics) versus soft real-time (e.g., media streaming), using UML extensions for schedulability analysis. == Key concepts == RTUML adapts UML diagrams and techniques for real-time needs: Statecharts and Behaviour Modelling: Extended state machines model reactive behaviour, using and-states for concurrency, pseudostates for transitions, and timing constraints (e.g., {duration < 10ms}). Examples include cardiac pacemaker models. Sequence and Interaction Diagrams: Capture message timing, priorities, and resource allocation in multi-threaded systems. Architectural Patterns: Define logical and physical architectures with active objects for concurrency and patterns like observer or publisher-subscriber. Timing and Constraints: Use Object Constraint Language (OCL) for specifying deadlines and priorities. Profiles and Extensions: OMG’s UML Profile for Schedulability, Performance, and Time (SPT) and MARTE add stereotypes like RT::ActiveObject. These support iterative development, from requirements to deployment, often with tools like IBM Rhapsody or Enterprise Architect. == Applications == RTUML is used in: Embedded Systems: Modelling automotive ECUs or UAV controls. Avionics and Defence: DO-178C-compliant designs for fault tolerance. Medical Devices: Pacemakers or ventilators with precise timing. Industrial Automation: RTOS task visualisation via sequence diagrams. Tools like IBM Rhapsody support RTUML for model-based development and code generation in C/C++. == Criticism and adoption == RTUML’s complexity can overwhelm simple systems, and its use in agile environments is limited, where lightweight diagrams are preferred. Surveys indicate UML (including RTUML) is used in 30–50% of embedded projects, often for documentation rather than full model-driven engineering. It remains standard in academia and certified industries like aerospace.
Spanish Network of Excellence on Cybersecurity Research
The Spanish Network of Excellence on Cybersecurity Research (RENIC), is a research initiative to promote cybersecurity interests in Spain. == Members == === Board of Directors (2018) === President: Universidad de Málaga Vice president: CSIC Treasurer: Universidad Politécnica de Madrid Secretary: Universidad de Granada Vocals: Tecnalia, Universidad de La Laguna and Universidad de Modragón === Board of Directors (2016) === President: Universidad Carlos III de Madrid Vice president: Universidad Politécnica de Madrid Treasurer: Universidad de Granada Secretary: Universidad de León Vocals: Gradiant, Tecnalia, Universidad de Málaga === Founding Members === Centro Andaluz de Innovación y Tecnologías de la Información y las Comunicaciones (CITIC). Consejo Superior de Investigaciones Científicas (CSIC). Centro Tecnolóxico de Telecomunicaciones de Galicia (Gradiant). Instituto Imdea Software. Instituto Nacional de Ciberseguridad (INCIBE). Mondragón Unibertsitatea. Tecnalia. Universidad Carlos III de Madrid. Universidad Castilla la Mancha. Universidad de Granada. Universidad de la Laguna. Universidad de León. Universidad de Málaga. Universidad de Murcia. Universidad de Vigo. Universidad Internacional de la Rioja. Universidad Politécnica de Madrid. Universidad Rey Juan Carlos. === Members === Consejo Superior de Investigaciones Científicas (CSIC). Centro Tecnolóxico de Telecomunicaciones de Galicia (Gradiant). Instituto Imdea Software. Instituto Nacional de Ciberseguridad (INCIBE). Mondragón Unibertsitatea. Tecnalia. Universidad Carlos III de Madrid. Universidad de Castilla-La Mancha. Universidad de Granada. Universidad de la Laguna. Universidad de León. Universidad de Málaga. Universidad de Murcia. Universidad de Vigo. Universidad Politécnica de Madrid. Universidad Rey Juan Carlos. Universitat Oberta de Catalunya. IKERLAN. === Honorary Members === Centre for the Development of Industrial Technology (CDTI). (2017) Instituto Nacional de Ciberseguridad (INCIBE). (2016) == Initiatives and Participations == RENIC is ECSO member, and is also a member of its board of directors. A collaboration agreement between RENIC and the Innovative Business Cluster on Cybersecurity (AEI Cybersecurity) has been signed. RENIC is pleased to sponsor the Cybersecurity Research National Conferences (JNIC) JNIC2017 edition, organized by Universidad Rey Juan Carlos. RENIC is pleased to announce the publication of the online version of the Catalog and knowledge map of cybersecurity research
SQL/PSM
SQL/PSM (SQL/Persistent Stored Modules) is an ISO standard mainly defining an extension of SQL with a procedural language for use in stored procedures. Initially published in 1996 as an extension of SQL-92 (ISO/IEC 9075-4:1996, a version sometimes called PSM-96 or even SQL-92/PSM), SQL/PSM was later incorporated into the multi-part SQL:1999 standard, and has been part 4 of that standard since then, most recently in SQL:2023. The SQL:1999 part 4 covered less than the original PSM-96 because the SQL statements for defining, managing, and invoking routines were actually incorporated into part 2 SQL/Foundation, leaving only the procedural language itself as SQL/PSM. The SQL/PSM facilities are still optional as far as the SQL standard is concerned; most of them are grouped in Features P001-P008. SQL/PSM standardizes syntax and semantics for control flow, exception handling (called "condition handling" in SQL/PSM), local variables, assignment of expressions to variables and parameters, and (procedural) use of cursors. It also defines an information schema (metadata) for stored procedures. SQL/PSM is one language in which methods for the SQL:1999 structured types can be defined. The other is Java, via SQL/JRT. SQL/PSM is derived, seemingly directly, from Oracle's PL/SQL. Oracle developed PL/SQL and released it in 1991, basing the language on the US Department of Defense's Ada programming language. However, Oracle has maintained a distance from the standard in its documentation. IBM's SQL PL (used in DB2) and Mimer SQL's PSM were the first two products officially implementing SQL/PSM. It is commonly thought that these two languages, and perhaps also MySQL/MariaDB's procedural language, are closest to the SQL/PSM standard. However, a PostgreSQL addon implements SQL/PSM (alongside its other procedural languages like the PL/SQL-derived plpgsql), although it is not part of the core product. RDF functionality in OpenLink Virtuoso was developed entirely through SQL/PSM, combined with custom datatypes (e.g., ANY for handling URI and Literal relation objects), sophisticated indexing, and flexible physical storage choices (column-wise or row-wise).
List of information schools
This list of information schools, sometimes abbreviated to iSchools, includes members of the iSchools organization. The iSchools organization reflects a consortium of over 130 information schools across the globe. == History == The first iSchools Caucus was formed in 1988 by Syracuse, Pittsburgh, and Drexel and was called the Gang of Three (sometimes gang of four with Rutgers). Syracuse renamed the School of Library Science as the School of Information Studies in 1974, and is considered as the first “iSchool” in history. The group was formally named "the iSchools Caucus" or more casually, the iCaucus. By 2003, the group expanded to include the Universities of Michigan, Washington, Illinois, UNC, Florida State, Indiana, and Texas, and was called the Gang of Ten. The current iSchools Caucus organization was formalized by 2005, with additions of UC Berkeley, UC Irvine, UCLA, Penn State, Georgia Tech, Maryland, Toronto, Carnegie Mellon and Singapore Management University. == iSchools organization == The iSchools promote an interdisciplinary approach to understanding the opportunities and challenges of information management, with a core commitment to concepts like universal access and user-centered organization of information. The field is concerned broadly with questions of design and preservation across information spaces, from digital and virtual spaces such as online communities, social networking, the World Wide Web, and databases to physical spaces such as libraries, museums, collections, and other repositories. "School of Information", "Department of Information Studies", or "Information Department" are often the names of the participating organizations. Degree programs at iSchools include course offerings in areas such as information architecture, design, policy, and economics; knowledge management, user experience design, and usability; preservation and conservation; librarianship and library administration; the sociology of information; and human-computer interaction and computer science. === Leadership === The executive committee of the iSchools is made up of the current chair (Ina Fourie, University of Pretoria, South Africa), past chair (Gillian Oliver, Monash University, Australia) and the chair elect (Javed Mostafa, University of Toronto Canada), plus representatives from the three regions (North America, Europe, and Asia-Pacific). The current executive director is Slava Sterzer. == Member institutions == Between 2010 and 2026, the organization expanded globally beyond North America, growing to 133 member schools as of March 2026. For an updated and complete list of member schools, please visit the member database of the iSchools. == iConferences == Members of the iSchools organize a regular academic conference, known as the iConference, hosted by a different member institution each year. September 2005: Pennsylvania State University October 2006: University of Michigan February 2008: University of California, Los Angeles February 2009: University of North Carolina February 2010: University of Illinois at Urbana-Champaign February 2011: University of Washington, Seattle February 2012: University of Toronto February 2013: University of North Texas March 2014: Humboldt-Universität zu Berlin March 2015: University of California, Irvine March 2016: Drexel University March 2017: Wuhan University March 2018: University of Sheffield and Northumbria University March 2019: University of Maryland March 2020: University of Borås (virtual only) March 2021: Renmin University of China (virtual only) February/March 2022: University of Texas at Austin, University College Dublin & Kyushu University (virtual only) March 2023: Universitat Oberta de Catalunya March 2024: Jilin University March 2025: Indiana University March/April 2026: Edinburgh Napier University 2027: Victoria University of Wellington == Other schools of information == Other information schools and programs include: Documentation Research and Training Centre, Indian Statistical Institute, Bangalore San Jose State University, School of Information University of Southern California Library Science Degree Ankara University, Department of Information and Records Management, Ankara/Turkey Marmara University, Department of Information and Records Management, Istanbul/Turkey University of Kelaniya, Department of Library and Information Science, Kelaniya/Sri Lanka University of Colombo, National Institute of Library and Information Science (NILIS), Colombo/Sri Lanka Chicago State University, Department of Information Studies
Driver scheduling problem
The driver scheduling problem (DSP) is type of problem in operations research and theoretical computer science. The DSP consists of selecting a set of duties (assignments) for the drivers or pilots of vehicles (e.g., buses, trains, boats, or planes) involved in the transportation of passengers or goods, within the constraints of various legislative and logistical criteria. == Criteria and modelling == This very complex problem involves several constraints related to labour and company rules and also different evaluation criteria and objectives. Being able to solve this problem efficiently can have a great impact on costs and quality of service for public transportation companies. There is a large number of different rules that a feasible duty might be required to satisfy, such as Minimum and maximum stretch duration Minimum and maximum break duration Minimum and maximum work duration Minimum and maximum total duration Maximum extra work duration Maximum number of vehicle changes Minimum driving duration of a particular vehicle Operations research has provided optimization models and algorithms that lead to efficient solutions for this problem. Among the most common models proposed to solve the DSP are the Set Covering and Set Partitioning Models (SPP/SCP). In the SPP model, each work piece (task) is covered by only one duty. In the SCP model, it is possible to have more than one duty covering a given work piece. In both models, the set of work pieces that needs to be covered is laid out in rows, and the set of previously defined feasible duties available for covering specific work pieces is arranged in columns. The DSP resolution, based on either of these models, is the selection of the set of feasible duties that guarantees that there is one (SPP) or more (SCP) duties covering each work piece while minimizing the total cost of the final schedule.
Description logic
Description logics (DL) are a family of formal knowledge representation languages. Many DLs are more expressive than propositional logic but less expressive than first-order logic. In contrast to the latter, the core reasoning problems for DLs are (usually) decidable, and efficient decision procedures have been designed and implemented for these problems. There are general, spatial, temporal, spatiotemporal, and fuzzy description logics, and each description logic features a different balance between expressive power and reasoning complexity by supporting different sets of mathematical constructors. DLs are used in artificial intelligence to describe and reason about the relevant concepts of an application domain (known as terminological knowledge). It is of particular importance in providing a logical formalism for ontologies and the Semantic Web: the Web Ontology Language (OWL) and its profiles are based on DLs. A major area of application of DLs and OWL is in biomedical informatics, where they assist in the codification of biomedical knowledge. DLs and OWL are also applied in other domains, including defense, climate modeling, and large-scale industrial knowledge graphs. == Introduction == A DL models concepts, roles and individuals, and their relationships. The fundamental modeling concept of a DL is the axiom—a logical statement relating roles and/or concepts. This is a key difference from the frames paradigm where a frame specification declares and completely defines a class. == Nomenclature == === Terminology compared to FOL and OWL === The description logic community uses different terminology than the first-order logic (FOL) community for operationally equivalent notions; some examples are given below. The Web Ontology Language (OWL) uses again a different terminology, also given in the table below. === Naming convention === There are many varieties of description logics and there is an informal naming convention, roughly describing the operators allowed. The expressivity is encoded in the label for a logic starting with one of the following basic logics: Followed by any of the following extensions: ==== Exceptions ==== Some canonical DLs that do not exactly fit this convention are: ==== Examples ==== As an example, A L C {\displaystyle {\mathcal {ALC}}} is a centrally important description logic from which comparisons with other varieties can be made. A L C {\displaystyle {\mathcal {ALC}}} is simply A L {\displaystyle {\mathcal {AL}}} with complement of any concept allowed, not just atomic concepts. A L C {\displaystyle {\mathcal {ALC}}} is used instead of the equivalent A L U E {\displaystyle {\mathcal {ALUE}}} . A further example, the description logic S H I Q {\displaystyle {\mathcal {SHIQ}}} is the logic A L C {\displaystyle {\mathcal {ALC}}} plus extended cardinality restrictions, and transitive and inverse roles. The naming conventions aren't purely systematic so that the logic A L C O I N {\displaystyle {\mathcal {ALCOIN}}} might be referred to as A L C N I O {\displaystyle {\mathcal {ALCNIO}}} and other abbreviations are also made where possible. The Protégé ontology editor supports S H O I N ( D ) {\displaystyle {\mathcal {SHOIN}}^{\mathcal {(D)}}} . Three major biomedical informatics terminology bases, SNOMED CT, GALEN, and GO, are expressible in E L {\displaystyle {\mathcal {EL}}} (with additional role properties). OWL 2 provides the expressiveness of S R O I Q ( D ) {\displaystyle {\mathcal {SROIQ}}^{\mathcal {(D)}}} , OWL-DL is based on S H O I N ( D ) {\displaystyle {\mathcal {SHOIN}}^{\mathcal {(D)}}} , and for OWL-Lite it is S H I F ( D ) {\displaystyle {\mathcal {SHIF}}^{\mathcal {(D)}}} . == History == Description logic was given its current name in the 1980s. Previous to this it was called (chronologically): terminological systems, and concept languages. === Knowledge representation === Frames and semantic networks lack formal (logic-based) semantics. DL was first introduced into knowledge representation (KR) systems to overcome this deficiency. The first DL-based KR system was KL-ONE (by Ronald J. Brachman and Schmolze, 1985). During the '80s other DL-based systems using structural subsumption algorithms were developed including KRYPTON (1983), LOOM (1987), BACK (1988), K-REP (1991) and CLASSIC (1991). This approach featured DL with limited expressiveness but relatively efficient (polynomial time) reasoning. In the early '90s, the introduction of a new tableau based algorithm paradigm allowed efficient reasoning on more expressive DL. DL-based systems using these algorithms — such as KRIS (1991) — show acceptable reasoning performance on typical inference problems even though the worst case complexity is no longer polynomial. From the mid '90s, reasoners were created with good practical performance on very expressive DL with high worst case complexity. Examples from this period include FaCT, RACER (2001), CEL (2005), and KAON 2 (2005). DL reasoners, such as FaCT, FaCT++, RACER, DLP and Pellet, implement the method of analytic tableaux. KAON2 is implemented by algorithms which reduce a SHIQ(D) knowledge base to a disjunctive datalog program. === Semantic web === The DARPA Agent Markup Language (DAML) and Ontology Inference Layer (OIL) ontology languages for the Semantic Web can be viewed as syntactic variants of DL. In particular, the formal semantics and reasoning in OIL use the S H I Q {\displaystyle {\mathcal {SHIQ}}} DL. The DAML+OIL DL was developed as a submission to—and formed the starting point of—the World Wide Web Consortium (W3C) Web Ontology Working Group. In 2004, the Web Ontology Working Group completed its work by issuing the OWL recommendation. The design of OWL is based on the S H {\displaystyle {\mathcal {SH}}} family of DL with OWL DL and OWL Lite based on S H O I N ( D ) {\displaystyle {\mathcal {SHOIN}}^{\mathcal {(D)}}} and S H I F ( D ) {\displaystyle {\mathcal {SHIF}}^{\mathcal {(D)}}} respectively. The W3C OWL Working Group began work in 2007 on a refinement of - and extension to - OWL. In 2009, this was completed by the issuance of the OWL2 recommendation. OWL2 is based on the description logic S R O I Q ( D ) {\displaystyle {\mathcal {SROIQ}}^{\mathcal {(D)}}} . Practical experience demonstrated that OWL DL lacked several key features necessary to model complex domains. == Modeling == === TBox vs Abox === In DL, a distinction is drawn between the so-called TBox (terminological box) and the ABox (assertional box). In general, the TBox contains sentences describing concept hierarchies (i.e., relations between concepts) while the ABox contains ground sentences stating where in the hierarchy, individuals belong (i.e., relations between individuals and concepts). For example, the statement: belongs in the TBox, while the statement: belongs in the ABox. Note that the TBox/ABox distinction is not significant, in the same sense that the two "kinds" of sentences are not treated differently in first-order logic (which subsumes most DL). When translated into first-order logic, a subsumption axiom like (1) is simply a conditional restriction to unary predicates (concepts) with only variables appearing in it. Clearly, a sentence of this form is not privileged or special over sentences in which only constants ("grounded" values) appear like (2). === Motivation for having Tbox and Abox === So why was the distinction introduced? The primary reason is that the separation can be useful when describing and formulating decision-procedures for various DL. For example, a reasoner might process the TBox and ABox separately, in part because certain key inference problems are tied to one but not the other one ('classification' is related to the TBox, 'instance checking' to the ABox). Another example is that the complexity of the TBox can greatly affect the performance of a given decision-procedure for a certain DL, independently of the ABox. Thus, it is useful to have a way to talk about that specific part of the knowledge base. The secondary reason is that the distinction can make sense from the knowledge base modeler's perspective. It is plausible to distinguish between our conception of terms/concepts in the world (class axioms in the TBox) and particular manifestations of those terms/concepts (instance assertions in the ABox). In the above example: when the hierarchy within a company is the same in every branch but the assignment to employees is different in every department (because there are other people working there), it makes sense to reuse the TBox for different branches that do not use the same ABox. There are two features of description logic that are not shared by most other data description formalisms: DL does not make the unique name assumption (UNA) or the closed-world assumption (CWA). Not having UNA means that two concepts with different names may be allowed by some inference to be shown to be equivalent. Not having CWA, or rather having the open world assumption (OWA) means that
TurboQuant
TurboQuant is an online vector quantization algorithm for compressing high-dimensional Euclidean vectors while preserving their geometric structure. It was proposed in 2025 by Amir Zandieh, Majid Daliri, Majid Hadian, and Vahab Mirrokni in the paper TurboQuant: Online Vector Quantization with Near-optimal Distortion Rate. The paper lists Zandieh and Mirrokni as affiliated with Google Research, Daliri with New York University, and Hadian with Google DeepMind. The method was developed for applications including large language model (LLM) inference, key–value (KV) cache compression, vector databases, and nearest neighbor search. TurboQuant consists of two related algorithms: TurboQuantmse, which is optimized for mean squared error (MSE), and TurboQuantprod, which is optimized for unbiased inner product estimation. The algorithm uses a random rotation of input vectors, applies scalar quantizers to the rotated coordinates, and, for inner-product estimation, applies a one-bit Quantized Johnson–Lindenstrauss (QJL) transform to the residual error. == Background == Vector quantization is a compression method that maps high-dimensional vectors to a finite set of codewords. The problem has roots in Shannon's source coding theory and rate–distortion theory. In machine learning and information retrieval, vector quantization is used to reduce the memory required to store embeddings, activation vectors, and other numerical representations. In Transformer-based large language models, the KV cache stores key and value vectors from previous tokens during autoregressive decoding. The size of this cache grows with context length, the number of attention heads, and the number of concurrent requests, making it a major memory bottleneck in LLM serving. Similar compression problems appear in vector search, where large collections of embedding vectors must be stored and searched efficiently. Earlier approaches to vector quantization include product quantization, scalar quantization, and data-dependent k-means codebook construction. The TurboQuant paper argues that many existing methods either require offline preprocessing and calibration or suffer from suboptimal distortion guarantees in online settings. == Algorithm == === TurboQuantmse === TurboQuantmse is the version of the algorithm optimized for mean-squared error. For a unit vector x ∈ S d − 1 {\displaystyle x\in S^{d-1}} , the algorithm first applies a random rotation matrix Π ∈ R d × d {\displaystyle \Pi \in \mathbb {R} ^{d\times d}} and sets z = Π x {\displaystyle z=\Pi x} . Each coordinate of the rotated vector follows a shifted and scaled beta distribution, which converges to a normal distribution in high dimensions. In high dimensions, distinct coordinates also become nearly independent, allowing the algorithm to apply scalar quantizers independently to each coordinate. The scalar quantizer is constructed by solving a one-dimensional continuous k-means or Lloyd–Max quantization problem. If the centroids are c 1 , c 2 , … , c 2 b {\displaystyle c_{1},c_{2},\ldots ,c_{2^{b}}} , the quantization step stores, for each coordinate, i d x j = a r g m i n k ∈ [ 2 b ] | z j − c k | . {\displaystyle \mathrm {idx} _{j}=\operatorname {} {arg\,min}_{k\in [2^{b}]}|z_{j}-c_{k}|.} During dequantization, the stored index for each coordinate is replaced by the corresponding centroid, giving a reconstructed rotated vector z ~ {\displaystyle {\tilde {z}}} . The algorithm then rotates back: x ~ = Π ⊤ z ~ . {\displaystyle {\tilde {x}}=\Pi ^{\top }{\tilde {z}}.} The paper gives the following bound for TurboQuantmse: D m s e ≤ 3 π 2 ⋅ 1 4 b . {\displaystyle D_{\mathrm {mse} }\leq {\frac {\sqrt {3\pi }}{2}}\cdot {\frac {1}{4^{b}}}.} It also reports finer-grained MSE values of approximately 0.36, 0.117, 0.03, and 0.009 for bit-widths b = 1 , 2 , 3 , 4 {\displaystyle b=1,2,3,4} , respectively. === TurboQuantprod === TurboQuantprod is optimized for unbiased inner-product estimation. The authors note that an MSE-optimized quantizer may introduce bias when used to estimate inner products. To address this, TurboQuantprod first applies TurboQuantmse with bit-width b − 1 {\displaystyle b-1} , then applies a one-bit Quantized Johnson–Lindenstrauss transform to the remaining residual vector. Let r = x − Q m s e − 1 ( Q m s e ( x ) ) {\displaystyle r=x-Q_{\mathrm {mse} }^{-1}(Q_{\mathrm {mse} }(x))} be the residual after MSE quantization, and let γ = ‖ r ‖ 2 {\displaystyle \gamma =\|r\|_{2}} . The QJL step stores a sign vector for the residual. For γ ≠ 0 {\displaystyle \gamma \neq 0} , this can be written using the normalized residual u = r / γ {\displaystyle u=r/\gamma } : q j l = sign ( S u ) , {\displaystyle qjl=\operatorname {sign} (Su),} where S ∈ R d × d {\displaystyle S\in \mathbb {R} ^{d\times d}} is a random projection matrix. Since the sign function is invariant under positive rescaling, this is equivalent to sign ( S r ) {\displaystyle \operatorname {sign} (Sr)} when r ≠ 0 {\displaystyle r\neq 0} . If γ = 0 {\displaystyle \gamma =0} , the residual correction is zero. TurboQuantprod stores the MSE quantization, the QJL sign vector, and the residual norm: Q p r o d ( x ) = [ Q m s e ( x ) , q j l , γ ] . {\displaystyle Q_{\mathrm {prod} }(x)=\left[Q_{\mathrm {mse} }(x),qjl,\gamma \right].} The dequantized vector is reconstructed as x ~ = x ~ m s e + π / 2 d γ S ⊤ q j l . {\displaystyle {\tilde {x}}={\tilde {x}}_{\mathrm {mse} }+{\frac {\sqrt {\pi /2}}{d}}\,\gamma S^{\top }qjl.} The paper proves that TurboQuantprod is unbiased for inner-product estimation: E x ~ [ ⟨ y , x ~ ⟩ ] = ⟨ y , x ⟩ . {\displaystyle \mathbb {E} _{\tilde {x}}\left[\langle y,{\tilde {x}}\rangle \right]=\langle y,x\rangle .} It also gives the distortion bound D p r o d ≤ 3 π 2 ⋅ ‖ y ‖ 2 2 d ⋅ 1 4 b . {\displaystyle D_{\mathrm {prod} }\leq {\frac {\sqrt {3\pi }}{2}}\cdot {\frac {\|y\|_{2}^{2}}{d}}\cdot {\frac {1}{4^{b}}}.} == Performance and applications == The TurboQuant paper reports that the algorithm achieves near-optimal distortion rates within a small constant factor of information-theoretic lower bounds. The authors report that, for KV cache quantization, TurboQuant achieved quality neutrality at 3.5 bits per channel and marginal degradation at 2.5 bits per channel. In long-context LLM experiments using Llama 3.1 8B Instruct, the paper evaluated the method on a "needle-in-a-haystack" retrieval task with document lengths from 4,000 to 104,000 tokens. It reported that TurboQuant matched the uncompressed full-precision baseline while using more than 4× compression, and compared the method against PolarQuant, SnapKV, PyramidKV, and KIVI. Google Research stated that TurboQuant was evaluated on long-context benchmarks including LongBench, Needle in a Haystack, ZeroSCROLLS, RULER, and L-Eval using open-source models including Gemma and Mistral. According to a report in Tom's Hardware, Google described the method as reducing KV-cache memory by at least six times and achieving up to an eightfold improvement in attention-logit computation on Nvidia H100 GPUs compared with unquantized 32-bit keys. TurboQuant has also been applied to nearest-neighbor vector search. The original paper reports experiments on DBpedia entity embeddings and GloVe embeddings, comparing TurboQuant with product quantization and other vector-search quantization baselines. == Relationship to other methods == TurboQuant is related to several methods for efficient large language model inference and high-dimensional search: Product quantization – a vector quantization technique widely used for approximate nearest-neighbor search Quantization (machine learning) – reducing the numerical precision of weights, activations, or cached tensors in machine learning models PagedAttention – a memory-management algorithm for LLM serving that reduces fragmentation in the KV cache Johnson–Lindenstrauss lemma – a result in high-dimensional geometry used in random projection methods Lloyd's algorithm – an algorithm for scalar and vector quantization, including k-means-style codebook construction Unlike PagedAttention, which focuses on memory allocation and cache layout, TurboQuant reduces the numerical storage cost of the vectors themselves. Unlike many product-quantization methods, TurboQuant is designed to be data-oblivious and online, avoiding dataset-specific codebook training. == Limitations == The strongest performance claims for TurboQuant come from the original paper and Google Research's own publication. Coverage in technology media has noted that the broader impact of the method will depend on real-world implementation details, workloads, and hardware architectures.