Large Language Model (LLM) Training Algorithm

A Large Language Model (LLM) Training Algorithm is a deep neural model training algorithm that can be implemented by an LLM training system (optimizes large language model parameters) to support LLM training tasks.

• AKA: Language Model Training Method, LLM Optimization Algorithm.
• Context:
  • It can (typically) employ gradient descent or stochastic gradient descent techniques to optimize model parameters.
  • It can (typically) utilize backpropagation to compute gradients through the neural network.
  • It can (typically) minimize a loss function such as cross-entropy loss or perplexity.
  • It can (typically) implement optimization strategies like Adam, AdamW, or SGD with momentum.
  • It can (typically) incorporate regularization techniques to prevent overfitting.
  • It can (often) apply gradient accumulation to handle large batch sizes with limited memory.
  • It can (often) use gradient clipping to prevent exploding gradients.
  • It can (often) implement learning rate scheduling to improve convergence.
  • It can (often) utilize mixed precision training to reduce memory usage and increase throughput.
  • It can (often) employ activation recomputation (also known as gradient checkpointing) to trade computation for memory savings.
  • It can (often) implement parallelism strategies to distribute computation across multiple processing units.
  • It can (often) use attention optimization techniques such as FlashAttention to reduce memory overhead.
  • ...
  • It can range form being a Pre-Training LLM Training Algorithm to being a Post-Training LLM Training Algorithm, depending on ...
  • It can range from being a Single-Token Prediction Algorithm to being a Multi-Token Prediction Algorithm, depending on its prediction target.
  • It can range from being a Causal Language Modeling Algorithm to being a Masked Language Modeling Algorithm, depending on its attention pattern.
  • It can range from being a Standard Optimization Algorithm to being a Parameter-Efficient Fine-Tuning Algorithm, depending on its parameter update scope.
  • It can range from being a Single-GPU Algorithm to being a Multi-GPU Distributed Algorithm, depending on its computational scale.
  • It can have Algorithm Input: model architecture, tokenized data, optimization hyperparameters
  • It can have Algorithm Output: updated model weights, loss metrics, gradient statistics
  • It can have Algorithm Performance Measures such as convergence rate, computational efficiency, and memory utilization
  • ...
• Examples:
  • Next-Token Prediction Algorithms, such as:
    • Autoregressive Training Algorithms, such as:
      • Causal Language Modeling with left-to-right attention for generative capabilities.
      • Teacher Forcing to stabilize sequence-to-sequence training.
    • Multi-Token Prediction Algorithms, such as:
      • Parallel Token Prediction with shared representations for improved efficiency.
      • Future Token Prediction with multiple output heads for faster convergence.
  • Masked Language Modeling Algorithms, such as:
    • BERT-style Training Algorithms, such as:
      • Random Token Masking with bidirectional attention for language understanding.
      • Whole Word Masking to preserve linguistic units.
    • RoBERTa-style Training Algorithms, such as:
      • Dynamic Masking for preventing memorization during extended training.
      • Byte-Pair Encoding Model for tokenization alignment.
  • Parameter-Efficient Training Algorithms, such as:
    • Adapter-Based Methods, such as:
      • Low-Rank Adaptation (LoRA) for efficient fine-tuning.
      • Prefix Tuning for parameter-efficient adaptation.
    • Quantization Methods, such as:
      • Quantization-Aware Training to reduce bit precision.
      • Post-Training Quantization for model compression.
  • Distributed Training Algorithms, such as:
    • Parallelism Strategy Algorithms, such as:
      • Data Parallelism Algorithm for gradient synchronization across replicated models.
      • ZeRO (Zero Redundancy Optimizer) for memory optimization in data parallel training.
      • Tensor Parallelism Algorithm for weight matrix sharding across multiple devices.
      • Pipeline Parallelism Algorithm for layer distribution across processing units.
      • Sequence Parallelism Algorithm for token sequence distribution to optimize memory usage.
      • Context Parallelism Algorithm for handling long contexts in transformer models.
      • Expert Parallelism Algorithm for distributing experts in Mixture-of-Experts models.
    • Hybrid Parallelism Algorithms, such as:
      • 3D Parallelism combining data, tensor, and pipeline parallelism.
      • 4D Parallelism adding expert parallelism to the standard 3D approach.
  • Memory Optimization Algorithms, such as:
    • Precision Reduction Algorithms, such as:
      • Mixed Precision Training with FP16 or BF16 formats.
      • FP8 Training for further memory reduction with calibration techniques.
    • Computation Trading Algorithms, such as:
      • Activation Recomputation to free memory by recomputing forward activations.
      • Selective Gradient Checkpointing for targeted memory savings.
  • Attention Optimization Algorithms, such as:
    • Memory-Efficient Attentions, such as:
      • FlashAttention for IO-aware attention computation.
      • FlashAttention 2 with improved tiling strategies.
      • Ring Attention for optimized multi-GPU attention.
    • Sparse Attentions, such as:
      • Block-Sparse Attention for efficient long-sequence processing.
      • Local Attention with windowed attention patterns.
  • ...
• Counter-Examples:
  • LLM Training Task, which describes the overall training process rather than the specific algorithmic approach.
  • LLM Training System, which refers to the hardware and software infrastructure rather than the mathematical method.
  • LLM Inference Algorithm, which focuses on model execution rather than parameter optimization.
  • Vision Model Training Algorithm, which optimizes for image understanding rather than language modeling.
  • Traditional Machine Learning Algorithm, which typically uses statistical methods rather than deep learning approaches.
• See: Backpropagation, Gradient Descent, Stochastic Gradient Descent, Adam Optimizer, Learning Rate Schedule, Cross-Entropy Loss, Transformer Architecture, Attention Mechanism, LLM Training Task, LLM Training System, Distributed Computing, GPU Optimization.

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References

• (Kumar et al., 2025) ⇒ Komal Kumar, Tajamul Ashraf, Omkar Thawakar, Rao Muhammad Anwer, Hisham Cholakkal, Mubarak Shah, Ming-Hsuan Yang, Phillip H. S. Torr, Salman Khan, and Fahad Shahbaz Khan. (2025). “LLM Post-Training: A Deep Dive Into Reasoning Large Language Models.” doi:10.48550/arXiv.2502.21321
  • NOTES:
    1. Post-Training LLM Algorithm Taxonomy: The paper establishes a clear taxonomy of post-training algorithms (Figure 1), demonstrating how LLM training algorithms extend beyond initial pre-training to include fine-tuning (SFT), reinforcement learning (PPO, DPO, GRPO), and test-time scaling—showcasing the complete optimization lifecycle for LLM parameters.
    2. Parameter-Efficient Training Algorithms: The paper's coverage of LoRA, QLoRA, and adapter methods (Section 4.7 and Table 2) illustrates how modern LLM training algorithms can optimize selective subsets of parameters rather than all weights, directly confirming your wiki's categorization of "Parameter-Efficient Training Algorithms."
    3. Reinforcement Learning for Sequential Decision-Making: The paper's explanation of how RL algorithms (Sections 3.1-3.2) adapt to token-by-token generation frames LLM training as a sequential decision process with specialized advantage functions and credit assignment mechanisms—extending beyond the traditional gradient descent approaches in your wiki.
    4. Process vs. Outcome Reward Optimization: The comparison between Process Reward Models and Outcome Reward Models (Sections 3.1.3-3.1.4) demonstrates a unique aspect of LLM training algorithms not explicitly covered in your wiki: optimization can target either intermediate reasoning steps or final outputs.
    5. Hybrid Training-Inference Algorithms: The paper's extensive coverage of test-time scaling methods (Section 5) reveals that modern LLM training algorithms can span the traditional training-inference boundary, with techniques like Monte Carlo Tree Search and Chain-of-Thought representing algorithmic approaches that continue model optimization during deployment.

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