Course Goal: This course delves into the intricacies of activation functions, exploring their theoretical underpinnings, practical implications, and impact on deep learning model performance. It will provide a comprehensive analysis of various activation functions, culminating in a deep dive into the TeLU activation function as presented in the paper "TELU ACTIVATION FUNCTION FOR FAST AND STABLE DEEP LEARNING." Students will gain the ability to critically evaluate, select, and implement activation functions for diverse deep learning tasks, as well as understand the cutting edge of activation function research.
Prerequisites:
- Completion of "Modern AI Development: From Transformers to Generative Models" or equivalent knowledge.
- Strong understanding of deep learning concepts (neural networks, backpropagation, optimization algorithms).
- Proficiency in Python and deep learning libraries (PyTorch preferred, TensorFlow acceptable).
- Solid foundation in calculus (derivatives, integrals) and linear algebra (vectors, matrices).
Course Duration: 8 weeks (flexible, can be adjusted to 6 or 10 weeks)
Tools:
- Python (>= 3.8)
- PyTorch (preferred) or TensorFlow
- Jupyter Notebooks/Google Colab
- Standard Python libraries (NumPy, Pandas, Matplotlib, etc.)
- (Optional) Visualization tools for activation functions and model behavior.
Curriculum Draft:
Module 1: Revisiting Activation Functions - Foundations and Landscape (Week 1)
- Topic 1.1: The Role of Activation Functions in Deep Learning
- Review: Non-linearity, feature extraction, decision boundaries.
- Impact on training dynamics: gradient flow, convergence speed, stability.
- Relationship to network architecture and depth.
- The interplay of activation functions with optimization, normalization and initialization
- Topic 1.2: Classical Activation Functions: A Deep Dive
- Sigmoid, Tanh: Properties, limitations (vanishing gradients), historical context.
- ReLU: Properties, advantages (sparsity, efficiency), and drawbacks (dying ReLU).
- Variants: Leaky ReLU, Parametric ReLU (PReLU) - Addressing the dying ReLU problem.
- Topic 1.3: Exploring the Activation Function Landscape
- Categorizing activation functions:
- Bounded vs. Unbounded
- Monotonic vs. Non-monotonic
- Smooth vs. Non-smooth
- Saturating vs. Non-saturating
- Properties and theoretical implications of each category.
- Categorizing activation functions:
- Topic 1.4: Design Principles and Desirable Properties
- Zero-centered output, computational efficiency, gradient behavior (avoiding vanishing/exploding gradients).
- Smoothness, differentiability, and implications for optimization.
- Approaching the identity function - benefits for learning.
- Robustness to noise and adversarial examples.
- Other considerations: Sparsity, biological plausibility, etc.
- Hands-on Exercises:
- Implement and visualize classical activation functions and their derivatives.
- Experiment with different activation functions in a simple neural network and compare training dynamics.
- Analyze the impact of activation function choice on model performance.
Module 2: Beyond ReLU - The Rise of Modern Activation Functions (Week 2)
- Topic 2.1: Exponential Linear Units (ELUs) and Scaled ELUs (SELUs)
- Motivation: Addressing limitations of ReLU, promoting faster learning.
- Mathematical formulation, properties, and benefits.
- Self-normalizing networks and SELUs - theoretical implications.
- Topic 2.2: Swish and the SiLU Family
- Discovery through neural architecture search.
- Mathematical formulation of SiLU and Swish.
- Properties: Smoothness, non-monotonicity, and their impact on training.
- Variants of Swish and their performance characteristics.
- Topic 2.3: Gaussian Error Linear Unit (GELU)
- Motivation: Stochastic regularization and connection to dropout.
- Mathematical definition and relationship to the Gaussian cumulative distribution function.
- Smoothness, non-monotonicity, and impact on model performance.
- Success in Transformer-based models.
- Topic 2.4: Mish and Other Advanced Activation Functions
- Mish: Formulation, properties (self-regularization), and empirical results.
- Other notable functions: Logish, Smish - key features and comparisons.
- Discussion: Strengths and weaknesses of these modern activation functions.
- Hands-on Exercises:
- Implement ELU, SELU, Swish, GELU, and Mish from scratch.
- Train models with these activation functions on benchmark datasets (e.g., CIFAR-10, a subset of ImageNet) and compare performance.
- Analyze the impact of hyperparameters (e.g., learning rate, weight decay) on training with different activation functions.
- Possible Extensions:
- Investigate the use of these activation functions in different architectures (CNNs, RNNs, Transformers).
Module 3: Introducing TeLU - A Novel Activation Function (Week 3)
- Topic 3.1: Motivation and Design Principles of TeLU
- Addressing limitations of existing activation functions.
- Combining the strengths of ReLU (efficiency, strong gradients) with desirable properties of smooth, non-monotonic functions.
- The "Hyperbolic Tangent Exponential Linear Unit" - intuition behind the name.
- Topic 3.2: Mathematical Formulation of TeLU
- Definition: TeLU(x) = x * tanh(e^x).
- Analysis of the function:
- Behavior for positive and negative inputs.
- Asymptotic behavior as x approaches positive and negative infinity.
- Derivative of TeLU and its properties.
- Topic 3.3: Theoretical Advantages of TeLU
- Near-linear behavior in the active region: Implications for convergence speed.
- Persistent gradients in the saturation region: Addressing the vanishing gradient problem.
- Smoothness and infinite differentiability: Benefits for optimization and robustness.
- Zero-centering: Implications for training dynamics and comparison to other functions.
- Topic 3.4: TeLU as a Universal Approximator
- Review of the Universal Approximation Theorem.
- Proof that TeLU satisfies the conditions for a universal approximator (referencing the paper's theoretical analysis).
- Implications for the expressive power of networks using TeLU.
- Hands-on Exercises:
- Implement TeLU from scratch in PyTorch/TensorFlow.
- Visualize TeLU and its derivative, comparing them to other activation functions.
- Train a simple neural network using TeLU and observe its behavior during training.
Module 4: Deep Dive into TeLU - Properties and Analysis (Week 4)
- Topic 4.1: Gradient Analysis of TeLU
- Detailed examination of the TeLU derivative:
- Behavior in the active and inactive regions.
- Comparison to the derivatives of ReLU, ELU, Swish, and GELU.
- Implications for gradient-based optimization.
- Visualizing gradient flow through a network using TeLU.
- Detailed examination of the TeLU derivative:
- Topic 4.2: Computational Efficiency of TeLU
- Benchmarking TeLU against other activation functions (ReLU, ELU, Swish, GELU, Mish).
- Analyzing the computational cost of forward and backward passes.
- Impact of TeLU on training time and inference speed.
- Topic 4.3: TeLU and Regularization
- Exploring the potential self-regularizing properties of TeLU (similar to Mish).
- Comparing the need for explicit regularization (e.g., weight decay, dropout) when using TeLU vs. other activation functions.
- Topic 4.4: Robustness Analysis of TeLU
- Evaluating the sensitivity of TeLU to input noise and small perturbations.
- Comparing the robustness of TeLU to adversarial examples with other activation functions.
- Theoretical connections to smoothness and robustness.
- Hands-on Exercises:
- Conduct experiments to measure the computational efficiency of TeLU.
- Train models with different levels of regularization and compare the performance of TeLU to other activation functions.
- Generate adversarial examples and evaluate the robustness of models using TeLU.
Module 5: TeLU in Practice - Empirical Evaluation (Week 5)
- Topic 5.1: Experimental Setup and Methodology
- Datasets: MNIST, CIFAR-10, CIFAR-100, ImageNet (or subsets), potentially other relevant datasets (e.g., text, time-series).
- Architectures: Multi-layer perceptrons (MLPs), convolutional neural networks (CNNs), recurrent neural networks (RNNs), and potentially Transformers.
- Metrics: Accuracy, loss, convergence speed, training time, and potentially other relevant metrics (e.g., F1-score, AUC).
- Baselines: Comparing TeLU to ReLU, ELU, Swish, GELU, and Mish.
- Topic 5.2: TeLU on Image Classification Tasks
- Training and evaluating models on image datasets (MNIST, CIFAR-10, CIFAR-100, ImageNet).
- Analyzing the performance of TeLU in different network architectures (MLPs, CNNs).
- Comparing convergence speed, accuracy, and generalization ability to baseline activation functions.
- Investigating the impact of network depth on performance.
- Topic 5.3: TeLU on Other Tasks
- (Optional) Exploring the use of TeLU in RNNs for sequence modeling or natural language processing.
- (Optional) Applying TeLU to other domains (e.g., time-series data, reinforcement learning).
- Topic 5.4: Hyperparameter Tuning and Optimization
- Investigating the impact of learning rate, batch size, weight decay, and other hyperparameters on TeLU performance.
- Comparing optimal hyperparameter settings for TeLU and other activation functions.
- Discussion: Does TeLU require different hyperparameter tuning strategies than other activation functions?
- Hands-on Exercises:
- Reproduce the experiments presented in the TeLU paper (or a subset of them).
- Conduct additional experiments to evaluate TeLU on different datasets and architectures.
- Perform hyperparameter tuning to optimize the performance of models using TeLU.
Module 6: Advanced Topics and Research Directions (Week 6)
- Topic 6.1: Activation Function Design - Lessons from TeLU
- Revisiting the design principles of activation functions.
- What can we learn from the development and analysis of TeLU?
- How can these insights inform the design of future activation functions?
- Topic 6.2: Beyond Fixed Activation Functions
- Learnable activation functions: Exploring approaches to learn activation functions during training.
- Adaptive activation functions: Dynamically adjusting activation functions based on input or network state.
- Neural architecture search for activation functions.
- Topic 6.3: Connections to Other Areas of Deep Learning
- Activation functions and normalization techniques (Batch Normalization, Layer Normalization).
- Activation functions and optimization algorithms (SGD, Adam, etc.).
- Activation functions and initialization strategies.
- Topic 6.4: Open Questions and Future Research
- What are the limitations of TeLU?
- Are there scenarios where other activation functions might be preferred?
- What are the most promising directions for future research on activation functions?
- Hands-on Exercises/Project:
- Explore learnable or adaptive activation functions.
- Design and implement a novel activation function based on the principles discussed in the course.
- Investigate the relationship between activation functions and other aspects of deep learning (e.g., normalization, optimization).
Module 7: Theoretical and Experimental Analysis of TeLU (Week 7)
- Topic 7.1: In-depth Analysis of TeLU's Mathematical Properties
- Revisit the mathematical definition of TeLU.
- Detailed analysis of TeLU's derivative and its implications for gradient-based learning.
- Explore the connection between TeLU's formulation and its observed properties (e.g., smoothness, near-linearity).
- Topic 7.2: Comparative Analysis with Other Activation Functions
- Formal comparison of TeLU with ReLU, ELU, Swish, GELU, and Mish on various theoretical aspects:
- Gradient behavior
- Computational complexity
- Regularization effects
- Robustness
- Use mathematical tools and visualizations to highlight the differences and similarities.
- Formal comparison of TeLU with ReLU, ELU, Swish, GELU, and Mish on various theoretical aspects:
- Topic 7.3: Detailed Examination of the TeLU Paper's Experiments
- Step-by-step walkthrough of the experimental methodology used in the TeLU paper.
- Critical analysis of the results and their statistical significance.
- Discussion of the strengths and limitations of the experimental evaluation.
- Topic 7.4: Reproducing and Extending the TeLU Paper's Results
- Provide code and instructions for reproducing the key experiments from the paper.
- Encourage students to extend the experiments by:
- Trying different datasets.
- Exploring different architectures.
- Modifying hyperparameters.
- Investigating variations of TeLU.
- Hands-on Exercises:
- Implement and analyze TeLU's mathematical properties using code.
- Reproduce and extend the experiments from the TeLU paper.
- Critically evaluate the paper's claims and findings.
Module 8: Project and Future of Activation Functions (Week 8)
- Topic 8.1: Project Presentations and Discussion
- Students present their projects, showcasing their understanding of activation functions and their ability to apply them in practice.
- Peer feedback and discussion of project findings.
- Topic 8.2: The Future of Activation Functions
- Emerging trends in activation function research.
- Potential for new activation functions to further improve deep learning models.
- Discussion of the role of activation functions in the broader context of AI research.
- Topic 8.3: Course Wrap-up and Key Takeaways
- Review of the main concepts and findings covered in the course.
- Discussion of the importance of activation functions in deep learning.
- Guidance on further learning and resources for staying up-to-date with the field.
- Project:
- Students will work on a final project that involves a significant exploration of activation functions. Possible project ideas include:
- Designing and evaluating a novel activation function.
- In-depth comparative study of different activation functions on a challenging task.
- Investigating the role of activation functions in a specific application area.
- Extending the theoretical analysis of TeLU or other activation functions.
- Developing tools for visualizing and analyzing the behavior of activation functions.
- Students will work on a final project that involves a significant exploration of activation functions. Possible project ideas include:
Assessment:
- Weekly quizzes or assignments to test understanding of key concepts.
- Hands-on exercises and coding assignments throughout the modules.
- Midterm project/assignment focusing on the analysis and comparison of different activation functions.
- Final project involving in-depth research and experimentation with activation functions.
- Class participation and engagement in discussions.
Key Pedagogical Considerations:
- Balance of Theory and Practice: The curriculum should strike a balance between theoretical analysis and practical implementation.
- Emphasis on Critical Thinking: Encourage students to critically evaluate the strengths and weaknesses of different activation functions.
- Hands-on Learning: Provide ample opportunities for students to implement and experiment with activation functions through coding exercises and projects.
- Connection to Research: Highlight the connection between the course material and current research in activation functions, particularly the TeLU paper.
- Interactive Learning: Foster a collaborative learning environment through discussions, peer feedback, and group projects.