Adaptive Rigor in AI System Evaluation using Temperature-Controlled Verdict Aggregation via Generalized Power Mean
Organizations: Independent Researcher, Budva, Montenegro.
Abstract
Existing evaluation methods for LLM-based AI systems, such as LLM-as-a-Judge, verdict systems, and NLI, do not always align well with human assessment because they cannot adapt their strictness to the application domain. This paper presents Temperature-Controlled Verdict Aggregation (TCVA), a method that combines a five-level verdict-scoring system with generalized power-mean aggregation and an intuitive temperature parameter T [0.1, 1.0] to control evaluation rigor. Low temperatures yield pessimistic scores suited for safety-critical domains; high temperatures produce lenient scores appropriate for conversational AI. Experimental evaluation on three benchmark datasets with human Likert-scale annotations (SummEval and USR) shows that TCVA achieves correlation with human judgments comparable to RAGAS on faithfulness (Spearman = 0.667 vs. 0.676) while consistently outperforming DeepEval. The method requires no additional LLM calls when adjusting the temperature parameter.
Figures & tables
| Level | Weight | Semantics | Example of usage |
|---|---|---|---|
| Fully | 1.0 | Fully satisfied | The atomic statement (part of the AI response text) is fully supported by facts from the context of the AI system |
| Mostly | 0.9 | Mostly satisfied | The atomic statement is completely based on facts, but the structure of the text is slightly changed |
| Partially | 0.7 | Partially satisfied | The atomic statement is about half generated from facts and half made up by the AI model, but overall the answer is still relevant to the query |
| Minor | 0.3 | Minimally affected | The atomic statement is not explicitly confirmed in the facts used for generation, but a number of phrases or individual words are still present in the facts |
| None | 0.0 | Not satisfied | There is no connection between the generated atomic statement and the facts used by the AI model to generate the answer |
| Name | Function | Characteristics | |
|---|---|---|---|
| Minimum | Extreme pessimism: only the worst value is taken into account | ||
| — | Strong shift to minimum | ||
| Harmonic | Shift to small values | ||
| Geometric | Multiplicative mean | ||
| Arithmetic | Standard average | ||
| Quadratic | Root Mean Square |
| Interpretation | ||
|---|---|---|
| 0.773 | Approximately , strict estimate | |
| 0.809 | Strong bias towards the minimum | |
| 0.838 | Noticeable bias towards the minimum | |
| 0.848 | Harmonic mean | |
| 0.857 | Geometric mean | |
| 0.867 | Arithmetic mean |
| Type of mean | Explanation | ||
|---|---|---|---|
| 0.1 | Close to minimum | Maximum strict, even one bad verdict is critical | |
| 0.3 | Close to Harmonic | Strict, focus on worst verdicts | |
| 0.5 | Arithmetic | Balanced, each verdict has equal contribution | |
| 0.7 | Quadratic | Forgiving, focus on best verdicts | |
| 0.9 | Close to maximum | Maximum lenient, good verdicts dominate the final score |
| Method | SummEval | SummEval-Rel | USR |
|---|---|---|---|
| (Faithfulness) | (Relevancy) | (Dialogue) | |
| TCVA ( ) | 0.642 | 0.476 | 0.153 |
| TCVA ( ) | 0.642 | 0.476 | 0.153 |
| TCVA ( ) | 0.663 | 0.480 | 0.168 |
| TCVA ( ) | 0.664 | 0.452 | 0.173 |
| SummEval | SummEval-Rel | USR | ||||
|---|---|---|---|---|---|---|
| Method | MAE | MAE | MAE | |||
| TCVA (best ) | 0.527 | 0.356 | 0.369 | 0.211 | 0.143 | 0.501 |
| RAGAS | 0.535 | 0.259 | 0.333 | 0.365 | 0.140 | 0.516 |
| DeepEval | 0.302 | 0.325 | 0.239 | 0.352 | 0.367 | |
| Weight scheme | SummEval | SummEval-Rel | USR |
|---|---|---|---|
| Default | 0.667 | 0.480 | 0.226 |
| Linear | 0.668 | 0.472 | 0.230 |
| Aggressive | 0.664 | 0.492 | 0.226 |
| Conservative | 0.669 | 0.478 | 0.230 |
| (variation) | 0.005 | 0.020 | 0.004 |
| Dataset | Method | 95% CI | Paired test | |
|---|---|---|---|---|
| SummEval | TCVA (best ) | 0.667 | [0.561, 0.755] | , |
| RAGAS | 0.676 | [0.571, 0.762] | ||
| DeepEval | 0.395 | [0.251, 0.525] | ||
| SummEval-Rel | TCVA (best ) | 0.480 | [0.367, 0.583] | , |
| RAGAS | 0.411 | [0.286, 0.528] | ||
| DeepEval | 0.315 | [0.183, 0.439] |
| SummEval | SummEval-Rel | USR | ||||
|---|---|---|---|---|---|---|
| Configuration | ||||||
| A. Full TCVA | 0.667 | — | 0.480 | — | 0.226 | — |
| B. w/o Penalty | 0.610 | 0.485 | 0.221 | |||
| C. Arithmetic Mean | 0.663 | 0.480 | 0.218 | |||
| D. Binary Verdicts | 0.615 | 0.236 | 0.256 | |||
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