Technology Tree - chunhualiao/public-docs GitHub Wiki

The concept you're describing, often referred to as 科技树 ("science and technology tree") in Chinese, aligns closely with the term "tech tree" or "technology tree" in English.

This term is commonly used in gaming and strategic discussions to represent a structured progression of knowledge or technological advancements, where mastering one discovery or invention unlocks subsequent possibilities. It's also metaphorically used in broader contexts, such as national development or personal learning, to depict the systematic acquisition of foundational skills and knowledge leading to more advanced capabilities.

For a beginner with basic programming and machine learning skills, understanding the core techniques of rStar-Math involves learning various concepts and technologies related to language models, search algorithms, reinforcement learning, and program synthesis. Here's a structured skill tree and learning roadmap:

agent-based system

supply chain management

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• Languages:

  • Python (primary language for most machine learning frameworks).
  • Familiarity with languages like C++ for understanding computational efficiency or program synthesis.

• Topics to Learn:

  • Basic programming constructs (variables, loops, functions).
  • Working with libraries for numerical computation (e.g., NumPy).
  • Understanding of Python debugging and testing frameworks.

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• Linear Algebra:

  • Vectors, matrices, dot products, and matrix multiplication.
  • Applications in deep learning (e.g., weights, activations).

• Probability and Statistics:

  • Basics of probability distributions (e.g., Gaussian, uniform).
  • Concepts of expectation, variance, and sampling.

• Optimization:

  • Gradient descent and its variants (SGD, Adam).
  • Understanding of loss functions and backpropagation.

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• Core Concepts:

  • Supervised learning (regression, classification).
  • Neural networks (feedforward, backpropagation).
  • Model evaluation metrics (accuracy, loss, etc.).

• Hands-On:

  • Train simple models (e.g., logistic regression, fully connected networks) using frameworks like TensorFlow or PyTorch.

• Projects:

  • Build and train models on datasets like MNIST or CIFAR-10.

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• Topics to Learn:

  • Sequence models (RNNs, LSTMs).
  • Transformer architecture (attention mechanism, self-attention).
  • Understanding pre-trained language models (e.g., GPT, BERT).

• Hands-On:

  • Use Hugging Face's Transformers library to fine-tune a pre-trained model for text classification or summarization.

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• Core Concepts:

  • Understanding Abstract Syntax Trees (ASTs).
  • Generating and validating code.
  • Tools: Familiarity with Python libraries like ast or external tools like CodeT5 or OpenAI Codex.

• Hands-On:

  • Write programs that generate or manipulate other programs.
  • Example: Convert a mathematical expression in string form to executable Python code.

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• Core Concepts:

  • Basics of search algorithms (DFS, BFS).
  • MCTS principles:
    • Selection, Expansion, Simulation, Backpropagation.
    • Concepts like Q-values, UCB (Upper Confidence Bound).

• Hands-On:

  • Implement MCTS for simple games (e.g., Tic-Tac-Toe, Connect Four).

• Resources:

  • Tutorials or guides on AlphaZero's use of MCTS.

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• Core Concepts:

  • Markov Decision Processes (MDPs): states, actions, rewards.
  • Policy learning vs. value learning.
  • Algorithms: Q-learning, policy gradient methods.

• Hands-On:

  • Use OpenAI Gym to implement RL for simple environments (e.g., CartPole, MountainCar).

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• Core Concepts:

  • Transfer learning: Fine-tuning pre-trained models for specific tasks.
  • Data augmentation and synthetic data generation.
  • Iterative model improvement.

• Hands-On:

  • Fine-tune language models for domain-specific tasks using custom datasets.

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• Core Concepts:

  • Pairing reasoning with code generation.
  • Executing and validating Python code during model training.
  • Filtering and scoring solutions using execution results.

• Hands-On:

  • Write a script to generate and validate Python code snippets for basic math problems.

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• Core Concepts:

  • Ranking systems (e.g., Bradley-Terry model).
  • Pairwise ranking loss functions.
  • Training models to evaluate and rank intermediate steps.

• Hands-On:

  • Implement a simple reward model for ranking candidates in a search problem.

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• Core Concepts:

  • Debugging tools for ML models (e.g., TensorBoard).
  • Understanding error types in program synthesis (e.g., syntax errors, runtime errors).

• Hands-On:

  • Write test cases for validating code generation outputs.
  • Use Python’s unittest or pytest libraries.

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• Programming (Python, basic C++).
• Machine Learning Fundamentals.

• Transformer models.
• Program synthesis and code execution.
• Search algorithms (MCTS).

• Reinforcement Learning (Q-learning, policy gradients).
• Code-augmented reasoning.
• Fine-tuning and iterative model improvement.

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1. Step 1: Learn Python programming and basic machine learning.
2. Step 2: Study sequence models and transformers.
3. Step 3: Implement simple search algorithms and MCTS.
4. Step 4: Practice program synthesis (code generation and execution).
5. Step 5: Train a simple language model using Hugging Face.
6. Step 6: Explore reinforcement learning and apply it to simple environments.
7. Step 7: Combine these skills into a project, such as building an MCTS-driven reasoning system for math problems or simple code tasks.

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• Books:
  • Deep Learning by Ian Goodfellow for ML basics.
  • Reinforcement Learning: An Introduction by Sutton and Barto.
• Courses:
  • Andrew Ng's Machine Learning and Deep Learning Specializations.
  • Hugging Face’s free course on transformers.
• Projects:
  • Start small (e.g., Tic-Tac-Toe with MCTS), then progress to reasoning tasks.

By following this roadmap, you'll gain the skills to understand and potentially implement systems like rStar-Math.