Showing 1-60 of 64 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
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
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
Broadcasting is the set of rules that lets element-wise operations (addition, subtraction, multiplication, division) act on arrays or tensors of different but...
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
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
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
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
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
Nonlinear
Nonlinear describes any function, model, or relationship that does not satisfy the property of linearity. In machine learning the term most often refers to the...
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
NumPy (short for Numerical Python) is the foundational open-source library for numerical and scientific computing in Python, providing an n-dimensional array...
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 the field of artificial intelligence. In natural language processing and information theory, perplexity (often...
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
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
Sigmoid Function
See also: Machine learning terms The sigmoid function is a mathematical function that maps any real number to a value between 0 and 1 using the formula ,...
Deep LearningMachine Learning
Similarity Measure
A similarity measure (also called a similarity function or similarity metric) is a real-valued function that quantifies the degree of resemblance between two...
Information RetrievalMachine Learning
Singular value decomposition
See also: principal component analysis, eigenvalue decomposition, linear algebra, matrix factorization, pseudoinverse, low-rank adaptation, Eckart-Young...
Machine Learning
Sparse Vector
A sparse vector is a vector in which most of the elements are zero, in contrast to a dense vector, in which most elements are non-zero. Google's Machine...
Computer ScienceMachine Learning
Statistical learning theory
Statistical learning theory (SLT) is the mathematical framework that explains when and why machine learning algorithms generalize from a finite training sample...
Machine LearningStatistics
Tensor
In machine learning, a tensor is a multi-dimensional array of numbers that serves as the fundamental data structure for representing and manipulating data....
Deep LearningMachine Learning
Tensor Rank
The rank of a tensor, also referred to as its order or degree, is the number of dimensions (axes or indices) needed to describe the tensor. A scalar has rank...
Machine Learning
Tensor Shape
A tensor shape is a tuple of integers that describes the number of elements along each dimension (or axis) of a tensor. For a tensor of rank r, the shape is...
Deep LearningMachine Learning