parameter count

Parameter count refers to the total number of trainable weights and biases in a neural network model, serving as the primary indicator of model capacity — its ability to learn and represent complex patterns in data. Parameters are the numerical values that the model adjusts during training through gradient-based optimization to minimize the loss function. In transformer-based language models, parameters are distributed across several component types: embedding layers (vocabulary size × hidden dimension — mapping tokens to vectors), self-attention layers (4 × hidden² per layer for query, key, value, and output projection matrices, plus smaller bias terms), feedforward layers (2 × hidden × intermediate_size per layer — typically the largest component, with intermediate_size usually 4× hidden), layer normalization parameters (2 × hidden per normalization layer — scale and shift), and the output projection/language model head (hidden × vocabulary). For a standard transformer: total parameters ≈ 12 × num_layers × hidden² + 2 × vocab_size × hidden. Notable parameter counts include: BERT-Base (110M), GPT-2 (1.5B), GPT-3 (175B), LLaMA-2 (7B/13B/70B), GPT-4 (~1.8T estimated, MoE), and Gemini Ultra (undisclosed). Parameter count affects model behavior in several ways: larger models generally achieve lower training loss (scaling laws predict performance as a power law of parameters), larger models demonstrate emergent capabilities (abilities appearing suddenly at specific scales), and larger models require more memory (each parameter in FP16 requires 2 bytes — a 70B model needs ~140GB just for weights). However, parameter count alone does not determine model quality — training data quantity and quality, architecture design, and training methodology all significantly influence performance. The Chinchilla scaling laws showed that many models were over-parameterized and under-trained, and efficient architectures like MoE can achieve large parameter counts with proportionally lower computational cost.