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CIRCE read a problem's constraint structure to predict whether an LLM would get it right, before the attempt

AspireAI community · arXiv
Knowing whether a problem is too hard for a model before the model tries can guide routing, test-time compute allocation, and whether an agent needs a new tool. Existing estimators use the problem text, LLM-annotated difficulty labels, or post-hoc signals such as hidden states, and none use the constraint structure inherent in the problem: which variables to assign and how the constraints over them interact. CIRCE extracts that structure by using a cheap LLM to build a constraint intermediate representation which compiles deterministically into a constraint graph. Across seven reasoning benchmarks spanning SAT, logic and math, and four LLMs, even a randomly initialised GNN encoder improved predictions of response correctness, cutting negative log-likelihood from 0.465 to 0.423 and raising AUROC from 0.691 to 0.727 against the strongest baseline for each metric.
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One distance function matched sparse-autoencoder features across layers and compressed feature circuits into supernodes
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.
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