AI 中文总结
本文提出锐度感知模式连通性（SMC），将模式连通性重构为邻域鲁棒路径优化问题，通过一阶锐度感知近似强制整条曲线平坦，在CIFAR-10-C上提升高达6.09%准确率，并产生负损失屏障，验证了路径级平坦性对鲁棒权重空间插值的有效性。
AI 中文摘要
独立训练且性能相近的深度神经网络可以通过权重空间中的低损失参数曲线连接起来，这一现象被称为模式连通性（MC）。这一几何性质支撑了权重平均、模型集成和模型合并等实用技术。我们认为低损失连通性是一个不完整的几何标准：它仅控制一维轨迹上的损失，而对其周围的权重空间邻域不加约束，因此优化得到的曲线可能穿越在分布偏移下变得脆弱的尖锐脊线。因此，我们将模式连通性重新表述为一个邻域鲁棒的路径优化问题，寻求一条其整个局部邻域都保持低损失的曲线。我们提出了锐度模式连通性（SMC），该方法对由此产生的极小极大泛函应用一阶锐度感知近似，强制整条曲线而非仅曲线本身保持平坦。我们推导了一种在该锐度感知目标下用于连通路径的实用优化算法。在CIFAR-10-C的严重模糊损坏下，SMC相比标准MC实现了高达6.09%的绝对准确率提升。值得注意的是，SMC产生了负的损失屏障，这意味着在优化路径内部点获得的模型可以优于端点损失的平均值。这些结果在CIFAR-10和ImageNet-100上的ResNet-18、VGG16-BN和ViT-Tiny上得到验证，确立了路径级平坦性作为鲁棒权重空间插值的实用原则。
英文摘要
Deep neural networks that are independently trained to similar performance can be connected by low-loss parametric curves in weight space, a phenomenon known as Mode Connectivity (MC). This geometric property underpins practical techniques such as weight averaging, model ensembling, and model merging. We argue that low-loss connectivity is an incomplete geometric criterion: it controls loss only along a one-dimensional trajectory while leaving the surrounding weight-space neighborhood unconstrained, so the optimized curve may traverse sharp ridges that become fragile under distribution shift. We therefore reformulate mode connectivity as a neighborhood-robust path optimization problem, seeking a curve whose entire local neighborhood maintains low loss. We propose Sharp Mode Connectivity (SMC), which applies a first-order sharpness-aware approximation to the resulting minimax functional, enforcing flatness along the entire curve rather than only on it. We derive a practical optimization algorithm for connectivity paths under this sharpness-aware objective. Under severe blur corruptions from CIFAR-10-C, SMC achieves up to 6.09\% absolute accuracy improvement over standard MC. Remarkably, SMC produces negative loss barriers, meaning that models obtained at interior points of the optimized path can outperform the average endpoint loss. These results, validated across ResNet-18, VGG16-BN, and ViT-Tiny on CIFAR-10 and ImageNet-100, establish path-wise flatness as a practical principle for robust weight-space interpolation.
