Jürgen Schmidhuber
Publications
Interestingness as an Inductive Heuristic for Future Compression Progress
One of the bottlenecks on the way towards recursively self-improving systems is the challenge of interestingness: the ability to prospectively identify which tasks or data hold the potential for future progress. We formalize interestingness as an inductive heuristic for future compression progress and investigate its predictability using tools from Kolmogorov Complexity and Algorithmic Statistics. By analyzing complexity-runtime profiles under Length, Algorithmic, and Speed priors, we demonstrate that the inductive property of interestingness -- the capacity for past progress to signal future discovery -- is theoretically viable and empirically supported. We prove that expected future progress depends exponentially on the recency of the last observed breakthrough. Furthermore, we show that the Algorithmic Prior is significantly more optimistic than the Length Prior, yielding a quadratic increase in expected discovery for the same observed profile. These findings are experimentally confirmed across three diverse universal computational paradigms.
RPRA: Predicting an LLM-Judge for Efficient but Performant Inference
Large language models (LLMs) face a fundamental trade-off between computational efficiency (e.g., number of parameters) and output quality, especially when deployed on computationally limited devices such as phones or laptops. One way to address this challenge is by following the example of humans and have models ask for help when they believe they are incapable of solving a problem on their own; we can overcome this trade-off by allowing smaller models to respond to queries when they believe they can provide good responses, and deferring to larger models when they do not believe they can. To this end, in this paper, we investigate the viability of Predict-Answer/Act (PA) and Reason-Predict-Reason-Answer/Act (RPRA) paradigms where models predict -- prior to responding -- how an LLM judge would score their output. We evaluate three approaches: zero-shot prediction, prediction using an in-context report card, and supervised fine-tuning. Our results show that larger models (particularly reasoning models) perform well when predicting generic LLM judges zero-shot, while smaller models can reliably predict such judges well after being fine-tuned or provided with an in-context report card. Altogether, both approaches can substantially improve the prediction accuracy of smaller models, with report cards and fine-tuning achieving mean improvements of up to 55% and 52% across datasets, respectively. These findings suggest that models can learn to predict their own performance limitations, paving the way for more efficient and self-aware AI systems.
Planning to Explore: Curiosity-Driven Planning for LLM Test Generation
The use of LLMs for code generation has naturally extended to code testing and evaluation. As codebases grow in size and complexity, so does the need for automated test generation. Current approaches for LLM-based test generation rely on strategies that maximize immediate coverage gain, a greedy approach that plateaus on code where reaching deep branches requires setup steps that individually yield zero new coverage. Drawing on principles of Bayesian exploration, we treat the program's branch structure as an unknown environment, and an evolving coverage map as a proxy probabilistic posterior representing what the LLM has discovered so far. Our method, CovQValue, feeds the coverage map back to the LLM, generates diverse candidate plans in parallel, and selects the most informative plan by LLM-estimated Q-values, seeking actions that balance immediate branch discovery with future reachability. Our method outperforms greedy selection on TestGenEval Lite, achieving 51-77% higher branch coverage across three popular LLMs and winning on 77-84% of targets. In addition, we build a benchmark for iterative test generation, RepoExploreBench, where they achieve 40-74%. These results show the potential of curiosity-driven planning methods for LLM-based exploration, enabling more effective discovery of program behavior through sequential interaction