SuperARC: A Test for General and Super Intelligence Based on First Principles of Recursion Theory and Algorithmic Probability

Alberto Hernández-Espinosa, Luan Ozelim, Felipe S. Abrahão, Hector Zenil

Abstract: We introduce an open-ended test grounded in algorithmic probability that can avoid benchmark contamination in the quantitative evaluation of frontier models in the context of their Artificial General Intelligence (AGI) and Superintelligence (ASI) claims. Unlike other tests, this test does not rely on statistical compression methods (such as GZIP or LZW), which are more closely related to Shannon entropy than to Kolmogorov complexity and are not able to test beyond simple pattern matching. The test challenges aspects of AI, in particular LLMs, related to features of intelligence of fundamental nature such as synthesis and model creation in the context of inverse problems (generating new knowledge from observation). We argue that metrics based on model abstraction and abduction (optimal Bayesian `inference') for predictive `planning' can provide a robust framework for testing intelligence, including natural intelligence (human and animal), narrow AI, AGI, and ASI. We found that LLM model versions tend to be fragile and incremental as a result of memorisation only with progress likely driven by the size of training data. The results were compared with a hybrid neurosymbolic approach that theoretically guarantees universal intelligence based on the principles of algorithmic probability and Kolmogorov complexity. The method outperforms LLMs in a proof-of-concept on short binary sequences. We prove that compression is equivalent and directly proportional to a system's predictive power and vice versa. That is, if a system can better predict it can better compress, and if it can better compress, then it can better predict. Our findings strengthen the suspicion regarding the fundamental limitations of LLMs, exposing them as systems optimised for the perception of mastery over human language.