## 2 Inference and the INFINITE Methodology  
To develop the INFINITE methodology for assessing AI-generated codes, we discuss key concepts that facilitate problem understanding and simplify the methodology and solution procedure. We define various questions (attempts) that can guide the LLM towards the desired answer. Whenever a question is posed, whether the same or a different one, it is treated as a single query. Following a query, the response may either be a \"Server Busy\" (SB) response or an answer, whether desirable or not. For example, if the same question is asked five times, with the first four yielding an SB response and the fifth providing any answer (desirable or otherwise), this counts as one attempt and five queries. If a non-satisfactory answer is received, a new question--considered a new attempt--is posed. To calculate the average response time per query (\(ARTpQ\)) of a framework, we calculate the mean of the total response times, where response time (\(RT\)) is defined as the duration between a query and the framework's response:  
\[ARTpQ=\frac{\Sigma_{i=1}^{N}RT}{N} \tag{1}\]  
where \(N\) is the total number of queries. When evaluating the performance of LLMs, including the OpenAI family frameworks, it is crucial to assess all intermediate steps in the process \"from the initial question to the desired outcome\". Therefore, we consider and quantify factors such as the adequacy of computational resources needed for output generation, the time required to process each query and provide a response, the number of queries necessary to obtain the desired answer, and the quality of the responses. As previously mentioned, no standard metric for assessing inference effectiveness is found in the existing literature. Some attempts have shown promise, particularly causal inference, in improving the predictive accuracy, fairness, robustness, and explainability of LLMs [37]. Causal inference evaluates assumptions, study designs, and estimation strategies to draw causal conclusions from data. It originates from three frameworks: potential outcomes, causal graphs, and structural equations. Potentialoutcomes concentrate on estimating causal effects, whereas graphical models--especially those based on [PERSON]'s causal graphs--demonstrate causal pathways using directed acyclic graphs (DAGs) to illustrate conditional independence among variables [38; 39; 40]. However, for code-generating tasks, causality is linked to the accuracy of results, particularly regarding whether a change in a model (for instance, switching from manually written code to AI-generated code) causes a genuine improvement in accuracy [41]. It is widely accepted that there are three major components impacting inference performance: Efficiency, Consistency and Accuracy [42; 43; 44]. Efficiency refers to how quickly the model processes and returns responses. It is influenced by (a) Response Time (i.e., the time taken for the model to generate a response after receiving a query); (b) Server Busy Rate (SBR, i.e., the proportion of queries that cannot be processed due to system overload or resource constraints). Consistency refers to how \"clever\" and well trained the model is to be able to produce satisfactory responses with as few attempts as possible. A key indicator is the number of attempts by the user until an acceptable response is obtained. Accuracy refers to the model's reliability in providing a correct answer or making accurate predictions. Numerical predictions may be quantified through a mean relative error, which expresses how closely predicted values match the actual (ground truth) values. To determine and quantify the corresponding parameters that allow for the assessment of these components influencing inference, we propose the INFINITE methodology (Inference Index In Testing Model Effectiveness) along with the introduction of an Inference Index (InI). The steps of the methodology are as follows:  
* First, we identify the key parameters involved in submitting a query, allowing us to measure Efficiency, Consistency, and Accuracy.