Cheatsheet of Latex Code for Most Popular Natural Language Processing Equations

rockingdingo 2022-05-03 #nlp #latex #bert
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Cheatsheet of Latex Code for Most Popular Natural Language Processing Equations

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Sequential Labeling

  • Hidden Markov Model

    Equation


    Latex Code
                Q=\{q_{1},q_{2},...,q_{N}\}, V=\{v_{1},v_{2},...,v_{M}\} \\
            I=\{i_{1},i_{2},...,i_{T}\},O=\{o_{1},o_{2},...,o_{T}\} \\
            A=[a_{ij}]_{N \times N}, a_{ij}=P(i_{t+1}=q_{j}|i_{t}=q_{i}) \\
            B=[b_{j}(k)]_{N \times M},b_{j}(k)=P(o_{t}=v_{k}|i_{t}=q_{j}) \\
    Explanation

    Q denotes the set of states and V denotes the set of obvervations. Let's assume we have state sequence I of length T, and observation sequence O of length T, Hidden Markov Model(HMM) use transition matrix A to denote the transition probability a_{ij} and matrix B to denote observation probability matrix b_jk.

  • Conditional Random Field

    Equation




    Latex Code
            P(y|x)=\frac{1}{Z(x)}\exp(\sum_{i,k}\lambda_{k}t_{k}(y_{i-1},y_{i},x,i))+\sum_{i,l}\mu_{l}s_{l}(y_{i},x,i)) \\
        Z(x)=\sum_{y}\exp(\sum_{i,k}\lambda_{k}t_{k}(y_{i-1},y_{i},x,i))+\sum_{i,l}\mu_{l}s_{l}(y_{i},x,i))
    Explanation

    p(Y|x) denotes the linear chain Conditional Random Field(CRF). t_k denotes the function on the transition, s_l denote function on the node. lambda_k and mu_l denotes the weight coefficient.

  • Transformer

    Equation


    Latex Code
            Attention(Q, K, V) = softmax(\frac{QK^T}{\sqrt{d_k}})V
    Explanation




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