Mathematics
75 AI Wiki articles on Mathematics. The most referenced are Perplexity, Cross-Entropy and Scalar.
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Showing 1-60 of 75 articles
AI Co-Mathematician
AI Co-Mathematician is an interactive, agentic research system built by Google DeepMind to help professional mathematicians work on open-ended research...
AI for ScienceGoogle DeepMind
AIME (American Invitational Mathematics Examination)
The American Invitational Mathematics Examination (AIME) is a 15-question, 3-hour mathematics competition for high school students in the United States and...
AI Benchmarks
Ada Lovelace
Augusta Ada King, Countess of Lovelace (born Augusta Ada Byron; 10 December 1815 to 27 November 1852), usually called Ada Lovelace, was an English...
AI HistoryComputer Science
AlphaGeometry 2
AlphaGeometry 2 (often abbreviated AG2) is a neuro-symbolic artificial intelligence system built by Google DeepMind that solves Olympiad-level Euclidean...
AI for ScienceGoogle DeepMind
AlphaProof Nexus
AlphaProof Nexus is a formal proof search system from Google DeepMind that pairs a general-purpose language model with the Lean proof assistant in an agentic...
AI ResearchAI for Science
AlphaTensor
AlphaTensor is an artificial-intelligence system from DeepMind that uses deep reinforcement learning to discover faster algorithms for matrix multiplication....
Google DeepMindReinforcement Learning
Automatic Differentiation
Automatic differentiation (abbreviated AD, also called algorithmic differentiation, autodiff, or autograd) is a family of techniques for computing exact...
AI InfrastructureMachine Learning
Bayes' theorem
Bayes' theorem (also called Bayes' rule or Bayes' law) is a fundamental theorem of probability theory that describes how to update the probability of a...
Machine LearningStatistics
Bayesian statistics
Bayesian statistics is a statistical paradigm in which probability expresses a degree of belief that is updated as evidence arrives, using Bayes' theorem. The...
Statistics
Bellman Equation
See also: reinforcement learning, Markov decision process, Q-learning, dynamic programming, value function, Machine learning terms The Bellman equation is a...
Machine LearningReinforcement Learning
Bias (Math) or Bias Term
See also: Machine learning terms The bias term is a learnable additive constant b added to the weighted sum of a neuron's inputs before an activation function...
Machine LearningNeural Networks
Broadcasting
See also: Machine learning terms Broadcasting is the set of rules that lets element-wise operations (addition, subtraction, multiplication, division) act on...
Deep LearningMachine Learning
Control theory
Control theory is the mathematical and engineering discipline concerned with designing and analysing systems that achieve desired behaviour through measurement...
Reinforcement LearningRobotics
Convergence
Convergence in machine learning is the point at which an iterative optimization algorithm reaches a stable solution, meaning the loss function stops decreasing...
Machine LearningTraining & Optimization
Convex Function
A convex function is a real-valued function whose graph curves upward into a bowl or cup shape, so that the line segment (chord) connecting any two points on...
Machine LearningTraining & Optimization
Convex Optimization
Convex optimization is the branch of mathematical optimization that minimizes a convex function over a convex set, a problem class with one defining advantage:...
Machine LearningTraining & Optimization
Convex Set
A convex set is a set of points in which the line segment connecting any two points of the set lies entirely within the set [1][3]. Formally, a set in a real...
Machine LearningTraining & Optimization
Convolution
See also: Machine learning terms, Convolutional layer, Convolutional filter Convolution is a mathematical operation that combines two functions to produce a...
Deep LearningMachine Learning
Cross-Entropy
See also: Machine learning terms, Loss function, Entropy Cross-entropy is a measure from information theory of how many bits (or nats) are needed to encode...
Deep LearningMachine Learning
Curse of Dimensionality
See also: Machine learning, Feature engineering, Dimensionality reduction The curse of dimensionality is the set of problems that arise when data has a large...
Machine LearningStatistics
Distributionally Robust Optimization
Distributionally robust optimization (DRO) is a framework for making decisions when the probability distribution of uncertain inputs is not known exactly....
Machine LearningStatistics
Earth Mover's Distance
Earth Mover's Distance (EMD), also known as the Wasserstein-1 distance, Kantorovich-Rubinstein metric, or Mallows's distance, is a measure of dissimilarity...
Computer VisionMachine Learning
Entropy
Entropy is a quantitative measure of the uncertainty, randomness, or average information content in a probability distribution: for a discrete random variable...
Machine Learning
FrontierMath
FrontierMath: A Benchmark for Evaluating Advanced Mathematical Reasoning in AI Abbreviation A benchmark of research-level mathematics problems designed to...
AI BenchmarksArtificial Intelligence
FunSearch
FunSearch is a method from Google DeepMind that pairs a large language model with an automated evaluator to discover new solutions to hard problems in...
AI for ScienceGoogle DeepMind
Gradient
In machine learning, the gradient is the vector of partial derivatives of a loss function with respect to every model parameter, and it points in the direction...
Machine LearningTraining & Optimization
Hyperplane
A hyperplane is a flat, affine subspace of dimension n-1 embedded in an n-dimensional space, defined by the linear equation , where w is a normal vector and b...
Machine Learning
Independently and Identically Distributed (i.i.d.)
See also: Machine learning terms, Probability, Statistics, Distribution shift, Out-of-distribution detection Independently and identically distributed...
Machine LearningStatistics
Inductive bias
Inductive bias (also called learning bias) is the set of assumptions that a learning algorithm uses to predict outputs for previously unseen inputs. Without an...
Deep LearningMachine Learning
Information Gain
Information Gain (IG) is a measure from information theory that quantifies the reduction in entropy (uncertainty) achieved by partitioning a dataset on a...
Machine Learning
Information theory
Information theory is the mathematical study of the quantification, storage, and communication of information, founded by Claude Shannon in his 1948 paper "A...
Statistics
KL Divergence (Kullback-Leibler Divergence)
Kullback-Leibler divergence, often abbreviated KL divergence and written , is a measure of how one probability distribution P differs from a second reference...
Machine LearningStatistics
Lambda
See also: Machine learning terms Lambda (the Greek letter λ) is a symbol used across machine learning, statistics, and computer science to denote several...
Machine Learning
Lambda Calculus
Lambda calculus (often written λ-calculus) is a formal system in mathematical logic for expressing computation based on function abstraction and application...
Computer ScienceProgramming Languages
Latent semantic analysis (LSA)
Latent semantic analysis (LSA), called latent semantic indexing (LSI) in information retrieval contexts, is an unsupervised technique that maps both terms and...
Information RetrievalNatural Language Processing
Lean (Theorem Prover)
Lean is an open source interactive theorem prover and dependently typed functional programming language created by Leonardo de Moura, first launched at...
Programming Languages
Linear
See also: Machine learning terms In machine learning and mathematics, linear describes a function or relationship in which the output is built from the inputs...
Machine Learning
Log Loss
Log loss is the negative log-likelihood of the predicted probabilities and the standard loss function for probabilistic classification: for binary labels it is...
Machine LearningTraining & Optimization
Log-Odds
Log-odds, also known as the logit, is a mathematical transformation that converts a probability value between 0 and 1 into a real number spanning from negative...
Machine LearningStatistics
MATH-500
MATH-500 is a 500-problem benchmark for evaluating the mathematical reasoning of large language models, formed by holding out 500 problems from the test split...
AI Benchmarks
Manifold Hypothesis
The manifold hypothesis is the conjecture that real-world high-dimensional data, such as natural images, speech, and text representations, concentrates on or...
Deep LearningMachine Learning
Markov Decision Process (MDP)
See also: Machine learning terms A Markov Decision Process (MDP) is a mathematical framework for modeling sequential decision-making in stochastic...
Machine LearningReinforcement Learning
Markov chain
A Markov chain is a stochastic process in which the probability of the next state depends only on the current state and not on the sequence of states that came...
Statistics
Mathematical reasoning in AI
Mathematical reasoning in AI is the ability of computer systems to solve mathematical problems: carrying out multi-step calculations, proving theorems, and...
AI BenchmarksAI Research
Mathlib
Mathlib (formally mathlib4, the active Lean 4 incarnation) is the community-maintained, open-source unified library of formalized mathematics for the lean...
Software Development
Matrix factorization
Matrix factorization is a family of mathematical techniques that decompose a matrix into a product of two or more smaller matrices. Originally rooted in linear...
Machine Learning
Matrix multiplication
Matrix multiplication combines an M by K matrix A with a K by N matrix B to produce an M by N matrix C, in which every entry of C is the dot product of one row...
AI HardwareAlgorithms
Minerva (language model)
Minerva is a large language model developed by Google Research that specializes in quantitative reasoning, meaning it answers mathematics, science, and...
GoogleLarge Language Models
Minimax Loss
Minimax loss is a loss function rooted in game theory and decision theory that measures the worst-case performance of a strategy, algorithm, or model. In...
Generative AIMachine Learning
Nash equilibrium
A Nash equilibrium is a combination of strategies, one for each player in a game, such that no player can raise their own payoff by changing strategy alone...
AlgorithmsComputer Science
Nonlinear
See also: Machine learning terms Nonlinear describes any function, model, or relationship that does not satisfy the property of linearity. In machine learning...
Machine Learning
Normal distribution
The normal distribution, also called the Gaussian distribution, is a continuous probability distribution defined by two parameters, a mean and a variance ,...
Statistics
NumPy
See also: Machine learning terms, pandas, scikit-learn NumPy (short for Numerical Python) is the foundational open-source library for numerical and scientific...
AI Tools & ProductsMachine Learning
NuminaMath
NuminaMath is a family of openly licensed competition-mathematics resources developed by the non-profit Project Numina, spanning the largest public dataset of...
Data & DatasetsOpen Source AI
Partial derivative
See also: Machine learning terms A partial derivative measures how a multivariable function changes when one of its inputs is varied while every other input is...
Machine Learning
Perplexity
Perplexity has two distinct meanings in artificial intelligence. In information theory and natural language processing, perplexity (PPL) is an intrinsic score...
Machine LearningNatural Language Processing
Principal Component Analysis (PCA)
Principal component analysis (PCA) is an unsupervised learning technique for dimensionality reduction that identifies the orthogonal directions of maximum...
Machine LearningStatistics
Qwen2-Math
Qwen2-Math is a series of mathematics-specialized large language models released by the Qwen team at Alibaba on 8 August 2024. The series consists of three...
Chinese AILarge Language Models
Qwen2.5-Math
Qwen2.5-Math is a family of mathematics-specialized large language models developed by the Qwen team at Alibaba Cloud and released in September 2024. The...
Chinese AILarge Language Models
Scalar
See also: vector, matrix, tensor, linear algebra, gradient descent A scalar is a single numerical value, a quantity with magnitude but no direction, and the...
Machine Learning