On the Geometry of On-Policy Distillation

On-policy distillation (OPD) is increasingly used to improve large language model reasoning, but its training dynamics remain poorly understood. We characterize the trajectory of OPD updates in parameter space and compare it with supervised fine-tuning (SFT) and reinforcement learning with verifiable rewards (RLVR). A suite of parameter-space diagnostics consistently places OPD in a relaxed off-principal regime: compared with SFT, its updates affect fewer weights and avoid principal directions more strongly, while compared with RLVR, they remain less tightly constrained. Beyond this static localization, OPD exhibits subspace locking: its cumulative updates rapidly enter a narrow low-dimensional channel. Constraining training to the update subspace formed early in training preserves OPD performance but substantially degrades SFT, indicating that the locked subspace is functionally sufficient for OPD. Control experiments further show that sparsifying the update tokens and shifting rollout generation off-policy preserve the rank dynamics, whereas mixing the OPD objective with RLVR changes them. Overall, these results suggest that OPD is not merely an intermediate point between SFT and RLVR, but induces its own update geometry in parameter space.

QUBRIC: Co-Designing Queries and Rubrics for RL Beyond Verifiable Rewards

Rubric-based RL is a promising route for extending reinforcement learning beyond verifiable rewards, yet existing methods optimize rubrics while treating the query distribution as fixed. We identify a structural bottleneck: rubric quality is constrained by query structure. Open-ended queries yield vague rubrics; naively narrowing them introduces fabricated references that no model can verify, so all responses fail and training receives no reward signal. We present QUBRIC, a framework that co-designs queries and rubrics. Teacher-derived key points ground the rewriting of open-ended queries into scenario-based, evaluable questions. Contrastive rubric generation then turns teacher-policy gaps into query-level criteria, and learnability filtering retains only informative query-rubric pairs for GRPO training. QUBRIC achieves a +5.5 point gain on ArenaHard over the SFT baseline. Trained only on instruction-following data, it further transfers to three held-out benchmarks spanning legal, moral, and narrative reasoning (+6.3 points on average), with improvements concentrated in reasoning-related dimensions. These results provide evidence that co-designing queries and rubrics can make rubric-based RL a practical complement to RLVR beyond strictly verifiable tasks.

Controllable and Verifiable Tool-Use Data Synthesis for Agentic Reinforcement Learning

Existing synthetic tool-use corpora are primarily designed for offline supervised fine-tuning, yet reinforcement learning (RL) requires executable environments that support reward-checkable online rollouts. We propose COVERT, a two-stage pipeline that first generates reliable base tool-use trajectories through self-evolving synthesis with multi-level validation, and then applies oracle-preserving augmentations that systematically increase environmental complexity. These augmentations introduce distractor tools, indirect or ambiguous user queries, and noisy, multi-format, or erroneous tool outputs, while strictly preserving oracle tool calls and final answers as ground truth. This design enables automatic reward computation via reference matching for standard cases and lightweight judge-assisted verification for special behaviors such as error detection, supporting RL optimization of tool-calling policies. On Qwen2.5-Instruct-14B, COVERT-RL improves overall accuracy on BFCL v3 from 56.5 to 59.9 and on ACEBench from 53.0 to 59.3, with minimal regressions on general-ability benchmarks; when stacked on SFT, it further reaches 62.1 and 61.8, confirming additive gains. These results suggest that oracle-preserving synthetic environments offer a practical RL refinement stage, complementary to SFT, for improving tool-use robustness under ambiguity and unreliable tool feedback.

JoyAI-LLM Flash: Advancing Mid-Scale LLMs with Token Efficiency

We introduce JoyAI-LLM Flash, an efficient Mixture-of-Experts (MoE) language model designed to redefine the trade-off between strong performance and token efficiency in the sub-50B parameter regime. JoyAI-LLM Flash is pretrained on a massive corpus of 20 trillion tokens and further optimized through a rigorous post-training pipeline, including supervised fine-tuning (SFT), Direct Preference Optimization (DPO), and large-scale reinforcement learning (RL) across diverse environments. To improve token efficiency, JoyAI-LLM Flash strategically balances \emph{thinking} and \emph{non-thinking} cognitive modes and introduces FiberPO, a novel RL algorithm inspired by fibration theory that decomposes trust-region maintenance into global and local components, providing unified multi-scale stability control for LLM policy optimization. To enhance architectural sparsity, the model comprises 48B total parameters while activating only 2.7B parameters per forward pass, achieving a substantially higher sparsity ratio than contemporary industry leading models of comparable scale. To further improve inference throughput, we adopt a joint training-inference co-design that incorporates dense Multi-Token Prediction (MTP) and Quantization-Aware Training (QAT). We release the checkpoints for both JoyAI-LLM-48B-A3B Base and its post-trained variants on Hugging Face to support the open-source community.

Training LLMs for Multi-Step Tool Orchestration with Constrained Data Synthesis and Graduated Rewards

Multi-step tool orchestration, where LLMs must invoke multiple dependent APIs in the correct order while propagating intermediate outputs, remains challenging. State-of-the-art models frequently fail on full sequence execution, with parameter value errors accounting for a significant portion of failures. Training models to handle such workflows faces two obstacles: existing environments focus on simple per-turn function calls with simulated data, and binary rewards provide no signal for partial correctness. We present a framework addressing both challenges. First, we construct a reinforcement learning environment backed by a large-scale cache of real API responses, enabling a data synthesis pipeline that samples valid multi-step orchestration traces with controllable complexity and significantly higher generation efficiency than unconstrained methods. Second, we propose a graduated reward design that decomposes correctness into atomic validity (individual function call correctness at increasing granularity) and orchestration (correct tool sequencing with dependency respect). On ComplexFuncBench, our approach demonstrates substantial improvements in turn accuracy. Ablation studies confirm both reward components are essential: using either alone significantly degrades performance.

HeaPA: Difficulty-Aware Heap Sampling and On-Policy Query Augmentation for LLM Reinforcement Learning

RLVR is now a standard way to train LLMs on reasoning tasks with verifiable outcomes, but when rollout generation dominates the cost, efficiency depends heavily on which prompts you sample and when. In practice, prompt pools are often static or only loosely tied to the model's learning progress, so uniform sampling can't keep up with the shifting capability frontier and ends up wasting rollouts on prompts that are already solved or still out of reach. Existing approaches improve efficiency through filtering, curricula, adaptive rollout allocation, or teacher guidance, but they typically assume a fixed pool-which makes it hard to support stable on-policy pool growth-or they add extra teacher cost and latency. We introduce HeaPA (Heap Sampling and On-Policy Query Augmentation), which maintains a bounded, evolving pool, tracks the frontier using heap-based boundary sampling, expands the pool via on-policy augmentation with lightweight asynchronous validation, and stabilizes correlated queries through topology-aware re-estimation of pool statistics and controlled reinsertion. Across two training corpora, two training recipes, and seven benchmarks, HeaPA consistently improves accuracy and reaches target performance with fewer computations while keeping wall-clock time comparable. Our analyses suggest these gains come from frontier-focused sampling and on-policy pool growth, with the benefits becoming larger as model scale increases. Our code is available at https://github.com/horizon-rl/HeaPA.

Vision-DeepResearch: Incentivizing DeepResearch Capability in Multimodal Large Language Models

Multimodal large language models (MLLMs) have achieved remarkable success across a broad range of vision tasks. However, constrained by the capacity of their internal world knowledge, prior work has proposed augmenting MLLMs by ``reasoning-then-tool-call'' for visual and textual search engines to obtain substantial gains on tasks requiring extensive factual information. However, these approaches typically define multimodal search in a naive setting, assuming that a single full-level or entity-level image query and few text query suffices to retrieve the key evidence needed to answer the question, which is unrealistic in real-world scenarios with substantial visual noise. Moreover, they are often limited in the reasoning depth and search breadth, making it difficult to solve complex questions that require aggregating evidence from diverse visual and textual sources. Building on this, we propose Vision-DeepResearch, which proposes one new multimodal deep-research paradigm, i.e., performs multi-turn, multi-entity and multi-scale visual and textual search to robustly hit real-world search engines under heavy noise. Our Vision-DeepResearch supports dozens of reasoning steps and hundreds of engine interactions, while internalizing deep-research capabilities into the MLLM via cold-start supervision and RL training, resulting in a strong end-to-end multimodal deep-research MLLM. It substantially outperforming existing multimodal deep-research MLLMs, and workflows built on strong closed-source foundation model such as GPT-5, Gemini-2.5-pro and Claude-4-Sonnet. The code will be released in https://github.com/Osilly/Vision-DeepResearch.

Finding RELIEF: Shaping Reasoning Behavior without Reasoning Supervision via Belief Engineering

Large reasoning models (LRMs) have achieved remarkable success in complex problem-solving, yet they often suffer from computational redundancy or reasoning unfaithfulness. Current methods for shaping LRM behavior typically rely on reinforcement learning or fine-tuning with gold-standard reasoning traces, a paradigm that is both computationally expensive and difficult to scale. In this paper, we reveal that LRMs possess latent \textit{reasoning beliefs} that internally track their own reasoning traits, which can be captured through simple logit probing. Building upon this insight, we propose Reasoning Belief Engineering (RELIEF), a simple yet effective framework that shapes LRM behavior by aligning the model's self-concept with a target belief blueprint. Crucially, RELIEF completely bypasses the need for reasoning-trace supervision. It internalizes desired traits by fine-tuning on synthesized, self-reflective question-answering pairs that affirm the target belief. Extensive experiments on efficiency and faithfulness tasks demonstrate that RELIEF matches or outperforms behavior-supervised and preference-based baselines while requiring lower training costs. Further analysis validates that shifting a model's reasoning belief effectively shapes its actual behavior.

Evaluating Parameter Efficient Methods for RLVR

We systematically evaluate Parameter-Efficient Fine-Tuning (PEFT) methods under the paradigm of Reinforcement Learning with Verifiable Rewards (RLVR). RLVR incentivizes language models to enhance their reasoning capabilities through verifiable feedback; however, while methods like LoRA are commonly used, the optimal PEFT architecture for RLVR remains unidentified. In this work, we conduct the first comprehensive evaluation of over 12 PEFT methodologies across the DeepSeek-R1-Distill families on mathematical reasoning benchmarks. Our empirical results challenge the default adoption of standard LoRA with three main findings. First, we demonstrate that structural variants, such as DoRA, AdaLoRA, and MiSS, consistently outperform LoRA. Second, we uncover a spectral collapse phenomenon in SVD-informed initialization strategies (\textit{e.g.,} PiSSA, MiLoRA), attributing their failure to a fundamental misalignment between principal-component updates and RL optimization. Furthermore, our ablations reveal that extreme parameter reduction (\textit{e.g.,} VeRA, Rank-1) severely bottlenecks reasoning capacity. We further conduct ablation studies and scaling experiments to validate our findings. This work provides a definitive guide for advocating for more exploration for parameter-efficient RL methods.

Interleaving Reasoning for Better Text-to-Image Generation

Unified multimodal understanding and generation models recently have achieve significant improvement in image generation capability, yet a large gap remains in instruction following and detail preservation compared to systems that tightly couple comprehension with generation such as GPT-4o. Motivated by recent advances in interleaving reasoning, we explore whether such reasoning can further improve Text-to-Image (T2I) generation. We introduce Interleaving Reasoning Generation (IRG), a framework that alternates between text-based thinking and image synthesis: the model first produces a text-based thinking to guide an initial image, then reflects on the result to refine fine-grained details, visual quality, and aesthetics while preserving semantics. To train IRG effectively, we propose Interleaving Reasoning Generation Learning (IRGL), which targets two sub-goals: (1) strengthening the initial think-and-generate stage to establish core content and base quality, and (2) enabling high-quality textual reflection and faithful implementation of those refinements in a subsequent image. We curate IRGL-300K, a dataset organized into six decomposed learning modes that jointly cover learning text-based thinking, and full thinking-image trajectories. Starting from a unified foundation model that natively emits interleaved text-image outputs, our two-stage training first builds robust thinking and reflection, then efficiently tunes the IRG pipeline in the full thinking-image trajectory data. Extensive experiments show SoTA performance, yielding absolute gains of 5-10 points on GenEval, WISE, TIIF, GenAI-Bench, and OneIG-EN, alongside substantial improvements in visual quality and fine-grained fidelity. The code, model weights and datasets will be released in: https://github.com/Osilly/Interleaving-Reasoning-Generation .