# A Cycle-Consistency Constrained Framework for Dynamic Solution Space Reduction in Noninjective Regression

arXiv: https://arxiv.org/abs/2507.04659 · HTML: https://mlsanity.com/paper/2507.04659/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 35 references that are in the map.
- First posted on arXiv 7 Jul 2025.

## Builds on (most cited first, 10 of 10)

- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [A Review of Formal Methods applied to Machine Learning](https://mlsanity.com/paper/2104.02466/) (2021)
- [PINNACLE: PINN Adaptive ColLocation and Experimental points selection](https://mlsanity.com/paper/2404.07662/) (2024)
- [Some Fundamental Aspects about Lipschitz Continuity of Neural Networks](https://mlsanity.com/paper/2302.10886/) (2023)
- [OneFlow: Redesign the Distributed Deep Learning Framework from Scratch](https://mlsanity.com/paper/2110.15032/) (2021)
- [Universal Approximation Theorem for Vector- and Hypercomplex-Valued Neural Networks](https://mlsanity.com/paper/2401.02277/) (2024)
- [Lipschitz Properties for Deep Convolutional Networks](https://mlsanity.com/paper/1701.05217/) (2017)
- [Deep Generative Models: Complexity, Dimensionality, and Approximation](https://mlsanity.com/paper/2504.00820/) (2025)
- [ExoMDN: Rapid characterization of exoplanet interior structures with Mixture Density Networks](https://mlsanity.com/paper/2306.09002/) (2023)
- [Deep convolutional networks for automated detection of posterior-element fractures on spine CT](https://mlsanity.com/paper/1602.00020/) (2016)

## Abstract (arXiv)

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 Phi: X to Y and a backward model Psi: Y to X, where the cycle consistency loss is defined as L cycleb equal L(Y reduce Phi(Psi(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.