Machine-learnable Sets

Standard machine learning pipelines often admit many near-optimal models. These "Rashomon sets" pose a range of challenges and opportunities for uncertainty-aware, robust decision making. They allow users to incorporate domain knowledge and preferences that would otherwise be difficult to specify directly in an objective, and they quantify diversity among valid models for a given training dataset and objective function. However, computation of Rashomon sets, even for simple, interpretable model classes such as sparse decision trees, continues to require immense memory and runtime resources. We present PRAXIS, an algorithm to approximate this Rashomon set with orders of magnitude improvement in runtime and memory usage. We validate that PRAXIS regularly recovers almost all of the full Rashomon set. PRAXIS allows researchers and practitioners to scalably model the Rashomon set for real-world datasets. Code for PRAXIS is available at https://github.com/zakk-h/PRAXIS

The Rashomon effect describes the phenomenon that many models can achieve nearly equivalent performance on the same learning task, with significant ramifications for robustness, feature importance, and customizability. These use cases motivate the computation of Rashomon sets: the set of all models whose regularized loss is near-optimal. Decision trees are one of the few model classes for which Rashomon sets can be fully enumerated, but this computation has always been conditional on a binarization of the original data, either restricting which splits each tree is allowed to make or substantially increasing the complexity of an already difficult combinatorial problem. We introduce the first algorithm that exactly enumerates decision-tree Rashomon sets while exploiting the ordered structure of continuous features. We further develop a relaxation for approximate enumeration and an anytime algorithm that progressively refines the set of candidate thresholds, producing increasingly detailed approximations that converge to the continuous-feature Rashomon set. Experiments show that coarse binarization can miss many trees, important features, and predictive multiplicity; our algorithms achieve orders-of-magnitude speedups over existing enumeration methods, with approximations providing further speedups while maintaining near-perfect recall.

Shani et al. (2026) show that LLM representations broadly recover human category boundaries, while failing to reflect fine-grained typicality structure. Their analysis uses cosine similarity over dense model representations. We revisit their approach using overlap over active sparse autoencoder (SAE) latent sets as a more interpretable similarity measure. We first verify that this set-level measure is meaningful: SAE latent sets can recover union-like compositional structure in controlled toy models and induce semantically coherent neighborhoods in natural text. Extending the human-concepts analysis to SAE set similarities, we find that SAE activation sets do not recover human category boundaries or within-category typicality more faithfully than dense embeddings or residual-stream states, but instead track model-internal similarity structure. To probe this gap further, we study active latent sets under well-controlled semantic modifications, revealing a substantial mismatch between human judgements of conceptual change and change in the SAE active set. We interpret this as evidence that, outside idealised settings, SAE features do not compose via simple bag-of-features semantics.