## 3 Methods
### Language Models
#### 3.3.2 Decoder-Based Models  
The evolution of LLMs continued with the release of the GPT (Generative Pretrained Transformer) series, including GPT-2 in 2019 [21], GPT-3 in 2020 [15], and GPT-4 in 2023 [22], which introduced autoregressive modeling for generating coherent and contextually accurate paragraphs. Unlike BERT and ELECTRA, which focus on understanding text, GPT models excel in generating and completing sentences, making them versatile for a wider range of language tasks, from text generation to nuanced error correction.  
Following GPT, Meta AI's Llama (Large Language Model Meta AI) [14] has aimed to combine high performance with greater accessibility. Llama offers several advantages over previous models, including being open-source, which allows researchers and developers to access its model weights and code freely. This openness encourages innovation, enabling the community to fine-tune the model for specific applications or research needs. Additionally, Llama is designed with efficiency in mind, requiring fewer computational resources compared to models like GPT-4. It is able to run effectively on smaller hardware setups while still achieving competitive performance, making it an attractive option for those without access to extensive computing infrastructure.  
To evaluate the capabilities of various LLMs in performing nuanced linguistic tasks, we conducted a zero-shot evaluation on five models: GPT-4o, Llama-3.2-1B, Llama-3.2-3B, Llama-3.1-8B, and Llama-3.1-70B. In this context, zero-shot evaluation refers to assessing each model's ability to perform grammatical error detection and correction on a dataset of German children's literature without any additional fine-tuning specific to this task. Zero-shot learning allows the models to rely on their inherent language processing capabilities derived from extensive pretraining, providing insights into their adaptability to tasks they were not explicitly trained to handle.  
Each model brings unique attributes to this evaluation. GPT-4o, the latest high-intelligence flagship model, is designed for complex, multi-step tasks and represents an advancement in the GPT series with over 200 billion parameters, which surpasses GPT-4's 175 billion. This allows for nuanced and highly detailed responses while maintaining efficiency and speed, making GPT-4o suitable for intricate tasks at a lower cost and faster response time than its predecessor, GPT-4 Turbo. However, using GPT-4o still incurs a cost, with pricing set at USD 2.50 per million input tokens and CAD 10.00 per million output tokens, with a discounted rate of CAD 1.25 per million input tokens and CAD 5.00 per million output tokens through the Batch API. Llama-3.2, a more recent release from Meta AI, offers lightweight and highly efficient models with parameter counts of 1.24 billion for Llama-3.2-1B and 3.21 billion for Llama-3.2-3B, aimed at decoder-based text applications. Meanwhile, Llama-3.1, an earlier model, includes larger parameter versions like the 8B and 70B we tested, delivering potentially richer linguistic and contextual understanding due to their higher parameter counts. Unlike GPT-4o, all Llama models are open-source and freely accessible on the Hugging Face and Meta websites, allowing for broader experimentation and customization without associated usage costs. For this evaluation, we utilized the OpenAI API to access GPT-4o, while all Llama models were tested through their instruct versions available on Hugging Face.