## 2 Key Concepts in Natural Language Processing
### Impact of Prompts and Temperature  
Prompts and temperature settings play a crucial role in the performance of LLMs, particularly in tasks requiring nuanced understanding and accurate predictions.  
The way input prompts are crafted significantly influences the model's output. Techniques such as zero-shot prompting, few-shot prompting, and Retrieval-Augmented Generation (RAG) allow for diverse ways of guiding the model's reasoning process. For instance, zero-shot prompting requires no additional examples and relies entirely on the model's general knowledge, making it efficient for straightforward cases. Few-shot prompting incorporates a small set of examples \(K\) within the input prompt, enabling the model to infer patterns and produce more contextually accurate results:  
\[D_{K}=\{(X_{i},y_{i})\}_{i=1}^{K} \tag{7}\]  
where \(X_{i}\) represents the input text (clinical case), and \(y_{i}\) is the corresponding diagnosis. This set helps the model learn the structure of the input and apply it to a new case. Retrieval-Augmented Generation leverages external knowledge sources to supplement the model's responses, improving precision in complex scenarios.  
The temperature \(T\) is a hyperparameter that controls the randomness of the model's output. Temperature adjusts the probability distribution of the model's predictions, with lower temperatures constraining the model to produce more deterministic and focused responses, which is beneficial for tasks demanding accuracy, such as medical diagnoses. Conversely, higher temperatures introduce variability, which may lead to creative but less consistent outputs. Mathematically, the softmax function, used in generating predictions, is modified by temperature as follows:  
\[P(y|X)=\frac{\exp\Bigl{(}\frac{z_{y}}{T}\Bigr{)}}{\sum_{y^{\prime}}\exp\Bigl{(} \frac{z_{y^{\prime}}}{T}\Bigr{)}} \tag{8}\]  
where \(Z_{y}\) is the score (logit) for the class \(y\), \(P(y\,|\,X)\) is the probability of a particular class \(y\) given input \(X\). When \(T\) is small (e.g., 0.1), the softmax output becomes more concentrated, meaning the model will tend to choose the most likely outcome. This is useful for precision when a clear diagnosis is present. When \(T\) is large (e.g., 2), the output becomes more uniform, allowing the model to explore a wider range of potential diagnoses, which is helpful for ensuring sensitivity to less obvious but relevant diagnoses, particularly in cases with rare or complex symptoms.  
By carefully selecting the input and tailoring the prompt techniques (zero-shot, few-shot, and RAG), we can maximize both precision and sensitivity in the diagnostic predictions. The model's ability to handle diverse and complex clinical cases, especially rare diseases, is enhanced by the combination of RAG, few-shot learning, and the dynamic adjustment of temperature. Zero-shot learning allows the model to make predictions from a baseline understanding, while few-shot learning helps it generalize from prior examples, and RAG enriches the model's knowledge with external, case-specific information.  
By leveraging these techniques, we ensure that the model remains flexible and capable of delivering accurate and reliable diagnoses. Temperature plays a key role in fine-tuning the balance between precision (focusing on the most probable diagnoses) and sensitivity (exploring less common but relevant possibilities), making the overall diagnostic system more robust and adaptable to various clinical scenarios. This study sheds light on the optimal configurations for leveraging LLMs in medical diagnosis prediction, particularly for Spanish-language clinical cases.