Convergence occurs when training loss stops meaningfully improving, indicating the model has learned available patterns. Signs of convergence: Loss plateaus, validation metrics stable, gradient norms decrease, weight changes diminish. Types: Loss convergence: Training loss stops decreasing. Validation convergence: Validation metrics plateau (may diverge from train = overfitting). Weight convergence: Parameters stabilize. Factors affecting convergence: Learning rate (too high = no convergence, too low = slow), model capacity, data quality, optimization algorithm. Convergence vs optimality: Converged model not necessarily optimal. May be local minimum or saddle point. Non-convergence issues: Loss oscillating, NaN, increasing - indicate training problems. Practical convergence: Rarely reach true minimum. Stop when good enough or overfitting. For LLMs: Often train until compute budget exhausted rather than waiting for convergence. Scaling laws predict loss at given compute. Monitoring: Watch loss curves, compare train/val, check learning rate wasnt too aggressive. Early stopping: If validation stops improving, stop before full convergence to prevent overfitting.