рдЕрдзреНрдпрд╛рдп 1: рдбреАрдк рд▓рд░реНрдирд┐рдВрдЧ рдХрд╛ рдкрд░рд┐рдЪрдп

(Chapter 1: Introduction to Deep Learning)


ЁЯФН 1.1 рдбреАрдк рд▓рд░реНрдирд┐рдВрдЧ рдХреНрдпрд╛ рд╣реИ?

(What is Deep Learning?)

Deep Learning рдорд╢реАрди рд▓рд░реНрдирд┐рдВрдЧ рдХреА рдПрдХ рд╢рд╛рдЦрд╛ рд╣реИ, рдЬреЛ рдорд╛рдирд╡ рдорд╕реНрддрд┐рд╖реНрдХ рдХреА рддрд░рд╣ рдХрд╛рд░реНрдп рдХрд░рдиреЗ рд╡рд╛рд▓реЗ Artificial Neural Networks (ANNs) рдкрд░ рдЖрдзрд╛рд░рд┐рдд рд╣реЛрддреА рд╣реИред рдЗрд╕рдореЗрдВ рдбреЗрдЯрд╛ рд╕реЗ рд╕реНрд╡рдд: рд╡рд┐рд╢реЗрд╖рддрд╛рдПрдБ (features) рд╕реАрдЦреА рдЬрд╛рддреА рд╣реИрдВ рдФрд░ рдирд┐рд░реНрдгрдп рд▓рд┐рдП рдЬрд╛рддреЗ рд╣реИрдВред рдЗрд╕реЗ “deep” рдЗрд╕рд▓рд┐рдП рдХрд╣рд╛ рдЬрд╛рддрд╛ рд╣реИ рдХреНрдпреЛрдВрдХрд┐ рдЗрд╕рдореЗрдВ рдХрдИ layers рд╣реЛрддреА рд╣реИрдВред

ЁЯза Deep Learning рдХреА рд╡рд┐рд╢реЗрд╖рддрд╛рдПрдВ:

  • рдпрд╣ рдбреЗрдЯрд╛ рд╕реЗ рд╕реНрд╡рдпрдВ рд╕реАрдЦрддрд╛ рд╣реИ, рдЙрд╕реЗ рдореИрдиреНрдпреБрдЕрд▓ рдкреНрд░реЛрдЧреНрд░рд╛рдорд┐рдВрдЧ рдХреА рдЬрд╝рд░реВрд░рдд рдирд╣реАрдВред
  • Deep рдЗрд╕рд▓рд┐рдП рдХрд╣рд╛ рдЬрд╛рддрд╛ рд╣реИ рдХреНрдпреЛрдВрдХрд┐ рдЗрд╕рдореЗрдВ рдХрдИ Hidden Layers рд╣реЛрддреА рд╣реИрдВред
  • рдпрд╣ рдмрд╣реБрдд рдмрдбрд╝реЗ рдорд╛рддреНрд░рд╛ рдореЗрдВ рдбреЗрдЯрд╛ рдФрд░ рд╢рдХреНрддрд┐рд╢рд╛рд▓реА рдХрдВрдкреНрдпреВрдЯрд┐рдВрдЧ рд╕рдВрд╕рд╛рдзрдиреЛрдВ (рдЬреИрд╕реЗ GPU) рдХрд╛ рдЙрдкрдпреЛрдЧ рдХрд░рддрд╛ рд╣реИред

ЁЯУМ рдЙрджрд╛рд╣рд░рдг:

  • рдЖрдк рдЬрдм Google Photos рдореЗрдВ рдХрд┐рд╕реА рдХреЛ “Dog” рд▓рд┐рдЦрдХрд░ рд╕рд░реНрдЪ рдХрд░рддреЗ рд╣реИрдВ рдФрд░ рд╡рд╣ рдЖрдкрдХреЛ рдХреБрддреНрддреЗ рдХреА рддрд╕реНрд╡реАрд░реЗрдВ рджрд┐рдЦрд╛ рджреЗрддрд╛ рд╣реИ тАУ рддреЛ рдпрд╣ Deep Learning рдХрд╛ рд╣реА рдХрдорд╛рд▓ рд╣реИред

ЁЯФБ 1.2 рдорд╢реАрди рд▓рд░реНрдирд┐рдВрдЧ рдФрд░ рдбреАрдк рд▓рд░реНрдирд┐рдВрдЧ рдореЗрдВ рдЕрдВрддрд░

(Difference between Machine Learning and Deep Learning)

рдЖрдзрд╛рд░рдорд╢реАрди рд▓рд░реНрдирд┐рдВрдЧ (ML)рдбреАрдк рд▓рд░реНрдирд┐рдВрдЧ (DL)
рдкрд░рд┐рднрд╛рд╖рд╛рдПрдХ рддрдХрдиреАрдХ рдЬрд┐рд╕рдореЗрдВ рдореЙрдбрд▓ рдЗрдВрд╕рд╛рдиреЛрдВ рджреНрд╡рд╛рд░рд╛ рджреА рдЧрдИ рд╡рд┐рд╢реЗрд╖рддрд╛рдУрдВ (features) рдкрд░ рдХрд╛рдо рдХрд░рддрд╛ рд╣реИрдПрдХ рддрдХрдиреАрдХ рдЬреЛ рд╕реНрд╡рдпрдВ рдбреЗрдЯрд╛ рд╕реЗ features рд╕реАрдЦрддрд╛ рд╣реИ
рдбреЗрдЯрд╛ рдХреА рдЖрд╡рд╢реНрдпрдХрддрд╛рдХрдордмрд╣реБрдд рдЕрдзрд┐рдХ
рдлреАрдЪрд░ рдПрдХреНрд╕рдЯреНрд░реИрдХреНрд╢рдирдореИрдиреБрдЕрд▓рдСрдЯреЛрдореЗрдЯрд┐рдХ
рдПрд▓реНрдЧреЛрд░рд┐рджреНрдоDecision Trees, SVM, kNNNeural Networks, CNN, RNN
рд╣рд╛рд░реНрдбрд╡реЗрдпрд░ рдбрд┐рдкреЗрдВрдбреЗрдВрд╕реАрдХрдоGPU рдХреА рдЖрд╡рд╢реНрдпрдХрддрд╛
рдкреНрд░рджрд░реНрд╢рди (рдмрдбрд╝реЗ рдбреЗрдЯрд╛ рдкрд░)рд╕реАрдорд┐рддрдмрд╣реБрдд рдкреНрд░рднрд╛рд╡рд╢рд╛рд▓реА
рдЯреНрд░реЗрдирд┐рдВрдЧ рдЯрд╛рдЗрдордХрдордЕрдзрд┐рдХ

ЁЯОп рдирд┐рд╖реНрдХрд░реНрд╖:

Deep Learning, Machine Learning рдХреА рддреБрд▓рдирд╛ рдореЗрдВ рдЕрдзрд┐рдХ рд╕реНрд╡рд╛рдпрддреНрдд, рд╕реНрдХреЗрд▓реЗрдмрд▓ рдФрд░ рдкреНрд░рднрд╛рд╡рд╢рд╛рд▓реА рд╣реИ, рд╡рд┐рд╢реЗрд╖рдХрд░ рдмрдбрд╝реЗ рдбреЗрдЯрд╛ рдкрд░ред


ЁЯЫая╕П 1.3 рдбреАрдк рд▓рд░реНрдирд┐рдВрдЧ рдХреЗ рдЕрдиреБрдкреНрд░рдпреЛрдЧ

(Applications of Deep Learning)

Deep Learning рдЖрдЬ рд▓рдЧрднрдЧ рд╣рд░ рдХреНрд╖реЗрддреНрд░ рдореЗрдВ рдЙрдкрдпреЛрдЧ рд╣реЛ рд░рд╣рд╛ рд╣реИ, рдЬреИрд╕реЗ:

рдХреНрд╖реЗрддреНрд░рдЕрдиреБрдкреНрд░рдпреЛрдЧ
ЁЯЦ╝я╕П рдХрдВрдкреНрдпреВрдЯрд░ рд╡рд┐рдЬрд╝рдиFace Recognition, Object Detection, Medical Image Analysis
ЁЯЧгя╕П NLP (рднрд╛рд╖рд╛)Machine Translation, Sentiment Analysis, Chatbots
ЁЯза рд╕реНрд╡рд╛рд╕реНрдереНрдпрдХреИрдВрд╕рд░ рдкрд╣рдЪрд╛рди, рд╣реГрджрдп рд░реЛрдЧ рднрд╡рд┐рд╖реНрдпрд╡рд╛рдгреА, MRI Scan Interpretation
ЁЯУИ рд╡рд┐рддреНрддFraud Detection, Stock Market Prediction
ЁЯЪЧ рдСрдЯреЛрдореЛрдмрд╛рдЗрд▓Self-Driving Cars (Tesla, Waymo)
ЁЯХ╣я╕П рдЧреЗрдорд┐рдВрдЧAI Game Agents (AlphaGo, OpenAI Five)
ЁЯОи рдХреНрд░рд┐рдПрдЯрд┐рд╡AI-generated Art, Music, Story Generation
ЁЯЫ░я╕П рдбрд┐рдлреЗрдВрд╕/рд╕реНрдкреЗрд╕Satellite Image Analysis, Surveillance

ЁЯУЬ 1.4 рдбреАрдк рд▓рд░реНрдирд┐рдВрдЧ рдХрд╛ рдЗрддрд┐рд╣рд╛рд╕ рдФрд░ рд╡рд┐рдХрд╛рд╕

(History and Evolution of Deep Learning)

рд╡рд░реНрд╖рдШрдЯрдирд╛ / рдпреЛрдЧрджрд╛рди
1943McCulloch & Pitts рдиреЗ рдкрд╣рд▓рд╛ рдХреГрддреНрд░рд┐рдо рдиреНрдпреВрд░реЙрди рдореЙрдбрд▓ рдкреНрд░рд╕реНрддреБрдд рдХрд┐рдпрд╛
1958Frank Rosenblatt рдиреЗ Perceptron рд╡рд┐рдХрд╕рд┐рдд рдХрд┐рдпрд╛ тАУ рдкрд╣рд▓рд╛ neural network рдореЙрдбрд▓
1986Backpropagation Algorithm (Rumelhart, Hinton) тАУ Learning Possible рд╣реБрдЖ
1998Yann LeCun рдиреЗ LeNet (CNN architecture) рдмрдирд╛рдпрд╛ тАУ Digit Recognition рдХреЗ рд▓рд┐рдП
2006Geoffrey Hinton рдиреЗ Deep Belief Networks рдкреНрд░рд╕реНрддреБрдд рдХрд┐рдП тАУ Deep Learning рд╢рдмреНрдж рдкреНрд░рдЪрд▓рди рдореЗрдВ рдЖрдпрд╛
2012AlexNet рдиреЗ ImageNet рдкреНрд░рддрд┐рдпреЛрдЧрд┐рддрд╛ рдЬреАрддреА тАУ CNN рдЖрдзрд╛рд░рд┐рдд рдмрдбрд╝реА рд╕рдлрд▓рддрд╛
2014GANs (Goodfellow) тАУ Image Generation рдХреА рд╢реБрд░реБрдЖрдд
2017Google рдиреЗ Transformer рдореЙрдбрд▓ рдкреНрд░рд╕реНрддреБрдд рдХрд┐рдпрд╛ тАУ NLP рдХреА рджрд┐рд╢рд╛ рдмрджрд▓реА
2018-2024BERT, GPT, CLIP, DALL┬╖E, Whisper, Sora рдЬреИрд╕реЗ рд╢рдХреНрддрд┐рд╢рд╛рд▓реА Deep Learning рдореЙрдбрд▓ рд╕рд╛рдордиреЗ рдЖрдП

ЁЯЪА рдирд┐рд╖реНрдХрд░реНрд╖:

Deep Learning рдХрд╛ рдЗрддрд┐рд╣рд╛рд╕ рд╢реЛрдз рдФрд░ рдХрдВрдкреНрдпреВрдЯрд┐рдВрдЧ рд╢рдХреНрддрд┐ рджреЛрдиреЛрдВ рдХреА рдорджрдж рд╕реЗ рд▓рдЧрд╛рддрд╛рд░ рд╡рд┐рдХрд╕рд┐рдд рд╣реЛрддрд╛ рд░рд╣рд╛ рд╣реИ рдФрд░ рдЖрдЬ рдпрд╣ AI рдХрд╛ рд╕рдмрд╕реЗ рд╢рдХреНрддрд┐рд╢рд╛рд▓реА рдШрдЯрдХ рдмрди рдЪреБрдХрд╛ рд╣реИред


ЁЯУМ рд╕рд╛рд░рд╛рдВрд╢ (Summary)

рдмрд┐рдВрджреБрд╡рд┐рд╡рд░рдг
Deep LearningNeural Networks рдкрд░ рдЖрдзрд╛рд░рд┐рдд рдорд╢реАрди рд▓рд░реНрдирд┐рдВрдЧ рдХрд╛ рдЙрдиреНрдирдд рд░реВрдк
рд╡рд┐рд╢реЗрд╖рддрд╛рдПрдБSelf-learning, Multiple layers, Automatic feature extraction
рдЕрдВрддрд░DL рдЬрд╝реНрдпрд╛рджрд╛ рд╢рдХреНрддрд┐рд╢рд╛рд▓реА рд▓реЗрдХрд┐рди рдЕрдзрд┐рдХ рдбреЗрдЯрд╛ рдФрд░ рд╕рдВрд╕рд╛рдзрдиреЛрдВ рдХреА рдЖрд╡рд╢реНрдпрдХрддрд╛ рд╣реЛрддреА рд╣реИ
рдЙрдкрдпреЛрдЧVision, NLP, Health, Finance, Games рдЖрджрд┐
рдЗрддрд┐рд╣рд╛рд╕1943 рд╕реЗ рд▓реЗрдХрд░ рдЖрдЬ рддрдХ рдХрд╛ рд╡рд┐рдХрд╛рд╕ тАУ Perceptron рд╕реЗ GPT рддрдХ

ЁЯза рдЕрднреНрдпрд╛рд╕ рдкреНрд░рд╢реНрди (Practice Questions)

  1. Deep Learning рдХреЛ тАЬDeepтАЭ рдХреНрдпреЛрдВ рдХрд╣рд╛ рдЬрд╛рддрд╛ рд╣реИ?
  2. Machine Learning рдФрд░ Deep Learning рдореЗрдВ рдХреНрдпрд╛ рдкреНрд░рдореБрдЦ рдЕрдВрддрд░ рд╣реИрдВ?
  3. Computer Vision рдореЗрдВ Deep Learning рдХрд╛ рдХреИрд╕реЗ рдЙрдкрдпреЛрдЧ рд╣реЛрддрд╛ рд╣реИ?
  4. AlexNet рдХрд┐рд╕ рдХреНрд╖реЗрддреНрд░ рдореЗрдВ рдХреНрд░рд╛рдВрддрд┐ рд▓реЗрдХрд░ рдЖрдпрд╛ рдФрд░ рдХрдм?
  5. GANs рдХреНрдпрд╛ рд╣реИрдВ рдФрд░ рдХрд┐рд╕рдиреЗ рдЗрдиреНрд╣реЗрдВ рдкреНрд░рд╕реНрддреБрдд рдХрд┐рдпрд╛?

Evolution of neural networks

Logic Gates (AND, OR, NOT, XOR, etc.)

Foundation of computationтАФbasic building blocks of digital circuits.

Perform simple boolean operations.

Example: AND gate outputs 1 only if both inputs are 1.

Perceptron (Single-layer Neural Network)

The simplest type of artificial neuron, inspired by biological neurons.

Can mimic logic gates using weights and bias.

Activation function: Step function (e.g., outputs 0 or 1).

Limitation: Cannot solve the XOR problem (i.e., non-linearly separable problems).

y=f(WтЛЕX+b)

W = weights,
X = input,
b = bias,
f = activation function.

Artificial Neural Network (ANN) (Multi-layer Perceptron – MLP)

Fixes XOR problem by introducing hidden layers.

Uses non-linear activation functions (e.g., ReLU, Sigmoid).

Multiple perceptrons stacked together.

Still struggles with deep learning tasks.

Algorithm (Training ANNs)

Introduced to update weights efficiently using gradient descent.

Error is propagated backward from output to input.

Uses partial derivatives to minimize loss.

ЁЯФ╣ Steps:

Forward pass: Compute output.

Loss calculation: Compare output with actual value.

Backward pass: Adjust weights using gradient descent.

Repeat until convergence.

Convolutional Neural Networks (CNNs)

Designed for image processing and computer vision tasks.

Uses convolutional layers to detect patterns like edges, textures, etc.

Pooling layers reduce dimensionality, improving efficiency.

Example applications: Image Captioning, Object Detection, Face Recognition.

ЁЯФ╣ Key components:

Convolutional layers (Feature extraction)

Pooling layers (Downsampling)

Fully Connected layers (Classification)

Recurrent Neural Networks (RNNs)

Designed for sequential data like text, speech, and time series.

Maintains a memory of previous inputs using loops.

Common problem: Vanishing gradient (solved by LSTM & GRU).

Example applications: Text Generation, Speech Recognition, Machine Translation.

ЁЯФ╣ Variants:

Vanilla RNN: Simple version, suffers from vanishing gradient.

LSTM (Long Short-Term Memory): Fixes vanishing gradient issue.

GRU (Gated Recurrent Unit): Similar to LSTM but computationally efficient.

Summary:


Logic Gates тЖТ Basis of computation.

Perceptron тЖТ Simple neuron that mimics logic gates.

ANN (MLP) тЖТ Multi-layer perceptron solves non-linear problems.

Backpropagation тЖТ Algorithm for training neural networks.

CNN тЖТ Best for images.

RNN тЖТ Best for sequential data.

Let me know if you need more details on any stage!

Detail Guide for image captionging all neccesary skills and tools

Creating an image captioning model is a complex task that requires a mix of skills in deep learning, computer vision, natural language processing (NLP), and software engineering. HereтАЩs a detailed guide covering the necessary skills, tools, and steps:

1. Core Concepts and Skills

a. Machine Learning & Deep Learning

  • Understanding ML Basics: Supervised vs. unsupervised learning, loss functions, optimization.
  • Neural Networks: Basics of neural networks, backpropagation, activation functions.
  • Convolutional Neural Networks (CNNs): Essential for image feature extraction.
  • Recurrent Neural Networks (RNNs) and LSTMs: Key for sequence generation in captions.
  • Attention Mechanisms: Important for aligning parts of the image with parts of the caption.

b. Computer Vision

  • Image Preprocessing: Techniques such as normalization, resizing, data augmentation.
  • Feature Extraction: Using pre-trained CNNs like VGG, ResNet for extracting image features.
  • Transfer Learning: Fine-tuning pre-trained models for specific tasks like captioning.

c. Natural Language Processing (NLP)

  • Text Preprocessing: Tokenization, stemming, lemmatization, handling out-of-vocabulary words.
  • Language Modeling: Understanding how to predict the next word in a sequence.
  • Word Embeddings: Techniques like Word2Vec, GloVe for representing words as vectors.

d. Data Handling

  • Datasets: Understanding and working with datasets like Flickr8k, Flickr30k, MS COCO.
  • Data Augmentation: Techniques to increase dataset size artificially.
  • Handling Large Datasets: Techniques for managing memory and processing power.

e. Programming and Software Engineering

  • Python: Essential language for machine learning, deep learning, and data handling.
  • Libraries: Familiarity with NumPy, Pandas, Matplotlib for data manipulation and visualization.
  • Version Control: Git for tracking changes and collaborating with others.
  • Cloud Computing: Familiarity with platforms like AWS, Google Cloud, or Azure for training large models.

2. Tools and Frameworks

a. Deep Learning Frameworks

  • TensorFlow/Keras: Widely used for building and training deep learning models.
  • PyTorch: Another popular framework that is highly flexible and widely used in research.
  • Hugging Face Transformers: Useful for integrating pre-trained models and handling NLP tasks.

b. Pre-trained Models

  • VGG16, ResNet, InceptionV3: Pre-trained CNNs for feature extraction.
  • GPT, BERT: Pre-trained language models for generating captions (if using transformers).
  • Show, Attend, and Tell: A classic model architecture for image captioning.

c. Data Handling and Visualization Tools

  • OpenCV: For image manipulation and preprocessing.
  • Pandas and NumPy: For data manipulation and numerical computation.
  • Matplotlib and Seaborn: For visualizing data and model performance.

3. Step-by-Step Process

Step 1: Data Collection and Preprocessing

  • Dataset Selection: Choose a dataset like Flickr8k, Flickr30k, or MS COCO.
  • Data Preprocessing: Clean captions, tokenize words, build a vocabulary, resize images.
  • Feature Extraction: Use a pre-trained CNN to extract features from the images.

Step 2: Model Architecture Design

  • Encoder-Decoder Structure: Common architecture for image captioning.
    • Encoder: CNN (e.g., ResNet) for extracting image features.
    • Decoder: RNN/LSTM for generating captions from the encoded features.
  • Attention Mechanism: To focus on specific parts of the image while generating each word.

Step 3: Model Training

  • Loss Function: Usually cross-entropy loss for caption generation.
  • Optimizer: Adam or RMSprop optimizers are commonly used.
  • Training Loop: Train the model on the dataset, monitor loss, and adjust hyperparameters.

Step 4: Evaluation

  • Evaluation Metrics: BLEU, METEOR, ROUGE, CIDEr are commonly used for captioning tasks.
  • Qualitative Analysis: Manually inspect generated captions for accuracy and relevance.
  • Hyperparameter Tuning: Fine-tune model hyperparameters for better performance.

Step 5: Deployment

  • Model Saving: Save the trained model using formats like .h5 for Keras or .pth for PyTorch.
  • Inference Pipeline: Create a pipeline to feed new images into the model and generate captions.
  • Deployment Platforms: Use platforms like Flask, FastAPI, or TensorFlow Serving for deployment.

4. Advanced Topics

  • Transformer-based Models: Explore transformer models for captioning tasks.
  • Reinforcement Learning: Fine-tune models using reinforcement learning techniques like Self-Critical Sequence Training (SCST).
  • Multimodal Learning: Integrating image captioning with other tasks like visual question answering (VQA).

5. Practical Project

  • Build an End-to-End Project: Start from dataset collection to deploying an image captioning model on a cloud platform.
  • Experiment and Iterate: Try different models, architectures, and training techniques to improve performance.

6. Resources

  • Books: “Deep Learning with Python” by Fran├зois Chollet, “Pattern Recognition and Machine Learning” by Christopher Bishop.
  • Courses:
    • Coursera: “Deep Learning Specialization” by Andrew Ng.
    • Udacity: “Computer Vision Nanodegree”.
  • Online Documentation: TensorFlow, PyTorch, and Hugging Face documentation.

This guide should give you a comprehensive roadmap for mastering image captioning and building a functional model. Start with the basics and progressively tackle more advanced concepts and tools.

A fully connected layer( Dense layer), : fundamental component of neural networks,

A fully connected layer, also known as a dense layer, is a fundamental component of neural networks, especially in feedforward neural networks and the later stages of Convolutional Neural Networks (CNNs). In a fully connected layer, each neuron is connected to every neuron in the previous layer. This layer performs a linear transformation followed by an activation function, enabling the model to learn complex representations.

Key Concepts

  1. Neurons:
    • Each neuron in a fully connected layer takes input from all neurons in the previous layer.
    • The connections between neurons are represented by weights, which are learned during training.
  2. Weights and Biases:
    • Weights: Each connection between neurons has an associated weight, which is adjusted during training to minimize the loss function.
    • Bias: Each neuron has an additional parameter called bias, which is added to the weighted sum of inputs.
  3. Activation Function:
    • After the linear transformation (weighted sum plus bias), an activation function is applied to introduce non-linearity.
    • Common activation functions include ReLU (Rectified Linear Unit), Sigmoid, and Tanh.

How It Works

  1. Input: A vector of activations from the previous layer.
  2. Linear Transformation: Each neuron computes a weighted sum of its inputs plus a bias. z=тИСi=1n(wiтЛЕxi)+bz = \sum_{i=1}^{n} (w_i \cdot x_i) + bz=i=1тИСnтАЛ(wiтАЛтЛЕxiтАЛ)+b where wiw_iwiтАЛ are the weights, xix_ixiтАЛ are the input activations, and bbb is the bias.
  3. Activation Function: An activation function is applied to the linear transformation to produce the output of the neuron.a=activation(z)a = \text{activation}(z)a=activation(z)
  4. Output: The outputs of the activation functions from all neurons in the layer are passed to the next layer.

Example in Keras

HereтАЩs an example of how to create a simple neural network with a fully connected layer using Keras:

pythonCopy codefrom tensorflow.keras.models import Sequential
from tensorflow.keras.layers import Dense

# Create a simple model with one hidden dense layer
model = Sequential()
model.add(Dense(units=64, activation='relu', input_shape=(784,)))  # Input layer with 784 neurons (e.g., flattened 28x28 image)
model.add(Dense(units=10, activation='softmax'))  # Output layer with 10 neurons (e.g., for 10 classes)

# Print the model summary
model.summary()

Explanation of the Example Code

  • Dense: This function creates a fully connected (dense) layer.
    • units=64: The number of neurons in the layer.
    • activation='relu': The activation function applied to the layerтАЩs output.
    • input_shape=(784,): The shape of the input data (e.g., a flattened 28×28 image).

Common Activation Functions

  1. ReLU (Rectified Linear Unit):ReLU(x)=maxтБб(0,x)\text{ReLU}(x) = \max(0, x)ReLU(x)=max(0,x)
    • Most commonly used activation function in hidden layers.
    • Efficient and helps mitigate the vanishing gradient problem.
  2. Sigmoid:╧Г(x)=11+eтИТx\sigma(x) = \frac{1}{1 + e^{-x}}╧Г(x)=1+eтИТx1тАЛ
    • Maps the input to a range between 0 and 1.
    • Used in the output layer for binary classification.
  3. Tanh (Hyperbolic Tangent):tanhтБб(x)=exтИТeтИТxex+eтИТx\tanh(x) = \frac{e^x – e^{-x}}{e^x + e^{-x}}tanh(x)=ex+eтИТxexтИТeтИТxтАЛ
    • Maps the input to a range between -1 and 1.
    • Can be used in hidden layers, especially when dealing with normalized input data.
  4. Softmax:softmax(xi)=exiтИСjexj\text{softmax}(x_i) = \frac{e^{x_i}}{\sum_{j} e^{x_j}}softmax(xiтАЛ)=тИСjтАЛexjтАЛexiтАЛтАЛ
    • Used in the output layer for multi-class classification.
    • Produces a probability distribution over multiple classes.

Importance of Fully Connected Layers

  • Feature Combination: Fully connected layers combine features learned by convolutional and pooling layers, helping to make final decisions based on the extracted features.
  • Flexibility: They can model complex relationships by learning the appropriate weights and biases.
  • Adaptability: Can be used in various types of neural networks and architectures, including CNNs, RNNs, and more.

Applications

  • Classification: Commonly used in the output layer of classification networks.
  • Regression: Can be used for regression tasks by having a single neuron with a linear activation function in the output layer.
  • Feature Extraction: In some networks, fully connected layers are used to extract high-level features before passing them to the final output layer.

Conclusion

Fully connected layers are crucial components in deep learning models, enabling the network to learn and make predictions based on the combined features from previous layers. They are versatile and can be used in various neural network architectures to solve a wide range of tasks.