LAF-Based Evaluation and UTTL-Based Learning Strategies with MIATTs

Abstract

In many real-world machine learning (ML) applications, the true target cannot be precisely defined due to ambiguity or subjectivity information. To address this challenge, under the assumption that the true target for a given ML task is not assumed to exist objectively in the real world, the EL-MIATTs (Evaluation and Learning with Multiple Inaccurate True Targets) framework has been proposed. Bridging theory and practice in implementing EL-MIATTs, in this paper, we develop two complementary mechanisms: LAF (Logical Assessment Formula)-based evaluation algorithms and UTTL (Undefinable True Target Learning)-based learning strategies with MIATTs, which together enable logically coherent and practically feasible modeling under uncertain supervision. We first analyze task-specific MIATTs, examining how their coverage and diversity determine their structural property and influence downstream evaluation and learning. Based on this understanding, we formulate LAF-grounded evaluation algorithms that operate either on original MIATTs or on ternary targets synthesized from them, balancing interpretability, soundness, and completeness. For model training, we introduce UTTL-grounded learning strategies using Dice and cross-entropy loss functions, comparing per-target and aggregated optimization schemes. We also discuss how the integration of LAF and UTTL bridges the gap between logical semantics and statistical optimization. Together, these components provide a coherent pathway for implementing EL-MIATTs, offering a principled foundation for developing ML systems in scenarios where the notion of "ground truth" is inherently uncertain. An application of this work's results is presented as part of the study available at https://www.qeios.com/read/EZWLSN.