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Wednesday, November 26, 2025

Machine learning

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Machine_learning

Machine learning (ML) is a field of study in artificial intelligence concerned with the development and study of statistical algorithms that can learn from data and generalise to unseen data, and thus perform tasks without explicit instructions. Within a subdiscipline in machine learning, advances in the field of deep learning have allowed neural networks, a class of statistical algorithms, to surpass many previous machine learning approaches in performance.

ML finds application in many fields, including natural language processing, computer vision, speech recognition, email filtering, agriculture, and medicine. The application of ML to business problems is known as predictive analytics.

Statistics and mathematical optimisation (mathematical programming) methods comprise the foundations of machine learning. Data mining is a related field of study, focusing on exploratory data analysis (EDA) via unsupervised learning.

From a theoretical viewpoint, probably approximately correct learning provides a mathematical and statistical framework for describing machine learning. Most traditional machine learning and deep learning algorithms can be described as empirical risk minimisation under this framework.

History

The term machine learning was coined in 1959 by Arthur Samuel, an IBM employee and pioneer in the field of computer gaming and artificial intelligence.The synonym self-teaching computers was also used in this time period.

The earliest machine learning program was introduced in the 1950s when Arthur Samuel invented a computer program that calculated the winning chance in checkers for each side, but the history of machine learning roots back to decades of human desire and effort to study human cognitive processes. In 1949, Canadian psychologist Donald Hebb published the book The Organization of Behavior, in which he introduced a theoretical neural structure formed by certain interactions among nerve cells. Hebb's model of neurons interacting with one another set a groundwork for how AIs and machine learning algorithms work under nodes, or artificial neurons used by computers to communicate data. Other researchers who have studied human cognitive systems contributed to the modern machine learning technologies as well, including logician Walter Pitts and Warren McCulloch, who proposed the early mathematical models of neural networks to come up with algorithms that mirror human thought processes.

By the early 1960s, an experimental "learning machine" with punched tape memory, called Cybertron, had been developed by Raytheon Company to analyse sonar signals, electrocardiograms, and speech patterns using rudimentary reinforcement learning. It was repetitively "trained" by a human operator/teacher to recognise patterns and equipped with a "goof" button to cause it to reevaluate incorrect decisions. A representative book on research into machine learning during the 1960s was Nils Nilsson's book on Learning Machines, dealing mostly with machine learning for pattern classification. Interest related to pattern recognition continued into the 1970s, as described by Duda and Hart in 1973. In 1981, a report was given on using teaching strategies so that an artificial neural network learns to recognise 40 characters (26 letters, 10 digits, and 4 special symbols) from a computer terminal.

Tom M. Mitchell provided a widely quoted, more formal definition of the algorithms studied in the machine learning field: "A computer program is said to learn from experience E with respect to some class of tasks T and performance measure P if its performance at tasks in T, as measured by P, improves with experience E." This definition of the tasks in which machine learning is concerned offers a fundamentally operational definition rather than defining the field in cognitive terms. This follows Alan Turing's proposal in his paper "Computing Machinery and Intelligence", in which the question, "Can machines think?", is replaced with the question, "Can machines do what we (as thinking entities) can do?"

Modern-day Machine Learning algorithms are broken into 3 algorithm types: Supervised Learning Algorithms, Unsupervised Learning Algorithms, and Reinforcement Learning Algorithms.

Current Supervised Learning Algorithms have objectives of classification and regression.
Current Unsupervised Learning Algorithms have objectives of clustering, dimensionality reduction, and association rule.
Current Reinforcement Learning Algorithms focus on decisions that must be made with respect to some previous, unknown time and are broken down to either be studies of model-based methods or model-free methods.

In 2014 Ian Goodfellow and others introduced generative adversarial networks (GANs) with realistic data synthesis. By 2016 AlphaGo obtained victory against top human players using reinforcement learning techniques.

Relationships to other fields

Artificial intelligence

As a scientific endeavour, machine learning grew out of the quest for artificial intelligence (AI). In the early days of AI as an academic discipline, some researchers were interested in having machines learn from data. They attempted to approach the problem with various symbolic methods, as well as what were then termed "neural networks"; these were mostly perceptrons and other models that were later found to be reinventions of the generalised linear models of statistics. Probabilistic reasoning was also employed, especially in automated medical diagnosis.

However, an increasing emphasis on the logical, knowledge-based approach caused a rift between AI and machine learning. Probabilistic systems were plagued by theoretical and practical problems of data acquisition and representation. By 1980, expert systems had come to dominate AI, and statistics was out of favour. Work on symbolic/knowledge-based learning did continue within AI, leading to inductive logic programming(ILP), but the more statistical line of research was now outside the field of AI proper, in pattern recognition and information retrieval. Neural networks research had been abandoned by AI and computer science around the same time. This line, too, was continued outside the AI/CS field, as "connectionism", by researchers from other disciplines, including John Hopfield, David Rumelhart, and Geoffrey Hinton. Their main success came in the mid-1980s with the reinvention of backpropagation.

Machine learning (ML), reorganised and recognised as its own field, started to flourish in the 1990s. The field changed its goal from achieving artificial intelligence to tackling solvable problems of a practical nature. It shifted focus away from the symbolic approaches it had inherited from AI, and toward methods and models borrowed from statistics, fuzzy logic, and probability theory.

Data compression

There is a close connection between machine learning and compression. A system that predicts the posterior probabilities of a sequence given its entire history can be used for optimal data compression (by using arithmetic coding on the output distribution). Conversely, an optimal compressor can be used for prediction (by finding the symbol that compresses best, given the previous history). This equivalence has been used as a justification for using data compression as a benchmark for "general intelligence".

An alternative view can show compression algorithms implicitly map strings into implicit feature space vectors, and compression-based similarity measures compute similarity within these feature spaces. For each compressor C(.) we define an associated vector space ℵ, such that C(.) maps an input string x, corresponding to the vector norm ||~x||. An exhaustive examination of the feature spaces underlying all compression algorithms is precluded by space; instead, feature vectors chooses to examine three representative lossless compression methods, LZW, LZ77, and PPM.

According to AIXI theory, a connection more directly explained in Hutter Prize, the best possible compression of x is the smallest possible software that generates x. For example, in that model, a zip file's compressed size includes both the zip file and the unzipping software, since you can not unzip it without both, but there may be an even smaller combined form.

Examples of AI-powered audio/video compression software include NVIDIA Maxine, AIVC. Examples of software that can perform AI-powered image compression include OpenCV, TensorFlow, MATLAB's Image Processing Toolbox (IPT) and High-Fidelity Generative Image Compression.

In unsupervised machine learning, k-means clustering can be utilized to compress data by grouping similar data points into clusters. This technique simplifies handling extensive datasets that lack predefined labels and finds widespread use in fields such as image compression.

Data compression aims to reduce the size of data files, enhancing storage efficiency and speeding up data transmission. K-means clustering, an unsupervised machine learning algorithm, is employed to partition a dataset into a specified number of clusters, k, each represented by the centroid of its points. This process condenses extensive datasets into a more compact set of representative points. Particularly beneficial in image and signal processing, k-means clustering aids in data reduction by replacing groups of data points with their centroids, thereby preserving the core information of the original data while significantly decreasing the required storage space.

Large language models (LLMs) are also efficient lossless data compressors on some data sets, as demonstrated by DeepMind's research with the Chinchilla 70B model. Developed by DeepMind, Chinchilla 70B effectively compressed data, outperforming conventional methods such as Portable Network Graphics (PNG) for images and Free Lossless Audio Codec (FLAC) for audio. It achieved compression of image and audio data to 43.4% and 16.4% of their original sizes, respectively. There is, however, some reason to be concerned that the data set used for testing overlaps the LLM training data set, making it possible that the Chinchilla 70B model is only an efficient compression tool on data it has already been trained on.

Data mining

Machine learning and data mining often employ the same methods and overlap significantly, but while machine learning focuses on prediction, based on known properties learned from the training data, data mining focuses on the discovery of (previously) unknown properties in the data (this is the analysis step of knowledge discovery in databases). Data mining uses many machine learning methods, but with different goals; on the other hand, machine learning also employs data mining methods as "unsupervised learning" or as a preprocessing step to improve learner accuracy. Much of the confusion between these two research communities (which do often have separate conferences and separate journals, ECML PKDD being a major exception) comes from the basic assumptions they work with: in machine learning, performance is usually evaluated with respect to the ability to reproduce known knowledge, while in knowledge discovery and data mining (KDD) the key task is the discovery of previously unknown knowledge. Evaluated with respect to known knowledge, an uninformed (unsupervised) method will easily be outperformed by other supervised methods, while in a typical KDD task, supervised methods cannot be used due to the unavailability of training data.

Machine learning also has intimate ties to optimisation: Many learning problems are formulated as minimisation of some loss function on a training set of examples. Loss functions express the discrepancy between the predictions of the model being trained and the actual problem instances (for example, in classification, one wants to assign a label to instances, and models are trained to correctly predict the preassigned labels of a set of examples).

Generalization

Characterizing the generalisation of various learning algorithms is an active topic of current research, especially for deep learning algorithms.

Statistics

Machine learning and statistics are closely related fields in terms of methods, but distinct in their principal goal: statistics draws population inferences from a sample, while machine learning finds generalisable predictive patterns.

Conventional statistical analyses require the a priori selection of a model most suitable for the study data set. In addition, only significant or theoretically relevant variables based on previous experience are included for analysis. In contrast, machine learning is not built on a pre-structured model; rather, the data shape the model by detecting underlying patterns. The more variables (input) used to train the model, the more accurate the ultimate model will be.

Leo Breiman distinguished two statistical modelling paradigms: data model and algorithmic model,^[37] wherein "algorithmic model" means more or less the machine learning algorithms like Random Forest.

Some statisticians have adopted methods from machine learning, leading to a combined field that they call statistical learning.

Statistical physics

Analytical and computational techniques derived from deep-rooted physics of disordered systems can be extended to large-scale problems, including machine learning, e.g., to analyse the weight space of deep neural networks. Statistical physics is thus finding applications in the area of medical diagnostics.

Theory

A core objective of a learner is to generalise from its experience. Generalization in this context is the ability of a learning machine to perform accurately on new, unseen examples/tasks after having experienced a learning data set. The training examples come from some generally unknown probability distribution (considered representative of the space of occurrences) and the learner has to build a general model about this space that enables it to produce sufficiently accurate predictions in new cases.

The computational analysis of machine learning algorithms and their performance is a branch of theoretical computer science known as computational learning theory via the probably approximately correct learning model. Because training sets are finite and the future is uncertain, learning theory usually does not yield guarantees of the performance of algorithms. Instead, probabilistic bounds on the performance are quite common. The bias–variance decomposition is one way to quantify generalisation error.

For the best performance in the context of generalisation, the complexity of the hypothesis should match the complexity of the function underlying the data. If the hypothesis is less complex than the function, then the model has underfitted the data. If the complexity of the model is increased in response, then the training error decreases. But if the hypothesis is too complex, then the model is subject to overfitting and generalisation will be poorer.

In addition to performance bounds, learning theorists study the time complexity and feasibility of learning. In computational learning theory, a computation is considered feasible if it can be done in polynomial time. There are two kinds of time complexity results: Positive results show that a certain class of functions can be learned in polynomial time. Negative results show that certain classes cannot be learned in polynomial time.

Approaches

Machine learning approaches are traditionally divided into three broad categories, which correspond to learning paradigms, depending on the nature of the "signal" or "feedback" available to the learning system:

Supervised learning: The computer is presented with example inputs and their desired outputs, given by a "teacher", and the goal is to learn a general rule that maps inputs to outputs.
Unsupervised learning: No labels are given to the learning algorithm, leaving it on its own to find structure in its input. Unsupervised learning can be a goal in itself (discovering hidden patterns in data) or a means towards an end (feature learning).
Reinforcement learning: A computer program interacts with a dynamic environment in which it must perform a certain goal (such as driving a vehicle or playing a game against an opponent). As it navigates its problem space, the program is provided feedback that's analogous to rewards, which it tries to maximise.

Although each algorithm has advantages and limitations, no single algorithm works for all problems.

Supervised learning

Supervised learning algorithms build a mathematical model of a set of data that contains both the inputs and the desired outputs. The data, known as training data, consists of a set of training examples. Each training example has one or more inputs and the desired output, also known as a supervisory signal. In the mathematical model, each training example is represented by an array or vector, sometimes called a feature vector, and the training data is represented by a matrix. Through iterative optimisation of an objective function, supervised learning algorithms learn a function that can be used to predict the output associated with new inputs. An optimal function allows the algorithm to correctly determine the output for inputs that were not a part of the training data. An algorithm that improves the accuracy of its outputs or predictions over time is said to have learned to perform that task.

Types of supervised-learning algorithms include active learning, classification and regression. Classification algorithms are used when the outputs are restricted to a limited set of values, while regression algorithms are used when the outputs can take any numerical value within a range. For example, in a classification algorithm that filters emails, the input is an incoming email, and the output is the folder in which to file the email. In contrast, regression is used for tasks such as predicting a person's height based on factors like age and genetics or forecasting future temperatures based on historical data.

Similarity learning is an area of supervised machine learning closely related to regression and classification, but the goal is to learn from examples using a similarity function that measures how similar or related two objects are. It has applications in ranking, recommendation systems, visual identity tracking, face verification, and speaker verification.

Unsupervised learning

Unsupervised learning algorithms find structures in data that has not been labelled, classified or categorised. Instead of responding to feedback, unsupervised learning algorithms identify commonalities in the data and react based on the presence or absence of such commonalities in each new piece of data. Central applications of unsupervised machine learning include clustering, dimensionality reduction, and density estimation.

Cluster analysis is the assignment of a set of observations into subsets (called clusters) so that observations within the same cluster are similar according to one or more predesignated criteria, while observations drawn from different clusters are dissimilar. Different clustering techniques make different assumptions on the structure of the data, often defined by some similarity metric and evaluated, for example, by internal compactness, or the similarity between members of the same cluster, and separation, the difference between clusters. Other methods are based on estimated density and graph connectivity.

A special type of unsupervised learning called, self-supervised learning involves training a model by generating the supervisory signal from the data itself.

Semi-supervised learning

Semi-supervised learning falls between unsupervised learning (without any labelled training data) and supervised learning (with completely labelled training data). Some of the training examples are missing training labels, yet many machine-learning researchers have found that unlabelled data, when used in conjunction with a small amount of labelled data, can produce a considerable improvement in learning accuracy.

In weakly supervised learning, the training labels are noisy, limited, or imprecise; however, these labels are often cheaper to obtain, resulting in larger effective training sets.

Reinforcement learning

Reinforcement learning is an area of machine learning concerned with how software agents ought to take actions in an environment to maximise some notion of cumulative reward. Due to its generality, the field is studied in many other disciplines, such as game theory, control theory, operations research, information theory, simulation-based optimisation, multi-agent systems, swarm intelligence, statistics and genetic algorithms. In reinforcement learning, the environment is typically represented as a Markov decision process (MDP). Many reinforcement learning algorithms use dynamic programming techniques. Reinforcement learning algorithms do not assume knowledge of an exact mathematical model of the MDP and are used when exact models are infeasible. Reinforcement learning algorithms are used in autonomous vehicles or in learning to play a game against a human opponent.

Dimensionality reduction

Dimensionality reduction is a process of reducing the number of random variables under consideration by obtaining a set of principal variables. In other words, it is a process of reducing the dimension of the feature set, also called the "number of features". Most of the dimensionality reduction techniques can be considered as either feature elimination or extraction. One of the popular methods of dimensionality reduction is principal component analysis (PCA). PCA involves changing higher-dimensional data (e.g., 3D) to a smaller space (e.g., 2D). The manifold hypothesis proposes that high-dimensional data sets lie along low-dimensional manifolds, and many dimensionality reduction techniques make this assumption, leading to the areas of manifold learning and manifold regularisation.

Other types

Other approaches have been developed which do not fit neatly into this three-fold categorisation, and sometimes more than one is used by the same machine learning system. For example, topic modelling, meta-learning.

Self-learning

Self-learning, as a machine learning paradigm, was introduced in 1982 along with a neural network capable of self-learning, named crossbar adaptive array (CAA). It gives a solution to the problem learning without any external reward, by introducing emotion as an internal reward. Emotion is used as a state evaluation of a self-learning agent. The CAA self-learning algorithm computes, in a crossbar fashion, both decisions about actions and emotions (feelings) about consequence situations. The system is driven by the interaction between cognition and emotion. The self-learning algorithm updates a memory matrix W =||w(a,s)|| such that in each iteration executes the following machine learning routine:

in situation s act a
receive a consequence situation s'
compute emotion of being in the consequence situation v(s')
update crossbar memory w'(a,s) = w(a,s) + v(s')

It is a system with only one input, situation, and only one output, action (or behaviour) a. There is neither a separate reinforcement input nor an advice input from the environment. The backpropagated value (secondary reinforcement) is the emotion toward the consequence situation. The CAA exists in two environments, one is the behavioural environment where it behaves, and the other is the genetic environment, wherefrom it initially and only once receives initial emotions about situations to be encountered in the behavioural environment. After receiving the genome (species) vector from the genetic environment, the CAA learns a goal-seeking behaviour in an environment that contains both desirable and undesirable situations.

Feature learning

Several learning algorithms aim at discovering better representations of the inputs provided during training. Classic examples include principal component analysis and cluster analysis. Feature learning algorithms, also called representation learning algorithms, often attempt to preserve the information in their input but also transform it in a way that makes it useful, often as a pre-processing step before performing classification or predictions. This technique allows reconstruction of the inputs coming from the unknown data-generating distribution, while not being necessarily faithful to configurations that are implausible under that distribution. This replaces manual feature engineering, and allows a machine to both learn the features and use them to perform a specific task.

Feature learning can be either supervised or unsupervised. In supervised feature learning, features are learned using labelled input data. Examples include artificial neural networks, multilayer perceptrons, and supervised dictionary learning. In unsupervised feature learning, features are learned with unlabelled input data. Examples include dictionary learning, independent component analysis, autoencoders, matrix factorisation and various forms of clustering.

Manifold learning algorithms attempt to do so under the constraint that the learned representation is low-dimensional. Sparse coding algorithms attempt to do so under the constraint that the learned representation is sparse, meaning that the mathematical model has many zeros. Multilinear subspace learning algorithms aim to learn low-dimensional representations directly from tensor representations for multidimensional data, without reshaping them into higher-dimensional vectors. Deep learning algorithms discover multiple levels of representation, or a hierarchy of features, with higher-level, more abstract features defined in terms of (or generating) lower-level features. It has been argued that an intelligent machine learns a representation that disentangles the underlying factors of variation that explain the observed data.

Feature learning is motivated by the fact that machine learning tasks such as classification often require input that is mathematically and computationally convenient to process. However, real-world data such as images, video, and sensory data have not yielded attempts to algorithmically define specific features. An alternative is to discover such features or representations through examination, without relying on explicit algorithms.

Sparse dictionary learning

Sparse dictionary learning is a feature learning method where a training example is represented as a linear combination of basis functions and assumed to be a sparse matrix. The method is strongly NP-hard and difficult to solve approximately. A popular heuristic method for sparse dictionary learning is the k-SVD algorithm. Sparse dictionary learning has been applied in several contexts. In classification, the problem is to determine the class to which a previously unseen training example belongs. For a dictionary where each class has already been built, a new training example is associated with the class that is best sparsely represented by the corresponding dictionary. Sparse dictionary learning has also been applied in image denoising. The key idea is that a clean image patch can be sparsely represented by an image dictionary, but the noise cannot.

Anomaly detection

In data mining, anomaly detection, also known as outlier detection, is the identification of rare items, events or observations that raise suspicions by differing significantly from the majority of the data. Typically, the anomalous items represent an issue such as bank fraud, a structural defect, medical problems or errors in a text. Anomalies are referred to as outliers, novelties, noise, deviations and exceptions.

In particular, in the context of abuse and network intrusion detection, the interesting objects are often not rare, but unexpected bursts of inactivity. This pattern does not adhere to the common statistical definition of an outlier as a rare object. Many outlier detection methods (in particular, unsupervised algorithms) will fail on such data unless aggregated appropriately. Instead, a cluster analysis algorithm may be able to detect the micro-clusters formed by these patterns.

Three broad categories of anomaly detection techniques exist. Unsupervised anomaly detection techniques detect anomalies in an unlabelled test data set under the assumption that the majority of the instances in the data set are normal, by looking for instances that seem to fit the least to the remainder of the data set. Supervised anomaly detection techniques require a data set that has been labelled as "normal" and "abnormal" and involves training a classifier (the key difference from many other statistical classification problems is the inherently unbalanced nature of outlier detection). Semi-supervised anomaly detection techniques construct a model representing normal behaviour from a given normal training data set and then test the likelihood of a test instance being generated by the model.

Robot learning

Robot learning is inspired by a multitude of machine learning methods, starting from supervised learning, reinforcement learning, and finally meta-learning (e.g. MAML).

Association rules

Association rule learning is a rule-based machine learning method for discovering relationships between variables in large databases. It is intended to identify strong rules discovered in databases using some measure of "interestingness".

Rule-based machine learning is a general term for any machine learning method that identifies, learns, or evolves "rules" to store, manipulate or apply knowledge. The defining characteristic of a rule-based machine learning algorithm is the identification and utilisation of a set of relational rules that collectively represent the knowledge captured by the system. This is in contrast to other machine learning algorithms that commonly identify a singular model that can be universally applied to any instance in order to make a prediction. Rule-based machine learning approaches include learning classifier systems, association rule learning, and artificial immune systems.

Based on the concept of strong rules, Rakesh Agrawal, Tomasz Imieliński and Arun Swami introduced association rules for discovering regularities between products in large-scale transaction data recorded by point-of-sale (POS) systems in supermarkets. For example, the rule ${o n i o n s, p o t a t o e s} \Rightarrow {b u r g e r}$ found in the sales data of a supermarket would indicate that if a customer buys onions and potatoes together, they are likely to also buy hamburger meat. Such information can be used as the basis for decisions about marketing activities such as promotional pricing or product placements. In addition to market basket analysis, association rules are employed today in application areas including Web usage mining, intrusion detection, continuous production, and bioinformatics. In contrast with sequence mining, association rule learning typically does not consider the order of items either within a transaction or across transactions.

Learning classifier systems (LCS) are a family of rule-based machine learning algorithms that combine a discovery component, typically a genetic algorithm, with a learning component, performing either supervised learning, reinforcement learning, or unsupervised learning. They seek to identify a set of context-dependent rules that collectively store and apply knowledge in a piecewise manner to make predictions.

Inductive logic programming (ILP) is an approach to rule learning using logic programming as a uniform representation for input examples, background knowledge, and hypotheses. Given an encoding of the known background knowledge and a set of examples represented as a logical database of facts, an ILP system will derive a hypothesized logic program that entails all positive and no negative examples. Inductive programming is a related field that considers any kind of programming language for representing hypotheses (and not only logic programming), such as functional programs.

Inductive logic programming is particularly useful in bioinformatics and natural language processing. Gordon Plotkin and Ehud Shapiro laid the initial theoretical foundation for inductive machine learning in a logical setting.^[80]^[81]^[82] Shapiro built their first implementation (Model Inference System) in 1981: a Prolog program that inductively inferred logic programs from positive and negative examples.^[83] The term inductive here refers to philosophical induction, suggesting a theory to explain observed facts, rather than mathematical induction, proving a property for all members of a well-ordered set.

Models

A machine learning model is a type of mathematical model that, once "trained" on a given dataset, can be used to make predictions or classifications on new data. During training, a learning algorithm iteratively adjusts the model's internal parameters to minimise errors in its predictions. By extension, the term "model" can refer to several levels of specificity, from a general class of models and their associated learning algorithms to a fully trained model with all its internal parameters tuned.

Various types of models have been used and researched for machine learning systems, picking the best model for a task is called model selection.

Artificial neural networks

Artificial neural networks (ANNs), or connectionist systems, are computing systems vaguely inspired by the biological neural networks that constitute animal brains. Such systems "learn" to perform tasks by considering examples, generally without being programmed with any task-specific rules.

An ANN is a model based on a collection of connected units or nodes called "artificial neurons", which loosely model the neurons in a biological brain. Each connection, like the synapses in a biological brain, can transmit information, a "signal", from one artificial neuron to another. An artificial neuron that receives a signal can process it and then signal additional artificial neurons connected to it. In common ANN implementations, the signal at a connection between artificial neurons is a real number, and the output of each artificial neuron is computed by some non-linear function of the sum of its inputs. The connections between artificial neurons are called "edges". Artificial neurons and edges typically have a weight that adjusts as learning proceeds. The weight increases or decreases the strength of the signal at a connection. Artificial neurons may have a threshold such that the signal is only sent if the aggregate signal crosses that threshold. Typically, artificial neurons are aggregated into layers. Different layers may perform different kinds of transformations on their inputs. Signals travel from the first layer (the input layer) to the last layer (the output layer), possibly after traversing the layers multiple times.

The original goal of the ANN approach was to solve problems in the same way that a human brain would. However, over time, attention moved to performing specific tasks, leading to deviations from biology. Artificial neural networks have been used on a variety of tasks, including computer vision, speech recognition, machine translation, social network filtering, playing board and video games and medical diagnosis.

Deep learning consists of multiple hidden layers in an artificial neural network. This approach tries to model the way the human brain processes light and sound into vision and hearing. Some successful applications of deep learning are computer vision and speech recognition.

Decision trees

Decision tree learning uses a decision tree as a predictive model to go from observations about an item (represented in the branches) to conclusions about the item's target value (represented in the leaves). It is one of the predictive modelling approaches used in statistics, data mining, and machine learning. Tree models where the target variable can take a discrete set of values are called classification trees; in these tree structures, leaves represent class labels, and branches represent conjunctions of features that lead to those class labels. Decision trees where the target variable can take continuous values (typically real numbers) are called regression trees. In decision analysis, a decision tree can be used to visually and explicitly represent decisions and decision making. In data mining, a decision tree describes data, but the resulting classification tree can be an input for decision-making.

Random forest regression

Random forest regression (RFR) falls under the umbrella of decision tree-based models. RFR is an ensemble learning method that builds multiple decision trees and averages their predictions to improve accuracy and to avoid overfitting. To build decision trees, RFR uses bootstrapped sampling; for instance, each decision tree is trained on random data from the training set. This random selection of RFR for training enables the model to reduce biased predictions and achieve a higher degree of accuracy. RFR generates independent decision trees, and it can work on single-output data as well as multiple regressor tasks. This makes RFR compatible to be use in various applications.

Support-vector machines

Support-vector machines (SVMs), also known as support-vector networks, are a set of related supervised learning methods used for classification and regression. Given a set of training examples, each marked as belonging to one of two categories, an SVM training algorithm builds a model that predicts whether a new example falls into one category. An SVM training algorithm is a non-probabilistic, binary, linear classifier, although methods such as Platt scaling exist to use SVM in a probabilistic classification setting. In addition to performing linear classification, SVMs can efficiently perform a non-linear classification using what is called the kernel trick, implicitly mapping their inputs into high-dimensional feature spaces.

Regression analysis

Regression analysis encompasses a large variety of statistical methods to estimate the relationship between input variables and their associated features. Its most common form is linear regression, where a single line is drawn to best fit the given data according to a mathematical criterion such as ordinary least squares. The latter is often extended by regularisation methods to mitigate overfitting and bias, as in ridge regression. When dealing with non-linear problems, go-to models include polynomial regression (for example, used for trendline fitting in Microsoft Excel), logistic regression (often used in statistical classification) or even kernel regression, which introduces non-linearity by taking advantage of the kernel trick to implicitly map input variables to higher-dimensional space.

Multivariate linear regression extends the concept of linear regression to handle multiple dependent variables simultaneously. This approach estimates the relationships between a set of input variables and several output variables by fitting a multidimensional linear model. It is particularly useful in scenarios where outputs are interdependent or share underlying patterns, such as predicting multiple economic indicators or reconstructing images, which are inherently multi-dimensional.

Bayesian networks

A simple Bayesian network. Rain influences whether the sprinkler is activated, and both rain and the sprinkler influence whether the grass is wet.

A Bayesian network, belief network, or directed acyclic graphical model is a probabilistic graphical model that represents a set of random variables and their conditional independence with a directed acyclic graph (DAG). For example, a Bayesian network could represent the probabilistic relationships between diseases and symptoms. Given symptoms, the network can be used to compute the probabilities of the presence of various diseases. Efficient algorithms exist that perform inference and learning. Bayesian networks that model sequences of variables, like speech signals or protein sequences, are called dynamic Bayesian networks. Generalisations of Bayesian networks that can represent and solve decision problems under uncertainty are called influence diagrams.

Gaussian processes

A Gaussian process is a stochastic process in which every finite collection of the random variables in the process has a multivariate normal distribution, and it relies on a pre-defined covariance function, or kernel, that models how pairs of points relate to each other depending on their locations.

Given a set of observed points, or input–output examples, the distribution of the (unobserved) output of a new point as a function of its input data can be directly computed by looking at the observed points and the covariances between those points and the new, unobserved point.

Gaussian processes are popular surrogate models in Bayesian optimisation used to do hyperparameter optimisation.

Genetic algorithms

A genetic algorithm (GA) is a search algorithm and heuristic technique that mimics the process of natural selection, using methods such as mutation and crossover to generate new genotypes in the hope of finding good solutions to a given problem. In machine learning, genetic algorithms were used in the 1980s and 1990s. Conversely, machine learning techniques have been used to improve the performance of genetic and evolutionary algorithms.

Belief functions

The theory of belief functions, also referred to as evidence theory or Dempster–Shafer theory, is a general framework for reasoning with uncertainty, with understood connections to other frameworks such as probability, possibility and imprecise probability theories. These theoretical frameworks can be thought of as a kind of learner and have some analogous properties of how evidence is combined (e.g., Dempster's rule of combination), just like how in a pmf-based Bayesian approach would combine probabilities. However, there are many caveats to these beliefs functions when compared to Bayesian approaches to incorporate ignorance and uncertainty quantification. These belief function approaches that are implemented within the machine learning domain typically leverage a fusion approach of various ensemble methods to better handle the learner's decision boundary, low samples, and ambiguous class issues that standard machine learning approach tend to have difficulty resolving. However, the computational complexity of these algorithms is dependent on the number of propositions (classes), and can lead to a much higher computation time when compared to other machine learning approaches.

Rule-based models

Rule-based machine learning (RBML) is a branch of machine learning that automatically discovers and learns 'rules' from data. It provides interpretable models, making it useful for decision-making in fields like healthcare, fraud detection, and cybersecurity. Key RBML techniques includes learning classifier systems, association rule learning, artificial immune systems, and other similar models. These methods extract patterns from data and evolve rules over time.

Training models

Typically, machine learning models require a high quantity of reliable data to perform accurate predictions. When training a machine learning model, machine learning engineers need to target and collect a large and representative sample of data. Data from the training set can be as varied as a corpus of text, a collection of images, sensor data, and data collected from individual users of a service. Overfitting is something to watch out for when training a machine learning model. Trained models derived from biased or non-evaluated data can result in skewed or undesired predictions. Biased models may result in detrimental outcomes, thereby furthering the negative impacts on society or objectives. Algorithmic bias is a potential result of data not being fully prepared for training. Machine learning ethics is becoming a field of study and, notably, becoming integrated within machine learning engineering teams.

Federated learning

Federated learning is an adapted form of distributed artificial intelligence to train machine learning models that decentralises the training process, allowing for users' privacy to be maintained by not needing to send their data to a centralised server. This also increases efficiency by decentralising the training process to many devices. For example, Gboard uses federated machine learning to train search query prediction models on users' mobile phones without having to send individual searches back to Google.

Applications

There are many applications for machine learning, including:

In 2006, the media-services provider Netflix held the first "Netflix Prize" competition to find a program to better predict user preferences and improve the accuracy of its existing Cinematch movie recommendation algorithm by at least 10%. A joint team made up of researchers from AT&T Labs-Research in collaboration with the teams Big Chaos and Pragmatic Theory built an ensemble model to win the Grand Prize in 2009 for $1 million. Shortly after the prize was awarded, Netflix realised that viewers' ratings were not the best indicators of their viewing patterns ("everything is a recommendation") and they changed their recommendation engine accordingly. In 2010, an article in The Wall Street Journal noted the use of machine learning by Rebellion Research to predict the 2008 financial crisis. In 2012, co-founder of Sun Microsystems, Vinod Khosla, predicted that 80% of medical doctors jobs would be lost in the next two decades to automated machine learning medical diagnostic software. In 2014, it was reported that a machine learning algorithm had been applied in the field of art history to study fine art paintings and that it may have revealed previously unrecognised influences among artists. In 2019 Springer Nature published the first research book created using machine learning. In 2020, machine learning technology was used to help make diagnoses and aid researchers in developing a cure for COVID-19. Machine learning was recently applied to predict the pro-environmental behaviour of travellers. Recently, machine learning technology was also applied to optimise smartphone's performance and thermal behaviour based on the user's interaction with the phone. When applied correctly, machine learning algorithms (MLAs) can utilise a wide range of company characteristics to predict stock returns without overfitting. By employing effective feature engineering and combining forecasts, MLAs can generate results that far surpass those obtained from basic linear techniques like OLS.

Recent advancements in machine learning have extended into the field of quantum chemistry, where novel algorithms now enable the prediction of solvent effects on chemical reactions, thereby offering new tools for chemists to tailor experimental conditions for optimal outcomes.

Machine Learning is becoming a useful tool to investigate and predict evacuation decision-making in large-scale and small-scale disasters. Different solutions have been tested to predict if and when householders decide to evacuate during wildfires and hurricanes. Other applications have been focusing on pre evacuation decisions in building fires.

Limitations

Although machine learning has been transformative in some fields, machine-learning programs often fail to deliver expected results. Reasons for this are numerous: lack of (suitable) data, lack of access to the data, data bias, privacy problems, badly chosen tasks and algorithms, wrong tools and people, lack of resources, and evaluation problems.

The "black box theory" poses another yet significant challenge. Black box refers to a situation where the algorithm or the process of producing an output is entirely opaque, meaning that even the coders of the algorithm cannot audit the pattern that the machine extracted from the data. The House of Lords Select Committee, which claimed that such an "intelligence system" that could have a "substantial impact on an individual's life" would not be considered acceptable unless it provided "a full and satisfactory explanation for the decisions" it makes.

In 2018, a self-driving car from Uber failed to detect a pedestrian, who was killed after a collision. Attempts to use machine learning in healthcare with the IBM Watson system failed to deliver even after years of time and billions of dollars invested. Microsoft's Bing Chat chatbot has been reported to produce hostile and offensive response against its users.

Machine learning has been used as a strategy to update the evidence related to a systematic review and increased reviewer burden related to the growth of biomedical literature. While it has improved with training sets, it has not yet developed sufficiently to reduce the workload burden without limiting the necessary sensitivity for the findings research itself.

Explainability

Explainable AI (XAI), or Interpretable AI, or Explainable Machine Learning (XML), is artificial intelligence (AI) in which humans can understand the decisions or predictions made by the AI. It contrasts with the "black box" concept in machine learning where even its designers cannot explain why an AI arrived at a specific decision. By refining the mental models of users of AI-powered systems and dismantling their misconceptions, XAI promises to help users perform more effectively. XAI may be an implementation of the social right to explanation.

Overfitting

Settling on a bad, overly complex theory gerrymandered to fit all the past training data is known as overfitting. Many systems attempt to reduce overfitting by rewarding a theory in accordance with how well it fits the data but penalising the theory in accordance with how complex the theory is.

Other limitations and vulnerabilities

Learners can also be disappointed by "learning the wrong lesson". A toy example is that an image classifier trained only on pictures of brown horses and black cats might conclude that all brown patches are likely to be horses. A real-world example is that, unlike humans, current image classifiers often do not primarily make judgments from the spatial relationship between components of the picture, and they learn relationships between pixels that humans are oblivious to, but that still correlate with images of certain types of real objects. Modifying these patterns on a legitimate image can result in "adversarial" images that the system misclassifies.

Adversarial vulnerabilities can also result in nonlinear systems or from non-pattern perturbations. For some systems, it is possible to change the output by only changing a single adversarially chosen pixel. Machine learning models are often vulnerable to manipulation or evasion via adversarial machine learning.

Researchers have demonstrated how backdoors can be placed undetectably into classifying (e.g., for categories "spam" and "not spam" of posts) machine learning models that are often developed or trained by third parties. Parties can change the classification of any input, including in cases for which a type of data/software transparency is provided, possibly including white-box access.

Model assessments

Classification of machine learning models can be validated by accuracy estimation techniques like the holdout method, which splits the data into a training and test set (conventionally 2/3 training set and 1/3 test set designation) and evaluates the performance of the training model on the test set. In comparison, the K-fold-cross-validation method randomly partitions the data into K subsets and then K experiments are performed each considering 1 subset for evaluation and the remaining K-1 subsets for training the model. In addition to the holdout and cross-validation methods, bootstrap, which samples n instances with replacement from the dataset, can be used to assess model accuracy.

In addition to overall accuracy, investigators frequently report sensitivity and specificity, meaning true positive rate (TPR) and true negative rate (TNR), respectively. Similarly, investigators sometimes report the false positive rate (FPR) as well as the false negative rate (FNR). However, these rates are ratios that fail to reveal their numerators and denominators. Receiver operating characteristic (ROC), along with the accompanying Area Under the ROC Curve (AUC), offer additional tools for classification model assessment. Higher AUC is associated with a better performing model.^[145]

Ethics

The ethics of artificial intelligence covers a broad range of topics within AI that are considered to have particular ethical stakes. This includes algorithmic biases, fairness, automated decision-making, accountability, privacy, and regulation. It also covers various emerging or potential future challenges such as machine ethics (how to make machines that behave ethically), lethal autonomous weapon systems, arms race dynamics, AI safety and alignment, technological unemployment, AI-enabled misinformation, how to treat certain AI systems if they have a moral status (AI welfare and rights), artificial superintelligence and existential risks.

Some application areas may also have particularly important ethical implications, like healthcare, education, criminal justice, or the military.

Bias

Different machine learning approaches can suffer from different data biases. A machine learning system trained specifically on current customers may not be able to predict the needs of new customer groups that are not represented in the training data. When trained on human-made data, machine learning is likely to pick up the constitutional and unconscious biases already present in society.

Systems that are trained on datasets collected with biases may exhibit these biases upon use (algorithmic bias), thus digitising cultural prejudices. For example, in 1988, the UK's Commission for Racial Equality found that St. George's Medical School had been using a computer program trained from data of previous admissions staff and this program had denied nearly 60 candidates who were found to either be women or have non-European-sounding names. Using job hiring data from a firm with racist hiring policies may lead to a machine learning system duplicating the bias by scoring job applicants by similarity to previous successful applicants. Another example includes predictive policing company Geolitica's predictive algorithm that resulted in "disproportionately high levels of over-policing in low-income and minority communities" after being trained with historical crime data.

While responsible collection of data and documentation of algorithmic rules used by a system is considered a critical part of machine learning, some researchers blame the lack of participation and representation of minority populations in the field of AI for machine learning's vulnerability to biases. In fact, according to research carried out by the Computing Research Association in 2021, "female faculty make up just 16.1%" of all faculty members who focus on AI among several universities around the world. Furthermore, among the group of "new U.S. resident AI PhD graduates," 45% identified as white, 22.4% as Asian, 3.2% as Hispanic, and 2.4% as African American, which further demonstrates a lack of diversity in the field of AI.

Language models learned from data have been shown to contain human-like biases. Because human languages contain biases, machines trained on language corpora will necessarily also learn these biases. In 2016, Microsoft tested Tay, a chatbot that learned from Twitter, and it quickly picked up racist and sexist language.

In an experiment carried out by ProPublica, an investigative journalism organisation, a machine learning algorithm's insight into the recidivism rates among prisoners falsely flagged "black defendants high risk twice as often as white defendants". In 2015, Google Photos once tagged a couple of black people as gorillas, which caused controversy. The gorilla label was subsequently removed, and in 2023, it still cannot recognise gorillas. Similar issues with recognising non-white people have been found in many other systems.

Because of such challenges, the effective use of machine learning may take longer to be adopted in other domains. Concern for fairness in machine learning, that is, reducing bias in machine learning and propelling its use for human good, is increasingly expressed by artificial intelligence scientists, including Fei-Fei Li, who said that "[t]here's nothing artificial about AI. It's inspired by people, it's created by people, and—most importantly—it impacts people. It is a powerful tool we are only just beginning to understand, and that is a profound responsibility."

Financial incentives

There are concerns among health care professionals that these systems might not be designed in the public's interest but as income-generating machines. This is especially true in the United States, where there is a long-standing ethical dilemma of improving health care, but also increasing profits. For example, the algorithms could be designed to provide patients with unnecessary tests or medication in which the algorithm's proprietary owners hold stakes. There is potential for machine learning in health care to provide professionals with an additional tool to diagnose, medicate, and plan recovery paths for patients, but this requires these biases to be mitigated.

Hardware

Since the 2010s, advances in both machine learning algorithms and computer hardware have led to more efficient methods for training deep neural networks (a particular narrow subdomain of machine learning) that contain many layers of nonlinear hidden units. By 2019, graphics processing units (GPUs), often with AI-specific enhancements, had displaced CPUs as the dominant method of training large-scale commercial cloud AI. OpenAI estimated the hardware compute used in the largest deep learning projects from AlexNet (2012) to AlphaZero (2017), and found a 300,000-fold increase in the amount of compute required, with a doubling-time trendline of 3.4 months.

Tensor Processing Units (TPUs)

Tensor Processing Units (TPUs) are specialised hardware accelerators developed by Google specifically for machine learning workloads. Unlike general-purpose GPUs and FPGAs, TPUs are optimised for tensor computations, making them particularly efficient for deep learning tasks such as training and inference. They are widely used in Google Cloud AI services and large-scale machine learning models like Google's DeepMind AlphaFold and large language models. TPUs leverage matrix multiplication units and high-bandwidth memory to accelerate computations while maintaining energy efficiency. Since their introduction in 2016, TPUs have become a key component of AI infrastructure, especially in cloud-based environments.

Neuromorphic computing

Neuromorphic computing refers to a class of computing systems designed to emulate the structure and functionality of biological neural networks. These systems may be implemented through software-based simulations on conventional hardware or through specialised hardware architectures.

Physical neural networks

A physical neural network is a specific type of neuromorphic hardware that relies on electrically adjustable materials, such as memristors, to emulate the function of neural synapses. The term "physical neural network" highlights the use of physical hardware for computation, as opposed to software-based implementations. It broadly refers to artificial neural networks that use materials with adjustable resistance to replicate neural synapses.

Embedded machine learning

Embedded machine learning is a sub-field of machine learning where models are deployed on embedded systems with limited computing resources, such as wearable computers, edge devices and microcontrollers. Running models directly on these devices eliminates the need to transfer and store data on cloud servers for further processing, thereby reducing the risk of data breaches, privacy leaks and theft of intellectual property, personal data and business secrets. Embedded machine learning can be achieved through various techniques, such as hardware acceleration, approximate computing, and model optimisation. Common optimisation techniques include pruning, quantisation, knowledge distillation, low-rank factorisation, network architecture search, and parameter sharing.

Creator in Buddhism

From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/Creator_in_Buddhism

Generally speaking, Buddhism is a religion that does not include the belief in a monotheistic creator deity. As such, it has often been described as either (non-materialistic) atheism or as nontheism. However, other scholars have challenged these descriptions since some forms of Buddhism do posit different kinds of transcendent, unborn, and unconditioned ultimate realities (e.g., Buddha-nature).

Buddhist teachings state that there are divine beings called devas (sometimes translated as 'gods') and other Buddhist deities, heavens, and rebirths in its doctrine of saṃsāra, or cyclical rebirth. Buddhism teaches that none of these gods are creators or eternal beings. However, they can live very long lives. In Buddhism, the devas are also trapped in the cycle of rebirth and are not necessarily virtuous. Thus, while Buddhism includes multiple "gods", its main focus is not on them. Peter Harvey calls this "trans-polytheism".

Buddhist texts also posit that mundane deities, such as Mahabrahma, are misconstrued to be creators. Buddhist ontology follows the doctrine of dependent origination, whereby all phenomena arise in dependence on other phenomena, hence no primal unmoved mover could be acknowledged or discerned. Gautama Buddha, in the early Buddhist texts, is also shown as stating that he saw no single beginning to the universe.

During the medieval period, Buddhist philosophers like Vasubandhu developed extensive refutations of creationism and Hindu theism. Because of this, some modern scholars, such as Matthew Kapstein, have described this later stage of Buddhism as anti-theistic. Buddhist anti-theistic writings were also common during the modern era, in response to the presence of Christian missionaries and their critiques of Buddhism.

Despite this, some writers, such as B. Alan Wallace and Douglas Duckworth, have noted that certain doctrines in Vajrayana Buddhism can be seen as being similar to certain theistic doctrines like Neoplatonic theology and pantheism. Various scholars have also compared East Asian Buddhist doctrines regarding the supreme and eternal Buddhas like Vairocana or Amitabha with certain forms of theism, such as pantheism and process theism.

Early Buddhist texts

Damien Keown notes that in the Saṃyutta Nikāya, the Buddha sees the cycle of rebirths as stretching back "many hundreds of thousands of aeons without discernible beginning." Saṃyutta Nikāya 15:1 and 15:2 states: "This samsara is without discoverable beginning. A first point is not discerned of beings roaming and wandering on hindered by ignorance and fettered by craving."

According to Buddhologist Richard Hayes, the early Buddhist Nikaya literature treats the question of the existence of a creator god "primarily from either an epistemological point of view or a moral point of view". In these texts, the Buddha is portrayed not as a creator-denying atheist who claims to be able to prove such a god's nonexistence, but rather his focus is other teachers' claims that their teachings lead to the highest good.

According to Hayes, in the Tevijja Sutta (DN 13), there is an account of a dispute between two brahmins about how best to reach union with Brahma (Brahmasahavyata), who is seen as the highest god over whom no other being has mastery and who sees all. However, after being questioned by the Buddha, it is revealed that they do not have any direct experience of this Brahma. The Buddha calls their religious goal laughable, vain, and empty.

Hayes also notes that in the early texts, the Buddha is not depicted as an atheist, but more as a sceptic who is against religious speculations, including speculations about a creator god. Citing the Devadaha Sutta (Majjhima Nikaya 101), Hayes states, "while the reader is left to conclude that it is attachment rather than God, actions in past lives, fate, type of birth or efforts in this life that is responsible for our experiences of sorrow, no systematic argument is given in an attempt to disprove the existence of God."

Narada Thera also notes that the Buddha specifically calls out the doctrine of creation by a supreme deity (termed Ishvara) for criticism in the Aṅguttara Nikāya. This doctrine of creation by a supreme lord is defined as follows: "Whatever happiness or pain or neutral feeling this person experiences, all that is due to the creation of a supreme deity (issaranimmāṇahetu)." The Buddha criticized this view because he saw it as a fatalistic teaching that would lead to inaction or laziness:

"So, then, owing to the creation of a supreme deity, men will become murderers, thieves, unchaste, liars, slanderers, abusive, babblers, covetous, malicious and perverse in view. Thus for those who fall back on the creation of a god as the essential reason, there is neither desire nor effort nor necessity to do this deed or abstain from that deed."

In another early sutta (Devadahasutta, Majjhima Nikāya 101), the Buddha sees the pain and suffering that is experienced by certain individuals as indicating that if they were created by a god, then this is likely to be an evil god:

"If the pleasure and pain that beings feel are caused by the creative act of a Supreme God, then the Nigaṇṭhas surely must have been created by an evil Supreme God, since they now feel such painful, racking, piercing feelings."

High gods who are mistaken as creator

According to Peter Harvey, Buddhism assumes that the universe has no ultimate beginning to it and thus sees no need for a creator god. In the early texts, the nearest term to this concept is "Great Brahma" (Maha Brahma), such as in Digha Nikaya 1.18. However, "[w]hile being kind and compassionate, none of the brahmās are world-creators."

In the Pali Canon, Buddhism includes the concept of reborn gods. According to this theory, periodically, the physical world system ends and beings of that world system are reborn as gods in lower heavens. This too ends, according to Buddhist cosmology, and god Mahabrahma is then born, who is alone. He longs for the presence of others, and the other gods are reborn as his ministers and companions. In Buddhist suttas, such as DN 1, Mahabrahma forgets his past lives and falsely believes himself to be the Creator, Maker, All-Seeing, Lord. This belief, state the Buddhist texts, is then shared by other gods. Eventually, however, one of the gods dies and is reborn as human, with the power to remember his previous life. He teaches what he remembers from his previous life in lower heaven, that Mahabrahma is the Creator. It is this that leads to the human belief in a creator, according to the Pali Canon.

A similar story of a high god (brahma) who mistakes himself as the all-powerful creator can be seen in the Brahma-nimantanika Sutta (MN 49). In this sutta, the Buddha displays his superior knowledge by explaining how a high god named Baka Brahma, who believes himself to be supremely powerful, actually does not know of certain spiritual realms. The Buddha also demonstrates his superior psychic power by disappearing from Baka Brahma's sight, to a realm that he cannot reach, and then challenges him to do the same. Baka Brahma fails in this, demonstrating the Buddha's superiority. The text also depicts Mara, an evil trickster figure, as attempting to support the Brahma's misconception of himself. As noted by Michael D. Nichols, MN 49 seems to show that "belief in an eternal creator figure is a devious ploy put forward by the Evil One to mislead humanity, and the implication is that Brahmins who believe in the power and permanence of Brahma have fallen for it."

The Problem of Evil in the Jatakas

Some stories in the Buddhist Jataka collections outline a critique of a Creator deity that is similar to the Problem of Evil.

One Jataka story (VI.208) states:

If Brahma is lord of the whole world and Creator of the multitude of beings, then why has he ordained misfortune in the world without making the whole world happy; or for what purpose has he made the world full of injustice, falsehood and conceit; or is the lord of beings evil in that he ordained injustice when there could have been justice?

The Pali Bhūridatta Jātaka (No. 543) has the bodhisattva (future Buddha) state:

"He who has eyes can see the sickening sight,

Why does not Brahmā set his creatures right?

If his wide power no limit can restrain,

Why is his hand so rarely spread to bless?

Why are his creatures all condemned to pain?

Why does he not to all give happiness?

Why do fraud, lies, and ignorance prevail?

Why triumphs falsehood—truth and justice fail?

I count you Brahmā one th'unjust among,

Who made a world in which to shelter wrong."

In the Pali Mahābodhi Jātaka (No. 528), the bodhisattva says:

"If there exists some Lord all powerful to fulfil

In every creature bliss or woe, and action good or ill;

That Lord is stained with sin.

Man does but work his will."

Medieval philosophers

While Early Buddhism was not as concerned with critiquing concepts of God or Īśvara (since theism was not as prominent in India until the medieval era), medieval Indian Buddhists engaged much more thoroughly with the emerging Hindu theisms (mainly by attempting to refute them). According to Matthew Kapstein, medieval Buddhist philosophers deployed a host of arguments, including the argument from evil and others that "stressed formal problems in the conception of a supreme deity". Kapstein outlines this second line of argumentation as follows:

God, the theists affirm, must be eternal, and an eternal entity must be supposed to be altogether free from corruption and change. That same eternal being is held to be the creator, that is, the causal basis, of this world of corruption and change. The changing state, however, of a thing that is caused implies there to be change also in its causal basis, for a changeless cause cannot explain alteration in the result. The hypothesis of a creator god, therefore, either fails to explain our changing world, or else God himself must be subject to change and corruption, and hence cannot be eternal. Creation, in other words, entails the impermanence of the creator. Theism, the Buddhist philosophers concluded, could not as a system of thought be saved from such contradictions.

Kapstein also notes that by this time, "Buddhism's earlier refusal of theism had indeed given way to a well-formed antitheism." However, Kapstein notes that these criticisms remained mostly philosophical, since Buddhist antitheism "was conceived primarily in terms of the logical requirements of Buddhist philosophical systems, for which the concept of a personal god violated the rational demands of an impersonal, moral and causal order".

Madhyamaka philosophers

In the Twelve Gate Treatise (十二門論, Shih-erh-men-lun), the Buddhist philosopher Nagarjuna (c. 1st–2nd century) works to refute the belief of certain Indian non-Buddhists in a god called Isvara, who is "the creator, ruler and destroyer of the world". Nagarjuna makes several arguments against a creator God, including the following:

"If all living beings are the sons of God, He should use happiness to cover suffering and should not give them suffering. And those who worship Him should not have suffering but should enjoy happiness. But this is not true in reality."
"If God is self-existent, He should need nothing. If He needs something, He should not be called self-existent. If He does not need anything, why did He [cause] change, like a small boy who plays a game, to make all creatures?"
"Again, if God created all living beings, who created Him? That God created Himself, cannot be true, for nothing can create itself. If He were created by another creator, He would not be self-existent."
"Again, if all living beings come from God, they should respect and love Him just as sons love their father. But actually this is not the case; some hate God and some love Him."
"Again, if God is the maker [of all things], why did He not create men all happy or all unhappy? Why did He make some happy and others unhappy? We would know that He acts out of hate and love, and hence is not self-existent. Since He is not self-existent, all things are not made by Him."

In his Hymn to the Inconceivable (Acintyastava), Nagarjuna attacks this belief in two verses:

33. Just as the work of a magician is empty of substance, all the rest of the world has been said by you to be empty of substance—including a creator deity. 34. If the creator is created by another, he cannot avoid being created and, consequently, is not permanent. Alternatively, if he creates himself, it implies that the creator is the agent of the activity affecting himself, which is absurd.

Nagarjuna also argues against a Creator in his Bodhicittavivaraṇa. Furthermore, in his Letter to a Friend, he also rejects the idea of a creator deity:

The aggregates (come) not from a triumph of wishing, not from (permanent) time, not from primal matter, not from an essential nature, not from the Powerful Creator Ishvara, and not from having no cause. Know that they arise from unawareness, karmic actions, and craving.

Bhāviveka (c. 500 – c. 578) also critiques the idea in his Madhyamakahṛdaya (Heart of the Middle Way, ch. III).

A later Madhyamaka philosopher, Candrakīrti, states in his Introduction to the Middle Way (6.114): "Because things (bhava) are not produced without a cause (hetu), from a creator god (isvara), from themselves, another or both, they are always produced in dependence [on conditions]."

Shantideva (c. 8th century), in the 9th chapter of his Bodhicaryāvatāra, states:

'God is the cause of the world.' Tell me, who is God? The elements? Then why all the trouble about a mere word? (119) Besides, the elements are manifold, impermanent, without intelligence or activity; without anything divine or venerable; impure. Also such elements as earth, etc., are not God.(120) Neither is space God; space lacks activity, nor is atman—that we have already excluded. Would you say that God is too great to conceive? An unthinkable creator is likewise unthinkable, so that nothing further can be said.

Vasubandhu

The 5th-century Buddhist philosopher Vasubandhu argued that a creator's singular identity is incompatible with creating the world in his Abhidharmakosha. He states (AKB, chapter 2):

The universe does not originate from one single cause (ekaṃ kāraṇam) which may be called God/Supreme Lord (Īśvara), Self (Puruṣa), Primal Source (Pradhāna) or any other name.

Vasubandhu then proceeds to outline various arguments for and against the existence of a creator deity or single cause. In the argument that follows, the Buddhist non-theist begins by stating that if the universe arose from a single cause, "things would arise all at the same time: but everyone sees that they arise successively". The theist responds that things arise in succession because of the power of God's wishes; he thus wills things to arise in succession. The Buddhist responds: "then things do not arise from a single cause, because the desires (of God) are multiple". Furthermore, these desires would have to be simultaneous, but since God is not multiple, things would all arise at the same time.

The theist now responds that God's desires are not simultaneous, "because God, in order to produce his desires, takes into account other causes". The Buddhist replies that if this is the case, then God is not the single cause of everything, and furthermore, he then relies on causes that are also dependent on other causes (and so on).

Then the question of why God creates the world is taken up. The theist states that it is for God's own joy. The Buddhist responds that in this case, God is not lord over his own joy since he cannot create it without an external mean, and "if he is not Sovereign with respect to his own joy, how can he be Sovereign with respect to the world?" Furthermore, the Buddhist also adds:

Besides, do you say that God finds joy in seeing the creatures which he has created in the prey of all the distress of existence, including the tortures of the hells? Homage to this kind of God! The profane stanza expresses it well: "One calls him Rudra because he burns, because he is sharp, fierce, redoubtable, an eater of flesh, blood and marrow.

Furthermore, the Buddhist states that the followers of God as a single cause deny observable cause and effect. If they modify their position to accept observable causes and effects as auxiliaries to their God, "this is nothing more than a pious affirmation, because we do not see the activity of a (Divine) Cause next to the activity of the causes called secondary".

The Buddhist also argues that since God did not have a beginning, the creation of the world by God would also not have a beginning (contrary to the claims of the theists). Vasubandhu states: "the Theist might say that the work of God is the [first] creation [of the world] (ādisarga): but it would follow that creation, dependent only on God, would never have a beginning, like God himself. This is a consequence which the Theist rejects."

Vasubandhu finishes this section of his commentary by stating that sentient beings wander from birth to birth doing various actions, experiencing the effects of their karma and "falsely thinking that God is the cause of this effect. We must explain the truth in order to put an end to this false conception."

Other Yogacara philosophers

The Chinese monk Xuanzang (fl. c. 602–664) studied Buddhism in India during the seventh century, staying at Nalanda. There, he studied the Yogacara teachings passed down from Asanga and Vasubandhu and taught to him by the abbot Śīlabhadra. In his work Cheng Weishi Lun (Skt. Vijñāptimātratāsiddhi śāstra), Xuanzang refutes a "Great Lord" or Great Brahmā doctrine:

According to one doctrine, there is a great, self-existent deity whose substance is real and who is all-pervading, eternal, and the producer of all phenomena. This doctrine is unreasonable. If something produces something, it is not eternal, the non-eternal is not all-pervading, and what is not all-pervading is not real. If the deity's substance is all-pervading and eternal, it must contain all powers and be able to produce all dharmas everywhere, at all times, and simultaneously. If he produces dharma when a desire arises, or according to conditions, this contradicts the doctrine of a single cause. Or else, desires and conditions would arise spontaneously since the cause is eternal. Other doctrines claim that there is a great Brahma, a Time, a Space, a Starting Point, a Nature, an Ether, a Self, etc., that is eternal and really exists, is endowed with all powers, and is able to produce all dharmas. We refute all these in the same way we did the concept of the Great Lord.

The 7th-century Buddhist scholar Dharmakīrti advances a number of arguments against the existence of a creator god in his Pramāṇavārtika, following in the footsteps of Vasubandhu.

Later Mahayana scholars, such as Śāntarakṣita, Kamalaśīla, Śaṅkaranandana (fl. c. 9th or 10th century), and Jñānaśrīmitra (fl. 975–1025), also continued to write and develop the Buddhist anti-theistic arguments.

The 11th-century Buddhist philosopher Ratnakīrti, at the former university at Vikramashila (now Bhagalpur, Bihar), criticized the arguments for the existence of a God-like being called Isvara that emerged in the Navya-Nyaya sub-school of Hinduism in his "Refutation of Arguments Establishing Īśvara" (Īśvara-sādhana-dūṣaṇa). These arguments are similar to those used by other sub-schools of Hinduism and Jainism that questioned the Navya-Nyaya theory of a dualistic creator.

Theravada Buddhists

The Theravada commentator Buddhaghosa also specifically denied the concept of a Creator. He wrote:

"For there is no god Brahma. The maker of the conditioned world of rebirths. Phenomena alone flow on. Conditioned by the coming together of causes." (Visuddhimagga 603).

Mahayana and theism

Mahayana Buddhist traditions have more complex Buddhologies, which often contain a figure variously termed the Eternal Buddha, Supreme Buddha, Original Buddha, or Adi-Buddha (primordial Buddha or first Buddha).

Mahayana buddhology and theism

Mahayana Buddhist interpretations of the Buddha as a supreme being, which is eternal, all-compassionate, and existing on a cosmic scale, have been compared to theism by various scholars. For example, Guang Xing describes the Mahayana Buddha as an omnipotent and almighty divinity "endowed with numerous supernatural attributes and qualities". In Mahayana, a fully awakened Buddha (such as Amitābha) is held to be omniscient as well as having other qualities, such as infinite wisdom, an immeasurable life, and boundless compassion. In East Asian Buddhism, Buddhas are often seen as also having eternal life. According to Paul Williams, in Mahayana, a Buddha is often seen as "a spiritual king, relating to and caring for the world".

Various authors, such as F. Sueki, Douglas Duckworth, and Fabio Rambelli, have described Mahayana Buddhist views using the term "pantheism" (the belief that God and the universe are identical). Similarly, Geoffrey Samuel has compared Tibetan Buddhist Buddhology with the related view of panentheism.

Duckworth draws on positive Mahayana conceptions of Buddha-nature, which he explains as a "positive foundation" and "a pure essence residing in temporarily obscured sentient beings". He compares various Mahayana interpretations of Buddha-nature (Tibetan and East Asian) with a pantheist view that sees all things as divine and that "undoes the duality between the divine and the world". In a similar fashion, Eva K. Neumaier compares Mahayana Buddha-nature teachings that point to a source of all things with the theology of Nicholas of Cusa (1401–1464), who described God as an essence and the world as a manifestation of God.

José Ignacio Cabezón notes that while Mahayana sources reject a universal creator God that stands apart from the world, as well as any single creation event for the entire universe, Mahayanists do accept "localized" creation of specific worlds by the Buddhas and bodhisattvas as well as the idea that any world is jointly created by the collective karmic forces of all the beings who reside in them. Buddha-created worlds are termed "Buddha-fields" (or "pure lands"), and their creation is seen as a key activity of the Buddhas and bodhisattvas.

Much comparative work has also been done on Mahayana Buddhist thought and Whiteheadian process theology. Scholars who have worked in this include Jay B. McDaniel, John B. Cobb, Jr., David R. Griffin, Vincent Shen, John S. Yokota, Steve Odin, and Linyin Gu. Some of these figures have also been involved in Buddhist–Christian dialogue.Cobb sees many affinities with the Buddhist ideas of emptiness and not-self and Whitehead's view of God. He has incorporated these into his own process theology. In a similar fashion, some Buddhist thinkers, like Dennis Hirota and John S. Yokota, have developed Buddhist theologies that draw on process theology.

East Asian Buddhism and theism

In Huayan Buddhism, the supreme Buddha Vairocana is seen as the "cosmic Buddha", with an infinite body that comprises the entire universe and whose light penetrates every particle in the cosmos. According to a religious pamphlet from Tōdai-ji temple in Japan (the headquarters of Japanese Huayan), "Vairocana Buddha exists everywhere and every time in the Universe, and the Universe itself is his body. At the same time, the songs of birds, the colors of flowers, the currents of streams, the figures of clouds—all these are the sermon of Buddha".^[However, Francis Cook argues that Vairocana is not a god, nor has the functions of a monotheistic god, since he is not a creator of the universe, nor a judge or father who governs the world.

Thích Nhất Hạnh, meanwhile, has written that the idea of the Buddha's "cosmic body", who is both the cosmos and its creator, "is very close to the idea of God in the theistic religions". Similarly, Lin Weiyu writes that the Huayan school interprets Vairocana as "omnipresent, omnipotent and identical to the universe itself". According to Lin, the Huayan commentator Fazang's conception of Vairocana contains "elements that approach Vairocana to the monotheistic God". However, Lin also notes that this Buddha is contained within a broader Buddhist metaphysics of emptiness, which tempers the reification of this Buddha as a monotheistic creator god.

The Shingon Buddhist view of the Supreme Buddha Mahāvairocana, whose body is seen as being the whole universe, has also been called "cosmotheism" (the idea that the cosmos is God) by scholars like Charles Eliot, Hajime Nakamura, and Masaharu Anesaki.^[67]^[68]^[69] Fabio Rambelli terms it a kind of pantheism, the main doctrine of which is that Mahāvairocana's Dharma body is co-substantial with the universe and is the very substance that the universe consists of. Furthermore, this cosmic Buddha is seen as making use of all the sounds, thoughts, and forms in the universe to preach the Buddha's teaching to others. Thus, all forms, thoughts, and sounds in the universe are seen as manifestations and teachings of the Buddha.

Tantric Adi-Buddha theory and theism

B. Alan Wallace writes on how the Tibetan Buddhist Vajrayana concept of the primordial Buddha (Adi-Buddha) is sometimes seen as forming the foundation of both saṃsāra (the world of suffering) and nirvana (liberation). This view, according to Wallace, holds that "the entire universe consists of nothing other than displays of this infinite, radiant, empty awareness."

Furthermore, Wallace notes similarities between these Vajrayana doctrines and notions of a divine creative "ground of being". He writes: "a careful analysis of Vajrayana Buddhist cosmogony, specifically as presented in the Atiyoga (Dzogchen) tradition of Indo-Tibetan Buddhism, which presents itself as the culmination of all Buddhist teachings, reveals a theory of a transcendent ground of being and a process of creation that bear remarkable similarities with views presented in Vedanta and Neoplatonic Western Christian theories of creation." He further comments that the three views "have so much in common that they could almost be regarded as varying interpretations of a single theory".

Douglas Duckworth sees Tibetan tantric Buddhism as "pantheist to the core", since "in its most profound expressions (e.g., highest Yoga tantra), all dualities between the divine and the world are radically undone". According to Duckworth, in Vajrayana, "the divine is seen within the world, and the infinite within the finite."

Eva K. Neumaier-Dargyay notes that the Dzogchen tantra called the Kunjed Gyalpo ("all-creating king") uses symbolic language for the Adi-Buddha Samantabhadra, which is reminiscent of theism. Neumaier-Dargyay considers the Kunjed Gyalpo to contain theistic-sounding language, such as positing a single "cause of all that exists" (including all Buddhas). However, she also writes that this language is symbolic and points to an impersonal "ground of all existence", or primordial basis, which is "the mind of perfect purity" that underlies all that exists.

Alexander Studholme also points to how the Kāraṇḍavyūhasūtra presents the great bodhisattva Avalokiteśvara as a kind of supreme lord of the cosmos and as the progenitor of various heavenly bodies and divinities (such as the Sun and Moon, the deities Shiva and Vishnu, etc.) Avalokiteśvara himself is seen, in the versified version of the sutra, to be an emanation of the first Buddha, the Adi-Buddha, who is called svayambhu (self-existent, not born from anything or anyone) and the "primordial lord" (Adinatha).

Adi-Buddha as non-theistic

The 14th Dalai Lama sees this deity (called Samantabhadra) as a symbol for ultimate reality, "the realm of the Dharmakaya – the space of emptiness". He is also quite clear that "the theory that God is the creator, is almighty, and permanent is in contradiction to Buddhist teachings... For Buddhists the universe has no first cause, and hence no creator, nor can there be such a thing as a permanent, primordially pure being."

Further discussing the doctrine of the Adi-Buddha, the Dalai Lama writes that the tantric Buddhist tradition explains ultimate reality in terms of "inherent clear light, the essential nature of the mind" and that this seems to imply "that all phenomena, samsara and nirvana, arise from this clear and luminous source".^[52] This doctrine of an "ultimate source", says the Dalai Lama, seems "close to the notion of a Creator, since all phenomena, whether they belong to samsara or nirvana, originate therein". However, he warns that we not think of this as a Creator God, since the clear light is not "a sort of collective clear light, analogous to the non-Buddhist concept of Brahman as a substratum. We must not be inclined to deify this luminous space. We must understand that when we speak of ultimate or inherent clear light, we are speaking on an individual level. When, in the tantric context, we say that all worlds appear out of clear light, we do not visualize this source as a unique entity, but as the ultimate clear light of each being... It would be a grave error to conceive of it as an independent and autonomous existence from beginningless time."

The Dzogchen master Namkhai Norbu also argued that this figure is not a Creator God but is a symbol for a state of consciousness and a personification of the ground or basis (ghzi) in Dzogchen thought. Norbu explains that the Dzogchen idea of the Adi-Buddha Samantabhadra "should be mainly understood as a metaphor to enable us to discover our real condition". He further adds that:

If we deem Samantabhadra an individual being, we are far from the true meaning. In reality, he denotes our potentiality that, even though at the present moment we are in samsara, has never been conditioned by dualism. From the beginning, the state of the individual has been pure and always remains pure: this is what Samantabhadra represents. But when we fall into conditioning, it is as if we are no longer Samantabhadra because we are ignorant of our true nature. So what is called the primordial Buddha, or Adibuddha, is only a metaphor for our true condition.

Regarding the term Adi-Buddha as used in the tantric Kalachakra tradition, Vesna Wallace notes:

when the Kalacakra tradition speaks of the Adibuddha in the sense of a beginningless and endless Buddha, it is referring to the innate gnosis that pervades the minds of all sentient beings and stands as the basis of both samsara and nirvana. Whereas, when it speaks of the Adibuddha as the one who first attained perfect enlightenment by means of imperishable bliss, and when it asserts the necessity of acquiring merit and knowledge in order to attain perfect Buddhahood, it is referring to the actual realization of one's own innate gnosis. Thus, one could say that in the Kalacakra tradition, Adibuddha refers to the ultimate nature of one's own mind and to the one who has realized the innate nature of one's own mind by means of purificatory practices.

Jim Valby notes that the "All-Creating King" (Kunjed Gyalpo, i.e., the primordial Buddha) of Dzogchen thought and its companion deities "are not gods, but are symbols for different aspects of our primordial enlightenment. Kunjed Gyalpo is our timeless Pure Perfect Presence beyond cause and effect. Sattvavajra is our ordinary, analytical, judgmental presence inside time that depends upon cause and effect."

Modern Buddhist anti-theism

Ouyi Zhixu, a Chinese Buddhist figure of the Ming dynasty

The modern era brought Buddhists into contact with the Abrahamic religions, especially Christianity. Attempts to convert Buddhist nations to Christianity through missionary work were countered by Buddhist attempts at refutations of Christian doctrine and led to the development of Buddhist Modernism. The earliest Christian attempts to refute Buddhism and criticize its teachings were those of Jesuits like Alessandro Valignano, Michele Ruggieri, and Matteo Ricci.

These attacks were answered by Asian Buddhists, who wrote critiques of Christianity, often centered on refuting Christian theism. Perhaps the earliest such attempt was that of the Chinese monk Zhu Hong (祩宏, 1535–1615), who authored Four Essays on Heaven (天說四端). Another influential Chinese Buddhist critic of Christian theism was Xu Dashou (許大受), who wrote a long and systematic refutation of Christianity, titled Zuopi (佐闢, "help to the refutation"), which attempts to refute Christianity from the point of view of three Chinese traditions (Confucianism, Buddhism, and Taoism).

The monk Ouyi Zhixu (蕅益智旭, 1599–1655) later wrote the Bixie ji ("Collected Essays Refuting Heterodoxy"), which specifically attacks Christianity on the grounds of theodicy as well as relying on classical Confucian ethics. According to Beverley Foulks, in his essays, Zhixu "objects to the way Jesuits invest God with qualities of love, hatred, and the power to punish. He criticizes the notion that God would create humans to be both good and evil, and finally he questions why God would allow Lucifer to tempt humans towards evil."

Modern Japanese Buddhists also wrote their own works to refute Christian theism. Fukansai Habian (1565–1621) is perhaps one of the best-known of these critics, especially because he was a convert to Christianity who then became an apostate and wrote an anti-Christian polemic, titled Deus Destroyed (Ha Daiusu), in 1620. The Zen monk Sessō Sōsai also wrote an important anti-Christian work, the Argument for the Extinction of Heresy (Taiji Jashū Ron), in which he argued that the Christian God is just the Vedic Brahma and that Christianity was a heretical form of Buddhism. His critiques were particularly influential on the leadership of the Tokugawa shogunate.

Later Japanese Buddhists continued to write anti-theist critiques, focusing on Christianity. These figures include Kiyū Dōjin (a.k.a. Ugai Tetsujō 1814–91, who was a head of Jōdo-shū), who wrote Laughing at Christianity (1869), and Inoue Enryō. According to Kiri Paramore, the 19th-century Japanese attacks on Christianity tended to rely on more rationalistic and philosophical critiques than the Tokugawa-era critiques (which tended to be more driven by nationalism and xenophobia).

Modern Theravada Buddhists have also written various critiques of a Creator God, which reference Christian and modern theories of God. These works include A.L. De Silva's Beyond Belief, Nyanaponika Thera's Buddhism and the God Idea (1985), and Gunapala Dharmasiri's A Buddhist critique of the Christian concept of God (1988).

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