Plane Finder is a United Kingdom-based real-time flight tracking service launched in 2009, that is able to show flight data globally. The data available includes flight numbers, how fast an aircraft is moving, its elevation and destination of travel. Several variants of the service are available as mobile apps including free, premium 3D and augmented reality versions. The flight tracking map and database can be accessed by web browsers. Plane Finder allows registered users to share their ADS-B and MLAT data via the Plane Finder ADS-B Client, available for macOS, Windows and Linux. Plane Finder supports VFR charts from NATS, and was the first major flight tracking app to introduce a replay feature, allowing users to replay flights dating back to 2011. == Flight tracking == Plane Finder collects data from its own global network of receivers, using the following sources. === Automatic dependent surveillance-broadcast (ADS-B) === A network of automatic dependent surveillance-broadcast (ADS-B) receivers gathers aircraft data such as callsign, position and speed. Plane Finder serves to supplement this data with additional information, including aircraft registration/tail number, departure airport, destination, artwork, and photographs. Plane Finder users can apply for an ADS-B receiver in exchange for their flight data. === Multilateration (MLAT) === To deliver aircraft position data where ADS-B is unavailable, Plane Finder uses multilateration (MLAT). Using three or more receivers running Plane Finder client software, monitoring the aircraft simultaneously, the aircraft’s position is calculated using receiver location and accurate timestamps. While European airspace is widely covered, only some parts of North American airspace are covered. === Federal Aviation Administration (FAA) feed === ADS-B is prevalent across Europe and Australia, but not in North America. Where MLAT or ADS-B data is unavailable, a feed from the Federal Aviation Administration provides flight information. The FAA feed covers United States and Canadian airspace, including bordering areas of the Atlantic and Pacific Oceans. === FLARM feed === Plane Finder collects data from a centralised FLARM feed, for monitoring small aircraft and gliders. == Flight data source == The Plane Finder website and database is widely used as an information source to support articles in the media. The Independent used Plane Finder flight tracking to demonstrate to readers the flight path of flight MT2706, which turned back as a result of last minute Egyptian government flight restrictions on 6 November 2015. The Independent also used Plane Finder information to demonstrate a timeline of the speed/altitude of flight 7K 9268, a Russian plane which crashed on 31 October 2015. The BBC cited Plane Finder in regard to the point at which at British Airways flight turned back to Heathrow Airport to make an emergency landing after smoke was seen coming from its engines. Plane Finder data has also been used to create original imagery for the media, such as the Washington Post, which used Plane Finder as a source to show flight patterns immediately after the Brussels bombings in March 2016.
Speculative decoding
Speculative decoding is an inference-time optimization for autoregressive large language models (LLMs) that generates multiple tokens per decoding step instead of one. A smaller draft model proposes a sequence of candidate tokens, and the larger target model verifies them in a single forward pass through a modified rejection sampling scheme. The verification preserves the target model's original output distribution, so the technique produces the same results as standard decoding while cutting latency by roughly two to three times. The name is an analogy to speculative execution in CPU design, where a processor runs instructions along a predicted branch before the outcome is known. == Background == Standard autoregressive decoding in large language models generates one token at a time. The model computes a probability distribution over its vocabulary, samples the next token, and feeds that token back as input. For large models, this process is bottlenecked by memory bandwidth rather than arithmetic throughput: loading the model's parameters from high-bandwidth memory (HBM) to the processor takes up most of the wall-clock time at each step. Because of this, a forward pass over one token and a forward pass over several tokens in a batch take roughly the same time. Speculative decoding relies on this property. == Mechanism == The technique alternates between two phases: drafting and verification. During drafting, a fast approximation model generates a short run of K candidate tokens, typically between 3 and 12. The draft model is usually a much smaller version of the target model or a lightweight auxiliary network. During verification, the target model scores the entire draft sequence in one batched forward pass. A modified rejection sampling algorithm compares the draft and target probabilities at each position. If the target model would have been at least as likely to produce a given token, that token is accepted; the first token that fails is resampled from a corrected distribution, and everything after it is thrown out. The result is that the output distribution is the same as if each token had been generated one at a time. How many tokens get accepted per cycle depends on how well the draft model matches the target. For common words and predictable continuations the match tends to be good, so the target model can confirm several tokens at once. == History == An early precursor was blockwise parallel decoding, proposed in 2018 by Stern, Shazeer, and Uszkoreit. Their method predicted multiple future tokens through auxiliary prediction heads and validated them against the autoregressive model, but it only worked with greedy decoding and did not preserve the full sampling distribution. The modern form of the technique came from Yaniv Leviathan, Matan Kalman, and Yossi Matias at Google Research, who posted "Fast Inference from Transformers via Speculative Decoding" on arXiv in November 2022. Separately and at about the same time, Charlie Chen and colleagues at DeepMind arrived at a closely related method they called speculative sampling, published in February 2023. Both papers introduced the use of rejection sampling to guarantee that the output distribution is unchanged. Leviathan et al. showed roughly 2–3x speedup on T5-XXL (11 billion parameters); Chen et al. reported 2–2.5x on the Chinchilla model (70 billion parameters). The Leviathan et al. paper was presented as an oral at the International Conference on Machine Learning in July 2023. == Variants == SpecInfer (Miao et al., 2024) uses multiple small language models to jointly build a tree of candidate continuations rather than a single chain. The target model verifies the whole tree in parallel and keeps the longest valid path, with reported speedups of 1.5–3.5x. Medusa (Cai et al., 2024) takes a different approach by not using a separate draft model at all. Extra lightweight decoding heads are attached to the target model itself, and each one predicts a token at a different future position. The candidates are evaluated through a tree-structured attention mechanism. The authors measured 2.2–3.6x speedup. EAGLE (Li et al., 2024) performs autoregression on the target model's internal feature representations (specifically the second-to-top layer) rather than on tokens directly. On LLaMA 2 Chat 70B, this gave a 2.7–3.5x latency reduction. Later versions added dynamic draft trees (EAGLE-2) and further optimizations (EAGLE-3), reaching 3–6.5x speedup. == Adoption == By 2024, speculative decoding had become a standard part of production LLM serving. Google uses it in the AI Overviews feature of Google Search. Open-source inference frameworks such as vLLM, NVIDIA's TensorRT-LLM, and SGLang all include built-in support for speculative decoding and its variants. Apple, AWS, and Meta have also published research extending the method or deploying it at scale.
Tensor (machine learning)
In machine learning, the term tensor informally refers to two different concepts: (i) a way of organizing data and (ii) a multilinear (tensor) transformation. Data may be organized in a multidimensional array (M-way array), informally referred to as a "data tensor"; however, in the strict mathematical sense, a tensor is a multilinear mapping over a set of domain vector spaces to a range vector space. Observations, such as images, movies, volumes, sounds, and relationships among words and concepts, stored in an M-way array ("data tensor"), may be analyzed either by artificial neural networks or tensor methods. Tensor decomposition factors data tensors into smaller tensors. Operations on data tensors can be expressed in terms of matrix multiplication and the Kronecker product. The computation of gradients, a crucial aspect of backpropagation, can be performed using software libraries such as PyTorch and TensorFlow. Computations are often performed on graphics processing units (GPUs) using CUDA, and on dedicated hardware such as Google's Tensor Processing Unit or Nvidia's Tensor core. These developments have greatly accelerated neural network architectures, and increased the size and complexity of models that can be trained. == History == A tensor is by definition a multilinear map. In mathematics, this may express a multilinear relationship between sets of algebraic objects. In physics, tensor fields, considered as tensors at each point in space, are useful in expressing mechanics such as stress or elasticity. In machine learning, the exact use of tensors depends on the statistical approach being used. In 2001, the field of signal processing and statistics were making use of tensor methods. Pierre Comon surveys the early adoption of tensor methods in the fields of telecommunications, radio surveillance, chemometrics and sensor processing. Linear tensor rank methods (such as, Parafac/CANDECOMP) analyzed M-way arrays ("data tensors") composed of higher order statistics that were employed in blind source separation problems to compute a linear model of the data. He noted several early limitations in determining the tensor rank and efficient tensor rank decomposition. In the early 2000s, multilinear tensor methods crossed over into computer vision, computer graphics and machine learning with papers by Vasilescu or in collaboration with Terzopoulos, such as Human Motion Signatures, TensorFaces TensorTextures and Multilinear Projection. Multilinear algebra, the algebra of higher-order tensors, is a suitable and transparent framework for analyzing the multifactor structure of an ensemble of observations and for addressing the difficult problem of disentangling the causal factors based on second order or higher order statistics associated with each causal factor. Tensor (multilinear) factor analysis disentangles and reduces the influence of different causal factors with multilinear subspace learning. When treating an image or a video as a 2- or 3-way array, i.e., "data matrix/tensor", tensor methods reduce spatial or time redundancies as demonstrated by Wang and Ahuja. Yoshua Bengio, Geoff Hinton and their collaborators briefly discuss the relationship between deep neural networks and tensor factor analysis beyond the use of M-way arrays ("data tensors") as inputs. One of the early uses of tensors for neural networks appeared in natural language processing. A single word can be expressed as a vector via Word2vec. Thus a relationship between two words can be encoded in a matrix. However, for more complex relationships such as subject-object-verb, it is necessary to build higher-dimensional networks. In 2009, the work of Sutskever introduced Bayesian Clustered Tensor Factorization to model relational concepts while reducing the parameter space. From 2014 to 2015, tensor methods become more common in convolutional neural networks (CNNs). Tensor methods organize neural network weights in a "data tensor", analyze and reduce the number of neural network weights. Lebedev et al. accelerated CNN networks for character classification (the recognition of letters and digits in images) by using 4D kernel tensors. == Definition == Let F {\displaystyle \mathbb {F} } be a field (such as the real numbers R {\displaystyle \mathbb {R} } or the complex numbers C {\displaystyle \mathbb {C} } ). A tensor T ∈ F I 1 × I 2 × … × I C {\displaystyle {\mathcal {T}}\in {\mathbb {F} }^{I_{1}\times I_{2}\times \ldots \times I_{C}}} is a multilinear transformation from a set of domain vector spaces to a range vector space: T : { F I 1 × F I 2 × … F I C } ↦ F I 0 {\displaystyle {\mathcal {T}}:\{{\mathbb {F} }^{I_{1}}\times {\mathbb {F} }^{I_{2}}\times \ldots {\mathbb {F} }^{I_{C}}\}\mapsto {\mathbb {F} }^{I_{0}}} Here, C {\displaystyle C} and I 0 , I 1 , … , I C {\displaystyle I_{0},I_{1},\ldots ,I_{C}} are positive integers, and ( C + 1 ) {\displaystyle (C+1)} is the number of modes of a tensor (also known as the number of ways of a multi-way array). The dimensionality of mode c {\displaystyle c} is I c {\displaystyle I_{c}} , for 0 ≤ c ≤ C {\displaystyle 0\leq c\leq C} . In statistics and machine learning, an image is vectorized when viewed as a single observation, and a collection of vectorized images is organized as a "data tensor". For example, a set of facial images { d i p , i e , i l , i v ∈ R I X } {\displaystyle \{{\mathbb {d} }_{i_{p},i_{e},i_{l},i_{v}}\in {\mathbb {R} }^{I_{X}}\}} with I X {\displaystyle I_{X}} pixels that are the consequences of multiple causal factors, such as a facial geometry i p ( 1 ≤ i p ≤ I P ) {\displaystyle i_{p}(1\leq i_{p}\leq I_{P})} , an expression i e ( 1 ≤ i e ≤ I E ) {\displaystyle i_{e}(1\leq i_{e}\leq I_{E})} , an illumination condition i l ( 1 ≤ i l ≤ I L ) {\displaystyle i_{l}(1\leq i_{l}\leq I_{L})} , and a viewing condition i v ( 1 ≤ i v ≤ I V ) {\displaystyle i_{v}(1\leq i_{v}\leq I_{V})} may be organized into a data tensor (ie. multiway array) D ∈ R I X × I P × I E × I L × V {\displaystyle {\mathcal {D}}\in {\mathbb {R} }^{I_{X}\times I_{P}\times I_{E}\times I_{L}\times V}} where I P {\displaystyle I_{P}} are the total number of facial geometries, I E {\displaystyle I_{E}} are the total number of expressions, I L {\displaystyle I_{L}} are the total number of illumination conditions, and I V {\displaystyle I_{V}} are the total number of viewing conditions. Tensor factorizations methods such as TensorFaces and multilinear (tensor) independent component analysis factorizes the data tensor into a set of vector spaces that span the causal factor representations, where an image is the result of tensor transformation T {\displaystyle {\mathcal {T}}} that maps a set of causal factor representations to the pixel space. Another approach to using tensors in machine learning is to embed various data types directly. For example, a grayscale image, commonly represented as a discrete 2-way array D ∈ R I R X × I C X {\displaystyle {\mathbf {D} }\in {\mathbb {R} }^{I_{RX}\times I_{CX}}} with dimensionality I R X × I C X {\displaystyle I_{RX}\times I_{CX}} where I R X {\displaystyle I_{RX}} are the number of rows and I C X {\displaystyle I_{CX}} are the number of columns. When an image is treated as 2-way array or 2nd order tensor (i.e. as a collection of column/row observations), tensor factorization methods compute the image column space, the image row space and the normalized PCA coefficients or the ICA coefficients. Similarly, a color image with RGB channels, D ∈ R N × M × 3 . {\displaystyle {\mathcal {D}}\in \mathbb {R} ^{N\times M\times 3}.} may be viewed as a 3rd order data tensor or 3-way array.-------- In natural language processing, a word might be expressed as a vector v {\displaystyle v} via the Word2vec algorithm. Thus v {\displaystyle v} becomes a mode-1 tensor v ↦ A ∈ R N . {\displaystyle v\mapsto {\mathcal {A}}\in \mathbb {R} ^{N}.} The embedding of subject-object-verb semantics requires embedding relationships among three words. Because a word is itself a vector, subject-object-verb semantics could be expressed using mode-3 tensors v a × v b × v c ↦ A ∈ R N × N × N . {\displaystyle v_{a}\times v_{b}\times v_{c}\mapsto {\mathcal {A}}\in \mathbb {R} ^{N\times N\times N}.} In practice the neural network designer is primarily concerned with the specification of embeddings, the connection of tensor layers, and the operations performed on them in a network. Modern machine learning frameworks manage the optimization, tensor factorization and backpropagation automatically. === As unit values === Tensors may be used as the unit values of neural networks which extend the concept of scalar, vector and matrix values to multiple dimensions. The output value of single layer unit y m {\displaystyle y_{m}} is the sum-product of its input units and the connection weights filtered through the activation function f {\displaystyle f} : y m = f ( ∑ n x n u m , n ) , {\displaystyle y_{m}=f\left(\sum _{n}x_{n}u_{m,n}\right),} where y m ∈ R .
Pedagogical agent
A pedagogical agent is a concept borrowed from computer science and artificial intelligence and applied to education, usually as part of an intelligent tutoring system (ITS). It is a simulated human-like interface between the learner and the content, in an educational environment. A pedagogical agent is designed to model the type of interactions between a student and another person. Mabanza and de Wet define it as "a character enacted by a computer that interacts with the user in a socially engaging manner". A pedagogical agent can be assigned different roles in the learning environment, such as tutor or co-learner, depending on the desired purpose of the agent. "A tutor agent plays the role of a teacher, while a co-learner agent plays the role of a learning companion". == History == The history of Pedagogical Agents is closely aligned with the history of computer animation. As computer animation progressed, it was adopted by educators to enhance computerized learning by including a lifelike interface between the program and the learner. The first versions of a pedagogical agent were more cartoon than person, like Microsoft's Clippy which helped users of Microsoft Office load and use the program's features in 1997. However, with developments in computer animation, pedagogical agents can now look lifelike. By 2006 there was a call to develop modular, reusable agents to decrease the time and expertise required to create a pedagogical agent. There was also a call in 2009 to enact agent standards. The standardization and re-usability of pedagogical agents is less of an issue since the decrease in cost and widespread availability of animation tools. Individualized pedagogical agents can be found across disciplines including medicine, math, law, language learning, automotive, and armed forces. They are used in applications directed to every age, from preschool to adult. == Learning theories related to pedagogical agent design == === Distributed cognition theory === Distributed cognition theory is the method in which cognition progresses in the context of collaboration with others. Pedagogical agents can be designed to assist the cognitive transfer to the learner, operating as artifacts or partners with collaborative role in learning. To support the performance of an action by the user, the pedagogical agent can act as a cognitive tool as long as the agent is equipped with the knowledge that the user lacks. The interactions between the user and the pedagogical agent can facilitate a social relationship. The pedagogical agent may fulfill the role of a working partner. === Socio-cultural learning theory === Socio-cultural learning theory is how the user develops when they are involved in learning activities in which there is interaction with other agents. A pedagogical agent can: intervene when the user requests, provide support for tasks that the user cannot address, and potentially extend the learners cognitive reach. Interaction with the pedagogical agent may elicit a variety of emotions from the learner. The learner may become excited, confused, frustrated, and/or discouraged. These emotions affect the learners' motivation. === Extraneous Cognitive Load === Extraneous cognitive load is the extra effort being exerted by an individual's working memory due to the way information is being presented. A pedagogical agent can increase the user's cognitive load by distracting them and becoming the focus of their attention, causing split attention between the instructional material and the agent. Agents can reduce the perceived cognitive load by providing narration and personalization that can also promote a user's interest and motivation. While research on the reduction of cognitive load from pedagogical agents is minimal, more studies have shown that agents do not increase it. == Effectiveness == It has been suggested by researchers that pedagogical agents may take on different roles in the learning environment. Examples of these roles are: supplanting, scaffolding, coaching, testing, or demonstrating or modelling a procedure. A pedagogical agent as a tutor has not been demonstrated to add any benefit to an educational strategy in equivalent lessons with and without a pedagogical agent. According to Richard Mayer, there is some support in research for pedagogical agent increasing learning, but only as a presenter of social cues. A co-learner pedagogical agent is believed to increase the student's self-efficacy. By pointing out important features of instructional content, a pedagogical agent can fulfill the signaling function, which research on multimedia learning has shown to enhance learning. Research has demonstrated that human-human interaction may not be completely replaced by pedagogical agents, but learners may prefer the agents to non-agent multimedia systems. This finding is supported by social agency theory. Much like the varying effectiveness of the pedagogical agent roles in the learning environment, agents that take into account the user's affect have had mixed results. Research has shown pedagogical agents that make use of the users’ affect have been found to increase user knowledge retention, motivation, and perceived self-efficacy. However, with such a broad range of modalities in affective expressions, it is often difficult to utilize them. Additionally, having agents detect a user's affective state with precision remains challenging, as displays of affect are different across individuals. == Design == === Attractiveness === The appearance of a pedagogical agent can be manipulated to meet the learning requirements. The attractiveness of a pedagogical agent can enhance student's learning when the users were the opposite gender of the pedagogical agent. Male students prefer a sexy appearance of a female pedagogical agents and dislike the sexy appearance of male agents. Female students were not attracted by the sexy appearance of either male or female pedagogical agents. === Affective Response === Pedagogical agents have reached a point where they can convey and elicit emotion, but also reason about and respond to it. These agents are often designed to elicit and respond to affective actions from users through various modalities such as speech, facial expressions, and body gestures. They respond to the affective state of the given user, and make use of these modalities using a wide array of sensors incorporated into the design of the agent. Specifically in education and training applications, pedagogical agents are often designed to increasingly recognize when users or learners exhibit frustration, boredom, confusion, and states of flow. The added recognition in these agents is a step toward making them more emotionally intelligent, comforting and motivating the users as they interact. === Digital Representation === The design of a pedagogical agent often begins with its digital representation, whether it will be 2D or 3D and static or animated. Several studies have developed pedagogical agents that were both static and animated, then evaluated the relative benefits. Similar to other design considerations, the improved learning from static or animated agents remains questionable. One study showed that the appearance of an agent portrayed using a static image can impact a user's recall, based on the visual appearance. Other research found results that suggest static agent images improve learning outcomes. However, several other studies found user's learned more when the pedagogical agent was animated rather than static. Recently a meta-analysis of such research found a negligible improvement in learning via pedagogical agents, suggesting more work needs to be done in the area to support any claims.
Automated machine learning
Automated machine learning (AutoML) is the process of automating the tasks of applying machine learning to real-world problems. It is the combination of automation and ML. AutoML potentially includes every stage from beginning with a raw dataset to building a machine learning model ready for deployment. AutoML was proposed as an artificial intelligence-based solution to the growing challenge of applying machine learning. The high degree of automation in AutoML aims to allow non-experts to make use of machine learning models and techniques without requiring them to become experts in machine learning. Automating the process of applying machine learning end-to-end additionally offers the advantages of producing simpler solutions, faster creation of those solutions, and models that often outperform hand-designed models. Common techniques used in AutoML include hyperparameter optimization, meta-learning and neural architecture search. == Comparison to the standard approach == In a typical machine learning application, practitioners have a set of input data points to be used for training. The raw data may not be in a form that all algorithms can be applied to. To make the data amenable for machine learning, an expert may have to apply appropriate data pre-processing, feature engineering, feature extraction, and feature selection methods. After these steps, practitioners must then perform algorithm selection and hyperparameter optimization to maximize the predictive performance of their model. If deep learning is used, the architecture of the neural network must also be chosen manually by the machine learning expert. Each of these steps may be challenging, resulting in significant hurdles to using machine learning. AutoML aims to simplify these steps for non-experts, and to make it easier for them to use machine learning techniques correctly and effectively. AutoML plays an important role within the broader approach of automating data science, which also includes challenging tasks such as data engineering, data exploration and model interpretation and prediction. == Targets of automation == Automated machine learning can target various stages of the machine learning process. Steps to automate are: Data preparation and ingestion (from raw data and miscellaneous formats) Column type detection; e.g., Boolean, discrete numerical, continuous numerical, or text Column intent detection; e.g., target/label, stratification field, numerical feature, categorical text feature, or free text feature Task detection; e.g., binary classification, regression, clustering, or ranking Feature engineering Feature selection Feature extraction Meta-learning and transfer learning Detection and handling of skewed data and/or missing values Model selection - choosing which machine learning algorithm to use, often including multiple competing software implementations Ensembling - a form of consensus where using multiple models often gives better results than any single model Hyperparameter optimization of the learning algorithm and featurization Neural architecture search Pipeline selection under time, memory, and complexity constraints Selection of evaluation metrics and validation procedures Problem checking Leakage detection Misconfiguration detection Analysis of obtained results Creating user interfaces and visualizations == Challenges and Limitations == There are a number of key challenges being tackled around automated machine learning. A big issue surrounding the field is referred to as "development as a cottage industry". This phrase refers to the issue in machine learning where development relies on manual decisions and biases of experts. This is contrasted to the goal of machine learning which is to create systems that can learn and improve from their own usage and analysis of the data. Basically, it's the struggle between how much experts should get involved in the learning of the systems versus how much freedom they should be giving the machines. However, experts and developers must help create and guide these machines to prepare them for their own learning. To create this system, it requires labor intensive work with knowledge of machine learning algorithms and system design. Additionally, other challenges include meta-learning and computational resource allocation.
Color clock
The color clock, or color timer, is a part of the video circuitry of computer graphics hardware that works with analog color television systems. The clock is timed to match the timing of the color standard it works with, typically NTSC or PAL, ensuring that the data being read from the computer memory to create the image on-screen is in sync with the display. Depending on the speed of the color clock, the product of the resolution and number of colors is defined. Slow color clocks of many early games consoles and home computers resulted in limited color palettes at the highest resolutions.
Nolot
Nolot is a chess test suite with 11 positions from real games. They were compiled by Pierre Nolot (French: [nɔ.lo]) for the French chess magazine Gambisco and posted on the rec.games.chess Usenet group in 1994. They were designed to be particularly hard to solve for chess engines to solve at the time, although modern engines can find a solution near-instantaneously. == Problem 1 == FEN: r3qb1k/1b4p1/p2pr2p/3n4/Pnp1N1N1/6RP/1B3PP1/1B1QR1K1 w - - 0 1 26.Nxh6!! c3 (26... Rxh6 27.Nxd6 Qh5 (best) 28.Rg5! Qxd1 29.Nf7+ Kg8 30.Nxh6+ Kh8 31.Rxd1 c3 32.Nf7+ Kg8 33.Bg6! Nf4 34.Bxc3 Nxg6 35.Bxb4 Kxf7 36.Rd7+ Kf6 37.Rxg6+ Kxg6 38.Rxb7 ±) 27.Nf5! cxb2 28.Qg4 Bc8 (28... g6!? 29.Kh2! 29.Qd7 30.Nh4 Bc6 31.Nc5! dxc 32.Rxe6 Nf6 33.Nxg6+ Kg7 34.Qg5 Nbd5 35.Ne5 Kh8 36.Nxd7 ±) 29.Qh4+ Rh6 30.Nxh6 gxh6 31.Kh2! Qe5 32.Ng5 Qf6 33.Re8 Bf5 34.Qxh6 (missing a mate in 6: 34.Nf7+ Qxf7 35.Qxh6+ Bh7 36.Rxa8 Nf6 37.Rxf8 Qxf8 38.Qxf8+ Ng8 39.Qg7#) 34...Qxh6 35.Nf7+ Kh7 36.Bxf5+ Qg6 37.Bxg6+ Kg7 38.Rxa8 Be7 39.Rb8 a5 40.Be4+ Kxf7 41.Bxd5+ 1–0 The best Novag computer, the Diablo 68000, finds 26. Nxh6 after seven and a half months (Pierre Nolot has let it run on the position for 14 months and one day, until a power failure stopped an analysis of over 80,000,000,000 nodes.) but for wrong reasons: it evaluates white's position as inferior and thinks this move would enable it to draw. Today Gambit Tiger 2.0 for example can find it quite quickly: Most free engines running on 64-bit processors in 2010 could solve this problem and the others in a few seconds. 1.Qd4 c3 2.Bxc3 Nxc3 3.Qxb4 Nxe4 4.Qxb7 Rb8 5.Qxb8 Qxb8 6.Bxe4 d5 7.Rb1 μ (-1.20) Depth: 12 00:00:09 6055 kN 1.Nxh6 c3 2.Nf5 cxb2 3.Qg4 Rb8 4.Nxg7 Rg6 5.Qxg6 Qxg6 6.Rxg6 Bxg7 7.Nxd6 ³ (-0.48) Depth: 12 00:00:21 14368 kN 1.Nxh6 c3 2.Nf5 cxb2 3.Qg4 Rc8 4.Nxg7 Rg6 5.Nxe8 Rxg4 6.Rxg4 Rxe8 7.Rg6 μ (-0.74) Depth: 13 00:00:55 38455 kN 1.Ne3 Rxe4 2.Bxe4 Qxe4 3.Nxd5 Qxd5 4.Qc1 Qf5 5.Qxh6+ Qh7 6.Qe6 Nd3 7.Re2 Nxb2 8.Rxb2 ³ (-0.58) Depth: 13 00:01:30 62979 kN 1.Ne3 Rxe4 ³ (-0.58) Depth: 14 00:02:02 84941 kN 1.Ne3 Nxe3 2.Rexe3 Bxe4 3.Qg4 Rg6 4.Qxe4 Qxe4 5.Bxe4 Rxg3 6.Rxg3 d5 7.Bf5 Re8 8.Bc3 ³ (-0.30) Depth: 15 00:03:05 128968 kN 1.Nxh6 ² (0.32) Depth: 15 00:07:58 350813 kN With the next ply showing a clear advantage. Stockfish 14dev 64bit 4CPU running on 2020 hardware recognises the significance of Nxh6!! in 1 second. Stockfish_21092606_x64_avx2: NNUE evaluation using nn-13406b1dcbe0.nnue enabled. 19/32 00:01 7708k 4882k +3,00 Nxh6 Rxh6 Nxd6 Qh5 Bg6 Qxd1 Nf7+ Kg8 Nxh6+ gxh6 Bh5+ Kh7 Rxd1 c3 Bxc3 Nxc3 Rd7+ Kh8 Rxb7 Ne4 Re3 Nxf2 Kxf2 Bc5 Ke2 Bxe3 Kxe3 Nd5+ Kf2 49/73 15:02 5118270k 5673k +6,15 Nxh6 Rxh6 Nxd6 Qh5 Rg5 Qxd1 Nf7+ Kg8 Nxh6+ Kh8 Rxd1 c3 Nf7+ Kg8 Bg6 Nf4 Bxc3 Nbd5 Rb1 Bc6 Bd2 Nxg6 Rxg6 Ne7 Rxc6 Nxc6 Rb6 Rc8 Ng5 a5 Ra6 Bb4 Be3 Ne5 Bd4 Nc6 Bb6 Bd2 h4 Kf8 Bc5+ Kg8 Be3 Bxe3 fxe3 Kf8 Kf2 Ke7 Nf3 Kd7 Rb6 Ne7 Rb5 Kd6 Rxa5 Rc2+ Kg3 Re2 Nd4 Rxe3+ Kf4 Rd3 Nf5+ Kc7 Nxe7 == Problem 2 == FEN: r4rk1/pp1n1p1p/1nqP2p1/2b1P1B1/4NQ2/1B3P2/PP2K2P/2R5 w - - 0 1 22.Rxc5!! Nxc5 23.Nf6+ Kh8 24.Qh4 Qb5+ (computers think there is perpetual check here, but...) 25.Ke3! 25... h5 26.Nxh5 Qxb3+ (26... d5+ 27.Bxd5 Qd3 28.Kf2 Ne4+ 29.Bxe4 Qd4+ 30.Kg2 Qxb2+ 31.Kh3 ±) and White won in 41 moves. Today Deep Junior 8.ZX for example finds it very quickly (around 1 minute): 1.Kd1 Rac8 2.Bh6 Qb5 3.Rc3 Qf1+ 4.Kc2 Rc6 5.Bxf8 −+ (-2.11) Depth: 12 00:00:04 10422 kN 1.Nxc5 Nxc5 2.Rxc5 Qxc5 3.e6 Rae8 4.e7 Nc8 5.Kf1 Nxd6 6.Bf6 b5 −+ (-2.10) Depth: 12 00:00:14 25054 kN 1.Bf6! μ (-1.35) Depth: 12 00:00:17 34601 kN 1.Bf6 Qb5+ 2.Ke1 Bb4+ 3.Kf2 Bc5+ = (0.00) Depth: 12 00:00:20 34601 kN 1.Bf6 Qb5+ 2.Ke1 Nxf6 3.Nxf6+ Kg7 4.Nh5+ gxh5 5.Qf6+ Kg8 6.Qg5+ Kh8 7.Qf6+ = (0.00) Depth: 15 00:01:01 130544 kN 1.Rxc5! = (0.15) Depth: 15 00:01:12 145875 kN 1.Rxc5 Nxc5 2.Nf6+ Kh8 3.Qh4 Qb5+ 4.Ke3 h5 5.Nxh5 Qd3+ 6.Kf2 Ne4+ 7.fxe4 Qd4+ 8.Kf1 Qd3+ 9.Ke1 Qb1+ 10.Bd1 ± (2.18) Depth: 15 00:01:18 145875 kN Stockfish 14dev 64bit 4CPU running on 2020 hardware recognises the significance of Rxc5!! in 1 second. Stockfish_21092606_x64_avx2: NNUE evaluation using nn-13406b1dcbe0.nnue enabled. 21/25 00:01 5822k 5545k +6,61 Rxc5 Qxc5 Nxc5 Nxc5 Bh6 Nbd7 Bxf8 Rxf8 Qe3 Rc8 f4 Nxe5 Qxe5 Ne6 Bxe6 Rc2+ Kd3 Rxh2 46/86 11:27 5057055k 7355k +7,61 Rxc5 Qxc5 Nxc5 Nxc5 Bf6 Ne6 Qh6 Nd4+ Kf2 Nf5 Qg5 Nd7 h4 Nxf6 Qxf6 Ng7 d7 b5 Bd5 Rab8 b4 Nh5 Bxf7+ Rxf7 d8R+ Rxd8 Qxd8+ Rf8 Qd5+ Kg7 e6 Kf6 Qd7 Ng7 Qd4+ Kxe6 Qxg7 Rf7 Qc3 Ke7 Qc5+ Ke8 Qc8+ Ke7 h5 gxh5 Kg3 h4+ Kh2 h6 Qc5+ Kf6 Qxb5 Kg7 f4 Rxf4 Qe5+ Rf6 b5 h3 Qd4 Kg8 Qxf6 h5 Blacks 22. .. Nxc5 is suboptimal and leads faster mate 77/44 09:18 6987714k 12518k +M22 Nf6+ Kh8 Qh4 Qb5+ Ke3 Qxb3+ axb3 h5 Nxh5 Nd5+ Kd4 Ne6+ Kxd5 Nxg5 Qxg5 gxh5 f4 Rad8 f5 f6 Qxh5+ Kg7 Qg6+ Kh8 e6 b6 e7 Rb8 exf8Q+ Rxf8 Ke6 b5 Ke7 Rb8 Qh5+ Kg7 Qf7+ Kh8 Kxf6 Rf8 Qxf8+ Kh7 Qg7+ == Problem 3 == FEN: r2qk2r/ppp1b1pp/2n1p3/3pP1n1/3P2b1/2PB1NN1/PP4PP/R1BQK2R w KQkq - 0 1 12.Nxg5!! Bxd1 13.Nxe6 Qb8 14.Nxg7+!! Kf8 15.Bh6! Bg4 16.0-0+ Kg8 17.Rf4 ± White wins with a queen sac but black has defensive resources. Stockfish 8 64bit 3CPU running on 2016 hardware recognizes the significance of Nxg5!! in 55 seconds. Stockfish 14 dev (Stockfish_21092606_x64_avx2) 64bit 4CPU running on 2020 hardware recognizes the significance of Nxg5!! in 1 second. NNUE evaluation using nn-13406b1dcbe0.nnue enabled. 21/34 00:01 8291k 4530k +2,78 Nxg5 Bxd1 Nxe6 Qb8 Nxg7+ Kd8 Kxd1 b5 N3f5 Bf8 Rf1 Kc8 Nh5 Kb7 Bxb5 Ne7 g4 a6 Ba4 Nxf5 gxf5 Ka7 Nf4 c5 47/59 37:49 10390430k 4578k +3,16 Nxg5 Bxd1 Nxe6 Qb8 Nxg7+ Kd8 Kxd1 b5 Rf1 Kc8 N3f5 Bf8 Ne6 Kd7 Nf4 Ne7 g4 a5 Ke2 Qb7 h4 Ra6 a3 Kc8 Be3 Kb8 Kf3 Rb6 Bd2 Qc8 Kg3 c5 Be3 c4 Nxe7 Bxe7 Bf5 Qd8 h5 Qg8 Kh3 Bg5 Rf3 Ra6 Raf1 b4 Nxd5 Qxd5 Bxg5 bxc3 bxc3 Rb6 Be3 Rb3 Blacks 14 .. Kf8 is suboptimal and leads loss fast 41/68 06:31 3269727k 8350k +9,28 Bh6 Kg8 Rxd1 Bf8 N3h5 Bxg7 Nxg7 Qf8 Nf5 Ne7 Bxf8 Nxf5 Bxf5 Rxf8 Be6+ Kg7 Rd3 Rf4 Bxd5 c6 Rg3+ Kf8 Rf3 Rxf3 Bxf3 Kg7 Rf1 Re8 Be4 Re6 Ke2 a5 Ke3 Rh6 h3 a4 Kf4 Re6 h4 Re8 Ke3 h6 h5 Rf8 Rxf8 Kxf8 == Problem 4 == FEN: r1b1kb1r/1p1n1ppp/p2ppn2/6BB/2qNP3/2N5/PPP2PPP/R2Q1RK1 w kq - 0 1 10.Nxe6!! Qxe6 11.Nd5 Kd8 12.Bg4 Qe5 13.f4 Qxe4 (13...Qxb2 stronger but not sufficient: 14.Bxd7 Bxd7 15.Rb1 Qa3 16.Nxf6 Bb5 17.Qd4 Qc5 18.Rfd1 ±) 14.Bxd7 Bxd7 15.Nxf6 gxf6 16.Bxf6+ Kc7 17.Bxh8 and Black resigned on move 27. Stockfish 14dev 64bit 4CPU running on 2020 hardware recognises the significance of 10.Nxe6 in 1 second. Stockfish_21092606_x64_avx2: NNUE evaluation using nn-13406b1dcbe0.nnue enabled. 22/37 00:01 6955k 5367k +4,00 Nxe6 Qxe6 Nd5 Kd8 Bg4 Qe5 f4 Qxb2 Rb1 Qa3 Bxd7 Bxd7 Nxf6 Bb5 Rf3 Qxa2 c4 Bxc4 Rf2 Qa5 Nd5+ f6 Nxf6 Kc7 Rc1 b5 Qd5 gxf6 Bxf6 Kb8 Rxc4 Qe1+ Rf1 51/70 47:10 14538911k 5137k +5,76 Nxe6 Qxe6 Nd5 Kd8 Bg4 Qe5 f4 Qxe4 Bxd7 Bxd7 Nxf6 Qf5 Qd4 Kc8 Nd5 Bc6 c4 f6 Nb6+ Kb8 Bh4 Be7 Rae1 Bd8 Nxa8 Kxa8 Bf2 Kb8 Qxd6+ Bc7 Ba7+ Kc8 Qe6+ Qxe6 Rxe6 h5 h4 Rd8 Re7 g6 Be3 Ba5 Kf2 Rd6 Rc1 Bd8 Rg7 Be4 Rg8 Kd7 c5 Rd3 Rc4 Bd5 Rg7+ Ke6 Rd4 Rxd4 Bxd4 Kf5 Rd7 Bc6 Rxd8 Kxf4 Bxf6 == Problem 5 == FEN: r2qrb1k/1p1b2p1/p2ppn1p/8/3NP3/1BN5/PPP3QP/1K3RR1 w - - 0 1 21.e5!! dxe5 22.Ne4! Nh5 23.Qg6!? (stronger is 23.Qg4!! Nf4 24.Nf3 Qc7 25.Nh4 ± ) 23...exd4? (23...Nf4 24.Rxf4! exf4 25.Nf3! Qb6 26.Rg5!! covering b5 and threatening Nf6 or Ne5-f7+) 24.Ng5 1−0 Stockfish 8 64bit 3CPU running on 2016 hardware recognises the significance of 21.e5 in 5 seconds. Stockfish 12 dev (Stockfish_20062212_x64_modern) 64bit 1CPU running on 2016 hardware recognizes the significance of 21.e5 in 11 seconds. 25/42 00:06 7 963k 1309k +6,93 e5 Nh5 Ne4 dxe5 Nf3 Nf4 Qg4 Qc7 Nh4 Bc6 Nf6 g5 Rxf4 exf4 Qh5 Qe7 Ng6+ Kg7 Nxe7 Rxe7 Ng4 37/62 03:12 298 083k 1545k +10,70 e5 Ng4 Qxg4 Qg5 Qh3 Qxe5 Nde2 g5 Rxf8+ Kg7 Rff1 Rf8 Re1 Qf5 Qg3 Rad8 Nd4 Qf4 Nxe6+ Bxe6 Rxe6 Qxg3 == Problem 6 == FEN: rnbqk2r/1p3ppp/p7/1NpPp3/QPP1P1n1/P4N2/4KbPP/R1B2B1R b kq - 0 1 13... axb5!! offers an exchange to keep the white queen out of play. 14.Qxa8 Bd4 15.Nxd4 cxd4 16.Qxb8 0-0! 17.Ke1 Qh4 18.g3 Qf6 19.Bf4 g5? (Ivanchuk found 19...d3! during post-game analysis.) 20.Rc1 exf4 21.Qxf4 Qd4 22.Rd1 bxc4 23.e5 Qc3+ 24.Rd2 Re8 25.Bxd3 cxd3 −+ Tasc R30 finds 19... d3! in 2 1/2 hours. 19... Bf5!! is even stronger than 19... d3. Position is already lost at 19... d3 +8.00 for black, ... Bf5 not much better Stockfish 14dev 64bit 4CPU running on 2020 hardware recognises the significance of axb5!! in 1 second. Stockfish_21092606_x64_avx2: NNUE evaluation using nn-13406b1dcbe0.nnue enabled. 21/28 00:01 9264k 4714k -1,22 axb5 Qxa8 Bd4 Nxd4 cxd4 h3 Nf6 Bg5 0-0 cxb5 h6 Bxf6 Qxf6 Re1 Nd7 Kd1 Qg6 Qa4 Qg3 Qc2 Qxa3 Bd3 Qxb4 Qb1 46/67 1:05:00 18113493k 4644k -2,40 axb5 Qxa8 Bd4 h3 Nf6 Nxd4 exd4 Kf2 Nxe4+ Kg1 Nd7 Bg5 Qxg5 Qxc8+ Ke7 Qc7 Qe5 d6+ Qxd6 Qxd6+ Kxd6 bxc5+ Ndxc5 cxb5 d3 h4 d2 Rh3 Ke5 Be2 f5 Ra2 Rd8 Bd1 Rd4 Re3 f4 Re2 b6 a4 Kd6 Rc2 Kd5 Ra2 h6 Rb2 Nxa4 Bxa4 Rxa4 Rexd2+ Nxd2 Rxd2+ Kc4 Rd7 g6 == Problem 7 == FEN 1r1bk2r/2R2ppp/p3p3/1b2P2q/4QP2/4N3/1B4PP/3R2K1 w k - 0 1 1.Rxd8+!! Rxd8 (1...Kxd8 2.Ra7! Qe2 3.Qd4+ Ke8 4.h3 Qe1+ 5.Kh2 Rd8 6.Qc5 Qh4 7.Ba3 Rd7 8.Ra8+ Rd8 9.g3 1−0)