通过循环一致性约束，实现无需先验的多输出回归动态空间压缩。
A Cycle-Consistency Constrained Framework for Dynamic Solution Space Reduction in Noninjective Regression
- 构建正反向模型闭环，以循环一致性损失驱动训练。
- 合成数据上重建误差低于0.003，性能提升约30%。
- 适合无监督场景，减少人工干预，适用于复杂逆问题。
针对多输出模型在非单射回归任务中对预设概率分布和先验知识的强依赖问题，本文提出一种基于循环一致性的数据驱动训练框架。该方法联合优化前向模型Φ: X → Y 和反向模型Ψ: Y → X，循环一致性损失定义为L_cycle = L(Y − Φ(Ψ(Y)))（反之亦然）。通过最小化该损失，框架建立生成与验证相融合的闭环机制，无需手动规则设计或先验分布假设。在归一化合成数据和模拟数据上的实验表明，所提方法实现的循环重建误差低于0.003，在评估指标上相较基线模型提升约30%。此外，该框架支持无监督学习，显著降低对人工干预的依赖，展现出在非单射回归任务中的潜在优势。
原文摘要 · Abstract (English)
To address the challenges posed by the heavy reliance of multi-output models on preset probability distributions and embedded prior knowledge in non-injective regression tasks, this paper proposes a cycle consistency-based data-driven training framework. The method jointly optimizes a forward model Φ: X to Y and a backward model Ψ: Y to X, where the cycle consistency loss is defined as L _cycleb equal L(Y reduce Φ(Ψ(Y))) (and vice versa). By minimizing this loss, the framework establishes a closed-loop mechanism integrating generation and validation phases, eliminating the need for manual rule design or prior distribution assumptions. Experiments on normalized synthetic and simulated datasets demonstrate that the proposed method achieves a cycle reconstruction error below 0.003, achieving an improvement of approximately 30% in evaluation metrics compared to baseline models without cycle consistency. Furthermore, the framework supports unsupervised learning and significantly reduces reliance on manual intervention, demonstrating potential advantages in non-injective regression tasks.
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