Fisher信息可用于分离神经网络中的泛化与记忆
Fisher information and the geometry of memorization in neural networks
这篇论文解释了模型怎么分配容量来记噪声还是学规律，用 Fisher 信息几何就能看清楚，做可解释性研究的可以看看。
研究者在 CIFAR-10 上训练视觉模型，并注入只能靠记忆学习的受控噪声。结果表明，将模型权重投影到 Fisher 信息的前几个特征向量上，可以把通用任务性能与噪声样本的记忆行为分离开。这种解耦在不同网络层之间表现不同。同样的现象也出现在解决合成 in-context learning 任务的小型 transformer 中，并在线性模型里得到解析解的复现。
Fisher information and the geometry of memorization in neural networks
A fruitful approach towards understanding generalization in machine learning involves characterizing how models separate generalizable structure from idiosyncratic or even corrupted features of training data. Fisher information has emerged as a diagnostic tool for this separation, leveraging loss geometry to distinguish generalization from memorization. Here we investigate this connection in vision models trained on CIFAR-10 with controlled noise that can be learned only through memorization. We show that projecting model weights onto the top Fisher eigenvectors decouples general task performance from noisy sample memorization, and we investigate how this decoupling presents differentially across layers. We show that the same phenomena are present in small transformers trained to solve a synthetic in-context learning task, and are reproduced in closed form in a simple, analytically solvable linear model. Our results reveal that Fisher information captures aspects of the geometric structure underlying how neural networks allocate capacity between generalization and memorization.
