AI Generator Za Darmo

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  Pixel aspect ratio

  A pixel aspect ratio (PAR) is a mathematical ratio that describes how the width of a pixel in a digital image compares to the height of that pixel. Most digital imaging systems display an image as a grid of tiny, square pixels. However, some imaging systems, especially those that must be compatible with standard-definition television motion pictures, display an image as a grid of rectangular pixels, in which the pixel width and height are different. Pixel aspect ratio describes this difference. Use of pixel aspect ratio mostly involves pictures pertaining to standard-definition television and some other exceptional cases. Most other imaging systems, including those that comply with SMPTE standards and practices, use square pixels. PAR is also known as sample aspect ratio and abbreviated SAR, though it can be confused with storage aspect ratio. == Introduction == The ratio of the width to the height of an image is known as the aspect ratio, or more precisely the display aspect ratio (DAR) – the aspect ratio of the image as displayed; for TV, DAR was traditionally 4:3 (a.k.a. fullscreen), with 16:9 (a.k.a. widescreen) now the standard for HDTV. In digital images, there is a distinction with the storage aspect ratio (SAR), which is the ratio of pixel dimensions. If an image is displayed with square pixels, then these ratios agree; if not, then non-square, "rectangular" pixels are used, and these ratios disagree. The aspect ratio of the pixels themselves is known as the pixel aspect ratio (PAR) – for square pixels this is 1:1 – and these are related by the identity: Rearranging (solving for PAR) yields: For example: A 640 × 480 VGA image has a SAR of 640/480 = 4:3, and if displayed on a 4:3 display (DAR = 4:3) has square pixels, hence a PAR of 1:1. By contrast, a 720 × 576 D-1 PAL image has a SAR of 720/576 = 5:4, but if displayed on a 4:3 display (DAR = 4:3) the PAR is 4/3 : 5/4 = 16:15 ≈ 1.066. This means that the pixels of the PAL picture must be "stretched" by this amount to fit in the 4:3 display. In analog images such as film there is no notion of pixel, nor notion of SAR or PAR, but in the digitization of analog images the resulting digital image has pixels, hence SAR (and accordingly PAR, if displayed at the same aspect ratio as the original). Non-square pixels arise often in early digital TV standards, related to digitalization of analog TV signals – whose vertical and "effective" horizontal resolutions differ and are thus best described by non-square pixels – and also in some digital video cameras and computer display modes, such as Color Graphics Adapter (CGA). Today they arise also in transcoding between resolutions with different SARs. Actual displays do not generally have non-square pixels, though digital sensors might; they are rather a mathematical abstraction used in resampling images to convert between resolutions. There are several complicating factors in understanding PAR, particularly as it pertains to digitization of analog video: First, analog video does not have pixels, but rather a raster scan, and thus has a well-defined vertical resolution (the lines of the raster), but not a well-defined horizontal resolution, since each line is an analog signal. However, by a standardized sampling rate, the effective horizontal resolution can be determined by the sampling theorem, as is done below. Second, due to overscan, some of the lines at the top and bottom of the raster are not visible, as are some of the possible image on the left and right – see Overscan: Analog to digital resolution issues. Also, the resolution may be rounded (DV NTSC uses 480 lines, rather than the 486 that are possible). Third, analog video signals are interlaced – each image (frame) is sent as two "fields", each with half the lines. Thus either the pixels are twice as tall as they would be without interlacing, or the image is deinterlaced. == Background == Video is presented as a sequential series of images called video frames. Historically, video frames were created and recorded in analog form. As digital display technology, digital broadcast technology, and digital video compression evolved separately, it resulted in video frame differences that must be addressed using pixel aspect ratio. Digital video frames are generally defined as a grid of pixels used to present each sequential image. The horizontal component is defined by pixels (or samples), and is known as a video line. The vertical component is defined by the number of lines, as in 480 lines. Standard-definition television standards and practices were developed as broadcast technologies and intended for terrestrial broadcasting, and were therefore not designed for digital video presentation. Such standards define an image as an array of well-defined horizontal "Lines", well-defined vertical "Line Duration" and a well-defined picture center. However, there is not a standard-definition television standard that properly defines image edges or explicitly demands a certain number of picture elements per line. Furthermore, analog video systems such as NTSC 480i and PAL 576i, instead of employing progressively displayed frames, employ fields or interlaced half-frames displayed in an interwoven manner to reduce flicker and double the image rate for smoother motion. === Analog-to-digital conversion === As a result of computers becoming powerful enough to serve as video editing tools, video digital-to-analog converters and analog-to-digital converters were made to overcome this incompatibility. To convert analog video lines into a series of square pixels, the industry adopted a default sampling rate at which luma values were extracted into pixels. The luma sampling rate for 480i pictures was 12+3⁄11 MHz and for 576i pictures was 14+3⁄4 MHz. The term pixel aspect ratio was first coined when ITU-R BT.601 (commonly known as Rec. 601) specified that standard-definition television pictures are made of lines of exactly 720 non-square pixels. ITU-R BT.601 did not define the exact pixel aspect ratio but did provide enough information to calculate the exact pixel aspect ratio based on industry practices: The standard luma sampling rate of precisely 13+1⁄2 MHz. Based on this information: The pixel aspect ratio for 480i would be 10:11 as: 12 3 11 ÷ 13 1 2 = 10 11 {\displaystyle 12{\tfrac {3}{11}}\div 13{\tfrac {1}{2}}={\tfrac {10}{11}}} The pixel aspect ratio for 576i would be 59:54 as: 14 3 4 ÷ 13 1 2 = 59 54 {\displaystyle 14{\tfrac {3}{4}}\div 13{\tfrac {1}{2}}={\tfrac {59}{54}}} SMPTE RP 187 further attempted to standardize the pixel aspect ratio values for 480i and 576i. It designated 177:160 for 480i or 1035:1132 for 576i. However, due to significant difference with practices in effect by industry and the computational load that they imposed upon the involved hardware, SMPTE RP 187 was simply ignored. SMPTE RP 187 information annex A.4 further suggested the use of 10:11 for 480i. As of this writing, ITU-R BT.601-6, which is the latest edition of ITU-R BT.601, still implies that the pixel aspect ratios mentioned above are correct. === Digital video processing === As stated above, ITU-R BT.601 specified that standard-definition television pictures are made of lines of 720 non-square pixels, sampled with a precisely specified sampling rate. A simple mathematical calculation reveals that a 704 pixel width would be enough to contain a 480i or 576i standard 4:3 picture: A 4:3 480-line picture, digitized with the Rec. 601-recommended sampling rate, would be 704 non-square pixels wide. x 480 × 10 11 = 4 3 ⇒ x = 480 × 11 × 4 10 × 3 = 704 {\displaystyle {\frac {x}{480}}\times {\frac {10}{11}}={\frac {4}{3}}\Rightarrow x={\frac {480\times 11\times 4}{10\times 3}}=704} A 4:3 576-line picture, digitized with the Rec. 601-recommended sampling rate, would be 702+54⁄59 non-square pixels wide. x 576 × 59 54 = 4 3 ⇒ x = 576 × 54 × 4 59 × 3 = 702 54 59 {\displaystyle {\frac {x}{576}}\times {\frac {59}{54}}={\frac {4}{3}}\Rightarrow x={\frac {576\times 54\times 4}{59\times 3}}=702{\tfrac {54}{59}}} Unfortunately, not all standard TV pictures are exactly 4:3: As mentioned earlier, in analog video, the center of a picture is well-defined but the edges of the picture are not standardized. As a result, some analog devices (mostly PAL devices but also some NTSC devices) generated motion pictures that were horizontally (slightly) wider. This also proportionately applies to anamorphic widescreen (16:9) pictures. Therefore, to maintain a safe margin of error, ITU-R BT.601 required sampling 16 more non-square pixels per line (8 more at each edge) to ensure saving all video data near the margins. This requirement, however, had implications for PAL motion pictures. PAL pixel aspect ratios for standard (4:3) and anamorphic wide screen (16:9), respectively 59:54 and 118:81, were awkward for digital image processing, especially for mixing PAL and NTSC video clips. Therefore, video editing products chose the almost equivalent value

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  Instance selection

  Instance selection (or dataset reduction, or dataset condensation) is an important data pre-processing step that can be applied in many machine learning (or data mining) tasks. Approaches for instance selection can be applied for reducing the original dataset to a manageable volume, leading to a reduction of the computational resources that are necessary for performing the learning process. Algorithms of instance selection can also be applied for removing noisy instances, before applying learning algorithms. This step can improve the accuracy in classification problems. Algorithm for instance selection should identify a subset of the total available data to achieve the original purpose of the data mining (or machine learning) application as if the whole data had been used. Considering this, the optimal outcome of IS would be the minimum data subset that can accomplish the same task with no performance loss, in comparison with the performance achieved when the task is performed using the whole available data. Therefore, every instance selection strategy should deal with a trade-off between the reduction rate of the dataset and the classification quality. == Instance selection algorithms == The literature provides several different algorithms for instance selection. They can be distinguished from each other according to several different criteria. Considering this, instance selection algorithms can be grouped in two main classes, according to what instances they select: algorithms that preserve the instances at the boundaries of classes and algorithms that preserve the internal instances of the classes. Within the category of algorithms that select instances at the boundaries it is possible to cite DROP3, ICF and LSBo. On the other hand, within the category of algorithms that select internal instances, it is possible to mention ENN and LSSm. In general, algorithm such as ENN and LSSm are used for removing harmful (noisy) instances from the dataset. They do not reduce the data as the algorithms that select border instances, but they remove instances at the boundaries that have a negative impact on the data mining task. They can be used by other instance selection algorithms, as a filtering step. For example, the ENN algorithm is used by DROP3 as the first step, and the LSSm algorithm is used by LSBo. There is also another group of algorithms that adopt different selection criteria. For example, the algorithms LDIS, CDIS and XLDIS select the densest instances in a given arbitrary neighborhood. The selected instances can include both, border and internal instances. The LDIS and CDIS algorithms are very simple and select subsets that are very representative of the original dataset. Besides that, since they search by the representative instances in each class separately, they are faster (in terms of time complexity and effective running time) than other algorithms, such as DROP3 and ICF. Besides that, there is a third category of algorithms that, instead of selecting actual instances of the dataset, select prototypes (that can be synthetic instances). In this category it is possible to include PSSA, PSDSP and PSSP. The three algorithms adopt the notion of spatial partition (a hyperrectangle) for identifying similar instances and extract prototypes for each set of similar instances. In general, these approaches can also be modified for selecting actual instances of the datasets. The algorithm ISDSP adopts a similar approach for selecting actual instances (instead of prototypes).

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  And–or tree

  An and–or tree is a graphical representation of the reduction of problems (or goals) to conjunctions and disjunctions of subproblems (or subgoals). == Example == The and–or tree: represents the search space for solving the problem P, using the goal-reduction methods: P if Q and R P if S Q if T Q if U == Definitions == Given an initial problem P0 and set of problem solving methods of the form: P if P1 and … and Pn the associated and–or tree is a set of labelled nodes such that: The root of the tree is a node labelled by P0. For every node N labelled by a problem or sub-problem P and for every method of the form P if P1 and ... and Pn, there exists a set of children nodes N1, ..., Nn of the node N, such that each node Ni is labelled by Pi. The nodes are conjoined by an arc, to distinguish them from children of N that might be associated with other methods. A node N, labelled by a problem P, is a success node if there is a method of the form P if nothing (i.e., P is a "fact"). The node is a failure node if there is no method for solving P. If all of the children of a node N, conjoined by the same arc, are success nodes, then the node N is also a success node. Otherwise the node is a failure node. == Search strategies == An and–or tree specifies only the search space for solving a problem. Different search strategies for searching the space are possible. These include searching the tree depth-first, breadth-first, or best-first using some measure of desirability of solutions. The search strategy can be sequential, searching or generating one node at a time, or parallel, searching or generating several nodes in parallel. == Relationship with logic programming == The methods used for generating and–or trees are propositional logic programs (without variables). In the case of logic programs containing variables, the solutions of conjoint sub-problems must be compatible. Subject to this complication, sequential and parallel search strategies for and–or trees provide a computational model for executing logic programs. == Relationship with two-player games == And–or trees can also be used to represent the search spaces for two-person games. The root node of such a tree represents the problem of one of the players winning the game, starting from the initial state of the game. Given a node N, labelled by the problem P of the player winning the game from a particular state of play, there exists a single set of conjoint children nodes, corresponding to all of the opponents responding moves. For each of these children nodes, there exists a set of non-conjoint children nodes, corresponding to all of the player's defending moves. For solving game trees with proof-number search family of algorithms, game trees are to be mapped to and–or trees. MAX-nodes (i.e. maximizing player to move) are represented as OR nodes, MIN-nodes map to AND nodes. The mapping is possible, when the search is done with only a binary goal, which usually is "player to move wins the game".

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  Purged cross-validation

  Purged cross-validation is a variant of k-fold cross-validation designed to prevent look-ahead bias in time series and other structured data, developed in 2017 by Marcos López de Prado at Guggenheim Partners and Cornell University. It is primarily used in financial machine learning to ensure the independence of training and testing samples when labels depend on future events. It provides an alternative to conventional cross-validation and walk-forward backtesting methods, which often yield overly optimistic performance estimates due to information leakage and overfitting. == Motivation == Standard cross-validation assumes that observations are independently and identically distributed (IID), which often does not hold in time series or financial datasets. If the label of a test sample overlaps in time with the features or labels in the training set, the result may be data leakage and overfitting. Purged cross-validation addresses this issue by removing overlapping observations and, optionally, adding a temporal buffer ("embargo") around the test set to further reduce the risk of leakage. The figure below illustrates standard 5 Fold Cross-Validation == Purging == Purging removes from the training set any observation whose timestamp falls within the time range of formation of a label in the test set. This can be the case for train set observations before and after the test set. Their removal ensures that the algorithm cannot learn during train time information that will be used to assess the performance of the algorithm. See the figure below for an illustration of purging. == Embargoing == Embargoing addresses a more subtle form of leakage: even if an observation does not directly overlap the test set, it may still be affected by test events due to market reaction lag or downstream dependencies. To guard against this, a percentage-based embargo is imposed after each test fold. For example, with a 5% embargo and 1000 observations, the 50 observations following each test fold are excluded from training. Unlike purging, embargoing can only occur after the test set. The figure below illustrates the application of embargo: == Applications == Purged and embargoed cross-validation has been useful in: Backtesting of trading strategies Validation of classifiers on labeled event-driven returns Any machine learning task with overlapping label horizons == Example == To illustrate the effect of purging and embargoing, consider the figures below. Both diagrams show the structure of 5-fold cross-validation over a 20-day period. In each row, blue squares indicate training samples and red squares denote test samples. Each label is defined based on the value of the next two observations, hence creating an overlap. If this overlap is left untreated, test set information leaks into the train set. The second figure applies the Purged CV procedure. Notice how purging removes overlapping observations from the training set and the embargo widens the gap between test and training data. This approach ensures that the evaluation more closely resembles a true out-of-sample test and reduces the risk of backtest overfitting. == Combinatorial Purged Cross-Validation == Walk-forward backtesting analysis, another common cross-validation technique in finance, preserves temporal order but evaluates the model on a single sequence of test sets. This leads to high variance in performance estimation, as results are contingent on a specific historical path. Combinatorial Purged Cross-Validation (CPCV) addresses this limitation by systematically constructing multiple train-test splits, purging overlapping samples, and enforcing an embargo period to prevent information leakage. The result is a distribution of out-of-sample performance estimates, enabling robust statistical inference and more realistic assessment of a model's predictive power. === Methodology === CPCV divides a time-series dataset into N sequential, non-overlapping groups. These groups preserve the temporal order of observations. Then, all combinations of k groups (where k < N) are selected as test sets, with the remaining N − k groups used for training. For each combination, the model is trained and evaluated under strict controls to prevent leakage. To eliminate potential contamination between training and test sets, CPCV introduces two additional mechanisms: Purging: Any training observations whose label horizon overlaps with the test period are excluded. This ensures that future information does not influence model training. Embargoing: After the end of each test period, a fixed number of observations (typically a small percentage) are removed from the training set. This prevents leakage due to delayed market reactions or auto-correlated features. Each data point appears in multiple test sets across different combinations. Because test groups are drawn combinatorially, this process produces multiple backtest "paths," each of which simulates a plausible market scenario. From these paths, practitioners can compute a distribution of performance statistics such as the Sharpe ratio, drawdown, or classification accuracy. === Formal definition === Let N be the number of sequential groups into which the dataset is divided, and let k be the number of groups selected as the test set for each split. Then: The number of unique train-test combinations is given by the binomial coefficient: ( N k ) {\displaystyle {\binom {N}{k}}} Each observation is used in k {\displaystyle k} test sets and contributes to φ [ N , k ] {\displaystyle \varphi [N,k]} unique backtest paths: φ [ N , k ] = k N ( N k ) {\displaystyle \varphi [N,k]={\frac {k}{N}}{\binom {N}{k}}} This yields a distribution of performance metrics rather than a single point estimate, making it possible to apply Monte Carlo-based or probabilistic techniques to assess model robustness. === Illustrative example === Consider the case where N = 6 and k = 2. The number of possible test set combinations is ( 6 2 ) = 15 {\displaystyle {\binom {6}{2}}=15} . Each of the six groups appears in five test splits. Consequently, five distinct backtest paths can be constructed, each incorporating one appearance from every group. ==== Test group assignment matrix ==== This table shows the 15 test combinations. An "x" indicates that the corresponding group is included in the test set for that split. ==== Backtest path assignment ==== Each group contributes to five different backtest paths. The number in each cell indicates the path to which the group's result is assigned for that split. === Advantages === Combinatorial Purged Cross-Validation offers several key benefits over conventional methods: It produces a distribution of performance metrics, enabling more rigorous statistical inference. The method systematically eliminates lookahead bias through purging and embargoing. By simulating multiple historical scenarios, it reduces the dependence on any single market regime or realization. It supports high-confidence comparisons between competing models or strategies. CPCV is commonly used in quantitative strategy research, especially for evaluating predictive models such as classifiers, regressors, and portfolio optimizers. It has been applied to estimate realistic Sharpe ratios, assess the risk of overfitting, and support the use of statistical tools such as the Deflated Sharpe Ratio (DSR). === Limitations === The main limitation of CPCV stems from its high computational cost. However, this cost can be managed by sampling a finite number of splits from the space of all possible combinations.

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  Phase correlation

  Phase correlation is an approach to estimate the relative translative offset between two similar images (digital image correlation) or other data sets. It is commonly used in image registration and relies on a frequency-domain representation of the data, usually calculated by fast Fourier transforms. The term is applied particularly to a subset of cross-correlation techniques that isolate the phase information from the Fourier-space representation of the cross-correlogram. == Example == The following image demonstrates the usage of phase correlation to determine relative translative movement between two images corrupted by independent Gaussian noise. The image was translated by (20,23) pixels. Accordingly, one can clearly see a peak in the phase-correlation representation at approximately (20,23). == Method == Given two input images g a {\displaystyle \ g_{a}} and g b {\displaystyle \ g_{b}} : Apply a window function (e.g., a Hamming window) on both images to reduce edge effects (this may be optional depending on the image characteristics). Then, calculate the discrete 2D Fourier transform of both images. G a = F { g a } , G b = F { g b } {\displaystyle \ \mathbf {G} _{a}={\mathcal {F}}\{g_{a}\},\;\mathbf {G} _{b}={\mathcal {F}}\{g_{b}\}} Calculate the cross-power spectrum by taking the complex conjugate of the second result, multiplying the Fourier transforms together elementwise, and normalizing this product elementwise. R = G a ∘ G b ∗ | G a ∘ G b ∗ | {\displaystyle \ R={\frac {\mathbf {G} _{a}\circ \mathbf {G} _{b}^{}}{|\mathbf {G} _{a}\circ \mathbf {G} _{b}^{}|}}} Where ∘ {\displaystyle \circ } is the Hadamard product (entry-wise product) and the absolute values are taken entry-wise as well. Written out entry-wise for element index ( j , k ) {\displaystyle (j,k)} : R j k = G a , j k ⋅ G b , j k ∗ | G a , j k ⋅ G b , j k ∗ | {\displaystyle \ R_{jk}={\frac {G_{a,jk}\cdot G_{b,jk}^{}}{|G_{a,jk}\cdot G_{b,jk}^{}|}}} Obtain the normalized cross-correlation by applying the inverse Fourier transform. r = F − 1 { R } {\displaystyle \ r={\mathcal {F}}^{-1}\{R\}} Determine the location of the peak in r {\displaystyle \ r} . ( Δ x , Δ y ) = arg ⁡ max ( x , y ) { r } {\displaystyle \ (\Delta x,\Delta y)=\arg \max _{(x,y)}\{r\}} === Subpixel registration === Commonly, interpolation methods are used to estimate the peak location in the cross-correlogram to non-integer values, despite the fact that the data are discrete, and this procedure is often termed 'subpixel registration'. A large variety of subpixel interpolation methods are given in the technical literature. Common peak interpolation methods such as parabolic interpolation have been used, and the OpenCV computer vision package uses a centroid-based method, though these generally have inferior accuracy compared to more sophisticated methods. Because the Fourier representation of the data has already been computed, it is especially convenient to use the Fourier shift theorem with real-valued (sub-integer) shifts for this purpose, which essentially interpolates using the sinusoidal basis functions of the Fourier transform. An especially popular FT-based estimator is given by Foroosh et al. In this method, the subpixel peak location is approximated by a simple formula involving peak pixel value and the values of its nearest neighbors, where r ( 0 , 0 ) {\displaystyle r_{(0,0)}} is the peak value and r ( 1 , 0 ) {\displaystyle r_{(1,0)}} is the nearest neighbor in the x direction (assuming, as in most approaches, that the integer shift has already been found and the comparand images differ only by a subpixel shift). Δ x = r ( 1 , 0 ) r ( 1 , 0 ) ± r ( 0 , 0 ) {\displaystyle \ \Delta x={\frac {r_{(1,0)}}{r_{(1,0)}\pm r_{(0,0)}}}} The Foroosh et al. method is quite fast compared to most methods, though it is not always the most accurate. Some methods shift the peak in Fourier space and apply non-linear optimization to maximize the correlogram peak, but these tend to be very slow since they must apply an inverse Fourier transform or its equivalent in the objective function. It is also possible to infer the peak location from phase characteristics in Fourier space without the inverse transformation, as noted by Stone. These methods usually use a linear least squares (LLS) fit of the phase angles to a planar model. The long latency of the phase angle computation in these methods is a disadvantage, but the speed can sometimes be comparable to the Foroosh et al. method depending on the image size. They often compare favorably in speed to the multiple iterations of extremely slow objective functions in iterative non-linear methods. Since all subpixel shift computation methods are fundamentally interpolative, the performance of a particular method depends on how well the underlying data conform to the assumptions in the interpolator. This fact also may limit the usefulness of high numerical accuracy in an algorithm, since the uncertainty due to interpolation method choice may be larger than any numerical or approximation error in the particular method. Subpixel methods are also particularly sensitive to noise in the images, and the utility of a particular algorithm is distinguished not only by its speed and accuracy but its resilience to the particular types of noise in the application. == Rationale == The method is based on the Fourier shift theorem. Let the two images g a {\displaystyle \ g_{a}} and g b {\displaystyle \ g_{b}} be circularly-shifted versions of each other: g b ( x , y ) = d e f g a ( ( x − Δ x ) mod M , ( y − Δ y ) mod N ) {\displaystyle \ g_{b}(x,y)\ {\stackrel {\mathrm {def} }{=}}\ g_{a}((x-\Delta x){\bmod {M}},(y-\Delta y){\bmod {N}})} (where the images are M × N {\displaystyle \ M\times N} in size). Then, the discrete Fourier transforms of the images will be shifted relatively in phase: G b ( u , v ) = G a ( u , v ) e − 2 π i ( u Δ x M + v Δ y N ) {\displaystyle \mathbf {G} _{b}(u,v)=\mathbf {G} _{a}(u,v)e^{-2\pi i({\frac {u\Delta x}{M}}+{\frac {v\Delta y}{N}})}} One can then calculate the normalized cross-power spectrum to factor out the phase difference: R ( u , v ) = G a G b ∗ | G a G b ∗ | = G a G a ∗ e 2 π i ( u Δ x M + v Δ y N ) | G a G a ∗ e 2 π i ( u Δ x M + v Δ y N ) | = G a G a ∗ e 2 π i ( u Δ x M + v Δ y N ) | G a G a ∗ | = e 2 π i ( u Δ x M + v Δ y N ) {\displaystyle {\begin{aligned}R(u,v)&={\frac {\mathbf {G} _{a}\mathbf {G} _{b}^{}}{|\mathbf {G} _{a}\mathbf {G} _{b}^{}|}}\\&={\frac {\mathbf {G} _{a}\mathbf {G} _{a}^{}e^{2\pi i({\frac {u\Delta x}{M}}+{\frac {v\Delta y}{N}})}}{|\mathbf {G} _{a}\mathbf {G} _{a}^{}e^{2\pi i({\frac {u\Delta x}{M}}+{\frac {v\Delta y}{N}})}|}}\\&={\frac {\mathbf {G} _{a}\mathbf {G} _{a}^{}e^{2\pi i({\frac {u\Delta x}{M}}+{\frac {v\Delta y}{N}})}}{|\mathbf {G} _{a}\mathbf {G} _{a}^{}|}}\\&=e^{2\pi i({\frac {u\Delta x}{M}}+{\frac {v\Delta y}{N}})}\end{aligned}}} since the magnitude of an imaginary exponential always is one, and the phase of G a G a ∗ {\displaystyle \ \mathbf {G} _{a}\mathbf {G} _{a}^{}} always is zero. The inverse Fourier transform of a complex exponential is a Dirac delta function, i.e. a single peak: r ( x , y ) = δ ( x + Δ x , y + Δ y ) {\displaystyle \ r(x,y)=\delta (x+\Delta x,y+\Delta y)} This result could have been obtained by calculating the cross correlation directly. The advantage of this method is that the discrete Fourier transform and its inverse can be performed using the fast Fourier transform, which is much faster than correlation for large images. === Benefits === Unlike many spatial-domain algorithms, the phase correlation method is resilient to noise, occlusions, and other defects typical of medical or satellite images. The method can be extended to determine rotation and scaling differences between two images by first converting the images to log-polar coordinates. Due to properties of the Fourier transform, the rotation and scaling parameters can be determined in a manner invariant to translation. === Limitations === In practice, it is more likely that g b {\displaystyle \ g_{b}} will be a simple linear shift of g a {\displaystyle \ g_{a}} , rather than a circular shift as required by the explanation above. In such cases, r {\displaystyle \ r} will not be a simple delta function, which will reduce the performance of the method. In such cases, a window function (such as a Gaussian or Tukey window) should be employed during the Fourier transform to reduce edge effects, or the images should be zero padded so that the edge effects can be ignored. If the images consist of a flat background, with all detail situated away from the edges, then a linear shift will be equivalent to a circular shift, and the above derivation will hold exactly. The peak can be sharpened by using edge or vector correlation. For periodic images (such as a chessboard or picket fence), phase correlation may yield ambiguous results with several peaks in the resulting output. == Applications == Phase correlation is the preferred m

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  AI safety

  AI safety is an interdisciplinary field focused on preventing accidents, misuse, or other harmful consequences arising from artificial intelligence systems. It encompasses AI alignment (which aims to ensure AI systems behave as intended), monitoring AI systems for risks, and enhancing their robustness. The field is particularly concerned with existential risks posed by advanced AI models. Beyond technical research, AI safety involves developing norms and policies that promote safety, including advocacy for regulations at different levels of government. The field gained significant popularity in 2023, with rapid progress in generative AI and public concerns voiced by researchers and CEOs about potential dangers. During the 2023 AI Safety Summit, the United States and the United Kingdom both established their own AI Safety Institute. However, researchers have expressed concern that AI safety measures are not keeping pace with the rapid development of AI capabilities. == Motivations == Scholars discuss current risks from critical systems failures, bias, and AI-enabled surveillance, as well as emerging risks like technological unemployment, digital manipulation, weaponization, AI-enabled cyberattacks and bioterrorism. They also discuss speculative risks from losing control of future artificial general intelligence (AGI) agents, or from AI enabling perpetually stable dictatorships. === Existential safety === Some have criticized concerns about AGI, such as Andrew Ng who compared them in 2015 to "worrying about overpopulation on Mars when we have not even set foot on the planet yet". Stuart J. Russell on the other side urges caution, arguing that "it is better to anticipate human ingenuity than to underestimate it". AI researchers have widely differing opinions about the severity and primary sources of risk posed by AI technology – though surveys suggest that experts take high consequence risks seriously. In two surveys of AI researchers, the median respondent was optimistic about AI overall, but placed a 5% probability on an "extremely bad (e.g. human extinction)" outcome of advanced AI. In a 2022 survey of the natural language processing community, 37% agreed or weakly agreed that it is plausible that AI decisions could lead to a catastrophe that is "at least as bad as an all-out nuclear war". == History == Risks from AI began to be seriously discussed at the start of the computer age: Moreover, if we move in the direction of making machines which learn and whose behavior is modified by experience, we must face the fact that every degree of independence we give the machine is a degree of possible defiance of our wishes. In 1988 Blay Whitby published a book outlining the need for AI to be developed along ethical and socially responsible lines. From 2008 to 2009, the Association for the Advancement of Artificial Intelligence (AAAI) commissioned a study to explore and address potential long-term societal influences of AI research and development. The panel was generally skeptical of the radical views expressed by science-fiction authors but agreed that "additional research would be valuable on methods for understanding and verifying the range of behaviors of complex computational systems to minimize unexpected outcomes". In 2011, Roman Yampolskiy introduced the term "AI safety engineering" at the Philosophy and Theory of Artificial Intelligence conference, listing prior failures of AI systems and arguing that "the frequency and seriousness of such events will steadily increase as AIs become more capable". In 2014, philosopher Nick Bostrom published the book Superintelligence: Paths, Dangers, Strategies. He has the opinion that the rise of AGI has the potential to create various societal issues, ranging from the displacement of the workforce by AI, manipulation of political and military structures, to even the possibility of human extinction. His argument that future advanced systems may pose a threat to human existence prompted Elon Musk, Bill Gates, and Stephen Hawking to voice similar concerns. In 2015, dozens of artificial intelligence experts signed an open letter on artificial intelligence calling for research on the societal impacts of AI and outlining concrete directions. To date, the letter has been signed by over 8000 people including Yann LeCun, Shane Legg, Yoshua Bengio, and Stuart Russell. In the same year, a group of academics led by professor Stuart J. Russell founded the Center for Human-Compatible AI at the University of California Berkeley and the Future of Life Institute awarded $6.5 million in grants for research aimed at "ensuring artificial intelligence (AI) remains safe, ethical and beneficial". In 2016, the White House Office of Science and Technology Policy and Carnegie Mellon University announced The Public Workshop on Safety and Control for Artificial Intelligence, which was one of a sequence of four White House workshops aimed at investigating "the advantages and drawbacks" of AI. In the same year, Concrete Problems in AI Safety – one of the first and most influential technical AI Safety agendas – was published. In 2017, the Future of Life Institute sponsored the Asilomar Conference on Beneficial AI, where more than 100 thought leaders formulated principles for beneficial AI including "Race Avoidance: Teams developing AI systems should actively cooperate to avoid corner-cutting on safety standards". In 2018, the DeepMind Safety team outlined AI safety problems in specification, robustness, and assurance. The following year, researchers organized a workshop at ICLR that focused on these problem areas. In 2021, Unsolved Problems in ML Safety was published, outlining research directions in robustness, monitoring, alignment, and systemic safety. In 2023, Rishi Sunak said he wants the United Kingdom to be the "geographical home of global AI safety regulation" and to host the first global summit on AI safety. The AI safety summit took place in November 2023, and focused on the risks of misuse and loss of control associated with frontier AI models. During the summit the intention to create the International Scientific Report on the Safety of Advanced AI was announced. In 2024, The US and UK forged a new partnership on the science of AI safety. The MoU was signed on 1 April 2024 by US commerce secretary Gina Raimondo and UK technology secretary Michelle Donelan to jointly develop advanced AI model testing, following commitments announced at an AI Safety Summit in Bletchley Park in November. In 2025, an international team of 96 experts chaired by Yoshua Bengio published the first International AI Safety Report. The report, commissioned by 30 nations and the United Nations, represents the first global scientific review of potential risks associated with advanced artificial intelligence. It details potential threats stemming from misuse, malfunction, and societal disruption, with the objective of informing policy through evidence-based findings, without providing specific recommendations. == Research focus == AI safety research areas include robustness, monitoring, and alignment. === Robustness === ==== Adversarial robustness ==== AI systems are often vulnerable to adversarial examples or "inputs to machine learning (ML) models that an attacker has intentionally designed to cause the model to make a mistake". For example, in 2013, Szegedy et al. discovered that adding specific imperceptible perturbations to an image could cause it to be misclassified with high confidence. This continues to be an issue with neural networks, though in recent work the perturbations are generally large enough to be perceptible. The image on the right is predicted to be an ostrich after the perturbation is applied. (Left) is a correctly predicted sample, (center) perturbation applied magnified by 10x, (right) adversarial example. Adversarial robustness is often associated with security. Researchers demonstrated that an audio signal could be imperceptibly modified so that speech-to-text systems transcribe it to any message the attacker chooses. Network intrusion and malware detection systems also must be adversarially robust since attackers may design their attacks to fool detectors. Models that represent objectives (reward models) must also be adversarially robust. For example, a reward model might estimate how helpful a text response is and a language model might be trained to maximize this score. Researchers have shown that if a language model is trained for long enough, it will leverage the vulnerabilities of the reward model to achieve a better score and perform worse on the intended task. This issue can be addressed by improving the adversarial robustness of the reward model. More generally, any AI system used to evaluate another AI system must be adversarially robust. This could include monitoring tools, since they could also potentially be tampered with to produce a higher reward. Large language models (LLMs) can be vulnerable to prom

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  AI browser

  An AI browser is a web browser with integrated artificial intelligence capabilities, such as automatically summarizing web page content or answering questions about it. A more specialized type is an agentic browser, based on the concept of agentic AI, which can take actions – such as navigating webpages or filling out forms – on behalf of the user. Several agentic browsers emerged in 2025, including ChatGPT Atlas (macOS only), Comet, and Dia. As of 2025, this is a recent development in the browser market, including new entrants from OpenAI, Opera and Perplexity. The designation of 'AI browser' also includes established browsers that later added non-agentic AI features, such as Microsoft Edge with the Copilot chatbot, Google Chrome with the Gemini chatbot (for Windows desktop users in the US with their language set to English), and Firefox with multiple chatbot providers (such as ChatGPT, Claude, Copilot, Gemini, and Le Chat). AI browsers have been noted to be susceptible to prompt injection attacks. == Browser extensions and integrations == Rather than creating entirely new browsers, some AI browsing solutions integrate with existing browsers through extensions or companion applications. These tools add agentic capabilities to established browsers without requiring users to switch platforms. Examples include Composite, which functions as a cross-browser agent that works with Chrome, Edge, and other browsers to automate web-based tasks for workers. == Cloud-based implementations == Cloud-based implementations of AI browsers allow users to run automated browsing agents without local installation. These systems operate on remote servers using frameworks such as Puppeteer or Playwright. Examples include Browserbase, Browser-use and AI Browser. The AI typically parses the Document Object Model (DOM) to locate and interact with page elements, and may also analyze browser screenshots to interpret layout and structure. == Criticisms and dangers == AI browsers have been noted to be susceptible to being vulnerable to prompt injection attacks, in which the content of websites can be used to hijack the control of the browser. Multiple organisations have argued against using AI browsers due to this vulnerability. The United Kingdom national cyber security centre and Gartner consider them to be too risky for adoption by most organisations. A study by the CISPA Helmholtz Center and Saarland University concluded that this vulnerability makes them easy targets for malware, fraud, automated defamation, disinformation and biased outputs.

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  Symbolic regression

  Symbolic regression (SR) is a type of regression analysis that searches the space of mathematical expressions to find the model that best fits a given dataset, both in terms of accuracy and simplicity. No particular model is provided as a starting point for symbolic regression. Instead, initial expressions are formed by randomly combining mathematical building blocks such as mathematical operators, analytic functions, constants, and state variables. Usually, a subset of these primitives will be specified by the person operating it, but that's not a requirement of the technique. The symbolic regression problem for mathematical functions has been tackled with a variety of methods, including recombining equations most commonly using genetic programming, as well as more recent methods utilizing Bayesian methods and neural networks. Another non-classical alternative method to SR is called Universal Functions Originator (UFO), which has a different mechanism, search-space, and building strategy. Further methods such as Exact Learning attempt to transform the fitting problem into a moments problem in a natural function space, usually built around generalizations of the Meijer-G function. By not requiring a priori specification of a model, symbolic regression isn't affected by human bias, or unknown gaps in domain knowledge. It attempts to uncover the intrinsic relationships of the dataset, by letting the patterns in the data itself reveal the appropriate models, rather than imposing a model structure that is deemed mathematically tractable from a human perspective. The fitness function that drives the evolution of the models takes into account not only error metrics (to ensure the models accurately predict the data), but also special complexity measures, thus ensuring that the resulting models reveal the data's underlying structure in a way that's understandable from a human perspective. This facilitates reasoning and favors the odds of getting insights about the data-generating system, as well as improving generalisability and extrapolation behaviour by preventing overfitting. Accuracy and simplicity may be left as two separate objectives of the regression—in which case the optimum solutions form a Pareto front—or they may be combined into a single objective by means of a model selection principle such as minimum description length. It has been proven that symbolic regression is an NP-hard problem. Nevertheless, if the sought-for equation is not too complex it is possible to solve the symbolic regression problem exactly by generating every possible function (built from some predefined set of operators) and evaluating them on the dataset in question. == Difference from classical regression == While conventional regression techniques seek to optimize the parameters for a pre-specified model structure, symbolic regression avoids imposing prior assumptions, and instead infers the model from the data. In other words, it attempts to discover both model structures and model parameters. This approach has the disadvantage of having a much larger space to search, because not only the search space in symbolic regression is infinite, but there are an infinite number of models which will perfectly fit a finite data set (provided that the model complexity isn't artificially limited). This means that it will possibly take a symbolic regression algorithm longer to find an appropriate model and parametrization, than traditional regression techniques. This can be attenuated by limiting the set of building blocks provided to the algorithm, based on existing knowledge of the system that produced the data; but in the end, using symbolic regression is a decision that has to be balanced with how much is known about the underlying system. Nevertheless, this characteristic of symbolic regression also has advantages: because the evolutionary algorithm requires diversity in order to effectively explore the search space, the result is likely to be a selection of high-scoring models (and their corresponding set of parameters). Examining this collection could provide better insight into the underlying process, and allows the user to identify an approximation that better fits their needs in terms of accuracy and simplicity. == Benchmarking == === SRBench === In 2021, SRBench was proposed as a large benchmark for symbolic regression. In its inception, SRBench featured 14 symbolic regression methods, 7 other ML methods, and 252 datasets from PMLB. The benchmark intends to be a living project: it encourages the submission of improvements, new datasets, and new methods, to keep track of the state of the art in SR. === SRBench Competition 2022 === In 2022, SRBench announced the competition Interpretable Symbolic Regression for Data Science, which was held at the GECCO conference in Boston, MA. The competition pitted nine leading symbolic regression algorithms against each other on a novel set of data problems and considered different evaluation criteria. The competition was organized in two tracks, a synthetic track and a real-world data track. ==== Synthetic Track ==== In the synthetic track, methods were compared according to five properties: re-discovery of exact expressions; feature selection; resistance to local optima; extrapolation; and sensitivity to noise. Rankings of the methods were: QLattice PySR (Python Symbolic Regression) uDSR (Deep Symbolic Optimization) ==== Real-world Track ==== In the real-world track, methods were trained to build interpretable predictive models for 14-day forecast counts of COVID-19 cases, hospitalizations, and deaths in New York State. These models were reviewed by a subject expert and assigned trust ratings and evaluated for accuracy and simplicity. The ranking of the methods was: uDSR (Deep Symbolic Optimization) QLattice geneticengine (Genetic Engine) == Non-standard methods == Most symbolic regression algorithms prevent combinatorial explosion by implementing evolutionary algorithms that iteratively improve the best-fit expression over many generations. Recently, researchers have proposed algorithms utilizing other tactics in AI. Silviu-Marian Udrescu and Max Tegmark developed the "AI Feynman" algorithm, which attempts symbolic regression by training a neural network to represent the mystery function, then runs tests against the neural network to attempt to break up the problem into smaller parts. For example, if f ( x 1 , . . . , x i , x i + 1 , . . . , x n ) = g ( x 1 , . . . , x i ) + h ( x i + 1 , . . . , x n ) {\displaystyle f(x_{1},...,x_{i},x_{i+1},...,x_{n})=g(x_{1},...,x_{i})+h(x_{i+1},...,x_{n})} , tests against the neural network can recognize the separation and proceed to solve for g {\displaystyle g} and h {\displaystyle h} separately and with different variables as inputs. This is an example of divide and conquer, which reduces the size of the problem to be more manageable. AI Feynman also transforms the inputs and outputs of the mystery function in order to produce a new function which can be solved with other techniques, and performs dimensional analysis to reduce the number of independent variables involved. The algorithm was able to "discover" 100 equations from The Feynman Lectures on Physics, while a leading software using evolutionary algorithms, Eureqa, solved only 71. AI Feynman, in contrast to classic symbolic regression methods, requires a very large dataset in order to first train the neural network and is naturally biased towards equations that are common in elementary physics.

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  Domain adaptation

  Domain adaptation is a field associated with machine learning and transfer learning. It addresses the challenge of training a model on one data distribution (the source domain) and applying it to a related but different data distribution (the target domain). A common example is spam filtering, where a model trained on emails from one user (source domain) is adapted to handle emails for another user with significantly different patterns (target domain). Domain adaptation techniques can also leverage unrelated data sources to improve learning. When multiple source distributions are involved, the problem extends to multi-source domain adaptation. Domain adaptation is a specific type of transfer learning. According to the taxonomy laid out by Pan and Yang (2010), it falls into the category of transductive transfer learning. In this setting, the source and target tasks are the same (e.g., both are object recognition), but the domains differ (different marginal distributions). This distinguishes it from inductive transfer learning (where labeled data is available for the target task) and unsupervised transfer learning (where labels are unavailable in both domains). == Classification of domain adaptation problems == Domain adaptation setups are classified in two different ways: according to the distribution shift between the domains, and according to the available data from the target domain. === Distribution shifts === Common distribution shifts are classified as follows: Covariate Shift occurs when the input distributions of the source and destination change, but the relationship between inputs and labels remains unchanged. The above-mentioned spam filtering example typically falls in this category. Namely, the distributions (patterns) of emails may differ between the domains, but emails labeled as spam in the one domain should similarly be labeled in another. Prior Shift (Label Shift) occurs when the label distribution differs between the source and target datasets, while the conditional distribution of features given labels remains the same. An example is a classifier of hair color in images from Italy (source domain) and Norway (target domain). The proportions of hair colors (labels) differ, but images within classes like blond and black-haired populations remain consistent across domains. A classifier for the Norway population can exploit this prior knowledge of class proportions to improve its estimates. Concept Shift (Conditional Shift) refers to changes in the relationship between features and labels, even if the input distribution remains the same. For instance, in medical diagnosis, the same symptoms (inputs) may indicate entirely different diseases (labels) in different populations (domains). === Data available during training === Domain adaptation problems typically assume that some data from the target domain is available during training. Problems can be classified according to the type of this available data: Unsupervised: Unlabeled data from the target domain is available, but no labeled data. In the above-mentioned example of spam filtering, this corresponds to the case where emails from the target domain (user) are available, but they are not labeled as spam. Domain adaptation methods can benefit from such unlabeled data, by comparing its distribution (patterns) with the labeled source domain data. Semi-supervised: Most data that is available from the target domain is unlabelled, but some labeled data is also available. In the above-mentioned case of spam filter design, this corresponds to the case that the target user has labeled some emails as being spam or not. Supervised: All data that is available from the target domain is labeled. In this case, domain adaptation reduces to refinement of the source domain predictor. In the above-mentioned example classification of hair-color from images, this could correspond to the refinement of a network already trained on a large dataset of labeled images from Italy, using newly available labeled images from Norway. == Formalization == Let X {\displaystyle X} be the input space (or description space) and let Y {\displaystyle Y} be the output space (or label space). The objective of a machine learning algorithm is to learn a mathematical model (a hypothesis) h : X → Y {\displaystyle h:X\to Y} able to attach a label from Y {\displaystyle Y} to an example from X {\displaystyle X} . This model is learned from a learning sample S = { ( x i , y i ) ∈ ( X × Y ) } i = 1 m {\displaystyle S=\{(x_{i},y_{i})\in (X\times Y)\}_{i=1}^{m}} . Usually in supervised learning (without domain adaptation), we suppose that the examples ( x i , y i ) ∈ S {\displaystyle (x_{i},y_{i})\in S} are drawn i.i.d. from a distribution D S {\displaystyle D_{S}} of support X × Y {\displaystyle X\times Y} (unknown and fixed). The objective is then to learn h {\displaystyle h} (from S {\displaystyle S} ) such that it commits the least error possible for labelling new examples coming from the distribution D S {\displaystyle D_{S}} . The main difference between supervised learning and domain adaptation is that in the latter situation we study two different (but related) distributions D S {\displaystyle D_{S}} and D T {\displaystyle D_{T}} on X × Y {\displaystyle X\times Y} . The domain adaptation task then consists of the transfer of knowledge from the source domain D S {\displaystyle D_{S}} to the target one D T {\displaystyle D_{T}} . The goal is then to learn h {\displaystyle h} (from labeled or unlabelled samples coming from the two domains) such that it commits as little error as possible on the target domain D T {\displaystyle D_{T}} . The major issue is the following: if a model is learned from a source domain, what is its capacity to correctly label data coming from the target domain? == Four algorithmic principles == === Reweighting algorithms === The objective is to reweight the source labeled sample such that it "looks like" the target sample (in terms of the error measure considered). === Iterative algorithms === A method for adapting consists in iteratively "auto-labeling" the target examples. The principle is simple: a model h {\displaystyle h} is learned from the labeled examples; h {\displaystyle h} automatically labels some target examples; a new model is learned from the new labeled examples. Note that there exist other iterative approaches, but they usually need target labeled examples. === Search of a common representation space === The goal is to find or construct a common representation space for the two domains. The objective is to obtain a space in which the domains are close to each other while keeping good performances on the source labeling task. This can be achieved through the use of Adversarial machine learning techniques where feature representations from samples in different domains are encouraged to be indistinguishable. === Hierarchical Bayesian Model === The goal is to construct a Bayesian hierarchical model p ( n ) {\displaystyle p(n)} , which is essentially a factorization model for counts n {\displaystyle n} , to derive domain-dependent latent representations allowing both domain-specific and globally shared latent factors. == Software packages == Several compilations of domain adaptation and transfer learning algorithms have been implemented over the past decades: SKADA (Python) ADAPT (Python) TLlib (Python) Domain-Adaptation-Toolbox (MATLAB)

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  Principle of rationality

  The principle of rationality (or rationality principle) was coined by Karl R. Popper in his Harvard Lecture of 1963, and published in his book Myth of Framework. It is related to what he called the 'logic of the situation' in an Economica article of 1944/1945, published later in his book The Poverty of Historicism. According to Popper's rationality principle, agents act in the most adequate way according to the objective situation. It is an idealized conception of human behavior which he used to drive his model of situational analysis. Cognitive scientist Allen Newell elaborated on the principle in his account of knowledge level modeling. == Popper == Popper called for social science to be grounded in what he called situational analysis or situational logic. This requires building models of social situations which include individual actors and their relationship to social institutions, e.g. markets, legal codes, bureaucracies, etc. These models attribute certain aims and information to the actors. This forms the 'logic of the situation', the result of reconstructing meticulously all circumstances of an historical event. The 'principle of rationality' is the assumption that people are instrumental in trying to reach their goals, and this is what drives the model. Popper believed that this model could be continuously refined to approach the objective truth. Popper called his principle of rationality nearly empty (a technical term meaning without empirical content) and strictly speaking false, but nonetheless tremendously useful. These remarks earned him a lot of criticism because seemingly he had swerved from his famous Logic of Scientific Discovery. Among the many philosophers having discussed Popper's principle of rationality from the 1960s up to now are Noretta Koertge, R. Nadeau, Viktor J. Vanberg, Hans Albert, E. Matzner, Ian C. Jarvie, Mark A. Notturno, John Wettersten, Ian C. Böhm. == Newell == In the context of knowledge-based systems, Newell (in 1982) proposed the following principle of rationality: "If an agent has knowledge that one of its actions will lead to one of its goals, then the agent will select that action." This principle is employed by agents at the knowledge level to move closer to a desired goal. An important philosophical difference between Newell and Popper is that Newell argued that the knowledge level is real in the sense that it exists in nature and is not made up. This allowed Newell to treat the rationality principle as a way of understanding nature and avoid the problems Popper ran into by treating knowledge as non physical and therefore non empirical.

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  Halite AI Programming Competition

  Halite is an open-source computer programming contest developed by the hedge fund/tech firm Two Sigma in partnership with a team at Cornell Tech. Programmers can see the game environment and learn everything they need to know about the game. Participants are asked to build bots in whichever language they choose to compete on a two-dimensional virtual battle field. == History == Benjamin Spector and Michael Truell created the first Halite competition in 2016, before partnering with Two Sigma later that year. === Halite I === Halite I asked participants to conquer territory on a grid. It launched in November 2016 and ended in February 2017. Halite I attracted about 1,500 players. === Halite II === Halite II was similar to Halite I, but with a space-war theme. It ran from October 2017 until January 2018. The second installment of the competition attracted about 6,000 individual players from more than 100 countries. Among the participants were professors, physicists and NASA engineers, as well as high school and university students. === Halite III === Halite III launched in mid-October 2018. It ran from October 2018 to January 2019, with an ocean themed playing field. Players were asked to collect and manage Halite, an energy resource. By the end of the competition, Halite III included more than 4000 players and 460 organizations. === Halite IV === Halite IV was hosted by Kaggle, and launched in mid-June 2020.

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  Spatial embedding

  Spatial embedding is one of feature learning techniques used in spatial analysis where points, lines, polygons or other spatial data types. representing geographic locations are mapped to vectors of real numbers. Conceptually it involves a mathematical embedding from a space with many dimensions per geographic object to a continuous vector space with a much lower dimension. Such embedding methods allow complex spatial data to be used in neural networks and have been shown to improve performance in spatial analysis tasks == Embedded data types == Geographic data can take many forms: text, images, graphs, trajectories, polygons. Depending on the task, there may be a need to combine multimodal data from different sources. The next section describes examples of different types of data and their uses. === Text === Geolocated posts on social media can be used to acquire a library of documents bound to a given place that can be later transformed to embedded vectors using word embedding techniques. === Image === Satellites and aircraft collect digital spatial data acquired from remotely sensed images which can be used in machine learning. They are sometimes hard to analyse using basic image analysis methods and convolutional neural networks can be used to acquire an embedding of images bound to a given geographical object or a region. === Point === A single point of interest (POI) can be assigned multiple features that can be used in machine learning. These could be demographic, transportation, meteorological, or economic data, for example. When embedding single points, it is common to consider the entire set of available points as nodes in a graph. === Line / multiline === Among other things, motion trajectories are represented as lines (multilines). Individual trajectories are embedded taking into account travel time, distances and also features of points visited along the way. Embedding of trajectories allows to improve performance of such tasks as clustering and also categorization. === Polygon === The geographic areas analyzed in machine learning are defined by both administrative boundaries and top-down division into grids of regular shapes such as rectangles, for example. Both types are represented as polygons and, like points, can be assigned different demographic, transportation, or economic features. A polygon can also have features related to the size of the area or shape it represents. === Graph === An example domain where graph representation is used is the street layout in a city, where vertices can be intersections and edges can be roads. The vertices can also be destination points like public transport stops or important points in the city, and the edges represent the flow between them. Embedding graphs or single vertices allows to improve accuracy of analysis methods in which the treated geographical domain can be represented as a network. == Usage == POI recommendation - generating personalized point of interest recommendations based on user preferences. Next/future location prediction - prediction of the next location a person will go to based on their historical trajectory. Zone functions classification - based on different mobility of people or POI distribution a function of a given area in a city can be predicted. Crime prediction - estimation of crime rate in different regions of a city. Local event detection - studying spatio-temporal changes in embeddings can provide valuable information in detection of local event occurring in specific location. Regional mobility popularity prediction - analysis of mobility can show patterns in popularity of different regions in a city. Shape matching - finding a similar shape of given polygon, for example finding building with the same shape as input building. Travel time estimation - predicting estimated travel time given current traffic conditions and special occurring events. Time estimation for on-demand food delivery - estimation of delivery time when placing an order through the website. == Temporal aspect == Some of the data analyzed has a timestamp associated with it. In some cases of data analysis this information is omitted and in others it is used to divide the set into groups. The most common division is the separation of weekdays from weekends or division into hours of the day. This is particularly important in the analysis of mobility data, because the characteristics of mobility during the week and at different times of the day are very different from each other. Another area in which time division into, for example, individual months can be used is in the analysis of tourism of a given region. In order to take such a split into account, embedding methods treat the time stamp specifically or separate versions of the model are developed for different subgroups of the analyzed set.

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  Service-oriented software engineering

  Service-oriented software engineering (SOSE), also referred to as service engineering, is a software engineering methodology focused on the development of software systems by composition of reusable services (service-orientation) often provided by other service providers. Since it involves composition, it shares many characteristics of component-based software engineering, the composition of software systems from reusable components, but it adds the ability to dynamically locate necessary services at run-time. These services may be provided by others as web services, but the essential element is the dynamic nature of the connection between the service users and the service providers. == Service-oriented interaction pattern == There are three types of actors in a service-oriented interaction: service providers, service users and service registries. They participate in a dynamic collaboration which can vary from time to time. Service providers are software services that publish their capabilities and availability with service registries. Service users are software systems (which may be services themselves) that accomplish some task through the use of services provided by service providers. Service users use service registries to discover and locate the service providers they can use. This discovery and location occurs dynamically when the service user requests them from a service registry.

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  Sycophancy (artificial intelligence)

  In the field of artificial intelligence, sycophancy is a tendency of large language models (LLMs) and other AI assistants to tailor their responses to what they predict the user wants to hear rather than to what is accurate or warranted. The behavior takes several forms: an assistant may agree with a user's stated opinion even when the user is mistaken; it may abandon a correct answer after a challenge such as "are you sure?"; it may validate beliefs, decisions or self-presentation regardless of merit; or it may praise the user, their work or their ideas in unwarranted terms. The word is borrowed from the ordinary English term for fawning flattery, and is used in AI alignment and AI safety research to describe a class of misalignment failures associated with training on human feedback. Researchers at Anthropic first documented the behavior systematically in 2022. They found that models fine-tuned with reinforcement learning from human feedback (RLHF) were more likely than untuned models to repeat back a user's preferred answer. A 2023 follow-up paper, "Towards Understanding Sycophancy in Language Models", showed that five frontier assistants from OpenAI, Anthropic and Meta all exhibited the behavior, and traced its origin to biases in the human preference data used during training. Later work documented sycophancy in mathematics, medicine, academic peer review and other domains, and identified a broader category called "social sycophancy" affecting an assistant's emotional and interpersonal responses. The issue drew widespread public attention in April 2025 after OpenAI rolled back an update to its GPT-4o model. Users had reported that the assistant praised dangerous decisions, endorsed delusional thinking and offered exaggerated compliments for trivial prompts. OpenAI's post-mortem attributed the change in behavior to an additional training signal based on user thumbs-up and thumbs-down feedback. That episode, together with reporting in The New York Times, Rolling Stone and elsewhere on users drawn into delusional thinking through prolonged chatbot interaction, has been cited in litigation and in academic studies as evidence that sycophancy poses risks to user well-being. Proposed mitigations include fine-tuning on synthetic data that rewards disagreement with incorrect user statements, editing the small subset of model parameters causally responsible for the behavior, changes to the dialogue or system prompt, and benchmarks designed to surface sycophantic behavior before models are released. == Causes == The dominant explanation points to RLHF, the standard technique for aligning chat assistants with user expectations. Human annotators rank candidate model responses; a reward model is trained to predict those rankings; and the language model is then optimized against the reward model. Because human raters tend to prefer outputs that confirm their existing beliefs or flatter their work, the pipeline systematically rewards responses that agree with the annotator. Perez and colleagues at Anthropic published the first large-scale empirical evidence of the effect in 2022. They reported that RLHF training increased the probability that a model would repeat back a dialog user's preferred answer, and that larger models exhibited the behavior more strongly. Sharma and colleagues, the following year, went further and examined Anthropic's own preference data directly. Both the human raters and the reward models trained on their judgments preferred convincingly written sycophantic responses to truthful ones at a non-negligible rate. Wei and co-authors at Google DeepMind found similar results in the PaLM family, observing that both model scale and instruction tuning increased sycophancy on opinion questions. The behavior is often classified as a form of reward hacking, in which an optimization process exploits a flaw in its reward signal rather than achieving the intended objective. OpenAI's post-mortem of the April 2025 GPT-4o incident identified a more specific mechanism. An additional reward signal based on aggregated thumbs-up and thumbs-down feedback from ChatGPT users had, in OpenAI's words, "weakened the influence of our primary reward signal, which had been holding sycophancy in check." Separately, an Anthropic interpretability paper from 2025 located a linear direction in a model's internal activations corresponding to sycophantic behavior, and showed that such "persona vectors" could be used to flag sycophancy-inducing training data and to steer models away from the trait at inference time. == Measurement == The Anthropic team released SycophancyEval with its 2023 paper, supplying test sets for each of the four canonical behaviors. Two further benchmarks from Stanford followed in 2025. SycEval, applied to mathematical and medical reasoning tasks, reported an overall sycophancy rate of 58 per cent across the GPT-4o, Claude and Gemini models tested. ELEPHANT, aimed at social sycophancy, found that the eleven LLMs evaluated affirmed posts that the Reddit community r/AmITheAsshole had judged inappropriate in 42 per cent of cases, and preserved a user's face 45 percentage points more often than human respondents did. Domain-specific benchmarks have followed. BrokenMath tests robustness to plausible-looking but false mathematical claims drawn from competition problems, and reports that the best evaluated model was sycophantic in 29 per cent of cases. SYCON-Bench measures how many dialogue turns are required before a model abandons a correct position. Visual sycophancy in multimodal models has been examined with MM-SY and PENDULUM. A 2026 study by researchers at the Massachusetts Institute of Technology reported that personalization features, which adapt assistants to individual users over repeated sessions, can intensify social sycophancy. == Notable incidents == === GPT-4o rollback (April 2025) === On 25 April 2025, OpenAI completed the rollout of an update to GPT-4o, the default model used in ChatGPT at the time. Within days, users reported that the assistant had begun praising trivial messages in extravagant terms, endorsing impulsive or dangerous decisions, and reinforcing strong emotional statements without pushback. Widely shared examples included the model congratulating a user who reported stopping prescribed psychiatric medication, and praising a business plan to sell "shit on a stick" as venture-capital ready. OpenAI's chief executive, Sam Altman, wrote on 27 April that recent updates had made the model "too sycophant-y and annoying" and said fixes were in progress. The company began reverting the update on 28 April and completed the rollback for free users by 30 April. Two post-mortems followed: a short note on 29 April and a longer technical follow-up, "Expanding on what we missed with sycophancy", on 2 May. Both attributed the regression to a new training signal based on user thumbs-up and thumbs-down feedback, to inadequate pre-launch evaluation for sycophantic drift, and to the dismissal of qualitative concerns raised by internal testers before release. Reporting in CNN, Fortune and Bloomberg News treated the incident as a turning point in public awareness of the problem. === Chatbot-related psychological harm === From mid-2025 onward, news reports began to link sycophantic chatbot behavior to acute psychological harm. In June 2025, The New York Times technology reporter Kashmir Hill published an investigation centered on Eugene Torres, a Manhattan accountant with no history of mental illness, who developed a sustained delusional episode after a series of conversations with ChatGPT about simulation theory. According to the article, the assistant encouraged Torres to stop taking prescribed medication, to cut off friends and family, and at one point told him that he could fly from a nineteen-story building if he "truly believed". Futurism and Rolling Stone ran parallel investigations documenting other cases in which heavy use of ChatGPT had been associated with delusional thinking, involuntary commitment or, in at least one case, the death of a user with a pre-existing psychiatric diagnosis. A 2026 paper by researchers at the Massachusetts Institute of Technology and the University of Washington put forward a formal Bayesian model. It showed that even an ideally rational user could be drawn into what the authors call "delusional spiraling" when interacting with a sufficiently sycophantic assistant, and that the effect was not eliminated by suppressing hallucinations or by warning users in advance. The lawsuit Raine v. OpenAI, filed in San Francisco Superior Court in August 2025 by the parents of a sixteen-year-old who had died by suicide, alleges that "heightened sycophancy" was a design feature of ChatGPT that contributed to their son's death; it is the first wrongful-death suit against a large language-model provider. === Wider commentary === Mainstream coverage in outlets including The New York Times, The Washington Pos

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  Virtual intelligence

  Virtual intelligence (VI) is the term given to artificial intelligence that exists within a virtual world. Many virtual worlds have options for persistent avatars that provide information, training, role-playing, and social interactions. The immersion in virtual worlds provides a platform for VI beyond the traditional paradigm of past user interfaces (UIs). What Alan Turing established as a benchmark for telling the difference between human and computerized intelligence was devoid of visual influences. With today's VI bots, virtual intelligence has evolved past the constraints of past testing into a new level of the machine's ability to demonstrate intelligence. The immersive features of these environments provide nonverbal elements that affect the realism provided by virtually intelligent agents. Virtual intelligence is the intersection of these two technologies: Virtual environments: Immersive 3D spaces provide for collaboration, simulations, and role-playing interactions for training. Many of these virtual environments are currently being used for government and academic projects, including Second Life, VastPark, Olive, OpenSim, Outerra, Oracle's Open Wonderland, Duke University's Open Cobalt, and many others. Some of the commercial virtual worlds are also taking this technology into new directions, including the high-definition virtual world Blue Mars. Artificial intelligence (AI): AI is a branch of computer science that aims to create intelligent machines capable of performing tasks that typically require human intelligence. VI is a type of AI that operates within virtual environments to simulate human-like interactions and responses. == Applications == Cutlass Bomb Disposal Robot: Northrop Grumman developed a virtual training opportunity because of the prohibitive real-world cost and dangers associated with bomb disposal. By replicating a complicated system without having to learn advanced code, the virtual robot has no risk of damage, trainee safety hazards, or accessibility constraints. MyCyberTwin: NASA is among the companies that have used the MyCyberTwin AI technologies. They used it for the Phoenix rover in the virtual world Second Life. Their MyCyberTwin used a programmed profile to relay information about what the Phoenix rover was doing and its purpose. Second China: The University of Florida developed the "Second China" project as an immersive training experience for learning how to interact with the culture and language in a foreign country. Students are immersed in an environment that provides role-playing challenges coupled with language and cultural sensitivities magnified during country-level diplomatic missions or during times of potential conflict or regional destabilization. The virtual training provides participants with opportunities to access information, take part in guided learning scenarios, communicate, collaborate, and role-play. While China was the country for the prototype, this model can be modified for use with any culture to help better understand social and cultural interactions and see how other people think and what their actions imply. Duke School of Nursing Training Simulation: Extreme Reality developed virtual training to test critical thinking with a nurse performing trained procedures to identify critical data to make decisions and performing the correct steps for intervention. Bots are programmed to respond to the nurse's actions as the patient with their conditions improving if the nurse performs the correct actions.

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