Making the reward a hyperbolic distance instead of a weighted sum let inverse reinforcement learning expose non-separable conjunctions between features
AspireAI community · arXiv
Inverse reinforcement learning seeks to infer the reward function underlying observed behavior, and its predictive accuracy and interpretability depend on how that reward is computed from underlying features. Prior reward functions were implemented with linear weights, neural networks or other approximators, none of which assume anything about the geometry of the feature space. Inspired by geometric organization observed in neural circuits, Hyperbolic inverse reinforcement learning parameterizes reward as a function of the hyperbolic distance between the feature vector and a learned parameter vector, alongside its Euclidean-distance variant. The hyperbolic approach matched state-of-the-art models on established benchmarks and did better in the low-data limit and across dense environments. Applied to human navigation among multiple exhibits in a museum room, it revealed reward structure depending not only on individual exhibit-distance features but also on non-separable conjunctions between them. The limitation is that the museum experiment is a single navigation dataset, so the interpretability payoff rests on one domain rather than on a broad behavioural suite.
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Two sparse-autoencoder analyses have resisted scaling: matching semantically similar features across layers, and compressing large feature circuits into interpretable supernodes. This paper argues both are the same underlying problem, estimating semantic distances between SAE features that sit on different activation manifolds. Its representation treats each feature not as a single decoder vector but as an activation-weighted distribution over the hidden states expressing it, projects those distributions into a shared reference space, and compares them with Wasserstein distance. The representation is proved invariant to activation rescaling and stable under perturbation, and recovers true matches under finite-sample margin conditions. Empirically it outperformed decoder-vector and LLM-based baselines and captured subtle functional distinctions between related features, and it compressed large feature circuits into interpretable supernodes automatically. The limitation is that this is interpretability tooling: the paper demonstrates better feature matching and circuit compression, not that downstream interpretability claims become more accurate.