Category

Mathematics

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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