Unpacking Interpretability: Human-Centered Criteria for Optimal Combinatorial Solutions

Human decision-makers often face choices about complex cases with many potentially relevant features, but limited bandwidth to inspect and integrate all available information. In such settings, we study algorithms that highlight a small subset of case-specific features for human consideration, rather than producing a single prediction or recommendation. We model highlighting as a constrained information policy that selects a small number of features to reveal. A central issue is how humans interpret the algorithm's choice of features: a sophisticated agent correctly conditions on the selection rule, while a naive agent updates only on revealed feature values and treats the selection event as exogenous. We show that optimizing highlighting for sophisticated agents can be computationally intractable, even in simple discrete and binary settings, whereas optimizing for naive agents is tractable as long as the maximal bandwidth is fixed. We also show that a highlighting policy that is optimal for sophisticated agents can perform arbitrarily poorly when deployed to naive agents, motivating robust, implementable alternatives. We illustrate our framework in a calibrated empirical exercise based on the American Housing Survey. Overall, our results establish the value of highlighting a context-specific set of features rather than a fixed one as a practically appealing and computationally feasible tool for achieving human-algorithm complementarity.

Humans often find good solutions to combinatorial optimization problems that are computationally hard even for advanced computer algorithms. In the Euclidean traveling salesman problems (TSP), people rapidly produce tours that are near-optimal, despite severe limits on time and computation. What makes a tour human-like, and how might such solutions be learned? Here we address these questions through a large-scale behavioral and computational investigation of human performance in Euclidean TSP. We sampled a broad space of TSP instances, collected human solutions, and compared them with neural policies based on Pointer Networks, which are recurrent neural networks with an attention-based pointing mechanism that define probability distributions over valid tours. We trained these networks under multiple objectives, including reinforcement learning (RL), supervised learning from optimal tours, supervised learning from human tours, and RL fine-tuning after optimal-supervised pretraining. Human tours were not identical to optimal tours, but occupied a near-optimal geometric basin: they shared many structural properties with optimal solutions while preserving systematic human-specific deviations. The best account of human tours was not direct imitation of optimal tours, but a model pretrained on optimal tours, fine-tuned by RL, and decoded through $\text{Best-of-}N$ sampling. These findings suggest that human-like solutions may emerge from a combination of structured supervised learning, RL, and test-time search, echoing computational principles underlying many modern artificial intelligence systems.

Mechanistic interpretability aims to explain neural model behaviour by reverse-engineering learned computational structure into human-understandable components. Without a formal framework, however, mechanistic explanations cannot be objectively verified, compared, or composed. We introduce compositional interpretability, a category-theoretic framework grounded in the principles of compositionality and minimum description length. Compositional interpretations are pairs of syntactic and semantic mappings that must commute to enforce consistency between a model's decomposition and its observed behaviour. We deconstruct explanation quality into measures of faithfulness and complexity to cast interpretability as a constrained optimisation problem, and introduce compressive refinement to systematically restructure models into simpler parts without altering their function. Finally, we derive a parsimony criterion under which syntactic compression theoretically guarantees more concise, human-aligned explanations. Our framework situates prominent mechanistic methods as subclasses of refinement, and clarifies why their compressibility heuristics tend to align with human interpretability. Our work provides a measurable, optimisable blueprint for automating the discovery and evaluation of mechanistic explanations.