"Which model should I use?" is easier once you know what a model is and what the labels mean. Prices below were verified against each provider's own pages on 13 November 2026.
What an LLM is
An LLM turns text into tokens, passes them through a neural network and outputs a probability for every possible next token; generating a reply means choosing one, appending it and repeating. Four papers explain the field: Attention Is All You Need (the Transformer, 2017), Scaling Laws for Neural Language Models (2020), Language Models are Few-Shot Learners (2020) and InstructGPT (2022).
Why attention shapes your bill
The Transformer paper's own complexity comparison lists self-attention as costing operations proportional to the square of the sequence length per layer. That is one reason context windows have limits and long prompts are expensive to serve.
Claude vs ChatGPT vs Gemini through their APIs
USD per million tokens, input / output (tier placement is ours): flagship Claude Fable 5.2 $8 / $40, GPT-6 Astra $10 / $50, Gemini 4 Carbon $2 / $10; smallest tier Claude Haiku 5.5 and GPT-6 Luna both $0.10 / $0.50. Gemini 4 Carbon and Argon double on 1 December 2026. Current Claude models list a 1M-token window, GPT-6 1.05M, Gemini 4 1M (Anthropic, OpenAI, Google). For 1,000 uncached chat turns of 1,500 input and 400 output tokens: Sonnet 5.5 $7.00, GPT-6.1 Terra $3.50, Gemini 4 Hydrogen $5.25. A side-by-side with caching and batch rules is in this Claude vs ChatGPT vs Gemini comparison.
Open weight vs open source
Open weight means the parameters are published. Under the Open Source Initiative's Open Source AI Definition 1.0, open source AI also needs sufficiently detailed training-data information and the complete training and running code, all under OSI-approved terms. Publisher examples: gpt-oss is Apache 2.0 and Whisper is MIT. Before building on a model, check the licence for weights and code, commercial limits, acceptable-use rules and hosting cost. A checklist is in this guide to open source vs open weight LLMs.
