The State of LLMs 2025: Progress, Progress, and Predictions (magazine.sebastianraschka.com)

As 2025 concludes, significant advancements in large language models (LLMs) have been highlighted, particularly through the release of DeepSeek's R1 paper, which introduced Reinforcement Learning with Verifiable Rewards (RLVR) and the GRPO algorithm. DeepSeek R1 stands out as it is an open-weight model achieving performance on par with proprietary models like ChatGPT while significantly reducing estimated training costs to around $5 million, challenging previous assumptions of expenses ranging from tens to hundreds of millions. This paper has sparked renewed interest in earlier methodologies and emphasized that reasoning-like behavior in LLMs can now be developed more efficiently through RLVR, leading to improvements in model accuracy and complexity. The implications of these advancements are profound for the AI/ML community, as they signal a shift towards more cost-effective and capable models that can learn from large datasets without the hefty price tag of traditional methods. The introduction of GRPO and its mathematical enhancements facilitates training updates without corrupting previous runs, increasing model reliability. Moreover, the ongoing exploration of reasoning models and their applications beyond math and code marks a pivotal direction for future LLM development. Predictions for the coming years include further enhancements to RLVR methodologies and expansion into continual learning, setting the stage for a more sophisticated approach to model training and data integration.