In this blog, we will summarize the latex code for statistics equations, ranging from the elementary statistics equations (e.g. mean and variance) to more advanced graduate-level statistics equations, e.g. Binomial, Poisson, Normal Distribution, Chi-Square Test, Skewness, Kurtosis, etc.

In this blog, we will summarize the latex code for most popular machine learning equations, including multiple distance measures, generative models, etc. There are various distance measurements of different data distribution, including KL-Divergence, JS-Divergence, Wasserstein Distance(Optimal Transport), Maximum Mean Discrepancy(MMD) and so on. We will provide the latex code for machine learning models in the following sections. We will also provide latex code of Generative Adversarial Networks(GAN), Variational AutoEncoder(VAE), Diffusion Models(DDPM) for generative models in the second section.

In this blog, we will give you a brief introduction of what are multimodal models and what can multimodal generative models accomplish. OpenAI just released their latest text-to-video multimodal generative model "SORA" in Feb, 2024 which becomes extremely popular. SORA can generate short videos of up to 1 minute's length. Before SORA, there are also many generative multi-modal models released by various companies, such as BLIP, BLIP2, FLAMINGO, FlaVA, etc. We will summarize a complete list of these time tested multi-modal generative models, introduce the model architures (text and image encoder), the training process, tasks, latex equation of loss functions, the Vision Language capabilities (such as text-to-image, text-to-video, text-to-audio, visual question answering), etc. Tag: Multimodal, AIGC, Large Language Model

In this blog, we will summarize the latex code for Probability Formulas and Equations, including Binomial Distribution, Poisson Distribution, Normal Gaussian Distribution, Exponential Distribution, Gamma Distribution, Uniform Distribution, Beta Distribution, Bernoulli Distribution, Geometric Distribution, Beta Binomial Distribution, Poisson Binomial Distribution, Chi-Squared Distribution, Gumbel Distribution, Student t-Distribution, Laplace Distribution, etc. And for multivariate distributions, we will also cover Multinomial Distribution, MultiVariate Normal Distribution, MultiVariate Gamma Distribution, MultiVariate t-Distribution and others.

In this blog, we will summarize the latex code of most fundamental equations of transfer learning(TL). Different from multi-task learning, transfer learning models aims to achieve the best performance on target domain (minimized target domain test errors), not the performance of source domain. Typical transfer learning methods including domain adaptation(DA), feature sub-space alignment, etc. In this post, we will dicuss more details of TL equations, including many sub-areas like domain adaptation, H-divergence, Domain-Adversarial Neural Networks(DANN), which are useful as quick reference for your research.

In this blog, we will summarize the latex code for equations and formula sheet of CFA Level II exam, Formula Sheet Equations and Latex Code. Topics include QUANTITATIVE METHODS, such as LINEAR REGRESSION, MULTIPLE REGRESSION, TIME SERIES ANALYSIS, Machine Learning, ECONOMICS, Exchange rate, Covered interest rate parity, Uncovered interest rate parity, Relative purchasing power parity, Fisher and international Fisher effects, FX carry trade, Mundell-Fleming model, ECONOMIC GROWTH, Growth accounting equation, Labor productivity growth accounting equation, Classical growth model (Malthusian model), Neoclassical growth model (Solow’s model), Endogenous growth model, Convergence, ECONOMICS OF REGULATION. The data source of this blog is summarized from WILEY’S CFA PROGRAM LEVEL II quicksheet.

In this blog, we will introduce the DeepNLP Equation workspace, which helps users better manage, edit, share and display their equations. In the platform, users can manage their equations and latex code in a personal workspace, which enables users to create new equations (with latex code, personal tags), edit and save equations. It also creates a URL of your equation, which can be shared to the collaborators. In the following sections, we will give you the step by step instructions on how to create, edit and share an equation. Once you finish add the equation, you can copy the latex code of your equation to clipboard and paste the code to your preferred latex file system, e.g. Overleaf, etc.

Cheatsheet of Latex Code for Most Popular Natural Language Processing Equations

In this blog, we will summarize the latex code of most popular formulas and equations for Financial Engineering Formula and Equation (Continuous-Time Finance). We will cover important topics including Standard Brownian Motion (SBM), Geometric Brownian Motion (GBM), Ito Lemma, Stochastic Integrals, Solutions to Some Common SDEs, Brownian Motion Variation, Stock Prices as a GBM, Stock Prices are Lognormal, Sharpe Ratio and Hedging, The Black-Scholes Equation, Risk-Neutral Valuation and Power Contracts.

In this blog, we will summarize the latex code for differential equations formulas, including diffusion (conduction) equation, wave equation, heat equation, laplace equation, Legendre's equation, Bessel's equation, Spherical Harmonics Equation, etc.

In this blog, we will summarize the latex code of most popular formulas and equations for Financial Engineering Formula and Equation (Continuous-Time Finance). We will cover important topics including Standard Brownian Motion (SBM), Geometric Brownian Motion (GBM), Ito Lemma, Stochastic Integrals, Solutions to Some Common SDEs, Brownian Motion Variation, Stock Prices as a GBM, Stock Prices are Lognormal, Sharpe Ratio and Hedging, The Black-Scholes Equation, Risk-Neutral Valuation and Power Contracts.

In this blog, we will summarize the latex code for basic calculus formulas, including Limits, Differentiation and Integration. For integration formulas, we will cover the topic as standard form of integration, integration of 1/x, ln(x), Exponential e^{ax}, xe^{ax}, Integration by Parts, Differentiation of an Integral, Dirac Delta Function, etc.

In this blog, we will summarize the latex code for series formulas, including arithmetic and geometric progressions, convergence of series: the ratio test, Binomial expansion, Taylor and Maclaurin Series, Power Series with Real Variables e^{x},ln(1+x),sin(x),cos(x), Plane Wave Expansion, etc.

In this blog, we will summarize the latex code for linear matrix algebra formulas, including matrix multiplication, transpose, inverse matrix, determinants, hermitian matrices, determinants, eigenvalues and eigenvectors, orthogonal matrices, etc.

In this blog, we will summarize the latex code for basic calculus formulas, including Limits, Differentiation and Integration. For limits formulas, we will cover sections including: L'Hospital Rule, Limits of Power, Limits of xln(x), Limits of x^{n}/n!. For differentiation formulas, we will cover Differentiation of Polynomial Function, Chain Rule for Differentiation, Differentiation of Multiplication, Differentiation of Division, Differentiation of Trigonometric formulas (sin, cos, tan, sec), and Differentiation of Hyperbolic formulas (sinh, cosh, tanh, sech, coth, cosech).

In this blog, we will summarize the latex code for Curves and Shapes, Geometry Math Formulas. Topics include Distance Between Two Points 2D, Distance Between Two Points 3D, Eccentricity of a Hyperbola, Eccentricity of an Ellipse, Circle, Hyperbola, Hyperbolic Paraboloid, Parabola, Plane, Sphere, Ellipse, Ellipsoid, Elliptic Cone, Elliptic Cylinder, Elliptic Paraboloid, Spiral of Archimedes, etc.

In this blog, we will summarize the latex code of most popular formulas and equations for Financial Engineering Formula and Equation part I-Forwards, Puts, and Calls. We will cover important topics including Forwards, Put-Call Parity, Calls and Puts with Different Strikes, Calls and Puts Arbitrage, Call and Put Price Bounds, Varying Times to Expiration, Early Exercise for American Options, etc.

In this blog, we will summarize the latex code for Geometry, Math formulas and equations. Topics include Area of a Circle, Area of a Parallelogram, Area of a Rectangle, Area of a regular Polygon, Area of a Rhombus, Area of a Sector, Area of a Square, Area of a Trapezoid, Area of a Triangle,Area of an Ellipse, Area of an Equilateral Triangle.

In this blog, we will summarize the latex code for Geometry Coordinate Systems, Math Formulas. Topics include Cartesian to Cylindrical Coordinates, Cartesian to Polar Coordinates, Cartesian to Spherical Coordinates, Cylindrical to Spherical Coordinates, etc.

In this blog, we will summarize the latex code of most popular formulas and equations for Financial Engineering Formula and Equation Monte-Carlo Simulations and Interest Rate Models. We will cover important topics including Monte-Carlo Simulations, Bonds and Interest Rates, Black-Derman-Toy (BDT) model and Cox-Ingersoll-Ross (CIR) model.

In this blog, we will introduce most popuplar formulas in Mechanics, Physics. We will also provide latex code of the equations. Topics include velocity, stress, speed of sound, newton second law(force), shear_modulus, angular momentum, centripetal acceleration, continuity equation, displacement , Hydraulic Lift, Speed of sound waves in a fluid, etc.

In this blog, we will introduce most popuplar physics formulas in Relativity. We will also provide latex code of the equations. Topics include the Lorentz transformation, red and blue shift, general relativity, Riemannian Tensor and Einstein Field Equations, etc.

In this blog, we will introduce most popuplar physics formulas in Electricity & Magnetism. This blog covers topics, including the Maxwell equations, force and potential, Gauge Transformations, Energy of the Electromagnetic Field, etc.

In this blog, we will introduce most popuplar formulas in thermodynamics, Physics. We will also provide latex code of the equations. Topics include thermodynamics, heat capacity, conservation of energy, nernst's law, maxwell relations, adiabatic processes, isobaric processes, throttle processes, The Carnot Cycle, phase transitions, thermodynamic potential, ideal mixtures, thermodynamics statistical basis, etc.

In this blog, we will introduce most popuplar formulas in Wave, Physics. We will also provide latex code of the equations. Topics include Wave Equation, Plane Waves, Spherical Waves, Cylindrical Waves, The general solution of Wave Equation, The Stationary Phase Method, Green functions for the initial-value problem, Waveguides and resonating cavities, Non-linear wave equations, etc.

In this blog, we will introduce most popuplar formulas in Optics, Physics. We will also provide latex code of the equations. Topics include Bending of light, Snell's law, Fermat's principle, Paraxial geometrical, Mirrors, Magnification, Matrix Methods, Reflection and Transmission, Fresnel Equations, Polarization of Optics, Prisms and Dispersion, Diffraction, Birefringence and Dichroism, Retarders: waveplates and compensators, Fabry-Perot interferometer, etc.

In this blog, we will introduce most popuplar formulas in Oscillations, Physics. We will also provide latex code of the equations. Topics include harmonic oscillations, mechanic oscillations, electric oscillations, waves in long conductors, coupled conductors and transformers, pendulums, harmonic wave, etc.

In this blog, we will introduce most popuplar formulas in Quantum Physics. We will also provide latex code of the equations. Topics of Quantum Physics include Black Body Radiation, The Compton Effect, Quantum Wave Functions, Operators in Quantum Physics, The Uncertainty Principle, The Schrödinger Equation, Parity, The Tunnel Effect, Harmonic Oscillator, Angular momentum, Spin, the Dirac Formalism, and so on.

In this blog, we will summarize the latex code of most popular formulas and equations for Financial Engineering Formula and Equation (Continuous-Time Finance). We will cover important topics including Standard Brownian Motion (SBM), Geometric Brownian Motion (GBM), Ito Lemma, Stochastic Integrals, Solutions to Some Common SDEs, Brownian Motion Variation, Stock Prices as a GBM, Stock Prices are Lognormal, Sharpe Ratio and Hedging, The Black-Scholes Equation, Risk-Neutral Valuation and Power Contracts.

In this blog, we will summarize the latex code of most popular formulas and equations for Financial Engineering Formula and Equation (Continuous-Time Finance). We will cover important topics including Standard Brownian Motion (SBM), Geometric Brownian Motion (GBM), Ito Lemma, Stochastic Integrals, Solutions to Some Common SDEs, Brownian Motion Variation, Stock Prices as a GBM, Stock Prices are Lognormal, Sharpe Ratio and Hedging, The Black-Scholes Equation, Risk-Neutral Valuation and Power Contracts.

In this blog, we will summarize the latex code of most popular equations for financial engineering. We will cover important topics, including Black-Scholes formula, Value at Risk(VaR), etc.

In this blog, we will summarize the latex code of most popular formulas and equations for Financial Engineering Formula and Equation part I-Forwards, Puts, and Calls. We will cover important topics including Forwards, Put-Call Parity, Calls and Puts with Different Strikes, Calls and Puts Arbitrage, Call and Put Price Bounds, Varying Times to Expiration, Early Exercise for American Options, etc.

In this blog, we will summarize the latex code of most popular formulas and equations for Financial Engineering Formula and Equation Monte-Carlo Simulations and Interest Rate Models. We will cover important topics including Monte-Carlo Simulations, Bonds and Interest Rates, Black-Derman-Toy (BDT) model and Cox-Ingersoll-Ross (CIR) model.

In this blog, we will summarize the latex code of most popular formulas and equations for Microeconomics, Economics. We will cover important topics, including Allocative Efficiency Condition, Annuities Due, Average Fixed Cost, Average Product, Average Revenue, Average Total Cost, Average Variable Cost ,Compound Interest, Cross-Price Elasticity of Demand, Effective Rate, Elasticity of Supply, Factor of Production Hiring Rule, Future Value of Ordinary Annuities Marginal Cost, Marginal Revenue Product, Present Value of Ordinary Annuities, Simple Interest ,Distributive Efficiency Condition, Gini Coefficient, Marginal Factor Cost MFC, Marginal Product of Labor, Marginal Revenue, Marginal Revenue Product of Labor MRPL, Optimal Combination of Resources Condition, Optimal Consumption Rule, Price Elasticity of Demand, Price for a Competitive Firm, Production Efficiency Condition, Profit, Profit-Maximizing Output Level, Slope of the Total Product Curve, Socially Optimal Level of Output, Total Costs, etc.

In this blog, we will summarize the latex code for equations of CFA Level I exam, Formula Sheet Equations and Latex Code, and provide Chatbot as AI Assistant to facilitate your reading. You can ask question like what is "Real GDP" in the chatbox. Topics in the blog include three major parts of CFA Level I exam: QUANTITATIVE, ECONOMICS and FINANCIAL REPORTING. Detailed topics include THE TIME VALUE OF MONEY, Future Value, Present Value, Effective Annual Rate, Continuous Compounding, Ordinary Annuity, Annuity Due, Perpetuity, STATISTICAL CONCEPT AND MARKET RETURNS, Fisher Skewness, Kurtosis, Two-asset portfolio, Three-asset portfolio, Microeconomics, Simple Interest, Effective Rate, Future Value of Ordinary Annuities, Annuities Due, Present Value of Ordinary Annuities, Allocative Efficiency Condition, Average Fixed Cost; Macroeconomics Investment, Aggregate Expenditure Without Government or Foreign Sectors, Marginal Propensity to Consume MPC, Marginal Propensity Save MPS, Sum of Marginal Propensity to Save and Marginal Propensity to Consume, Autonomous Spending Multiplier, Balanced Budget Multiplier, Banks Reserve Ratio, Nominal Interest Rate, Real GDP, Real Interest Rate, Tax Multiplier, Unemployment Rate. FINANCIAL REPORTING and ANALYSIS, Basic EPS, Diluted EPS, Balance Sheet, Free Cash Flow to the Firm, Cash Flow Performance Ratio, Cash Flow To Revenue Ratio, Cash Return On Assets, Cash Return On Assets, Cash Return On Equity, Activity Ratio, Inventory Turnover, Days of Inventory On Hand (DOH), Receivables Turnover, Days of Sales Outstanding, etc.

In this blog, we will summarize the latex code for equations and formula sheet of CFA Level II exam, Formula Sheet Equations and Latex Code. Topics include QUANTITATIVE METHODS, such as LINEAR REGRESSION, MULTIPLE REGRESSION, TIME SERIES ANALYSIS, Machine Learning, ECONOMICS, Exchange rate, Covered interest rate parity, Uncovered interest rate parity, Relative purchasing power parity, Fisher and international Fisher effects, FX carry trade, Mundell-Fleming model, ECONOMIC GROWTH, Growth accounting equation, Labor productivity growth accounting equation, Classical growth model (Malthusian model), Neoclassical growth model (Solow’s model), Endogenous growth model, Convergence, ECONOMICS OF REGULATION. The data source of this blog is summarized from WILEY’S CFA PROGRAM LEVEL II quicksheet.

In this blog, we will summarize the latex code of most popular formulas and equations for Economics-MacroEconomics. We will cover important topics, including Investment, Aggregate Expenditure Without Government or Foreign Sectors, Marginal Propensity to Consume MPC, Marginal Propensity Save MPS, Sum of Marginal Propensity to Save and Marginal Propensity to Consume, Autonomous Spending Multiplier, Balanced Budget Multiplier, Banks Reserve Ratio, Budget Deficit, Financial Account Balance, Consumer Price Index CPI, Consumption Function, Current-Account Balance, Equality of Leakages and Injections, Equation of Exchange, Gross Domestic Product GDP, Gross Domestic Product Deflator, Inflation Between Two Years, Merchandise Trade Balance, Nominal Interest Rate, Real GDP, Real Interest Rate, Tax Multiplier, Unemployment Rate, etc.

In this blog, we will summarize the latex code for equations of CFA Level I exam, Formula Sheet Equations and Latex Code, and provide Chatbot as AI Assistant to facilitate your reading. You can ask question like what is "Real GDP" in the chatbox. Topics in the blog include three major parts of CFA Level I exam: QUANTITATIVE, ECONOMICS and FINANCIAL REPORTING. Detailed topics include THE TIME VALUE OF MONEY, Future Value, Present Value, Effective Annual Rate, Continuous Compounding, Ordinary Annuity, Annuity Due, Perpetuity, STATISTICAL CONCEPT AND MARKET RETURNS, Fisher Skewness, Kurtosis, Two-asset portfolio, Three-asset portfolio, Microeconomics, Simple Interest, Effective Rate, Future Value of Ordinary Annuities, Annuities Due, Present Value of Ordinary Annuities, Allocative Efficiency Condition, Average Fixed Cost; Macroeconomics Investment, Aggregate Expenditure Without Government or Foreign Sectors, Marginal Propensity to Consume MPC, Marginal Propensity Save MPS, Sum of Marginal Propensity to Save and Marginal Propensity to Consume, Autonomous Spending Multiplier, Balanced Budget Multiplier, Banks Reserve Ratio, Nominal Interest Rate, Real GDP, Real Interest Rate, Tax Multiplier, Unemployment Rate. FINANCIAL REPORTING and ANALYSIS, Basic EPS, Diluted EPS, Balance Sheet, Free Cash Flow to the Firm, Cash Flow Performance Ratio, Cash Flow To Revenue Ratio, Cash Return On Assets, Cash Return On Assets, Cash Return On Equity, Activity Ratio, Inventory Turnover, Days of Inventory On Hand (DOH), Receivables Turnover, Days of Sales Outstanding, etc.

In this blog, we will summarize the latex code for equations and formula sheet of CFA Level II exam, Formula Sheet Equations and Latex Code. Topics include QUANTITATIVE METHODS, such as LINEAR REGRESSION, MULTIPLE REGRESSION, TIME SERIES ANALYSIS, Machine Learning, ECONOMICS, Exchange rate, Covered interest rate parity, Uncovered interest rate parity, Relative purchasing power parity, Fisher and international Fisher effects, FX carry trade, Mundell-Fleming model, ECONOMIC GROWTH, Growth accounting equation, Labor productivity growth accounting equation, Classical growth model (Malthusian model), Neoclassical growth model (Solow’s model), Endogenous growth model, Convergence, ECONOMICS OF REGULATION. The data source of this blog is summarized from WILEY’S CFA PROGRAM LEVEL II quicksheet.

In this blog, we will summarize the latex code for equations and the formula sheet of CFA Level III exam- Section Portfolio Management. Topics include important concepts, formulas of portfolio management, including Total Wealth, Weight of risky asset in the portfolio, Effective Annual Rate EAR, Marginal contribution to total risk MCTR, Actual contribution to total risk ACTR, Percentage of risk contributed by position, Ratio of excess return to MCTR, The Fama-French model, Objective function to maximize utility, Expected after tax return of a bond, Expected after tax return of equities, Expected after tax standard deviation, and After tax rebalancing range. Tag: Portfolio Management,CFA III,AI course

In this blog, we will summarize the latex code of most popular equations and formulas for Equilibrium, Chemistry. The topics include Acid Ionization Constant, Base Ionization Constant, Relationship of Conjugate Acidâ??Base Pair, Negative Logarithms Relationship of Conjugate Acidâ??base Pair, Buffer Design Equation, Gas Pressure and Concentration Relationship, Ion Product Constant for Water, pH and pOH Relationship, pH Definition, pOH Definition, pKa Definition, pKb Definition, pOH and Base Ionization Equilibrium Constant Relationship.

In this blog, we will summarize the latex code for equations of CFA Level I exam, Formula Sheet Equations and Latex Code, and provide Chatbot as AI Assistant to facilitate your reading. You can ask question like what is "Real GDP" in the chatbox. Topics in the blog include three major parts of CFA Level I exam: QUANTITATIVE, ECONOMICS and FINANCIAL REPORTING. Detailed topics include THE TIME VALUE OF MONEY, Future Value, Present Value, Effective Annual Rate, Continuous Compounding, Ordinary Annuity, Annuity Due, Perpetuity, STATISTICAL CONCEPT AND MARKET RETURNS, Fisher Skewness, Kurtosis, Two-asset portfolio, Three-asset portfolio, Microeconomics, Simple Interest, Effective Rate, Future Value of Ordinary Annuities, Annuities Due, Present Value of Ordinary Annuities, Allocative Efficiency Condition, Average Fixed Cost; Macroeconomics Investment, Aggregate Expenditure Without Government or Foreign Sectors, Marginal Propensity to Consume MPC, Marginal Propensity Save MPS, Sum of Marginal Propensity to Save and Marginal Propensity to Consume, Autonomous Spending Multiplier, Balanced Budget Multiplier, Banks Reserve Ratio, Nominal Interest Rate, Real GDP, Real Interest Rate, Tax Multiplier, Unemployment Rate. FINANCIAL REPORTING and ANALYSIS, Basic EPS, Diluted EPS, Balance Sheet, Free Cash Flow to the Firm, Cash Flow Performance Ratio, Cash Flow To Revenue Ratio, Cash Return On Assets, Cash Return On Assets, Cash Return On Equity, Activity Ratio, Inventory Turnover, Days of Inventory On Hand (DOH), Receivables Turnover, Days of Sales Outstanding, etc.

In this blog, we will summarize the latex code for equations and formula sheet of CFA Level II exam, Formula Sheet Equations and Latex Code. Topics include QUANTITATIVE METHODS, such as LINEAR REGRESSION, MULTIPLE REGRESSION, TIME SERIES ANALYSIS, Machine Learning, ECONOMICS, Exchange rate, Covered interest rate parity, Uncovered interest rate parity, Relative purchasing power parity, Fisher and international Fisher effects, FX carry trade, Mundell-Fleming model, ECONOMIC GROWTH, Growth accounting equation, Labor productivity growth accounting equation, Classical growth model (Malthusian model), Neoclassical growth model (Solow’s model), Endogenous growth model, Convergence, ECONOMICS OF REGULATION. The data source of this blog is summarized from WILEY’S CFA PROGRAM LEVEL II quicksheet.

In this blog, we will summarize the latex code of most fundamental equations of multi-task learning(MTL) and transfer learning(TL). Multi-Task Learning aims to optimize N related tasks simultaneously and achieve the overall trade-off between multiple tasks. Typical network structure include shared-bottom models, Cross-Stitch Network, Multi-Gate Mixture of Experts (MMoE), Progressive Layered Extraction (PLE), Entire Space Multi-Task Model (ESSM) models and etc. Different from multi-task learning. In the following sections, we will dicuss more details of MTL equations, which is useful for your quick reference.

Cheatsheet of Latex Code for Most Popular Causual Inference and Uplift modelling Equations

In this blog, we will summarize the latex code of most popular kernel methods and Gaussian Process models, including Support Vector Machine (SVM), Gaussian Process (GP) and Deep Kernel Learning(DKL).

In this blog, we will summarize the latex code of most fundamental equations of Few-Shot Learning and Zero-Shot Learning. Few-Shot Learning learns from a few-labelled examples and better generalize to unseen examples. Typical works includes Prototypical Networks, Model-Agnostic Meta-Learning (MAML), etc.

In this blog, we will summarize the latex code of most popular equations and formulas for Atomic Structure, Electrochemistry, Thermochemistry, Chemistry. The topics include Bohr Radius, De Broglie Wavelength, Linear Momentum, Planck Quantized Energy Equation, Radii of stable orbits in Bohr model, Energy and Principal Quantum Number, Rydberg Equation, Speed of Light, Cell Voltage, Electric Current, Reaction Quotient, Equilibrium Constant and Cell Voltage, Enthalpy Change,Entropy Change, Gibb Free Energy Change, Specific Heat Capacity to Heat Equation, etc.

In this blog, we will summarize the latex code of most fundamental equations of GPT (Generative Pre-trained Transformer) Models. This blog will cover many popular GPT models, including GPT1, GPT2, GPT3, GPT4, InstructGPT, ChatGPT, etc.

In this blog, we will summarize the latex code of equations of Graph Neural Network(GNN) models, which are useful as quick reference for your research. For common notation, we denote G=(V,E) as the graph. V as the set of nodes with size |V|=N, and E as the set of N_e edges as |E| = N_e. A is denoted as the adjacency matrix. For each node v, we use h_v and o_v as hidde state and output vector of each node.

In this blog, we will summarize the latex code of most fundamental equations of reinforcement learning (RL). This blog will cover many topics, including Bellman Equation, Markov Decision Process(MDP), Partial Observable Markov Decision Process(POMDP), DQN, A3C, etc.

Ranking is a crucial part of modern commercial recommendation and advertisement system. It aims to solve the problem of accurate click-through rate(CTR) prediction. In this article, we will provides some of most popular ranking equations of commercial recommendation or ads system.

In this blog, we will summarize the latex code of most fundamental and popular knowledge graph (KG) Equations, with special focus on the link prediction tasks. We will cover a wide range of models, including TransE, TransR, TransE, RotatE, SME(Linear), SimplE etc. Knowledge Graph consists of a set of triples [(h, r, t)]. h and t denotes the head node and tail node respectively. And r denotes multiple relation types. One common solution to the link prediction tasks is to learn low-dimensional embeddings of entities(E) and relations (R), and infer the missing part of [(?, r, t), (h, ?, t), (h, r, ?)].

In this blog, we will summarize the latex code for complex variables formulas, including complex numbers, De Moivreâ??s theorem and power series for complex variables e^{z}, sin(z), cos(z), ln(1+z), (1+z)^{n}, etc.

In this blog, we will summarize the latex code of equations for Diffusion Models, which are among the top-performing generative models, including GAN, VAE and flow-based models. The basic idea of diffusion models are to inject random noise to the feature vector in the forward process as markov chain models, and in the reverse process gradualy reconstruct the feature vector for generation. See below blogpost as reference for more details: Weng, Lilian. (Jul 2021). What are diffusion models? Lilâ??Log. lilianweng.github.io/posts/2021-07-11-diffusion-models/