Given a random 200 conjectures instead of famous ones, frontier GPT models proposed solutions for about 60 percent, and roughly 60 percent of the counterexamples were off-the-shelf
AspireAI community · arXiv
AI-assisted mathematics is usually evaluated on the set of recent high-profile breakthroughs, which overstates how hard the average open problem is. This work builds OpenConjecture from conjectures in arXiv math papers published since February 2026 and applies frontier GPT models to a random sample of 200 over three passes with no problem-specific guidance. Models produced candidate solutions for roughly 60 percent of the conjectures, with counterexamples about 1.3 times more common than proofs; they proposed counterexamples to 70 conjectures and proofs to 55, and 84 percent of those held up to LLM review. Of the counterexamples from the first two passes that passed review, roughly 60 percent were classified as off-the-shelf and the remainder as standard constructions. The main caveat is that no expert verification was attempted, so the paper analyses the type of solution rather than confirming any of them.
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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.