As some of you know, I keep a running list of research papers I (want to) read and reference. About six months ago, I shared my 2024 list , which many readers found useful. So, I was thinking about doing this again. However, this time, I am incorporating that one piece of feedback kept coming up: "Can you organize the papers by topic instead of date?" The categories I came up with are: Reasoning Models - 1a. Training Reasoning Models - 1b. Inference-Time Reasoning Strategies - 1c. Evaluating LLMs and/or Understanding Reasoning Other Reinforcement Learning Methods for LLMs Other Inference-Time Scaling Methods Efficient Training & Architectures Diffusion-Based Language Models Multimodal & Vision-Language Models Data & Pre-training Datasets Also, as LLM research continues to be shared at a rapid pace, I have decided to break the list into bi-yearly updates. This way, the list stays digestible, timely, and hopefully useful for anyone looking for solid summer reading material. Please note that this is just a curated list for now. In future articles, I plan to revisit and discuss some of the more interesting or impactful papers in larger topic-specific write-ups. Stay tuned! Announcement: It's summer! And that means internship season, tech interviews, and lots of learning. To support those brushing up on intermediate to advanced machine learning and AI topics, I have made all 30 chapters of my Machine Learning Q and AI book freely available for the summer: 🔗 https://sebastianraschka.com/books/ml-q-and-ai/#table-of-contents Whether you are just curious and want to learn something new or prepping for interviews, hopefully this comes in handy. Happy reading, and best of luck if you are interviewing! 1. Reasoning Models This year, my list is very reasoning model-heavy. So, I decided to subdivide it into 3 categories: Training, inference-time scaling, and more general understanding/evaluation. 1a. Training Reasoning Models This subsection focuses on training strategies specifically designed to improve reasoning abilities in LLMs. As you may see, much of the recent progress has centered around reinforcement learning (with verifiable rewards), which I covered in more detail in a previous article. Annotated figure from Reinforcement Pre-Training, https://arxiv.org/abs/2506.08007 8 Jan, Towards System 2 Reasoning in LLMs: Learning How to Think With Meta Chain-of-Thought, https://arxiv.org/abs/2501.04682 13 Jan, The Lessons of Developing Process Reward Models in Mathematical Reasoning, https://arxiv.org/abs/2501.07301 16 Jan, Towards Large Reasoning Models: A Survey of Reinforced Reasoning with Large Language Models, https://arxiv.org/abs/2501.09686 20 Jan, Reasoning Language Models: A Blueprint, https://arxiv.org/abs/2501.11223 22 Jan, Kimi k1.5: Scaling Reinforcement Learning with LLMs, https://arxiv.org/abs//2501.12599 22 Jan, DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning, https://arxiv.org/abs/2501.12948 3 Feb, Competitive Programming with Large Reasoning Models, https://arxiv.org/abs/2502.06807 5 Feb, Demystifying Long Chain-of-Thought Reasoning in LLMs, Demystifying Long Chain-of-Thought Reasoning in LLMs, https://arxiv.org/abs/2502.03373 5 Feb, LIMO: Less is More for Reasoning, https://arxiv.org/abs/2502.03387 5 Feb, Teaching Language Models to Critique via Reinforcement Learning, https://arxiv.org/abs/2502.03492 6 Feb, Training Language Models to Reason Efficiently, https://arxiv.org/abs/2502.04463 10 Feb, Exploring the Limit of Outcome Reward for Learning Mathematical Reasoning, https://arxiv.org/abs/2502.06781 10 Feb, On the Emergence of Thinking in LLMs I: Searching for the Right Intuition, https://arxiv.org/abs/2502.06773 11 Feb, LLMs Can Easily Learn to Reason from Demonstrations Structure, not content, is what matters!, https://arxiv.org/abs/2502.07374 12 Feb, Fino1: On the Transferability of Reasoning Enhanced LLMs to Finance, https://arxiv.org/abs/2502.08127 13 Feb, Adapting Language-Specific LLMs to a Reasoning Model in One Day via Model Merging - An Open Recipe, https://arxiv.org/abs/2502.09056 20 Feb, Logic-RL: Unleashing LLM Reasoning with Rule-Based Reinforcement Learning, https://arxiv.org/abs/2502.14768 25 Feb, SWE-RL: Advancing LLM Reasoning via Reinforcement Learning on Open Software Evolution, https://arxiv.org/abs/2502.18449 4 Mar, Learning from Failures in Multi-Attempt Reinforcement Learning, https://arxiv.org/abs/2503.04808 4 Mar, The First Few Tokens Are All You Need: An Efficient and Effective Unsupervised Prefix Fine-Tuning Method for Reasoning Models, https://arxiv.org/abs/2503.02875 10 Mar, R1-Searcher: Incentivizing the Search Capability in LLMs via Reinforcement Learning, https://arxiv.org/abs/2503.05592 10 Mar, LMM-R1: Empowering 3B LMMs with Strong Reasoning Abilities Through Two-Stage Rule-Based RL, https://arxiv.org/abs/2503.07536 12 Mar, Search-R1: Training LLMs to Reason and Leverage Search Engines with Reinforcement Learning, https://arxiv.org/abs/2503.09516 16 Mar, Towards Hierarchical Multi-Step Reward Models for Enhanced Reasoning in Large Language Models, https://arxiv.org/abs/2503.13551 20 Mar, Reinforcement Learning for Reasoning in Small LLMs: What Works and What Doesn't, https://arxiv.org/abs/2503.16219 25 Mar, ReSearch: Learning to Reason with Search for LLMs via Reinforcement Learning, https://arxiv.org/abs/2503.19470 26 Mar, Understanding R1-Zero-Like Training: A Critical Perspective, https://arxiv.org/abs/2503.20783 30 Mar, RARE: Retrieval-Augmented Reasoning Modeling, https://arxiv.org/abs/2503.23513 31 Mar, Open-Reasoner-Zero: An Open Source Approach to Scaling Up Reinforcement Learning on the Base Model, https://arxiv.org/abs/2503.24290 31 Mar, JudgeLRM: Large Reasoning Models as a Judge, https://arxiv.org/abs/2504.00050 7 Apr, Concise Reasoning via Reinforcement Learning, https://arxiv.org/abs/2504.05185 10 Apr, VL-Rethinker: Incentivizing Self-Reflection of Vision-Language Models with Reinforcement Learning, https://arxiv.org/abs/2504.08837 11 Apr, Genius: A Generalizable and Purely Unsupervised Self-Training Framework For Advanced Reasoning, https://arxiv.org/abs/2504.08672 13 Apr, Leveraging Reasoning Model Answers to Enhance Non-Reasoning Model Capability, https://arxiv.org/abs/2504.09639 21 Apr, Learning to Reason under Off-Policy Guidance, https://arxiv.org/abs/2504.14945 22 Apr, Tina: Tiny Reasoning Models via LoRA, https://arxiv.org/abs/2504.15777 29 Apr, Reinforcement Learning for Reasoning in Large Language Models with One Training Example, https://arxiv.org/abs/2504.20571 30 Apr, Phi-4-Mini-Reasoning: Exploring the Limits of Small Reasoning Language Models in Math, https://arxiv.org/abs/2504.21233 2 May, Llama-Nemotron: Efficient Reasoning Models, https://arxiv.org/abs/2505.00949 5 May, RM-R1: Reward Modeling as Reasoning, https://arxiv.org/abs/2505.02387 6 May, Absolute Zero: Reinforced Self-play Reasoning with Zero Data, https://arxiv.org/abs/2505.03335 12 May, INTELLECT-2: A Reasoning Model Trained Through Globally Decentralized Reinforcement Learning, https://arxiv.org/abs/2505.07291 12 May, MiMo: Unlocking the Reasoning Potential of Language Model -- From Pretraining to Posttraining, https://arxiv.org/abs/2505.07608 14 May, Qwen3 Technical Report, https://arxiv.org/abs/2505.09388 15 May, Beyond 'Aha!': Toward Systematic Meta-Abilities Alignment in Large Reasoning Models, https://arxiv.org/abs/2505.10554 19 May, AdaptThink: Reasoning Models Can Learn When to Think, https://arxiv.org/abs/2505.13417 19 May, Thinkless: LLM Learns When to Think, https://arxiv.org/abs/2505.13379 20 May, General-Reasoner: Advancing LLM Reasoning Across All Domains, https://arxiv.org/abs/2505.14652 21 May, Learning to Reason via Mixture-of-Thought for Logical Reasoning, https://arxiv.org/abs/2505.15817 21 May, RL Tango: Reinforcing Generator and Verifier Together for Language Reasoning, https://arxiv.org/abs/2505.15034 23 May, QwenLong-L1: Towards Long-Context Large Reasoning Models with Reinforcement Learning, https://www.arxiv.org/abs/2505.17667 26 May, Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles, https://arxiv.org/abs/2505.19914 26 May, Learning to Reason without External Rewards, https://arxiv.org/abs/2505.19590 29 May, Darwin Godel Machine: Open-Ended Evolution of Self-Improving Agents, https://arxiv.org/abs/2505.22954 30 May, Reflect, Retry, Reward: Self-Improving LLMs via Reinforcement Learning, https://arxiv.org/abs/2505.24726 30 May, ProRL: Prolonged Reinforcement Learning Expands Reasoning Boundaries in Large Language Models, https://arxiv.org/abs/2505.24864 2 Jun, Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning, https://arxiv.org/abs/2506.01939 3 Jun, Rewarding the Unlikely: Lifting GRPO Beyond Distribution Sharpening, https://www.arxiv.org/abs/2506.02355 9 Jun, Reinforcement Pre-Training, https://arxiv.org/abs/2506.08007 10 Jun, RuleReasoner: Reinforced Rule-based Reasoning via Domain-aware Dynamic Sampling, https://arxiv.org/abs/2506.08672 10 Jun, Reinforcement Learning Teachers of Test Time Scaling, https://www.arxiv.org/abs/2506.08388 12 Jun, Magistral, https://arxiv.org/abs/2506.10910 12 Jun, Spurious Rewards: Rethinking Training Signals in RLVR, https://arxiv.org/abs/2506.10947 16 Jun, AlphaEvolve: A coding agent for scientific and algorithmic discovery, https://arxiv.org/abs/2506.13131 17 Jun, Reinforcement Learning with Verifiable Rewards Implicitly Incentivizes Correct Reasoning in Base LLMs, https://arxiv.org/abs/2506.14245 23 Jun, Programming by Backprop: LLMs Acquire Reusable Algorithmic Abstractions During Code Training, https://arxiv.org/abs/2506.18777 26 Jun, Bridging Offline and Online Reinforcement Learning for LLMs, https://arxiv.org/abs/2506.21495 1b. Inference-Time Reasoning Strategies This part of the list covers methods that improve reasoning dynamically at test time, without requiring retraining. Often, these papers are focused on trading of computational performance for modeling performance. Read more