ACM SIGEVO

The ACM SIGEVO is a Special Interest Group of the Association of Computing Machinery for members of that organization who are practitioners, academics, students or others with interests in evolutionary computation and related algorithms. == History == ACM SIGEVO was founded in 2005 when the International Society for Genetic and Evolutionary Computation (ISGEC) became an ACM Special Interest Group under its present title. The ISGEC had been formed in 1999 by the merger of the Genetic Programming conference organization with the International Conference on Genetic Algorithms (ICGA) leading to the first Genetic and Evolutionary Computation Conference (GECCO). == Membership == Members of this SIG pay a small fee in addition to the ACM membership fee. In return they have access to a quarterly online newsletter, but more importantly can obtain reduced registration rates at the two conferences organised by ACM SIGEVO: GECCO and the Foundations of Genetic Algorithms conference (FOGA). They can also access material on evolutionary computation and related topics in the ACM Digital Library. In addition they can subscribe to email mailing lists in order to keep informed about news over time. For students, ACM SIGEVO sponsors Travel Awards for attendance at the GECCO Conference and FOGA (the Foundations of Genetic Algorithms conference). ACM SIGEVO also sponsors a Graduate Student Workshop. ACM also sponsors Awards to be competed for by attendees at the conferences it organises. == Conferences == ACM SIGEVO organises two major conferences in the field of evolutionary computation. The Genetic and Evolutionary Conference (GECCO) is held annually, while the Foundations of Genetic Algorithms conference (FOGA) is held biennially. === GECCO === The first GECCO conference was held prior to the formation of ACM SIGEVO but since 2005 (see History above) it has been organised annually by ACM SIGEVO. The latest (2025) was held in Málaga, Spain. The next (2026) will be held in San José, Costa Rica. === FOGA === Foundations of Genetic Algorithms (FOGA) is a biennial peer-reviewed research conference focusing on the theoretical principles underlying genetic algorithms, other evolutionary algorithms and related heuristics. It is organized by ACM SIGEVO. Its relevance to the computer science research community has been reflected in an A-rating in the CORE computer science conference assessment system. The Foundations of Genetic Algorithms (FOGA) conference originated as a workshop in 1990 in order to create an opportunity for researchers on genetic algorithms and related areas of evolutionary computation to focus on the theoretical principles underlying their field. From the start its multi-day duration made it comparable to conferences in the field, and since 2015 its proceedings have used conference rather than workshop in their titles. In 2005 ACM SIGEVO the Association for Computing Machinery Special Interest Group on Genetic and Evolutionary Computation was formed and every FOGA conference since then has been supported by SIGEVO. The table below shows FOGA conferences by year, location, websites (where available) and publisher of proceedings. A citation follows the reference to the publisher giving the full details of each FOGA proceedings. Papers accepted at recent conferences have been presented as digital or print posters in poster sessions at the conference, before being published in written form in the conference proceedings. FOGA is comparable in its multi-day duration to other conferences on evolutionary computation such as CEC, GECCO and PPSN. The main difference is that FOGA focuses on the theoretical basis of evolutionary computation and related subjects. While the above conferences devote some time to theory they also cover a wide range of other topics including competitions and applications. This focus on theoretical computer science was reflected in the CORE computer science conference assessment exercise, where FOGA was given an A-ranking in the 2023 assessment. GECCO and PPSN also obtained A-rankings, but many other conferences in the field of evolutionary computation obtained lower rankings. This suggests that FOGA is a relevant conference in its field, comparable with others including the much larger CEC or GECCO. Keynote speakers at past conferences have been: == Awards == ACM SIGEVO sponsors a number of awards. === SIGEVO Outstanding Contribution Award === The SIGEVO Outstanding Contribution Award commenced in 2023, and these awards are designed to recognise distinctive contributions to the field of evolutionary computation when evaluated over a period of at least 15 years. As a result many recipients to date are notable academics or industrial practitioners, and include Anne Auger, Kalyanmoy Deb, Stephanie Forrest, Emma Hart and Hans-Paul Schwefel. === SIGEVO Dissertation Award === The SIGEVO Dissertation Award recognises thesis research in the field of evolutionary computation completed at least by the year prior to a GECCO conference. Theses are submitted and reviewed by a panel that selects one winner and a maximum of two honourable mentions. Awards will be made to the winner and any others at the next GECCO conference. === SIGEVO Chair Award === The SIGEVO Chair Award, established in 2016 is a lecture sponsored by ACM SIGEVO, to take place on the last day of the GECCO conference. It recognizes through the lectures that the lecturers are influential researchers in the field of evolutionary computation. The more recent lectures are available online. The 2024 Award winner was Una-May O'Reilly. === SIGEVO Impact Award === The SIGEVO Impact Award looks back to the GECCO conference ten years earlier and recognizes up to three papers a year which are considered by the current ACM SIGEVO Executive Committee to have had significant impact over the period since their first publication at the GECCO conference. An example (originally published in GECCO 2010) received this award in 2020. === GECCO Best Paper Award === The ACM SIGEVO sponsors awards for the best papers presented at the GECCO conference. Because GECCO conferences have very many parallel tracks there are multiple awards recognising presentations in the different tracks. At GECCO 2025 Best Paper Awards were presented across 12 tracks. === FOGA Best Paper Award === The ACM SIGEVO sponsors awards for the best papers presented at the FOGA conference. Because FOGA operates on a single track, it is easier to compare papers. Since 2019 this Award has been made (suggesting only four awards up to the latest conference in 2025). ACM SIGEVO records the 2019 award. === Humie Award === The Humies Awards are rewards for the best form of human-competitive results using evolutionary computation or related algorithms and published in the wider literature (they do not need to be published at a conference or in a journal sponsored by ACM SIGEVO or even the ACM.) They were established through a gift from John Koza and have been in operation from 2004 to the present. The link with ACM SIGEVO is that the winners of the competition (submissions are evaluated in advance) are presented with Humie Awards at GECCO conferences. The Humie Awards website provides full details for the rules and how to submit entries to the competition. == Journals == ACM SIGEVO sponsors the main journal covering evolutionary computation published by the ACM: ACM Transactions on Evolutionary Learning and Optimization. ACM SIGEVO refers to the preceding ISGEC organisation (see History above) as sponsoring two other important journals in the field: The Evolutionary Computation journal. Genetic Programming and Evolvable Machines. While these journals continue to be important in the field, the wording on the website of ACM SIGEVO suggests that ACM SIGEVO is not involved in their publication. == References and notes ==

Reverse correlation technique

The reverse correlation technique is a data driven study method used primarily in psychological and neurophysiological research. This method earned its name from its origins in neurophysiology, where cross-correlations between white noise stimuli and sparsely occurring neuronal spikes could be computed quicker when only computing it for segments preceding the spikes. The term has since been adopted in psychological experiments that usually do not analyze the temporal dimension, but also present noise to human participants. In contrast to the original meaning, the term is here thought to reflect that the standard psychological practice of presenting stimuli of defined categories to the participants is "reversed": Instead, the participant's mental representations of categories are estimated from interactions of the presented noise and the behavioral responses. It is used to create composite pictures of individual and/or group mental representations of various items (e.g. faces, bodies, and the self) that depict characteristics of said items (e.g. trustworthiness and self-body image). This technique is helpful when evaluating the mental representations of those with and without mental illnesses. == Terms == This technique utilizes spike-triggered average to explain what areas of signal and noise in an image are valuable for the given research question. Signal is information used to produce objects of value that help explain and connect the world around us. Noise is commonly referred to as unwanted signal that obscures the information that the signal is trying to present. Most importantly for reverse correlation studies, noise is randomly varying information. To determine the areas of importance using reverse correlation, noise is applied to a base image and then evaluated by observers. A base image is any image void of noise that relates to the research question. A base image that has noise superimposed on top is the stimuli that is presented to and evaluated by participants. Each time a new set of stimuli is presented to a participant, this is known as a trial. After a participant has responded to hundreds to thousands of trials, a researcher is ready to create a classification image. A classification image (abbreviated as "CI" in some studies) is a single image that represents the average noise patterns in the images selected by participants. A classification image can also be computed for groups by averaging the individuals’ classification images. These classification images are what researchers use to interpret the data and draw conclusions. As a whole, the reverse correlation method is a process that results in a composite image (from an individual or group) that can be used to estimate and interpret mental representations. == Basic study layout == The reverse correlation method is typically executed as an in-lab computer experiment. This method follows four broad steps. Each of the following steps are described in greater detail below. After creating a research question and determining that the reverse correlation method is the most suitable technique to answer the question, a researcher must (1) design randomly varying stimuli. After the stimuli have been prepared, a researcher should (2) collect data from participants who will see and respond to approximately 300 -1,000 trials. Each trial will either consist of one or two images (side by side) derived from the same base image with noise superimposed on top. Participant responses will depend on the chosen study design; if a researcher presents only one image at a time, participants rate the image on a 4pt scale, but when two images are shown, the participant is asked to choose which best aligns with the given category (e.g. choose the image that looks the most aggressive). Once all of the data is collected, the researcher will (3) compute classification images for each participant and using those images compute group classification images. Finally, with the classification images available, the researcher will (4) evaluate the images and draw conclusions about their results. === Step 1: making stimuli === When designing the stimuli for a reverse correlation study, the two primary factors that one should consider are (1) the base image and (2) the noise that will be used. While not all bases are images per se, the majority are and for this reason the base is typically referred to as a base image. The base image should represent whatever the research question is addressing. For example, if you are interested in peoples’ mental representations of Chinese people, it would not make sense to use a base image of a Spanish or Caucasian person. Again, if you are interested in the mental representations of male vocal patterns, it would make the most sense to use a base vocal pattern that has been produced by a male. Having a base is important because it provides a kind of anchor for participants to work from. When there is no base image, the number of trials that are required increases dramatically, thus making it harder to collect data. While there are studies that have excluded a base image, (e.g. the S study), for more elaborate and nuanced research questions, it is important to have a base image that is a fair representation of what participants are being asked to categorize. Photographs of faces are generally the most popular base image. Although the reverse correlation method is capable of investigating a wide variety of research questions, the most common application of the method is for evaluating faces on a single trait. Reverse correlation studies that address evaluations of the face are sometimes referred to as being a face space reverse correlation model (FSRCM). Thankfully, there are existing databases for face images of varying demographics and emotion that work well as base images. The reverse correlation method can also be used to help researchers identify what areas of an image (e.g. the areas on the face) have diagnostic value. In order to identify these areas of value, researchers start by minimizing the space a participant can pull information from. By imposing a “mask” on an image (e.g. blur an image while leaving random areas un-blurred), this reduces the information individuals might see, and forces them to focus on certain areas. Then, if/when participants are able to correctly identify an image with a trait repeatedly, we can draw conclusions about what areas have diagnostic value. While faces and visual stimuli are the most popular, this is not the only stimuli that can be used in a reverse correlation study. This method was originally designed for auditory stimuli which allows researchers to investigate how perceivers interpret auditory information and create trait based attributions to different sound patterns. For example, by segmenting a vocal recording of a single word (total sound time 426 ms) into six segments (71 ms each), and varying each segment's pitch using Gaussian distributions, researchers were able to uncover what vocal patterns people associated with certain traits. Specifically, this study investigated how listeners rated sound clips of the word “really” as sounding more interrogative (i.e. like the more common reverse correlation studies this study had participants listen to two sound clips per trial, choose which fit the category the best, and then created an average of the pitch contours). Beyond face and auditory perception, research utilizing the reverse correlation method has expanded to investigate how individuals see three-dimensional objects in images with noise (but no signal). After selecting your base image, regardless of what the image is, it is helpful to apply a Gaussian blur to smooth noise in the image. While noise will be applied later, it is helpful to reduce existing noise in the photo before applying your chosen noise. There are three primary choices when it comes to noise: white noise, sine-wave noise, and Gabor noise. The latter two of these constrain the configurations that the noise can have, and because of this white noise is usually the most commonly used. Regardless of the type of noise that is chosen, it is crucial that the noise randomly varies. === Step 2: data collection === Once the stimuli for the study has been developed, the researcher must make a few decisions before actually collecting the data. The researcher must come to a conclusion on how many stimuli will be presented at a time and how many trials the participants will see. In terms of stimuli presentation, a researcher can choose from either a 2-Image Forced Choice (2IFC) or a 4-Alternative Forced Choice (4AFC). The 2IFC presents two images at once (side by side) and requires participants to choose between the two on a specified category (e.g. which image looks the most like a male). Typically the noise from the left image is the mathematical inverse of the noise from the right image. This method was developed to better answer questions that could n

Neural Networks (journal)

Neural Networks is a monthly peer-reviewed scientific journal and an official journal of the International Neural Network Society, European Neural Network Society, and Japanese Neural Network Society. == History == The journal was established in 1988 and is published by Elsevier. It covers all aspects of research on artificial neural networks. The founding editor-in-chief was Stephen Grossberg (Boston University). The current editors-in-chief are DeLiang Wang (Ohio State University) and Taro Toyoizumi (RIKEN Center for Brain Science). == Abstracting and indexing == The journal is abstracted and indexed in Scopus and the Science Citation Index Expanded. According to the Journal Citation Reports, the journal has a 2022 impact factor of 7.8.

Abess

abess (Adaptive Best Subset Selection, also ABESS) is a machine learning method designed to address the problem of best subset selection. It aims to determine which features or variables are crucial for optimal model performance when provided with a dataset and a prediction task. abess was introduced by Zhu in 2020 and it dynamically selects the appropriate model size adaptively, eliminating the need for selecting regularization parameters. abess is applicable in various statistical and machine learning tasks, including linear regression, the Single-index model, and other common predictive models. abess can also be applied in biostatistics. == Basic Form == The basic form of abess is employed to address the optimal subset selection problem in general linear regression. abess is an l 0 {\displaystyle l_{0}} method, it is characterized by its polynomial time complexity and the property of providing both unbiased and consistent estimates. In the context of linear regression, assuming we have knowledge of n {\displaystyle n} independent samples ( x i , y i ) , i = 1 , … , n {\displaystyle (x_{i},y_{i}),i=1,\ldots ,n} , where x i ∈ R p × 1 {\displaystyle x_{i}\in \mathbb {R} ^{p\times 1}} and y i ∈ R {\displaystyle y_{i}\in \mathbb {R} } , we define X = ( x 1 , … , x n ) ⊤ {\displaystyle X=(x_{1},\ldots ,x_{n})^{\top }} and y = ( y 1 , … , y n ) ⊤ {\displaystyle y=(y_{1},\ldots ,y_{n})^{\top }} . The following equation represents the general linear regression model: y = X β + ε . {\displaystyle y=X\beta +\varepsilon .} To obtain appropriate parameters β {\displaystyle \beta } , one can consider the loss function for linear regression: L n LR ( β ; X , y ) = 1 2 n ‖ y − X β ‖ 2 2 . {\displaystyle {\mathcal {L}}_{n}^{\text{LR}}(\beta ;X,y)={\frac {1}{2n}}\|y-X\beta \|_{2}^{2}.} In abess, the initial focus is on optimizing the loss function under the l 0 {\displaystyle l_{0}} constraint. That is, we consider the following problem: min β ∈ R p × 1 L n LR ( β ; X , y ) , subject to ‖ β ‖ 0 ≤ s , {\displaystyle \min _{\beta \in \mathbb {R} ^{p\times 1}}{\mathcal {L}}_{n}^{\text{LR}}(\beta ;X,y),{\text{ subject to }}\|\beta \|_{0}\leq s,} where s {\displaystyle s} represents the desired size of the support set, and ‖ β ‖ 0 = ∑ i = 1 p I ( β i ≠ 0 ) {\displaystyle \|\beta \|_{0}=\sum _{i=1}^{p}{\mathcal {I}}_{(\beta _{i}\neq 0)}} is the l 0 {\displaystyle l_{0}} norm of the vector. To address the optimization problem described above, abess iteratively exchanges an equal number of variables between the active set and the inactive set. In each iteration, the concept of sacrifice is introduced as follows: For j in the active set ( j ∈ A ^ {\displaystyle j\in {\hat {\mathcal {A}}}} ): ξ j = L n LR ( β ^ A ∖ { j } ) − L n LR ( β ^ A ) = X j ⊤ X j 2 n ( β ^ j ) 2 {\displaystyle \xi _{j}={\mathcal {L}}_{n}^{\text{LR}}\left({\hat {\boldsymbol {\beta }}}^{{\mathcal {A}}\backslash \{j\}}\right)-{\mathcal {L}}_{n}^{\text{LR}}\left({\hat {\boldsymbol {\beta }}}^{\mathcal {A}}\right)={\frac {{\boldsymbol {X}}_{j}^{\top }{\boldsymbol {X}}_{j}}{2n}}\left({\hat {\beta }}_{j}\right)^{2}} For j in the inactive set ( j ∉ A ^ {\displaystyle j\notin {\hat {\mathcal {A}}}} ): ξ j = L n LR ( β ^ A ) − L n LR ( β ^ A + t ^ { j } ) = X j ⊤ X j 2 n ( d ^ j X j ⊤ X j / n ) 2 {\displaystyle \xi _{j}={\mathcal {L}}_{n}^{\text{LR}}\left({\hat {\boldsymbol {\beta }}}^{\mathcal {A}}\right)-{\mathcal {L}}_{n}^{\text{LR}}\left({\hat {\boldsymbol {\beta }}}^{\mathcal {A}}+{\hat {\boldsymbol {t}}}^{\{j\}}\right)={\frac {{\boldsymbol {X}}_{j}^{\top }{\boldsymbol {X}}_{j}}{2n}}\left({\frac {{\hat {\mathrm {d} }}_{j}}{{\boldsymbol {X}}_{j}^{\top }{\boldsymbol {X}}_{j}/n}}\right)^{2}} Here are the key elements in the above equations: β ^ A {\displaystyle {\hat {\beta }}^{\mathcal {A}}} : This represents the estimate of β {\displaystyle \beta } obtained in the previous iteration. A ^ {\displaystyle {\hat {\mathcal {A}}}} : It denotes the estimated active set from the previous iteration. β ^ A ∖ { j } {\displaystyle {\hat {\boldsymbol {\beta }}}^{{\mathcal {A}}\backslash \{j\}}} : This is a vector where the j-th element is set to 0, while the other elements are the same as β ^ A {\displaystyle {\hat {\beta }}^{\mathcal {A}}} . t ^ { j } = arg ⁡ min t L n LR ( β ^ A + t { j } ) {\displaystyle {\hat {\boldsymbol {t}}}^{\{j\}}=\arg \min _{t}{\mathcal {L}}_{n}^{\text{LR}}\left({\hat {\boldsymbol {\beta }}}^{\mathcal {A}}+{\boldsymbol {t}}^{\{j\}}\right)} : Here, t { j } {\displaystyle t^{\{j\}}} represents a vector where all elements are 0 except the j-th element. d ^ j = X j ⊤ ( y − X β ^ ) / n {\displaystyle {\hat {d}}_{j}={\boldsymbol {X}}_{j}^{\top }({\boldsymbol {y}}-{\boldsymbol {X}}{\hat {\boldsymbol {\beta }}})/n} : This is calculated based on the equation mentioned. The iterative process involves exchanging variables, with the aim of minimizing the sacrifices in the active set while maximizing the sacrifices in the inactive set during each iteration. This approach allows abess to efficiently search for the optimal feature subset. In abess, select an appropriate s max {\displaystyle s_{\max }} and optimize the above problem for active sets size s = 1 , … , s max {\displaystyle s=1,\ldots ,s_{\max }} using the information criterion GIC = n log ⁡ L n LR + s log ⁡ p log ⁡ log ⁡ n , {\displaystyle {\text{GIC}}=n\log {\mathcal {L}}_{n}^{\text{LR}}+s\log p\log \log n,} to adaptively choose the appropriate active set size s {\displaystyle s} and obtain its corresponding abess estimator. == Generalizations == The splicing algorithm in abess can be employed for subset selection in other models. === Distribution-Free Location-Scale Regression === In 2023, Siegfried extends abess to the case of Distribution-Free and Location-Scale. Specifically, it considers the optimization problem max ϑ ∈ R P , β ∈ R J , γ ∈ R J ∑ i = 1 N ℓ i ( ϑ , x i ⊤ β , exp ⁡ ( x i ⊤ γ ) − 1 ) , {\displaystyle \max _{{\boldsymbol {\vartheta }}\in \mathbb {R} ^{P},{\boldsymbol {\beta }}\in \mathbb {R} ^{J},{\boldsymbol {\gamma }}\in \mathbb {R} ^{J}}\sum _{i=1}^{N}\ell _{i}\left({\boldsymbol {\vartheta }},{\boldsymbol {x}}_{i}^{\top }{\boldsymbol {\beta }},{\sqrt {\exp \left({\boldsymbol {x}}_{i}^{\top }{\boldsymbol {\gamma }}\right)}}^{-1}\right),} subject to ‖ ( β ⊤ , γ ⊤ ) ⊤ ‖ 0 ≤ s , {\displaystyle \left\|\left({\boldsymbol {\beta }}^{\top },{\boldsymbol {\gamma }}^{\top }\right)^{\top }\right\|_{0}\leq s,} where ℓ i {\displaystyle \ell _{i}} is a loss function, ϑ {\displaystyle {\boldsymbol {\vartheta }}} is a parameter vector, β {\displaystyle {\boldsymbol {\beta }}} and γ {\displaystyle {\boldsymbol {\gamma }}} are vectors, and x i {\displaystyle {\boldsymbol {x}}_{i}} is a data vector. This approach, demonstrated across various applications, enables parsimonious regression modeling for arbitrary outcomes while maintaining interpretability through innovative subset selection procedures. === Groups Selection === In 2023, Zhang applied the splicing algorithm to group selection, optimizing the following model: min β ∈ R p L n LR ( β ; X , y ) subject to ∑ j = 1 J I ( ‖ β G j ‖ 2 ≠ 0 ) ≤ s {\displaystyle \min _{{\boldsymbol {\beta }}\in \mathbb {R} ^{p}}{\mathcal {L}}_{n}^{\text{LR}}(\beta ;X,y){\text{ subject to }}\sum _{j=1}^{J}I\left(\|{\boldsymbol {\beta }}_{G_{j}}\|_{2}\neq 0\right)\leq s} Here are the symbols involved: J {\displaystyle J} : Total number of feature groups, representing the existence of J {\displaystyle J} non-overlapping feature groups in the dataset. G j {\displaystyle G_{j}} : Index set for the j {\displaystyle j} -th feature group, where j {\displaystyle j} ranges from 1 to J {\displaystyle J} , representing the feature grouping structure in the data. s {\displaystyle s} : Model size, a positive integer determined from the data, limiting the number of selected feature groups. === Regression with Corrupted Data === Zhang applied the splicing algorithm to handle corrupted data. Corrupted data refers to information that has been disrupted or contains errors during the data collection or recording process. This interference may include sensor inaccuracies, recording errors, communication issues, or other external disturbances, leading to inaccurate or distorted observations within the dataset. === Single Index Models === In 2023, Tang applied the splicing algorithm to optimal subset selection in the Single-index model. The form of the Single Index Model (SIM) is given by y i = g ( b ⊤ x i , e i ) , i = 1 , … , n , {\displaystyle y_{i}=g({\boldsymbol {b}}^{\top }{\boldsymbol {x}}_{i},e_{i}),\quad i=1,\ldots ,n,} where b {\displaystyle {\boldsymbol {b}}} is the parameter vector, e i {\displaystyle e_{i}} is the error term. The corresponding loss function is defined as l n ( β ) = ∑ i = 1 n ( r i n − 1 2 − x i ⊤ β ) 2 , {\displaystyle l_{n}({\boldsymbol {\beta }})=\sum _{i=1}^{n}\left({\frac {r_{i}}{n}}-{\frac {1}{2}}-{\boldsymbol {x}}_{i}^{\top }{\boldsymbol {\beta }}\right)^{2},} where r {\disp

Linear genetic programming

"Linear genetic programming" is unrelated to "linear programming". Linear genetic programming (LGP) is a particular method of genetic programming wherein computer programs in a population are represented as a sequence of register-based instructions from an imperative programming language or machine language. The adjective "linear" stems from the fact that each LGP program is a sequence of instructions and the sequence of instructions is normally executed sequentially. Like in other programs, the data flow in LGP can be modeled as a graph that will visualize the potential multiple usage of register contents and the existence of structurally noneffective code (introns) which are two main differences of this genetic representation from the more common tree-based genetic programming (TGP) variant. Like other Genetic Programming methods, Linear genetic programming requires the input of data to run the program population on. Then, the output of the program (its behaviour) is judged against some target behaviour, using a fitness function. However, LGP is generally more efficient than tree genetic programming due to its two main differences mentioned above: Intermediate results (stored in registers) can be reused and a simple intron removal algorithm exists that can be executed to remove all non-effective code prior to programs being run on the intended data. These two differences often result in compact solutions and substantial computational savings compared to the highly constrained data flow in trees and the common method of executing all tree nodes in TGP. Furthermore, LGP naturally has multiple outputs by defining multiple output registers and easily cooperates with control flow operations. Linear genetic programming has been applied in many domains, including system modeling and system control with considerable success. Linear genetic programming should not be confused with linear tree programs in tree genetic programming, program composed of a variable number of unary functions and a single terminal. Note that linear tree GP differs from bit string genetic algorithms since a population may contain programs of different lengths and there may be more than two types of functions or more than two types of terminals. == Examples of LGP programs == Because LGP programs are basically represented by a linear sequence of instructions, they are simpler to read and to operate on than their tree-based counterparts. For example, a simple program written to solve a Boolean function problem with 3 inputs (in R1, R2, R3) and one output (in R0), could read like this: R1, R2, R3 have to be declared as input (read-only) registers, while R0 and R4 are declared as calculation (read-write) registers. This program is very simple, having just 5 instructions. But mutation and crossover operators could work to increase the length of the program, as well as the content of each of its instructions. Note that one instruction is non-effective or an intron (marked), since it does not impact the output register R0. Recognition of those instructions is the basis for the intron removal algorithm which is used analyze code prior to execution. Technically, this happens by copying an individual and then run the intron removal once. The copy with removed introns is then executed as many times as dictated by the number of training cases. Notably, the original individual is left intact, so as to continue participating in the evolutionary process. It is only the copy that is executed that is compressed by removing these "structural" introns. Another simple program, this one written in the LGP language Slash/A looks like a series of instructions separated by a slash: By representing such code in bytecode format, i.e. as an array of bytes each representing a different instruction, one can make mutation operations simply by changing an element of such an array.

Environmental impact of AI

The environmental impact of the design, training, deployment and use of artificial intelligence includes the greenhouse gas emissions from generating electricity for data centres and computing hardware, operational and upstream water use, and material impacts from hardware manufacturing, mining and electronic waste. Estimating AI's environmental effects can be difficult because results depend on how impacts are measured, including whether accounting includes only model computation or also data-centre overhead, idle capacity, hardware manufacture, and local electricity supply. As these issues have received greater attention, governments and regulators have increasingly considered data-centre reporting requirements, energy-efficiency standards, and broader transparency measures for AI-related resource use. == Carbon footprint and energy use == AI-related energy use arises at multiple stages, including model training, fine-tuning, inference, storage, networking, and supporting infrastructure such as cooling and power conversion. === Individual level === Published estimates of energy use per AI request vary widely across models, tasks and measurement methods. A benchmark study presented at the 2024 ACM Conference on Fairness, Accountability, and Transparency found substantial differences between task types, with lower energy use for some text tasks and much higher energy use for image generation in the study's test conditions. In that benchmark, simple classification tasks consumed about 0.002–0.007 Wh per prompt on average (about 9% of a smartphone charge for 1,000 prompts), while text generation and text summarisation each used about 0.05 Wh per prompt; image generation averaged 2.91 Wh per prompt, and the least efficient image model in the study used 11.49 Wh per image (roughly equivalent to half a smartphone charge). First-party measurements in production environments have also been published. A 2025 Google study on Gemini assistant serving reported median per-prompt energy, emissions, and water-use estimates under the authors' accounting framework, while noting that different system boundaries can produce substantially different results. The study reported a median text-prompt estimate of about 0.24 Wh, which is roughly as much energy as watching nine seconds of television. The study also stated that software and infrastructure improvements reduced energy use by a factor of 33 and carbon emissions by a factor of 44 for a typical prompt over one year within the authors' framework. Researchers at the University of Michigan measured the energy consumption of various Meta Llama 3.1 models released in 2024 and found that smaller language models (8 billion parameters) use about 114 joules (0.03167 Wh) per response, while larger models (405 billion parameters) require up to 6,700 joules (1.861 Wh) per response. This corresponds to the energy needed to run a microwave oven for roughly one-tenth of a second and eight seconds, respectively. Comparisons between AI systems and human labour for specific tasks have produced mixed results and remain sensitive to assumptions about output quality, workload and system boundaries. A 2024 study in Scientific Reports reported 130 to 2900 times lower estimated carbon emissions for selected AI systems than for human writers and illustrators under its assumptions. A later Scientific Reports paper reported a counterexample for programming tasks under its assumptions, finding 5 to 19 times higher estimated emissions for the evaluated AI system than for human programmers on the benchmark used in that study. === System level === ==== Energy use and efficiency ==== AI electricity intensity depends not only on model architecture but also on hardware and facility efficiency. Data-centre operators commonly report Power usage effectiveness (PUE), which measures the ratio of total facility energy to IT equipment energy; a lower PUE indicates less overhead energy for cooling and other supporting infrastructure. Operators may also publish metrics and case studies on hardware efficiency, cooling systems and power sourcing. In its 2024 environmental report, Google stated that its 2023 total greenhouse gas emissions increased 13% year over year, primarily because of increased data-centre energy consumption and supply-chain emissions, while also reporting lower PUE than industry averages for its own facilities. The International Energy Agency has also reported that data centres remain a relatively small share of global electricity use overall, but that their local effects can be much more pronounced because demand is geographically concentrated. ==== Carbon footprint ==== At system level, AI contributes to rising electricity demand in data centres and related infrastructure. The International Energy Agency estimated that data centres used about 415 TWh of electricity in 2024, or around 1.5% of global electricity consumption, and projected that data-centre electricity use could rise to about 945 TWh by 2030, with AI identified as the main driver of that growth alongside other digital services. The carbon footprint of AI systems depends strongly on electricity sources, hardware efficiency, utilisation rates, and what stages are included in the accounting. Training large models can require substantial electricity, while total lifecycle impacts also depend on deployment scale and the amount of inference performed after training. Early analyses of frontier-model development reported rapid historical growth in training compute for selected systems, although later trends have depended on changes in model design, hardware and efficiency gains. Accounting methods that include upstream or embodied impacts, such as hardware manufacture and facilities construction, can materially affect estimates of AI-related emissions. === Decisions and strategies by individual companies === Large technology companies have reported that the expansion of AI and cloud infrastructure affects their sustainability targets, electricity demand, and resource use. Google, for example, attributed part of its emissions growth in 2023 to increased data-centre energy consumption and supply-chain emissions in its 2024 environmental report. Cloud and AI companies have also announced measures intended to reduce environmental impacts, including investment in more efficient hardware, low-carbon electricity procurement, alternative cooling systems, and water stewardship programmes. The extent, comparability, and third-party verification of such disclosures vary between firms and jurisdictions. == Water usage == Data centres can use water directly for cooling and indirectly through the water used in electricity generation, depending on the local energy mix. Public reporting on data-centre water use has often been inconsistent, making comparisons between operators and regions difficult. To standardise operational reporting, The Green Grid proposed the metric water usage effectiveness (WUE), defined as annual site water use divided by IT equipment energy use. WUE does not by itself measure local water stress, source sustainability, or all upstream water impacts. Studies of AI water use also distinguish between water withdrawal and water consumption. Research on AI-specific water use has argued that the water footprint of AI systems can be difficult to observe and may vary substantially by location, cooling design, and electricity source. A 2025 Communications of the ACM article summarised methods for estimating AI water footprints and emphasised the distinction between water withdrawal and water consumption. Li and colleagues estimated that global AI water withdrawal could reach 4.2–6.6 billion cubic metres in 2027 under the scenarios examined in their article. Using GPT-3, released by OpenAI in 2020, as an example, they estimated that training the model in Microsoft's U.S. data centres could consume about 700,000 litres of onsite water and about 5.4 million litres in total when offsite electricity-related water use was included; they also estimated that 10–50 medium-length GPT-3 responses could consume about 500 mL of water, depending on when and where the model was deployed. Published prompt-level estimates have also varied by system and accounting framework: the 2025 Google study on Gemini assistant serving reported a median text-prompt estimate of about 0.26 mL under its framework. Location can materially affect the significance of data-centre water use. Research on U.S. data centres found that one-fifth of servers' direct water footprint came from moderately to highly water-stressed watersheds, while nearly half of servers were fully or partially powered by plants located in water-stressed regions. A 2025 Reuters report, citing data from Verisk Maplecroft and NatureFinance, said that an average mid-sized data centre uses about 1.4 million litres of water per day for cooling and that Phoenix would experience a 32% increase in annual water stress if currently pl

T-distributed stochastic neighbor embedding

t-distributed stochastic neighbor embedding (t-SNE) is a statistical method for visualizing high-dimensional data by giving each datapoint a location in a two or three-dimensional map. It is based on Stochastic Neighbor Embedding originally developed by Geoffrey Hinton and Sam Roweis, where Laurens van der Maaten and Hinton proposed the t-distributed variant. It is a nonlinear dimensionality reduction technique for embedding high-dimensional data for visualization in a low-dimensional space of two or three dimensions. Specifically, it models each high-dimensional object by a two- or three-dimensional point in such a way that similar objects are modeled by nearby points and dissimilar objects are modeled by distant points with high probability. The t-SNE algorithm comprises two main stages. First, t-SNE constructs a probability distribution over pairs of high-dimensional objects in such a way that similar objects are assigned a higher probability while dissimilar points are assigned a lower probability. Second, t-SNE defines a similar probability distribution over the points in the low-dimensional map, and it minimizes the Kullback–Leibler divergence (KL divergence) between the two distributions with respect to the locations of the points in the map. While the original algorithm uses the Euclidean distance between objects as the base of its similarity metric, this can be changed as appropriate. A Riemannian variant is UMAP. t-SNE has been used for visualization in a wide range of applications, including genomics, computer security research, natural language processing, music analysis, cancer research, bioinformatics, geological domain interpretation, and biomedical signal processing. For a data set with n {\displaystyle n} elements, t-SNE runs in O ( n 2 ) {\displaystyle O(n^{2})} time and requires O ( n 2 ) {\displaystyle O(n^{2})} space. == Details == Given a set of N {\displaystyle N} high-dimensional objects x 1 , … , x N {\displaystyle \mathbf {x} _{1},\dots ,\mathbf {x} _{N}} , t-SNE first computes probabilities p i j {\displaystyle p_{ij}} that are proportional to the similarity of objects x i {\displaystyle \mathbf {x} _{i}} and x j {\displaystyle \mathbf {x} _{j}} , as follows. For i ≠ j {\displaystyle i\neq j} , define p j ∣ i = exp ⁡ ( − ‖ x i − x j ‖ 2 / 2 σ i 2 ) ∑ k ≠ i exp ⁡ ( − ‖ x i − x k ‖ 2 / 2 σ i 2 ) {\displaystyle p_{j\mid i}={\frac {\exp(-\lVert \mathbf {x} _{i}-\mathbf {x} _{j}\rVert ^{2}/2\sigma _{i}^{2})}{\sum _{k\neq i}\exp(-\lVert \mathbf {x} _{i}-\mathbf {x} _{k}\rVert ^{2}/2\sigma _{i}^{2})}}} and set p i ∣ i = 0 {\displaystyle p_{i\mid i}=0} . Note the above denominator ensures ∑ j p j ∣ i = 1 {\displaystyle \sum _{j}p_{j\mid i}=1} for all i {\displaystyle i} . As van der Maaten and Hinton explained: "The similarity of datapoint x j {\displaystyle x_{j}} to datapoint x i {\displaystyle x_{i}} is the conditional probability, p j | i {\displaystyle p_{j|i}} , that x i {\displaystyle x_{i}} would pick x j {\displaystyle x_{j}} as its neighbor if neighbors were picked in proportion to their probability density under a Gaussian centered at x i {\displaystyle x_{i}} ." Now define p i j = p j ∣ i + p i ∣ j 2 N {\displaystyle p_{ij}={\frac {p_{j\mid i}+p_{i\mid j}}{2N}}} This is motivated because p i {\displaystyle p_{i}} and p j {\displaystyle p_{j}} from the N samples are estimated as 1/N, so the conditional probability can be written as p i ∣ j = N p i j {\displaystyle p_{i\mid j}=Np_{ij}} and p j ∣ i = N p j i {\displaystyle p_{j\mid i}=Np_{ji}} . Since p i j = p j i {\displaystyle p_{ij}=p_{ji}} , you can obtain previous formula. Also note that p i i = 0 {\displaystyle p_{ii}=0} and ∑ i , j p i j = 1 {\displaystyle \sum _{i,j}p_{ij}=1} . The bandwidth of the Gaussian kernels σ i {\displaystyle \sigma _{i}} is set in such a way that the entropy of the conditional distribution equals a predefined entropy using the bisection method. As a result, the bandwidth is adapted to the density of the data: smaller values of σ i {\displaystyle \sigma _{i}} are used in denser parts of the data space. The entropy increases with the perplexity of this distribution P i {\displaystyle P_{i}} ; this relation is seen as P e r p ( P i ) = 2 H ( P i ) {\displaystyle Perp(P_{i})=2^{H(P_{i})}} where H ( P i ) {\displaystyle H(P_{i})} is the Shannon entropy H ( P i ) = − ∑ j p j | i log 2 ⁡ p j | i . {\displaystyle H(P_{i})=-\sum _{j}p_{j|i}\log _{2}p_{j|i}.} The perplexity is a hand-chosen parameter of t-SNE, and as the authors state, "perplexity can be interpreted as a smooth measure of the effective number of neighbors. The performance of SNE is fairly robust to changes in the perplexity, and typical values are between 5 and 50.". Since the Gaussian kernel uses the Euclidean distance ‖ x i − x j ‖ {\displaystyle \lVert x_{i}-x_{j}\rVert } , it is affected by the curse of dimensionality, and in high dimensional data when distances lose the ability to discriminate, the p i j {\displaystyle p_{ij}} become too similar (asymptotically, they would converge to a constant). It has been proposed to adjust the distances with a power transform, based on the intrinsic dimension of each point, to alleviate this. t-SNE aims to learn a d {\displaystyle d} -dimensional map y 1 , … , y N {\displaystyle \mathbf {y} _{1},\dots ,\mathbf {y} _{N}} (with y i ∈ R d {\displaystyle \mathbf {y} _{i}\in \mathbb {R} ^{d}} and d {\displaystyle d} typically chosen as 2 or 3) that reflects the similarities p i j {\displaystyle p_{ij}} as well as possible. To this end, it measures similarities q i j {\displaystyle q_{ij}} between two points in the map y i {\displaystyle \mathbf {y} _{i}} and y j {\displaystyle \mathbf {y} _{j}} , using a very similar approach. Specifically, for i ≠ j {\displaystyle i\neq j} , define q i j {\displaystyle q_{ij}} as q i j = ( 1 + ‖ y i − y j ‖ 2 ) − 1 ∑ k ∑ l ≠ k ( 1 + ‖ y k − y l ‖ 2 ) − 1 {\displaystyle q_{ij}={\frac {(1+\lVert \mathbf {y} _{i}-\mathbf {y} _{j}\rVert ^{2})^{-1}}{\sum _{k}\sum _{l\neq k}(1+\lVert \mathbf {y} _{k}-\mathbf {y} _{l}\rVert ^{2})^{-1}}}} and set q i i = 0 {\displaystyle q_{ii}=0} . Herein a heavy-tailed Student t-distribution (with one-degree of freedom, which is the same as a Cauchy distribution) is used to measure similarities between low-dimensional points in order to allow dissimilar objects to be modeled far apart in the map. The locations of the points y i {\displaystyle \mathbf {y} _{i}} in the map are determined by minimizing the (non-symmetric) Kullback–Leibler divergence of the distribution P {\displaystyle P} from the distribution Q {\displaystyle Q} , that is: K L ( P ∥ Q ) = ∑ i ≠ j p i j log ⁡ p i j q i j {\displaystyle \mathrm {KL} \left(P\parallel Q\right)=\sum _{i\neq j}p_{ij}\log {\frac {p_{ij}}{q_{ij}}}} The minimization of the Kullback–Leibler divergence with respect to the points y i {\displaystyle \mathbf {y} _{i}} is performed using gradient descent. The result of this optimization is a map that reflects the similarities between the high-dimensional inputs. == Output == While t-SNE plots often seem to display clusters, the visual clusters can be strongly influenced by the chosen parameterization (especially the perplexity) and so a good understanding of the parameters for t-SNE is needed. Such "clusters" can be shown to even appear in structured data with no clear clustering, and so may be false findings. Similarly, the size of clusters produced by t-SNE is not informative, and neither is the distance between clusters. Thus, interactive exploration may be needed to choose parameters and validate results. It has been shown that t-SNE can often recover well-separated clusters, and with special parameter choices, approximates a simple form of spectral clustering. == Software == A C++ implementation of Barnes-Hut is available on the github account of one of the original authors. The R package Rtsne implements t-SNE in R. ELKI contains tSNE, also with Barnes-Hut approximation scikit-learn, a popular machine learning library in Python implements t-SNE with both exact solutions and the Barnes-Hut approximation. Tensorboard, the visualization kit associated with TensorFlow, also implements t-SNE (online version) The Julia package TSne implements t-SNE