Efficient Local Intrinsic Dimensionality Estimation in Evolving Deep Representations

Local intrinsic dimensionality (LID) provides insight into the behavior of individual training points in deep neural networks, with applications including adversarial detection, prevention of dimensional collapse in self-supervised learning, and identification of untruthful responses from large language models (LLMs). In such contexts, efficient LID estimation has depended on the use of mini-batches, due to the high cost of computing neighborhoods in latent space. However, estimation with respect to small subsets of the training data usually reflects the dimensionality of the global manifold structure rather than the intended local distribution around each point. In this paper, we propose the Nearest Distance Cache (NDC), a method that improves the locality of LID estimation by reusing nearest-neighbor distances observed in past mini-batches. This strategy faces two key challenges: representations evolve over time, and limited memory prevents storing all past distances. To address these, NDC maintains a compact cache of nearest distances per example and uses window-based change detection to discard outdated samples affected by distributional drift. We also evaluate NDC on two tasks: an autoencoder trained on synthetic data with known ground-truth LID, and a ResNet trained on CIFAR-10. Results show that NDC captures local properties of deep representations not revealed by single mini-batch estimates.