causal language modeling

**Causal Language Modeling** is **the fundamental training paradigm for autoregressive language models where each token predicts the next token sequentially — enabling generation of coherent text by learning conditional probability distributions P(token_i | token_1...token_i-1)**. **Training Architecture:** - **Causal Masking**: attention mechanism masks future tokens during training by setting attention scores to -∞ for positions beyond current token — prevents information leakage and enforces causal dependency structure in models like GPT-2, GPT-3, and Llama 2 - **Teacher Forcing**: ground truth tokens from training data fed as input at each step rather than model predictions — stabilizes training convergence and reduces error accumulation but creates train-test mismatch - **Cross-Entropy Loss**: standard loss function computing -log(p_correct_token) with softmax over vocabulary (typically 50K tokens in GPT-style models) — optimizes likelihood of actual next tokens - **Context Window**: fixed sequence length (e.g., 2048 tokens in GPT-2, 4096 in Llama 2, 8192 in recent models) determining maximum input length for attention computation **Decoding and Inference:** - **Greedy Decoding**: selecting highest probability token at each step — fast but prone to suboptimal solutions and error accumulation - **Temperature Scaling**: dividing logits by temperature parameter (T=0.7-1.0) before softmax — lower T sharpens distribution for deterministic outputs, higher T adds randomness - **Top-K and Top-P Sampling**: restricting vocabulary to top K highest probability tokens or cumulative probability P (nucleus sampling) — reduces hallucination probability by 40-60% compared to greedy - **Beam Search**: maintaining B best hypotheses (B=3-5 typical) and selecting highest likelihood complete sequence — computationally expensive but achieves better perplexity **Practical Challenges:** - **Exposure Bias**: model trained with teacher forcing but infers with own predictions — causes error compounding in long sequences with 15-25% performance degradation - **Token Distribution Shift**: training vs inference token distributions diverge, especially for rare tokens with <0.1% frequency - **Vocabulary Limitations**: fixed vocabulary cannot handle out-of-distribution words or proper nouns — subword tokenization mitigates this issue - **Sequence Length Limitations**: standard transformers with quadratic attention complexity cannot efficiently process sequences >16K tokens without approximations **Causal Language Modeling is the cornerstone of modern generative AI — enabling models like GPT-4, Claude, and Llama to generate coherent multi-paragraph text through probabilistic next-token prediction.**