# Delving into Cascaded Instability: A Lipschitz Continuity View on Image Restoration and Object Detection Synergy

arXiv: https://arxiv.org/abs/2510.24232 · HTML: https://mlsanity.com/paper/2510.24232/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 39 references that are in the map.
- First posted on arXiv 28 Oct 2025.

## Builds on (most cited first, 28 of 28)

- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Visualizing the Loss Landscape of Neural Nets](https://mlsanity.com/paper/1712.09913/) (2017)
- [DETRs Beat YOLOs on Real-time Object Detection](https://mlsanity.com/paper/2304.08069/) (2023)
- [YOLOv10: Real-Time End-to-End Object Detection](https://mlsanity.com/paper/2405.14458/) (2024)
- [Benchmarking Single Image Dehazing and Beyond](https://mlsanity.com/paper/1712.04143/) (2017)
- [Stronger generalization bounds for deep nets via a compression approach](https://mlsanity.com/paper/1802.05296/) (2018)
- [Retinexformer: One-stage Retinex-based Transformer for Low-light Image Enhancement](https://mlsanity.com/paper/2303.06705/) (2023)
- [Ultra-High-Definition Low-Light Image Enhancement: A Benchmark and Transformer-Based Method](https://mlsanity.com/paper/2212.11548/) (2022)
- [Getting to Know Low-light Images with The Exclusively Dark Dataset](https://mlsanity.com/paper/1805.11227/) (2018)
- [A Universal Law of Robustness via Isoperimetry](https://mlsanity.com/paper/2105.12806/) (2021)
- [InstructIR: High-Quality Image Restoration Following Human Instructions](https://mlsanity.com/paper/2401.16468/) (2024)
- [Globally-Robust Neural Networks](https://mlsanity.com/paper/2102.08452/) (2021)
- [Lipschitz constant estimation of Neural Networks via sparse polynomial optimization](https://mlsanity.com/paper/2004.08688/) (2020)
- [Image-Adaptive YOLO for Object Detection in Adverse Weather Conditions](https://mlsanity.com/paper/2112.08088/) (2021)
- [High-resolution Iterative Feedback Network for Camouflaged Object Detection](https://mlsanity.com/paper/2203.11624/) (2022)
- [A Dynamical System Perspective for Lipschitz Neural Networks](https://mlsanity.com/paper/2110.12690/) (2021)
- [A Unified Algebraic Perspective on Lipschitz Neural Networks](https://mlsanity.com/paper/2303.03169/) (2023)
- [Direct Parameterization of Lipschitz-Bounded Deep Networks](https://mlsanity.com/paper/2301.11526/) (2023)
- [LipsFormer: Introducing Lipschitz Continuity to Vision Transformers](https://mlsanity.com/paper/2304.09856/) (2023)
- [Some Fundamental Aspects about Lipschitz Continuity of Neural Networks](https://mlsanity.com/paper/2302.10886/) (2023)
- [FeatEnHancer: Enhancing Hierarchical Features for Object Detection and Beyond Under Low-Light Vision](https://mlsanity.com/paper/2308.03594/) (2023)
- [GDIP: Gated Differentiable Image Processing for Object-Detection in Adverse Conditions](https://mlsanity.com/paper/2209.14922/) (2022)
- [Beyond Image Super-Resolution for Image Recognition with Task-Driven Perceptual Loss](https://mlsanity.com/paper/2404.01692/) (2024)
- [Unsupervised Variational Translator for Bridging Image Restoration and High-Level Vision Tasks](https://mlsanity.com/paper/2408.08149/) (2024)

## Abstract (arXiv)

To improve detection robustness in adverse conditions (e.g., haze and low light), image restoration is commonly applied as a pre-processing step to enhance image quality for the detector. However, the functional mismatch between restoration and detection networks can introduce instability and hinder effective integration -- an issue that remains underexplored. We revisit this limitation through the lens of Lipschitz continuity, analyzing the functional differences between restoration and detection networks in both the input space and the parameter space. Our analysis shows that restoration networks perform smooth, continuous transformations, while object detectors operate with discontinuous decision boundaries, making them highly sensitive to minor perturbations. This mismatch introduces instability in traditional cascade frameworks, where even imperceptible noise from restoration is amplified during detection, disrupting gradient flow and hindering optimization. To address this, we propose Lipschitz-regularized object detection (LROD), a simple yet effective framework that integrates image restoration directly into the detector's feature learning, harmonizing the Lipschitz continuity of both tasks during training. We implement this framework as Lipschitz-regularized YOLO (LR-YOLO), extending seamlessly to existing YOLO detectors. Extensive experiments on haze and low-light benchmarks demonstrate that LR-YOLO consistently improves detection stability, optimization smoothness, and overall accuracy.