We introduce the cube bottleneck method, a procedure that repurposes neural-network compression from an efficiency technique into an analytical instrument for measuring sample difficulty. A 4×4×4 spatial bottleneck is inserted between the encoder and the classifier head of a convolutional network. After training, principal-component analysis (PCA) is applied to the bottleneck activations, and the resulting components are correlated with a per-sample difficulty score derived from the model's own confidence. Across five datasets spanning image classification (MNIST, CIFAR-10, CIFAR-100) and intrusion detection (CICIDS2017, UNSW-NB15), the principal components of the bottleneck consistently encode sample difficulty rather than class identity, with Fisher ratios below unity in four of the five datasets. The framework reframes compression as a diagnostic tool, with applications to active learning, curriculum learning, and analyst triage in cybersecurity. Code: https://github.com/Ivelin2022/3d-cube-bottleneck Acknowledgements: The author acknowledges the use of Anthropic's Claude (Claude Opus 4.7) as a writing and analysis assistant during preparation of this manuscript. All experimental design, code implementation, results, and scientific claims are the author's own.
Ivelin Likov (2026) studied this question.