Researchers at Google have trained a language model to improve itself using only a short list of topics, with no human-written questions or answers anywhere in the loop. The paper, posted to arXiv on 23 October 2026, calls the method On-Policy Self-Training, or OPST. Five of the six authors (Leon Sick, Lukas Hoyer, Yannick Strümpler, Christian Reisswig, and Federico Tombari) are listed with Google. The sixth, Timo Ropinski, is at Ulm University, and Sick did the work during a Google internship.

Here is how it works. The model gets a coarse topic description and invents its own practice questions. It then writes out reasoning for each one, which the paper treats as privileged information, and learns from that output. No stronger teacher model, answer key, or curated problem set takes part.

The headline numbers come from Gemma 4 E2B, the smaller of two Gemma models tested. In its non-thinking mode, MMLU rose from 37.5 to 47.7, GPQA from 28.8 to 32.8, and HellaSwag from 48.7 to 56.2. The average across the benchmarks moved from 38.3 to 45.6. With thinking switched on, GSM8K (grade-school math) climbed from 72.7 to 80.9, and the average went from 58.4 to 63.0.

The larger Gemma 4 E4B shows the same pattern at a smaller scale. Its non-thinking MMLU went from 54.3 to 61.9, and its thinking-mode GSM8K from 84.4 to 93.0. An appendix applies the method to Qwen3-4B-Base, a pretrained model with no instruction tuning, and reports an average gain from 66.7 to 72.7, with GSM8K jumping from 79.7 to 93.0.

The method also reaches images. Trained on unlabeled pictures alone, E2B improved its VQAv2 accuracy (a visual question-answering test) from 49.1 to 56.0. E4B went from 55.9 to 59.2 on the same test.

The paper’s claim that skills carry over to untrained domains deserves a careful reading. When the authors trained on three domains at once and tested on others, the out-of-domain average moved only from 43.6 to 44.4, and MATH-500 fell by 4.9 points. That is retention, not transfer. The model does not forget much, but it does not get better at material it never studied.

Two limits frame everything above. Every result is a comparison against the untouched starting model, so the paper establishes that self-training beats doing nothing. The experiments also stop at small models, in the E2B and E4B range plus a 4B Qwen. Nothing in the paper shows what happens at frontier scale, where benchmark headroom is thinner and a model’s own mistakes in its practice material could compound.

The cost structure is still what makes this worth tracking. Labeled data is the expensive part of tuning a model for a niche domain, and OPST swaps it for a topic list. A team with a small open model and no annotation budget now has a baseline to beat before it pays anyone to write training examples.

Reported from the arXiv paper “On-Policy Self-Training: Data-Free Self-Improvement in Large Language Models” (arXiv

.32770), submitted on 23 October 2026.