DeepNLP Blog: Machine learning,NLP,CV and related technical fields.

List of Statistics Equations Latex Code

rockingdingo 2022-11-06 #Binomial #Poisson #Normal Gaussian #Covariance #Chi-Square

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, etc.

Cheatsheet of Latex Code for Most Popular Machine Learning Equations

rockingdingo 2022-09-18 #GAN #VAE #KL-Divergence #Wasserstein #Mahalanobis

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.

List of Probability Distribution Formulas Latex Code

rockingdingo 2023-06-25 #statistics #match #probability

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.

Latex for Atomic Structure Electrochemistry Thermochemistry Chemical Equations and Formulas

rockingdingo 2023-05-28 #Chemistry #Atomic Structure #Electrochemistry

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.

Latex for Equilibrium Chemical Equations and Formulas Latex

rockingdingo 2023-05-28 #Chemical #Chemistry

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.

List of Curves and Shapes Geometry Math Formulas Latex Code

rockingdingo 2023-05-24 #Math #Geometry

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.

Latex for Financial Engineering Mathematics Formula-Brownian Motion Ito Lemma Risk-Neutral Valuation

rockingdingo 2023-05-21 #financial engineering #mathematics #finance

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.

Latex for Financial Engineering Mathematics Formula and Equations (Continuous-Time Finance)

rockingdingo 2023-05-14 #Financial Engineering #Mathematics #Finance

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.

Latex Code for Microeconomics, Economics Formula and Equation

rockingdingo 2023-05-14 #Economics #Microeconomics

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.

List of Quantum Physics Formulas Equations Latex Code

rockingdingo 2023-04-06 #physics #quantum

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 SchrÃ¶dinger Equation, Parity, The Tunnel Effect, Harmonic Oscillator, Angular momentum, Spin, the Dirac Formalism, and so on.

List of Physics Oscillations Formulas, Equations Latex Code

rockingdingo 2023-03-26 #physics #oscillations #wave

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.

List of Physics Mechanics Formulas, Equations Latex Code

rockingdingo 2023-03-20 #physics #mechanics

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.

List of Differential Equations Formulas Latex Code

rockingdingo 2023-01-28 #math #differential equations #laplace #bessel

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.

List of Physics Formulas Latex Code: Electricity & Magnetism (Graduate Level Physics)

physics_master 2022-12-24 #physics #electricity #magnetism

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.

List of Calculus Formulas Latex Code (First Part: Limits, Differentiation)

rockingdingo 2022-12-04 #calculus #differentiation #Math

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).

Cheatsheet of Latex Code for Reinforcement Learning Equations

rockingdingo 2022-07-18 #rl #reinforcement learning

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.

Cheatsheet of Latex Code for Financial Engineering and Quantitative equations

rockingdingo 2022-07-18 #financial engineering #black-sholes

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.

Cheatsheet of Latex Code for Graph Neural Network(GNN) Equations

rockingdingo 2022-07-17 #graph neural network #gnn #gcn #gat #graphsage

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.

Cheatsheet of Latex Code for Transfer Learning Equations

rockingdingo 2022-07-17 #machine learning #transfer learning #domain adaptation #Domain-Adversarial Neural Networks

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.

Cheatsheet of Latex Code for Multi-Task Learning Equations

rockingdingo 2022-07-11 #mtl #multi-task learning #mmoe #ple

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 Recommendation and Advertisement Ranking module Equations

rockingdingo 2022-06-20 #recommendation #advertisement #ranking #sequential modelling

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.

Cheatsheet of Latex Code for Most Popular Natural Language Processing Equations

rockingdingo 2022-05-03 #nlp #latex #bert

Cheatsheet of Latex Code for Most Popular Natural Language Processing Equations

List of Coordinate Systems Geometry Math Formulas Latex Code

rockingdingo 2023-05-23 #Geometry #Math

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.

List of Geometry Math Formulas and Equations Latex Code

rockingdingo 2023-05-22 #geometry #math

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.

Latex for Financial Engineering Mathematics Formula Monte-Carlo Simulations and Interest Rate Models

rockingdingo 2023-05-21 #financial engineering #mathematics #finance

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.

Latex for Financial Engineering Mathematics Formula (Forwards Puts and Calls)

rockingdingo 2023-05-14 #Financial Engineering

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.

Latex Code for MacroEconomics Formula and Equation

rockingdingo 2023-05-14 #Economics #MacroEconomics

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.

List of Physics Thermodynamics Formulas, Equations Latex Code

rockingdingo 2023-03-29 #physics #thermodynamics

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.

List of Physics Optics Formulas, Equations Latex Code

rockingdingo 2023-03-26 #physics #optics

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.

List of Physics Wave Formulas, Equations Latex Code

rockingdingo 2023-03-26 #physics #wave

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.

Introduction to GPT (Generative Pre-trained Transformer) Models, GPT4,ChatGPT Equations and Latex Code

rockingdingo 2023-03-22 #gpt #gpt4 #chatgpt #gpt3

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.

List of Complex Variables Formulas Latex Code

rockingdingo 2023-03-12 #Complex Variables #Conjugate #Power Series

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.

List of Series Formulas Latex Code

rockingdingo 2023-01-28 #math #series #taylor #binomial

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.

List of Physics Relativity Formulas Latex Code(First Part)

rockingdingo 2023-01-24 #physics #relativity #einstein

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.

List of Linear Matrix Algebra Formulas Latex Code

math_beginner 2023-01-16 #math #matrix #algebra #eigenvalues #determinants

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.

DeepNLP Equation Workspace: Manage, Edit, Share and Display Your Equations.

rockingdingo 2022-12-05 #equation editor #share #edit #display

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.

List of Calculus Formulas Latex Code (Second Part: Integration)

rockingdingo 2022-12-04 #Math #calculus #integration

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.

Knowledge Graph Link Prediction Equations And Latex Code

rockingdingo 2022-10-23 #Knowledge Graph #Link Prediction #KG

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, ?)].

Few-Shot Learning And Zero-Shot Learning Equations Latex Code

rockingdingo 2022-10-23 #Few-Shot #Zero-Shot #MAML #ProtoNets #Bregman Divergences

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.

Latex Code for Diffusion Models Equations

rockingdingo 2022-09-18 #Diffusion #VAE #GAN #Generative Models

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/

Cheatsheet of Latex Code for Kernel Methods and Gaussian Process

rockingdingo 2022-07-11 #kernel #svm #gaussian process #gp #deep kernel learning

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).

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

rockingdingo 2022-07-10 #causal inference #uplift modelling #auuc #qini

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

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