Partial derivative
A partial derivative measures how a multivariable function changes when one of its inputs is varied while every other input is held fixed.
Mathematics
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Showing 61-82 of 82 articles
Perplexity
Perplexity has two distinct meanings in artificial intelligence. In information theory and natural language processing, perplexity (PPL) is an intrinsic score for a probabilistic model: on a specified sequence
Principal Component Analysis (PCA)
Principal component analysis (PCA) is an unsupervised learning technique for dimensionality reduction that identifies the orthogonal directions of maximum variance in high-dimensional data and projects…
Prove2Me
Prove2Me is an open collaborative platform for formalizing mathematics in Lean 4, built by a group led by Tianyi Peng at Columbia University.
Qwen2-Math
Qwen2-Math is a series of mathematics-specialized large language models released by the Qwen team at Alibaba on 8 August 2024.
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.
Scalar
A scalar is a single numerical value, a quantity with magnitude but no direction, and the simplest object in linear algebra and machine learning.
Shapley value
The Shapley value is a rule from cooperative game theory for dividing the payoff of a group among its members.
Sigmoid Function
The sigmoid function is a mathematical function that maps any real number to a value between 0 and 1 using the formula $$\sigma(x) = \frac{1}{1 + e^{-x}}$$, producing a smooth S-shaped curve.
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 objects, returning a large value when the objects…
Singular value decomposition
Singular value decomposition (SVD) is a matrix factorization that writes any real or complex m x n matrix $$A$$ as the product $$A = U \Sigma V^\top$$, where U and V are orthogonal matrices (the left and right…
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.
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 to unseen data.
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.
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.
Tensor Shape
A tensor shape is a tuple of integers that describes the number of elements along each dimension (or axis) of a tensor.
Terence Tao
Terence Tao (born 1975 in Adelaide, Australia) is a mathematician at the University of California, Los Angeles, where he is a Distinguished Professor and holds the James and Carol Collins Chair in the College…
VC dimension
The Vapnik-Chervonenkis dimension, almost always shortened to VC dimension, measures the capacity of a class of binary classifiers by asking how many points the class can label in every possible way.
Wasserstein GAN (WGAN)
A Wasserstein GAN (WGAN) is a generative adversarial network that trains its two networks to minimise the Wasserstein-1 distance, also called the Earth mover's distance, between the real data distribution and…
Wasserstein Loss
Wasserstein loss is a loss function for training generative models that measures the distance between two probability distributions as the Wasserstein-1 distance
Weighted Sum
A weighted sum is a mathematical operation that combines multiple input values by multiplying each value by a corresponding weight (coefficient) and then summing the results.
Wolfram GPT
Wolfram GPT is the integration of Wolfram|Alpha and the Wolfram Language with OpenAI's ChatGPT, giving the language model on-demand access to authoritative computational knowledge, real-time data feeds…