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Fascinating World of Neural Networks.
What is a Neural Network? A neural network is a computational model that mimics the complex functions of the human brain. It consists of interconnected nodes or neurons that process and learn from data, enabling tasks such as pattern recognition and decision-making in machine learning¹. Here are the key components: 1. Neurons: These are the fundamental building blocks of neural networks. Neurons receive inputs, governed by thresholds and activation functions. 2. Connections: Neurons are interconnected through connections, which involve weights and biases regulating information transfer. 3. Learning Rule: Neural networks learn by adjusting weights and biases during three stages: input computation, output generation, and iterative refinement. This enhances the network's proficiency in diverse tasks. Evolution of Neural Networks Let's explore the historical milestones: - 1940s-1950s: Early Concepts - McCulloch and Pitts introduced the first mathematical model of artificial neurons, but computational constraints limited progress. - 1960s-1970s : Perceptrons - Rosenblatt's work on perceptrons led to single-layer networks, but their applicability was limited to linearly separable problems. - 1980s : Backpropagation and Connectionism - Rumelhart, Hinton, and Williams invented backpropagation, enabling multi-layer network training. Connectionism gained appeal. - 1990s : Boom and Winter - Neural networks found applications in image identification and finance but faced a "winter" due to computational costs and inflated expectations. - 2000s : Resurgence and Deep Learning - Larger datasets, innovative structures, and enhanced processing capability fueled a comeback. Deep learning, with its numerous layers, excelled in various disciplines. - 2010s-Present : Deep Learning Dominance - Convolutional neural networks (CNNs) and recurrent neural networks (RNNs) dominated machine learning, showcasing their power in gaming, image recognition, and natural language processing. In summary, neural networks extract features from data without pre-programmed understanding, making them essential for modern machine learning¹.
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What is Neural Networks ?
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Deep Learning
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Fascinating world of Neurons and Neural Networks.
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Why develop artificial Neural Networks?
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Key Feature 1
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Key Feature 2
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Origin of Neural Networks
Let's dive into the technical details of how neural networks are built. Neural networks, also known as artificial neural networks (ANNs), are composed of interconnected processing units called neurons. These neurons work together to learn patterns and make predictions based on input data. Here's a breakdown of the key components involved in building a neural network: 1. Neurons (Processing Units): - Neurons are the fundamental building blocks of neural networks. - Each neuron processes input data and produces an output. - In your example, you have six inputs (input1 to input6), which represent features or variables (like the shopping items). - Neurons are analogous to the simple processing units that perform calculations. 2. Weights (Analogous to Prices): - Neurons have associated weights, which determine the importance of each input. - Just like prices for shopping items, weights adjust the contribution of each input to the overall computation. - You mentioned weight1 to weight6, corresponding to the six inputs. 3. Intercept (Bias Term): - Similar to linear regression, neural networks often include an intercept term (bias). - The intercept accounts for any fixed additional charge or offset. - For example, it could represent the cost of processing a credit card payment. 4. Linear Combination: - The output of a neuron is calculated as a linear combination of the inputs and their associated weights. - The formula for the linear combination is: $$ text{linear combination} = text{intercept} + sum_{i=1}^{6} text{weight}_i times text{input}_i $$ - The summation includes all terms from input1 to input6. 5. Example Calculation: - Let's use the example numbers you provided: - Intercept = 10.0 - Weight1 = 5.4, Weight2 = -10.2, Weight3 = -0.1, Weight4 = 101.4, Weight5 = 0.0, Weight6 = 12.0 - Inputs: input1 = 8, input2 = 5, input3 = 22, input4 = -5, input5 = 2, input6 = -3 - The linear combination becomes: $$ 10.0 + 5.4 times 8 + (-10.2) times 5 + (-0.1) times 22 + 101.4 times (-5) + 0.0 times 2 + 12.0 times (-3) = -543.0 $$ This linear combination is then typically passed through an activation function (such as ReLU, sigmoid, or tanh) to produce the final output of the neuron. Neural networks consist of layers of interconnected neurons, allowing them to learn complex patterns from data.
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Value of weights and Inputs.
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Neural Network Activations and Output
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Perceptron
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Multilayer Perceptrons (MLPs) and Backpropagation
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Simple Classifier
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Advanced Neural Network Techniques
1. Data Parallelism : - Data parallelism involves distributing training data across multiple GPUs (often called "workers") and processing different examples simultaneously. - While each GPU computes gradients independently, the model's parameters are shared among all GPUs. - This approach allows you to utilize the compute power of multiple GPUs, but the model still needs to fit into a single GPU's memory¹. 2. Pipeline Parallelism : - With pipeline parallelism, we partition sequential chunks of the model across GPUs. - Each GPU processes a different part of the model, and the intermediate results are passed between GPUs. - This technique helps overcome memory limitations and accelerates training by overlapping computation and communication¹. 3. Tensor Parallelism : - Tensor parallelism breaks down complex operations (e.g., matrix multiplications) into smaller components that can be split across GPUs. - By distributing the computation, we can handle larger models and reduce memory requirements. - It's particularly useful for large-scale neural networks¹. 4. Mixture-of-Experts (MoE) : - In MoE, each example is processed by only a fraction of each layer. - Different experts specialize in different aspects of the data, and their outputs are combined to make predictions. - MoE can improve model robustness and adaptability¹. 5. Other Memory-Saving Designs : - Researchers continue to explore novel techniques for efficient neural network training. - These include quantization (reducing precision), model pruning (removing unnecessary connections), and weight sharing (sharing parameters across layers or models)¹. Remember that these techniques are powerful tools, but their effectiveness depends on the specific problem, model architecture, and available resources. As deep learning continues to evolve, we'll likely see even more innovative approaches emerge!
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Overview of Convolutional Neural Networks (CNNs)!
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How much CNNs is important for us?
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Do neural networks dream of electric sheep?
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Metaphors can indeed lead to misconceptions.
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LLMs have indeed revolutionized Natural Language processing.
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ChatGPT: AI for the masses
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Neural Networks
About Lesson

  1. Input Representation:

    • You’ve correctly represented the image pixels as numerical values (1 for colored and 0 for white).
    • The 25 pixels in the 5 × 5 grid serve as inputs to our classifier.

  2. Linear Combination and Weights:

    • Each input pixel corresponds to a weight in the neural network.
    • The linear combination of inputs is computed by multiplying each pixel value by its corresponding weight and summing them up.
    • In your example, all weights are set to 1, resulting in a linear combination of 9 for the cross image and 8 for the circle image.

  3. Activation Function:

    • You’ve used a step activation function.
    • If the linear combination is negative, the activation is 0 (signifying a cross).
    • If positive, the activation is 1 (signifying a circle).

  4. Improving Classification:

    • To improve classification, we adjust weights based on what distinguishes crosses from circles.
    • For example, assign weight -1 to the center pixel (13th pixel) and weight 1 to the middle pixels of each side.
    • The cross input now produces a negative total value (activation 0), correctly classifying it.
    • The circle input produces a positive total value (activation 1), correctly recognizing it.
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