The Era of Agentic Organization: Learning to Organize with Language Models

We envision a new era of AI, termed agentic organization, where agents solve complex problems by working collaboratively and concurrently, enabling outcomes beyond individual intelligence. To realize this vision, we introduce asynchronous thinking (AsyncThink) as a new paradigm of reasoning with large language models, which organizes the internal thinking process into concurrently executable structures. Specifically, we propose a thinking protocol where an organizer dynamically assigns sub-queries to workers, merges intermediate knowledge, and produces coherent solutions. More importantly, the thinking structure in this protocol can be further optimized through reinforcement learning. Experiments demonstrate that AsyncThink achieves 28% lower inference latency compared to parallel thinking while improving accuracy on mathematical reasoning. Moreover, AsyncThink generalizes its learned asynchronous thinking capabilities, effectively tackling unseen tasks without additional training.

Towards Stable and Effective Reinforcement Learning for Mixture-of-Experts

Recent advances in reinforcement learning (RL) have substantially improved the training of large-scale language models, leading to significant gains in generation quality and reasoning ability. However, most existing research focuses on dense models, while RL training for Mixture-of-Experts (MoE) architectures remains underexplored. To address the instability commonly observed in MoE training, we propose a novel router-aware approach to optimize importance sampling (IS) weights in off-policy RL. Specifically, we design a rescaling strategy guided by router logits, which effectively reduces gradient variance and mitigates training divergence. Experimental results demonstrate that our method significantly improves both the convergence stability and the final performance of MoE models, highlighting the potential of RL algorithmic innovations tailored to MoE architectures and providing a promising direction for efficient training of large-scale expert models.

Benefits and Pitfalls of Reinforcement Learning for Language Model Planning: A Theoretical Perspective

Recent reinforcement learning (RL) methods have substantially enhanced the planning capabilities of Large Language Models (LLMs), yet the theoretical basis for their effectiveness remains elusive. In this work, we investigate RL's benefits and limitations through a tractable graph-based abstraction, focusing on policy gradient (PG) and Q-learning methods. Our theoretical analyses reveal that supervised fine-tuning (SFT) may introduce co-occurrence-based spurious solutions, whereas RL achieves correct planning primarily through exploration, underscoring exploration's role in enabling better generalization. However, we also show that PG suffers from diversity collapse, where output diversity decreases during training and persists even after perfect accuracy is attained. By contrast, Q-learning provides two key advantages: off-policy learning and diversity preservation at convergence. We further demonstrate that careful reward design is necessary to prevent reward hacking in Q-learning. Finally, applying our framework to the real-world planning benchmark Blocksworld, we confirm that these behaviors manifest in practice.

Geometric-Mean Policy Optimization

Recent advancements, such as Group Relative Policy Optimization (GRPO), have enhanced the reasoning capabilities of large language models by optimizing the arithmetic mean of token-level rewards. However, GRPO suffers from unstable policy updates when processing tokens with outlier importance-weighted rewards, which manifests as extreme importance sampling ratios during training, i.e., the ratio between the sampling probabilities assigned to a token by the current and old policies. In this work, we propose Geometric-Mean Policy Optimization (GMPO), a stabilized variant of GRPO. Instead of optimizing the arithmetic mean, GMPO maximizes the geometric mean of token-level rewards, which is inherently less sensitive to outliers and maintains a more stable range of importance sampling ratio. In addition, we provide comprehensive theoretical and experimental analysis to justify the design and stability benefits of GMPO. Beyond improved stability, GMPO-7B outperforms GRPO by an average of 4.1% on multiple mathematical benchmarks and 1.4% on multimodal reasoning benchmark, including AIME24, AMC, MATH500, OlympiadBench, Minerva, and Geometry3K. Code is available at https://github.com/callsys/GMPO.

On-Policy RL with Optimal Reward Baseline

Reinforcement learning algorithms are fundamental to align large language models with human preferences and to enhance their reasoning capabilities. However, current reinforcement learning algorithms often suffer from training instability due to loose on-policy constraints and computational inefficiency due to auxiliary models. In this work, we propose On-Policy RL with Optimal reward baseline (OPO), a novel and simplified reinforcement learning algorithm designed to address these challenges. OPO emphasizes the importance of exact on-policy training, which empirically stabilizes the training process and enhances exploration. Moreover, OPO introduces the optimal reward baseline that theoretically minimizes gradient variance. We evaluate OPO on mathematical reasoning benchmarks. The results demonstrate its superior performance and training stability without additional models or regularization terms. Furthermore, OPO achieves lower policy shifts and higher output entropy, encouraging more diverse and less repetitive responses. These results highlight OPO as a promising direction for stable and effective reinforcement learning in large language model alignment and reasoning tasks. The implementation is provided at https://github.com/microsoft/LMOps/tree/main/opo.

Data Selection via Optimal Control for Language Models

This work investigates the selection of high-quality pre-training data from massive corpora to enhance LMs' capabilities for downstream usage. We formulate data selection as a generalized Optimal Control problem, which can be solved theoretically by Pontryagin's Maximum Principle (PMP), yielding a set of necessary conditions that characterize the relationship between optimal data selection and LM training dynamics. Based on these theoretical results, we introduce PMP-based Data Selection (PDS), a framework that approximates optimal data selection by solving the PMP conditions. In our experiments, we adopt PDS to select data from CommmonCrawl and show that the PDS-selected corpus accelerates the learning of LMs and constantly boosts their performance on a wide range of downstream tasks across various model sizes. Moreover, the benefits of PDS extend to ~400B models trained on ~10T tokens, as evidenced by the extrapolation of the test loss curves according to the Scaling Laws. PDS also improves data utilization when the pre-training data is limited, by reducing the data demand by 1.8 times, which mitigates the quick exhaustion of available web-crawled corpora. Our code, data, and model checkpoints can be found in https://github.com/microsoft/LMOps/tree/main/data_selection.

Towards Optimal Learning of Language Models

This work studies the general principles of improving the learning of language models (LMs), which aims at reducing the necessary training steps for achieving superior performance. Specifically, we present a theory for the optimal learning of LMs. We first propose an objective that optimizes LM learning by maximizing the data compression ratio in an "LM-training-as-lossless-compression" view. Then, we derive a theorem, named Learning Law, to reveal the properties of the dynamics in the optimal learning process under our objective. The theorem is then validated by experiments on a linear classification and a real-world language modeling task. Finally, we empirically verify that the optimal learning of LMs essentially stems from the improvement of the coefficients in the scaling law of LMs, indicating great promise and significance for designing practical learning acceleration methods. Our code can be found at https://aka.ms/LearningLaw.

Large Language Model for Science: A Study on P vs. NP

In this work, we use large language models (LLMs) to augment and accelerate research on the P versus NP problem, one of the most important open problems in theoretical computer science and mathematics. Specifically, we propose Socratic reasoning, a general framework that promotes in-depth thinking with LLMs for complex problem-solving. Socratic reasoning encourages LLMs to recursively discover, solve, and integrate problems while facilitating self-evaluation and refinement. Our pilot study on the P vs. NP problem shows that GPT-4 successfully produces a proof schema and engages in rigorous reasoning throughout 97 dialogue turns, concluding "P $\neq$ NP", which is in alignment with (Xu and Zhou, 2023). The investigation uncovers novel insights within the extensive solution space of LLMs, shedding light on LLM for Science.

Kosmos-2: Grounding Multimodal Large Language Models to the World

We introduce Kosmos-2, a Multimodal Large Language Model (MLLM), enabling new capabilities of perceiving object descriptions (e.g., bounding boxes) and grounding text to the visual world. Specifically, we represent refer expressions as links in Markdown, i.e., ``[text span](bounding boxes)'', where object descriptions are sequences of location tokens. Together with multimodal corpora, we construct large-scale data of grounded image-text pairs (called GrIT) to train the model. In addition to the existing capabilities of MLLMs (e.g., perceiving general modalities, following instructions, and performing in-context learning), Kosmos-2 integrates the grounding capability into downstream applications. We evaluate Kosmos-2 on a wide range of tasks, including (i) multimodal grounding, such as referring expression comprehension, and phrase grounding, (ii) multimodal referring, such as referring expression generation, (iii) perception-language tasks, and (iv) language understanding and generation. This work lays out the foundation for the development of Embodiment AI and sheds light on the big convergence of language, multimodal perception, action, and world modeling, which is a key step toward artificial general intelligence. Code and pretrained models are available at https://aka.ms/kosmos-2.

Language Is Not All You Need: Aligning Perception with Language Models

A big convergence of language, multimodal perception, action, and world modeling is a key step toward artificial general intelligence. In this work, we introduce Kosmos-1, a Multimodal Large Language Model (MLLM) that can perceive general modalities, learn in context (i.e., few-shot), and follow instructions (i.e., zero-shot). Specifically, we train Kosmos-1 from scratch on web-scale multimodal corpora, including arbitrarily interleaved text and images, image-caption pairs, and text data. We evaluate various settings, including zero-shot, few-shot, and multimodal chain-of-thought prompting, on a wide range of tasks without any gradient updates or finetuning. Experimental results show that Kosmos-1 achieves impressive performance on (i) language understanding, generation, and even OCR-free NLP (directly fed with document images), (ii) perception-language tasks, including multimodal dialogue, image captioning, visual question answering, and (iii) vision tasks, such as image recognition with descriptions (specifying classification via text instructions). We also show that MLLMs can benefit from cross-modal transfer, i.e., transfer knowledge from language to multimodal, and from multimodal to language. In addition, we introduce a dataset of Raven IQ test, which diagnoses the nonverbal reasoning capability of MLLMs.