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-  <title>LLMs in Lingustic Research 2024/25 – Week 02  Basics of Neural Networks (Part 2)</title>
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-  <h1 class="title"><font style="font-size:1em;">Week 02<br> Basics of Neural Networks (Part 2)</font></h1>
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   <p class="subtitle">LLMs in Lingustic Research WiSe 2024/25</p>
 
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     "text": "ReLU function\n\\[\nf(x) = \\max(0, x)\n\\]\nExample: \\(f(2) = 2\\)\nwhere:\n- f(x): This represents the output of the ReLU function for a given input x.\n- x: This is the input to the ReLU function.\n- max: This function returns the maximum of the two values.\n- 0: This is the threshold value.\n\nThe Rectified Linear Unit (ReLU) function is that outputs the input directly if it is positive, otherwise, it outputs zero.\nThe output of the ReLU function is between 0 and infinity.\nIt is a popular activation function used in deep learning models."
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     "text": "X-axis (Weight): Represents the value of the model parameter being optimized.\nY-axis (Loss): Represents the value of the loss function being minimized.\nThe goal is to find the value of the model parameter that minimizes the loss function."
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     "text": "The process starts at an initial weight with a corresponding loss, marked as “Initial weight + loss” on the graph\nGradient: The algorithm calculates the gradient (slope) at the current position. This gradient indicates the direction of steepest ascent."
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     "text": "The model then takes a step in the opposite direction of the gradient, as we want to minimize the loss.\nThis is why it’s called gradient descent - we descend along the gradient.\nThe “New weight + loss” point on the graph shows an intermediate step in this process, where the loss has decreased compared to the initial position."
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     "text": "As the algorithm progresses, it should ideally approach the bottom of the curve, labeled as “Theoretical minima” in the image.\nThe algorithm may not always reach the exact theoretical minima due to factors like step size (learning rate) and the complexity of the loss landscape.\nBut, it typically converges to a point close enough to be practically useful for model optimization."
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     "text": "flowchart LR\n    %% Input Layer\n    I1((I1)):::inputStyle\n    I2((I2)):::inputStyle\n    I3((I3)):::inputStyle\n    B1((Bias)):::biasStyle\n    %% Hidden Layer\n    H1((H1)):::hiddenStyle\n    H2((H2)):::hiddenStyle\n    H3((H3)):::hiddenStyle\n    B2((Bias)):::biasStyle\n    %% Output Layer\n    O1((O1)):::outputStyle\n    O2((O2)):::outputStyle\n    %% Connections\n    I1 -->|w11| H1\n    I1 -->|w12| H2\n    I1 -->|w13| H3\n    I2 -->|w21| H1\n    I2 -->|w22| H2\n    I2 -->|w23| H3\n    I3 -->|w31| H1\n    I3 -->|w32| H2\n    I3 -->|w33| H3\n    B1 -->|b1| H1\n    B1 -->|b2| H2\n    B1 -->|b3| H3\n    H1 -->|v11| O1\n    H1 -->|v12| O2\n    H2 -->|v21| O1\n    H2 -->|v22| O2\n    H3 -->|v31| O1\n    H3 -->|v32| O2\n    B2 -->|b4| O1\n    B2 -->|b5| O2\n    %% Styles\n    classDef inputStyle fill:#3498db,stroke:#333,stroke-width:2px;\n    classDef hiddenStyle fill:#e74c3c,stroke:#333,stroke-width:2px;\n    classDef outputStyle fill:#2ecc71,stroke:#333,stroke-width:2px;\n    classDef biasStyle fill:#f39c12,stroke:#333,stroke-width:2px;\n    %% Layer Labels\n    I2 -.- InputLabel[Input Layer]\n    H2 -.- HiddenLabel[Hidden Layer]\n    O1 -.- OutputLabel[Output Layer]\n    style InputLabel fill:none,stroke:none\n    style HiddenLabel fill:none,stroke:none\n    style OutputLabel fill:none,stroke:none"
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     "text": "The input layer consists of three nodes (I1, I2, I3) representing the input features.\nThe hidden layer consists of three nodes (H1, H2, H3) that process the input data.\nThe output layer consists of two nodes (O1, O2) that produce the final predictions.\nThe connections between nodes are represented by weights (w11, w12, …, v32) and biases (b1, b2, …, b5).\nThe weights and biases are adjusted during training to optimize the model.\nThe model makes predictions by passing the input data through the network and computing the output."
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     "text": "Training, development and test datasets\n\nThe training dataset is used to optimize the model parameters (weights and biases) using gradient descent.\nThe development dataset is used to tune the hyperparameters of the model, such as the learning rate and the number of hidden units.\nThe test dataset is used to evaluate the performance of the model on unseen data.\nIn order to avoid overfitting, it is important to have separate datasets for training, development, and testing.\nThe training dataset is typically the largest, followed by the development and test datasets.\nThe development and test datasets should be representative of the data the model will encounter in the real world.\nThe datasets should be randomly sampled to avoid bias and ensure that the model generalizes well."
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     "section": "Thank you!",
     "text": "Thank you!\n\n\n\n\nLLMs in Lingustic Research WiSe 2024/25"
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