Basic Mathematics of Artificial Intelligence
The mathematical foundation of artificial intelligence included many aspects:
** 1. Liner Algebra **
1. ** Vectors and Matrices **
- Vectors were one-dimensional arrays that could represent direction and size, while matrices were two-dimensional arrays that could represent linear transformations.
- For example, in artificial intelligence, linear algebra tools such as matrix multiplication were widely used in processing large data sets, image processing, and pattern recognition.
2. ** Transpose and Inverse Matrix **
- The transpose operation of the matrix is written as [A^{T}], and the inverse operation is written as [A^{-1}].
3. ** System of linear equations **
- It could be solved by the Gauss elimination method. The determinate was a scalar-value of the matrix, which was used to determine whether the matrix was inverse.
4. ** Eigen Value and Eigen Vectors **
- The eigen values represent the scaling factor of the matrix in certain directions, and the eigen values correspond to the eigen values, representing the invariants of the matrix in certain directions.
- Singular value decomposition (SVR) could decompose a matrix into the product of three matrices for dimensional reduction and data compression.
** 2. Theory of probability and statistics **
1. ** Basic Concepts **
- The probability represents the probability of an event occurring, ranging from 0 to 1.
- Condition probability (P(A| B) is the probability of an event occurring under a given condition.
- Bayes 'theorem (P(A| B)=\frac{P(B| A)P(A)}{P(B)} is used to calculate the posteriori probability.
2. ** Random variables and distribution **
- The value of a scattered random variable is considered to be scattered, such as the binormal distribution or the poisson distribution, while the value of a continuous random variable is considered to be continuous, such as the normal distribution or the exponential distribution.
- The expectation and the deviation represent the average and the degree of fluctuation of the random variable, respectively.
- Maximum likelihood estimation (MLE) estimates the parameters by maximized the likelihood function, and Bayes estimation involves the prior distribution (the prior probability distribution of the parameters) and the posteriori distribution (the probability distribution of the parameters after observing the data).
** 3. Derivative **
1. ** Limit and Derivative **
- The limit is the trend of the function around a certain point, the derivative is the instantaneous rate of change of the function at a certain point, recorded as <
Artificial Intelligence Mathematics
Artificial intelligence mathematics covers many important branches of mathematics. The following are some of the main aspects: ** 1. Liner Algebra ** 1. ** Basic Concepts ** - Vectors were one-dimensional arrays that could represent direction and size, while matrices were two-dimensional arrays that could represent linear transformations. - Operations such as transpose (noted as A^T) and inverse matrix (noted as A^{-1}) were important in artificial intelligence. 2. ** Field of application ** - In artificial intelligence, linear algebra was widely used in data representation, matrix operations, feature extraction, and so on. For example, when dealing with large data sets, image processing, and pattern recognition, linear algebra tools such as matrix multiplication, eigen values, and eigen matrices played a key role. ** 2. Theory of probability and statistics ** 1. ** Basic Concepts ** - The probability represents the probability of an event occurring, ranging from 0 to 1. Condition probability (P(A| B) is the probability of an event occurring under a given condition. Bayes 'theorem (P(A| B)=\frac{P(B| A)P(A)}{P(B)} is used to calculate the posteriori probability. - Random variables could be divided into two types, namely, the scattered random variables (such as the binormal distribution, the poisson distribution) and the continuous random variables (such as the normal distribution, the exponential distribution). There were also expectations and variations to represent their average value and degree of fluctuation. There was also the maximum likelihood estimation (MLE), which estimated the parameters by maximized the likelihood function. The Bayes estimation involved the prior distribution and the posteriori distribution. 2. ** Field of application ** - It was an important tool for dealing with uncertainty and data analysis, and was widely used in machine learning and deep learning. It is widely used in machine learning algorithms such as Bayes networks, decision trees, and cluster analysis. It can understand and predict the uncertainty of data, so as to make better decisions. ** 3. Derivative ** 1. ** Basic Concepts ** - The limit is the trend of a function around a certain point. The derivative is the instantaneous rate of change of the function at a certain point, and the partial derivative is the partial derivative. Integration was divided into uncertain integration (the process of finding the original function) and definite integration (the accumulation of the function in a certain interval). - The slope was the derivative of a multi-variable function, which represented the rate of change of the function in all directions. The slope descent gradually adjusted the parameters in the direction of the slope to minimize the objective function. 2. ** Field of application ** - It played an important role in artificial intelligence, especially in optimization problems. It could be used to find the optimal solution of a function to achieve optimal control of the objective function. It had applications in areas such as machine learning algorithm optimization and edge detection in image processing. ** 4. Theory of optimization ** 1. ** Basic Concepts ** - In unconstrained optimization, the gradient-descent method minimized the objective function by gradually adjusting the parameters in the direction of the gradients. Newton's method used the second-order derivative (Hessian matrix) to accelerate convergence. - The Lagrange Multipliers Method in constrained optimization transformed the constrained optimization problem into an unconstrained optimization problem by introducing the Lagrange Multipliers. The Karush-Kuhn- Tucker (KMT) condition was used to solve the optimization problem with unequal constraints. In the case of the Convex function, the line between any two points of the function image was above the function image. The Convex set was the line between any two points in the set. The Convex optimization problem (the optimization problem with both the objective function and the constraints being concave) had a global optimal solution. 2. ** Field of application ** - It was widely used in decision-making, path planning, and learning algorithms in artificial intelligence. It helped to find the best solution to the problem and improve the performance and efficiency of artificial intelligence. In addition, information theory provided the theoretical basis for data compression and signal processing of artificial intelligence. Graph theory was used in search algorithms, decision trees, and other aspects to provide the basis for reasoning and decision-making of intelligent systems. Dispersive mathematics played a key role in algorithm design and natural language processing. Mathematical logic was used in reasoning engines and intelligent search. The complexity theory provided scientific basis for evaluating the efficiency of artificial intelligence by analyzing the time complexity and space complexity of the algorithm. Group theory had applications in image processing, pattern recognition, and encryption, while tensors and subspace algebra were used in deep learning algorithms to better represent and process high-dimensional data. These branches of mathematics provided solid theoretical support for the development of artificial intelligence. "A Short History of the Future: Legends of the Intelligent Era" was equally exciting. Everyone was welcome to click and read it!
Artificial Intelligence Mathematics Foundation
"Mathematical Basics of Artificial Intelligence" was an e-book about the mathematical basics of artificial intelligence. It covers a variety of basic mathematical knowledge needed for artificial intelligence, such as linear algebra.(It involves concepts such as matrices, matrices, transpositions, inverse matrices, linear equations, determinants, eigen values, eigen matrices, singular value decomposition, etc.), calculus (Including limits, derivative, partial derivative, integral, and slope descent), probability theory and mathematical statistics (including probability, conditioned probability, Bayes 'theorem, random variables and distribution, expectation and variation, maximum likelihood estimation, Bayes estimation, etc.), and also introduced the commonly used statistics methods in machine learning, optimization theory, and neural networks. Some versions were based on calculus, linear algebra, probability theory, and mathematical statistics. They gave an in-depth introduction to function estimation, optimization theory, information theory, and graph theory. At the same time, they gave experimental cases in artificial intelligence algorithms. They might also implement relevant cases through Python to make abstract theory concrete. They might also provide 205 examples and 19 application projects to enhance practical use. It was suitable for high school students, college students, and junior high school students with strong abilities. Some of them were written by Dr. Chen Hua. They were one of the planning textbooks for artificial intelligence-related majors in colleges and universities for the cultivation of advanced artificial intelligence talents. They were published in April 2021. They might provide supporting PowerPoint, experimental and application cases, and other basic teaching materials for free. They could be downloaded at: "A Short History of the Future: Legends of the Intelligent Era" was equally exciting. Everyone was welcome to click and read it!
Basic Concepts of Artificial Intelligence
Artificial Intelligence (AI) was an emerging discipline that was based on computer science and was a combination of computer science, psychology, philosophy, and other disciplines. It researched and developed theories, methods, techniques, and application systems for simulating, extending, and expanding human intelligence. It was dedicated to solving common cognitive problems related to human intelligence, such as learning, creation, and image recognition. The goal was to establish a self-learning system that could obtain useful knowledge from data. Artificial intelligence could be divided into three levels: weak artificial intelligence, strong artificial intelligence, and super artificial intelligence. Weak artificial intelligence refers to machines or systems that can only display human intelligence in specific fields or tasks, such as voice recognition, image recognition, autonomous driving, etc. Strong artificial intelligence refers to machines or systems that can display human intelligence in any field or task, or even exceed human intelligence, such as general artificial intelligence, artificial life, etc. Super artificial intelligence referred to the intelligence of machines or systems that far surpassed humans in all fields or tasks, such as artificial neural networks, artificial super intelligence, etc. At present, the development of artificial intelligence was mainly concentrated on the weak artificial intelligence level. Strong artificial intelligence and super artificial intelligence were still in the theoretical and exploration stage. Artificial intelligence techniques and methods mainly included machine learning, deep learning, natural language processing, computer vision, robots, and so on. Machine learning is the core technology of artificial intelligence, including supervised learning, unsupervised learning, semi-supervised learning, reinforcement learning, etc. Deep learning is an important branch of machine learning, using multi-layer artificial neural networks to achieve machine learning, such as Consecutive neural networks, Cyclic neural networks, etc. Natural language processing is a technology that allows machines or systems to understand and generate natural language, covering speech recognition, Text To Speech, etc. Computer vision is a technology that allows machines or systems to perceive and understand images and videos, while robots are machines or systems that can simulate or extend human behavior and functions. In addition, Generative Artificial Intelligence (AIGC) was a branch of machine learning. It was an artificial intelligence that could create new content and ideas, including conversations, stories, pictures, videos, and music. General artificial intelligence (AGI) referred to an AI system that had the ability to self-control, reasonable self-understanding, and the ability to learn new skills. It could deal with complex problems that humans had never trained it to, reason when there were uncertain factors, and even use strategies to solve problems. At the same time, it had the ability to make decisions. "A Short History of the Future: Legends of the Intelligent Era" was equally exciting. Everyone was welcome to click and read it!
Basic application of artificial intelligence
The application foundation of artificial intelligence included many aspects: ** 1. Origin and Development ** 1. In the 1930s and 1940s, there were two important discoveries in the field of intelligence, namely mathematical logic and new computational ideas. Turing created a simple non-digital computing model to prove that computers could work in a way that could be understood as intelligent. 2. In 1969, the first joint conference on artificial intelligence was held. In 1970, the "International Journal of AI" was founded. This played a positive role in the international academic activities, exchanges, and research development of artificial intelligence. 3. Artificial intelligence research had made significant progress in the past few decades, and expert systems had shown great vitality. Feigenbaum was known as the "father of expert systems and knowledge engineering." In 1978, China incorporated artificial intelligence research into its national plan. ** 2. Main schools ** 1. Symbolism, also known as logicism, psychlogism, or computational science, was based on the assumption of a physical symbolic system and the principle of limited rationality. 2. Connectionism, also known as bionicism or physiologism, was based on the connection mechanism and learning algorithm between neural networks. 3. Actionism, also known as Evolutionism or Cyberneticism, was based on cybernetics and perception-action control systems. ** 3. Basic applications in different fields ** 1. In the field of software, SuperMap software combined artificial intelligence technology with natural language processing, computer vision, AI drawing, and other technologies to form a technical foundation. It was used to power the basic software of GPS and applied to natural resources, water conservancy, housing construction, and other industries. 2. In the field of new media operations, there was AI artificial intelligence that did not need to take videos or cut videos. It could automatically generate videos in a minute after entering a paragraph of text. It could be used in the e-commerce field to make product renderings (such as changing pictures in batches, changing backgrounds, Short videos, 3D product display, applying e-commerce templates to generate various scenes, etc.). It could help designers edit pictures and produce them in batches. It could also help farmers make Short videos to bring goods. 3. In terms of intelligent agents, the Azure AI Foundry was launched by the company, marking the shift from chatbots to agents and the use of artificial intelligence for business process automations. In the future, complex artificial intelligence applications will be built on artificial intelligence models such as the Large Language Model (ILM), becoming self-organizing software agents. 4. In terms of human-computer interaction, for example, Harvard students used Zuckerberg's AI glasses to combine web search and large models to develop new applications. They could sort out detailed files (including names, hobbies, studies or jobs, photos, etc.) from massive amounts of data within seconds of identifying passers-by's faces. "A Short History of the Future: Legends of the Intelligent Era" was equally exciting. Everyone was welcome to click and read it!
Basic Concepts of Artificial Intelligence
Artificial Intelligence (AI) was the general term for a series of technologies. It was the most extensive concept. It referred to the ability to make machines realize the abilities of humans and organizations, the ability to perform complex tasks, and the use of computers to simulate human intelligent behavior. It was a technology and application that achieved intelligence. It covered machine learning, deep learning, natural language processing, computer vision, and many other fields. Machine learning referred to the process of letting machines learn and improve algorithms through training data. Deep learning was a machine learning method based on neural networks, which could achieve more complex pattern recognition and data mining. It was essentially a neural network with more layers and was also one of the research directions of neural networks. Natural language processing referred to the application of computer technology to the language field to achieve functions such as text analysis and speech recognition. Computer vision referred to the application of computer technology to the field of images to achieve functions such as image recognition and target detection. The neural network was an important component of AI, mainly referring to artificial neural networks. In addition, spatial computing was a high-level application based on computer vision. Its core was to use AI computer vision and extended reality to integrate virtual experiences into the physical world. "A Short History of the Future: Legends of the Intelligent Era" was equally exciting. Everyone was welcome to click and read it!
Artificial intelligence mathematics foundation e-book
There was a book called " Mathematical Basics of Artificial Intelligence " that was available in a PDF-version. You could check the author's homepage to get the related book's PDF-version and implementation code for free. There was also an e-book titled " Basic Mathematical Theory for Artificial Intelligence ". It was one of the planned teaching materials for artificial intelligence-related majors in higher education institutions for the cultivation of advanced artificial intelligence talents. It would provide basic teaching materials such as PowerPoint, experiments, and application cases for free. " A Short History of the Future: Legends of the Intelligent Era " was equally exciting. Everyone was welcome to click and read it!
Artificial intelligence mathematics foundation after-school question answer
Based on the information provided, he could only obtain the answers to some of the questions in the " Foundation of Artificial Intelligence Mathematics ". For example, the answers to the questions about the sales of Dongfang Co., Ltd. in 2021, the bar chart of Yang Guang's college entrance examination score, and the calculation of fixed points. There was not enough information provided for the answers to the other after-school questions, so he could not give the complete answers to the after-school questions of the " Foundation of Artificial Intelligence Mathematics ". " A Short History of the Future: Legends of the Intelligent Era " was equally exciting. Everyone was welcome to click and read it!
The three most basic and core technologies of artificial intelligence
From the perspective of technology classification, the three core technologies of artificial intelligence were machine learning, natural language processing, and computer vision. Machine learning was one of the core technologies of artificial intelligence. It was a cross-disciplinary subject involving many fields. It studied how computers simulated or realized human learning behavior to obtain new knowledge or skills. Machine learning could be divided into supervised learning, unsupervised learning, reinforcement learning, traditional machine learning, and deep learning. It was a technology that allowed computers to learn, grow, and improve their performance from data. In simple terms, natural language processing allowed computers to understand human language and speak like humans. It was a technology in artificial intelligence that allowed machines to understand and process human language. It was widely used in intelligent customer service and intelligent translation software. Computer vision allowed computers to have " eyes " and be able to " understand " images and videos. For example, driverless cars could identify roads and obstacles, and Face Recognition technology could accurately identify faces. " A Short History of the Future: Legends of the Intelligent Era " was equally exciting. Everyone was welcome to click and read it!
The answers to the questions after the basic artificial intelligence class
The following are the answers to some of the post-class questions in "Basics of Artificial Intelligence": 1. What is intelligence? What are the characteristics of intelligence? - Intelligence could be understood as the sum of knowledge and intelligence. Knowledge was the foundation of intelligent behavior. Intelligence was the ability to acquire and apply knowledge to solve problems. It was the ability to make correct decisions and achieve goals in a given environment and goal. It originated from the thinking activity of the human brain. - The characteristics of intelligence included the ability to perceive (system input), the ability to remember and think, the ability to learn and adapt, and the ability to act (system output). 2. ** What are the schools of artificial intelligence? What were their core views? - At present, there were three main schools of thought in artificial intelligence: symbolism, Connectionist, and behavior. - Symbolism believes that knowledge can be expressed by logical symbols, and the cognitive process is a symbolic operation process. Humans and computers were both physical symbol systems. Computer symbols could be used to simulate human cognitive processes. He believed that the core problem of artificial intelligence was knowledge representation and knowledge reasoning, which could be realized by symbols. All cognitive activities were based on a unified architecture. - Connectionist principles were mainly neural networks and the connection mechanism and learning algorithm between neural networks. He believed that human thinking was based on neurons rather than symbolic operations. The human brain was different from a computer, and symbolic operations could not be used to simulate the working mode of the brain. - The principles of behaviour doctrine were cybernetics and the perception-action control system. This school of thought believed that intelligence depended on perception and action, and proposed the "perception-action" model of intelligent behavior. They believed that knowledge did not need to be expressed or reasoned. The research of artificial intelligence was based on a growing method, relying on perception and action to connect and interact with the outside world. 3. What are the short-term and long-term goals of artificial intelligence research? What is the relationship between them? - The immediate goal of artificial intelligence was to achieve machine intelligence, which was to study how to make existing computers smarter, so that they could use knowledge to deal with problems and simulate human intelligence. - The long-term goal was to create intelligent machines, that is, to reveal the fundamental mechanism of human intelligence, and to use intelligent machines to simulate, extend, and expand human intelligence. - There was no strict boundary between short-term goals and long-term goals. The two complemented each other. "A Short History of the Future: Legends of the Intelligent Era" was equally exciting. Everyone was welcome to click and read it!
AI artificial intelligence artificial intelligence
Artificial intelligence (AI) is a broad term used to describe applications that perform complex tasks that used to require human input. It includes subfields such as machine learning and deep learning. Machine learning focuses on building systems that can learn or improve performance based on the data they use. The goal of artificial intelligence is to create a self-learning system that can solve problems like humans. Artificial intelligence could be applied to various fields, such as online communication with customers, chess, image recognition, and so on. It also streamlines business processes, improves the customer experience, and speeds up innovation. The development of artificial intelligence had gone through many stages, from general-purpose computing devices to logical reasoning expert systems, to deep learning computing systems and large model computing systems. The current level of artificial intelligence is called narrow artificial intelligence (ANI). It performs well on specific tasks, but it cannot learn new skills or understand the world in depth. Super Artificial Intelligence (ASI) was a postulated future state with intelligence surpassing human intelligence. At present, artificial intelligence surpassed humans in some tasks, but still lagged behind in other tasks. The industry played a leading role in the cutting-edge research of artificial intelligence, and the cost of training cutting-edge models was getting higher and higher. In the future, the development of artificial intelligence might bring more breakthroughs and applications.