Daily Papers

Large-scale humanoid motion-tracking controllers are commonly improved by reallocating training effort: difficult motions are sampled more often, isolated into smaller subsets, or assigned to specialized experts. We show that this view is incomplete. In strong whole-body-control baselines, a residual set of feasible training clips remains unsolved even under targeted training, especially for high-dynamic transitions and balance-critical motions. These failures arise not only from insufficient exposure, but from a mismatch between the motion demands and the effective capability induced by the default training recipe. We propose Athena-WBC, a compact teacher-student pipeline with capability-aligned policy experts for long-tail humanoid whole-body control. Dynamic experts use a tracking-focused, constraint-aware objective that removes conservative effort and temporal-control penalties while preserving physical feasibility constraints; balance experts use a gravity curriculum to improve early-training survivability. The resulting privileged teachers are motion-routed for DAgger distillation and then compressed into a single controller with deployable observations followed by RL fine-tuning. Experiments on a full-size humanoid show improved recovery of training-set long-tail motions and better held-out tracking than a strong SONIC-recipe baseline, using only a small number of experts.

Large language models (LLMs) have recently advanced in reasoning when optimized with reinforcement learning (RL) under verifiable rewards. Existing methods primarily rely on outcome-based supervision to strengthen internal LLM reasoning, often leading to inefficient exploration and sparse rewards. To mitigate this issue, we propose Expert-Assisted Policy Optimization (EAPO), a novel RL framework that enhances exploration by incorporating multi-turn interactions with external experts during training. Unlike prior methods, where policies reason in isolation, EAPO incentivizes the policy to adaptively determine when and how to consult experts, yielding richer reward signals and more reliable reasoning trajectories. External assistance ultimately internalizes expert knowledge into the policy model, amplifying the model's inherent reasoning capabilities. During evaluation, the policy model has been well-optimized to solve questions independently, producing improved reasoning paths and more accurate solutions. Experiments on mathematical reasoning benchmarks, including AIME 2024, AIME 2025, and AIMO 2025, show that EAPO consistently outperforms expert-assisted workflow, expert-distilled models, and RL baselines, with an average gain of 5 points over self-exploratory models.

The ability to recognize one's own limitations and decide whether to solve a problem or delegate is fundamental for reliable intelligent systems. Yet we show that modern large language models systematically lack this ability: across diverse model families and scales, they overestimate their competence and attempt queries they cannot solve. We refer to this ability as Capability Self-Assessment (CSA) and formulate it as a policy-learning problem, aiming to improve self-assessment while preserving the model's original capabilities. Our results show that reinforcement learning teaches CSA effectively, significantly outperforming supervised fine-tuning while preserving original capabilities. In contrast, supervised fine-tuning severely degrades the capabilities the model is meant to assess. Moreover, learned self-assessment behavior generalizes well out of distribution, suggesting that CSA is a transferable model trait. Finally, CSA is practically useful: it improves local-cloud decision making at inference time and provides a signal for targeted data selection during training.

In long-horizon LLM agent reinforcement learning, weak policies often repeat similar failures, producing uninformative rollout trajectories and limiting effective policy optimization. Existing skill-centric methods improve exploration by optimizing, filtering, or internalizing reusable skills. However, they remain centered on the skills themselves rather than being designed as adaptive training-time support for the evolving policy. To address this, we propose a policy-centric training paradigm that reframes skills as a dynamic training scaffold. Our framework, Pats, converts rollout groups from the latest policy into evidence cards and uses task-specific evaluation to adjust the context used in subsequent rollouts. Concrete guidance helps weak policies to complete challenging tasks. As policy improves, redundant context is revised or removed to reduce reliance on explicit guidance while preserving useful rollout variation. The policy is optimized with environmental rewards using standard RLVR, and the training scaffold is discarded at deployment. On ALFWorld and WebShop, Pats improves over strong baselines by up to 18.6%. Across seven search-augmented QA benchmarks, it remains competitive while using 32.1% fewer prompt tokens than the baseline.

Long-horizon robotic tasks require diverse capabilities that no single policy can reliably provide. Heterogeneous policies offer complementary strengths, but orchestrating them requires reasoning over uncertain capability boundaries and cross-policy distribution mismatch, which are largely overlooked by existing planning methods built on homogeneous, predefined skills with fixed applicability. We propose RoboHarness, a unified framework that encapsulates independently developed robot control systems as reusable agentic skills. Although instantiated in this work with VLAs, RL policies, and task-and-motion planning (TAMP) systems, RoboHarness is designed as a general framework compatible with a broader range of robot policies, such as navigation policies, model predictive controllers, and world-action models. RoboHarness uses multi-modal execution memory and online evidence to characterize policy capability boundaries for capability-aware decomposition and routing. To stabilize policy handoffs, its Memory Bridge retrieves execution trajectories associated with the next policy, estimates its in-distribution state region, and guides the robot toward that region without joint policy retraining. Extensive experiments on three public benchmarks, 500 customized tasks, and 135 real-robot experiments demonstrate effective capability-aware routing and stable policy orchestration, yielding substantial improvements in zero-shot long-horizon planning and out-of-distribution robustness.

Agent skill libraries are becoming routable software assets: a retrieved skill can contribute instructions, scripts, resource bindings, and execution assumptions to an agent. This makes retrieval failures more specific than broad irrelevance. A system can find the right capability family yet expose the wrong same-capability representative. We study this failure as same-capability risk-exposure retrieval. Each benchmark unit pairs a helpful skill with a query-specific risky sibling that shares the capability family but differs on an execution-controlling contract, such as the required resource, precondition, procedure, or artifact. We introduce SameCapRisk-Bench, an auditable benchmark with 1,190 skill-risk units and 1,686 evaluation query cases: 694 marked-sibling units under public library pressure and 496 hard role-flip units where the same two skills swap helpful/risky roles across paired queries. The release records admission evidence, cue/leakage checks, source hashes, family relations, and fixed candidate pools. The benchmark reports helpful ranking together with harmful sibling rate (HSR@K), the top-K exposure of the marked risky sibling. On this benchmark, public SkillRouter, SkillRet, and R3-Skill retrieve helpful skills at high Recall@3 (0.848--0.888) but also expose marked risky siblings frequently (HSR@3 0.346--0.372). A fully public score-and-cluster pipeline lowers HSR@3 to 0.128--0.182, with Recall@3 of 0.713--0.776. Under a benchmark-trained reference scorer, public text-cluster and controlled resolvers reach HSR@3 0.012 and 0.007; the latter attains Recall@3 0.833. Skill retrieval should therefore report both capability matching and same-family risk exposure, with HSR serving as a targeted exposure certificate for fixed skill libraries.

Emotional dialogue research includes two influential strategy traditions. Empathetic dialogue prioritizes understanding a speaker's emotional experience. Emotional support conversation selects and sequences support for the seeker's current needs. Sustained use introduces a further goal. Effective support should sustain users' capacities for emotion regulation, coping, self-endorsed decisions, and social connection across the interaction lifecycle. We propose capability-sustaining emotional dialogue (CSED) as a longitudinal research paradigm that aligns supportive strategy with this goal and organizes data, models, system design, evaluation, and governance around repeated use, non-use, transition, and termination. A targeted literature-and-corpus audit motivates this position. In a PRISMA-ScR-guided sample, 95% of 60 system-building papers pursue relief-oriented goals. None evaluates capability or longitudinal outcomes, and only 1 considers dependency, autonomy, or termination risk. In 300 ESConv supporter turns, capability-relevant functions appear in 43.0%, while generic suggestions account for 22.0%, compared with 4.0% reappraisal, 6.7% self-efficacy support, and 0.3% boundary behavior. We release a protocol for extending the audit to model behavior. An illustrative process model connects latent user capability to six design commitments, four evaluation timescales, and lifecycle constraints. The resulting agenda makes CSED testable across data, policy design, training, evaluation, and governance.

The development and evaluation of Large Language Models (LLMs) have largely focused on individual capabilities. However, this overlooks the intersection of multiple abilities across different types of expertise that are often required for real-world tasks, which we term cross capabilities. To systematically explore this concept, we first define seven core individual capabilities and then pair them to form seven common cross capabilities, each supported by a manually constructed taxonomy. Building on these definitions, we introduce CrossEval, a benchmark comprising 1,400 human-annotated prompts, with 100 prompts for each individual and cross capability. To ensure reliable evaluation, we involve expert annotators to assess 4,200 model responses, gathering 8,400 human ratings with detailed explanations to serve as reference examples. Our findings reveal that, in both static evaluations and attempts to enhance specific abilities, current LLMs consistently exhibit the "Law of the Weakest Link," where cross-capability performance is significantly constrained by the weakest component. Specifically, across 58 cross-capability scores from 17 models, 38 scores are lower than all individual capabilities, while 20 fall between strong and weak, but closer to the weaker ability. These results highlight the under-performance of LLMs in cross-capability tasks, making the identification and improvement of the weakest capabilities a critical priority for future research to optimize performance in complex, multi-dimensional scenarios.

We investigate whether post-trained capabilities can be transferred across models without retraining, with a focus on transfer across different model scales. We propose the Master Key Hypothesis, which states that model capabilities correspond to directions in a low-dimensional latent subspace that induce specific behaviors and are transferable across models through linear alignment. Based on this hypothesis, we introduce UNLOCK, a training-free and label-free framework that extracts a capability direction by contrasting activations between capability-present and capability-absent Source variants, aligns it with a Target model through a low-rank linear transformation, and applies it at inference time to elicit the behavior. Experiments on reasoning behaviors, including Chain-of-Thought (CoT) and mathematical reasoning, demonstrate substantial improvements across model scales without training. For example, transferring CoT reasoning from Qwen1.5-14B to Qwen1.5-7B yields an accuracy gain of 12.1% on MATH, and transferring a mathematical reasoning direction from Qwen3-4B-Base to Qwen3-14B-Base improves AGIEval Math accuracy from 61.1% to 71.3%, surpassing the 67.8% achieved by the 14B post-trained model. Our analysis shows that the success of transfer depends on the capabilities learned during pre-training, and that our intervention amplifies latent capabilities by sharpening the output distribution toward successful reasoning trajectories.

Large-scale image generation has benefited from advances in data scale, quality, rebalancing, and recaptioning, yet conventional pipelines typically optimize task-specific datasets in isolation. A central challenge is not only how to curate each task-specific corpus, but also how to organize heterogeneous supervision according to the dependencies among generative capabilities. We present a capability-driven data infrastructure that couples capability-specific supervision construction with capability-aligned curriculum scheduling. Its three specialized yet interoperable data engines build complementary relational supervision for text-image grounding, inter-image transformation, and image-knowledge association, while caption experts align T2I and editing supervision across tasks and granularities. A multi-stage curriculum jointly evolves task composition, visual-concept distribution, data quality, and image resolution along the dependency order of capability acquisition, with capability-aware evaluation closing the loop through targeted retrieval, expert construction, and gap-aware resampling. At scale, the framework curates a 440M-image T2I corpus, 120M editing pairs, and over 27M image-entity pairs. With this infrastructure, we train multimodal diffusion models at two scales from scratch, with 3B and 6B sizes respectively. We conduct quantitative evaluation on CPI-Bench, along with qualitative evaluations across diverse text-to-image and editing scenarios. Experimental results present broad visual coverage, versatile rendering, and effective transfer across generative capabilities.

Large language model agents increasingly rely on reusable skills to extend their capabilities beyond parametric knowl- edge. However, retrieving the appropriate skill from a large- scale library remains challenging because realistic user re- quests are often concise and underspecified, stating only the task goal while leaving the required capabilities and execu- tion steps implicit. Existing benchmarks provide limited cov- erage of such requests. To address this gap, we introduce SkillReason-Bench, a large-scale cross-domain benchmark containing 3,729 queries and a retrieval corpus of 61,228 skills spanning nine domains. We further propose SkillRea- son, a two-stage framework that uses chain-of-thought rea- soning as training-time supervision for skill retrieval. In Stage I, capability reasoning traces generated by a stronger teacher provide explicit supervision through contrastive learning, re- trieval distribution alignment, and language modeling, en- couraging the retriever to internalize capability reasoning in its query representation. In Stage II, a retrieval-guided GRPO objective encourages the model to explore reasoning trajecto- ries better suited to its own capabilities and more effective for retrieval. At inference, SkillReason directly encodes the orig- inal query without autoregressive CoT generation, preserv- ing efficient query-only retrieval. Extensive experiments on SkillReason-Bench, SkillRet, and SRA-Bench show that Skill- Reason achieves state-of-the-art performance across all three benchmarks, demonstrating that reasoning-enhanced training better bridges the semantic gap between high-level task goals and skill capabilities.

Policy gradient methods rely on a baseline to measure the relative advantage of an action, ensuring the model reinforces behaviors that outperform its current average capability. In the training of Large Language Models (LLMs) using Actor-Critic methods (e.g., PPO), this baseline is typically estimated by a Value Model (Critic) often as large as the policy model itself. However, as the policy continuously evolves, the value model requires expensive, synchronous incremental training to accurately track the shifting capabilities of the policy. To avoid this overhead, Group Relative Policy Optimization (GRPO) eliminates the coupled value model by using the average reward of a group of rollouts as the baseline; yet, this approach necessitates extensive sampling to maintain estimation stability. In this paper, we propose V_0, a Generalist Value Model capable of estimating the expected performance of any model on unseen prompts without requiring parameter updates. We reframe value estimation by treating the policy's dynamic capability as an explicit context input; specifically, we leverage a history of instruction-performance pairs to dynamically profile the model, departing from the traditional paradigm that relies on parameter fitting to perceive capability shifts. Focusing on value estimation at State Zero (i.e., the initial prompt, hence V_0), our model serves as a critical resource scheduler. During GRPO training, V_0 predicts success rates prior to rollout, allowing for efficient sampling budget allocation; during deployment, it functions as a router, dispatching instructions to the most cost-effective and suitable model. Empirical results demonstrate that V_0 significantly outperforms heuristic budget allocation and achieves a Pareto-optimal trade-off between performance and cost in LLM routing tasks.

Trustworthy capability evaluations are crucial for ensuring the safety of AI systems, and are becoming a key component of AI regulation. However, the developers of an AI system, or the AI system itself, may have incentives for evaluations to understate the AI's actual capability. These conflicting interests lead to the problem of sandbagging, which we define as strategic underperformance on an evaluation. In this paper we assess sandbagging capabilities in contemporary language models (LMs). We prompt frontier LMs, like GPT-4 and Claude 3 Opus, to selectively underperform on dangerous capability evaluations, while maintaining performance on general (harmless) capability evaluations. Moreover, we find that models can be fine-tuned, on a synthetic dataset, to hide specific capabilities unless given a password. This behaviour generalizes to high-quality, held-out benchmarks such as WMDP. In addition, we show that both frontier and smaller models can be prompted or password-locked to target specific scores on a capability evaluation. We have mediocre success in password-locking a model to mimic the answers a weaker model would give. Overall, our results suggest that capability evaluations are vulnerable to sandbagging. This vulnerability decreases the trustworthiness of evaluations, and thereby undermines important safety decisions regarding the development and deployment of advanced AI systems.

Alignment methodologies have emerged as a critical pathway for enhancing language model alignment capabilities. While SFT (supervised fine-tuning) accelerates convergence through direct token-level loss intervention, its efficacy is constrained by offline policy trajectory. In contrast, RL(reinforcement learning) facilitates exploratory policy optimization, but suffers from low sample efficiency and stringent dependency on high-quality base models. To address these dual challenges, we propose GRAO (Group Relative Alignment Optimization), a unified framework that synergizes the respective strengths of SFT and RL through three key innovations: 1) A multi-sample generation strategy enabling comparative quality assessment via reward feedback; 2) A novel Group Direct Alignment Loss formulation leveraging intra-group relative advantage weighting; 3) Reference-aware parameter updates guided by pairwise preference dynamics. Our theoretical analysis establishes GRAO's convergence guarantees and sample efficiency advantages over conventional approaches. Comprehensive evaluations across complex human alignment tasks demonstrate GRAO's superior performance, achieving 57.70\%,17.65\% 7.95\% and 5.18\% relative improvements over SFT, DPO, PPO and GRPO baselines respectively. This work provides both a theoretically grounded alignment framework and empirical evidence for efficient capability evolution in language models.

Reinforcement learning from human feedback (RLHF) has emerged as a reliable approach to aligning large language models (LLMs) to human preferences. Among the plethora of RLHF techniques, proximal policy optimization (PPO) is of the most widely used methods. Despite its popularity, however, PPO may suffer from mode collapse, instability, and poor sample efficiency. We show that these issues can be alleviated by a novel algorithm that we refer to as Advantage-Induced Policy Alignment (APA), which leverages a squared error loss function based on the estimated advantages. We demonstrate empirically that APA consistently outperforms PPO in language tasks by a large margin, when a separate reward model is employed as the evaluator. In addition, compared with PPO, APA offers a more stable form of control over the deviation from the model's initial policy, ensuring that the model improves its performance without collapsing to deterministic output. In addition to empirical results, we also provide a theoretical justification supporting the design of our loss function.

Mainstream approaches to aligning large language models (LLMs) heavily rely on human preference data, particularly when models require periodic updates. The standard process for iterative alignment of LLMs involves collecting new human feedback for each update. However, the data collection process is costly and challenging to scale. To address this issue, we introduce the "TS-Align" framework, which fine-tunes a policy model using pairwise feedback data automatically mined from its outputs. This automatic mining process is efficiently accomplished through the collaboration between a large-scale teacher model and a small-scale student model. The policy fine-tuning process can be iteratively repeated using on-policy generations within our proposed teacher-student collaborative framework. Through extensive experiments, we demonstrate that our final aligned policy outperforms the base policy model with an average win rate of 69.7% across seven conversational or instruction-following datasets. Furthermore, we show that the ranking capability of the teacher is effectively distilled into the student through our pipeline, resulting in a small-scale yet effective reward model for policy model alignment.

Recent advances in post-training techniques have endowed Large Language Models (LLMs) with enhanced capabilities for tackling complex, logic-intensive tasks through the generation of supplementary planning tokens. This development raises a fundamental question: Are these models aware of what they "learn" and "think"? To address this, we define three core competencies: (1) awareness of learned latent policies, (2) generalization of these policies across domains, and (3) alignment between internal reasoning traces and final outputs. We empirically evaluate these abilities on several tasks, each designed to require learning a distinct policy. Furthermore, we contrast the profiles of models post-trained via Supervised Fine-Tuning (SFT), Direct Policy Optimization (DPO), and Group Relative Policy Optimization (GRPO). Our findings indicate that RL-trained models not only demonstrate greater awareness of their learned behaviors and stronger generalizability to novel, structurally similar tasks than SFT models but also often exhibit weak alignment between their reasoning traces and final outputs, an effect most pronounced in GRPO-trained models.

BalancedBio is a theoretically grounded framework for parameter-efficient biomedical reasoning, addressing multi-capability integration in domain-specific AI alignment. It establishes the Biomedical Multi-Capability Convergence Theorem, proving orthogonal gradient spaces are essential to prevent capability interference for safe deployment. Key innovations include: (1) Medical Knowledge Grounded Synthetic Generation (MKGSG), extending Source2Synth with clinical workflow constraints and medical ontology validation for factual accuracy and safety; and (2) Capability Aware Group Relative Policy Optimization, deriving optimal hybrid reward weighting to maintain orthogonality in RL, using a reward model with rule-based and model-based scores adapted to biomedical tasks. Mathematical analysis proves Pareto-optimal convergence, preserving performance across capabilities. It achieves state-of-the-art results in its parameter class: domain expertise (80.95% BIOMED-MMLU, +15.32% over baseline), reasoning (61.94%, +7.75%), instruction following (67.95%, +6.44%), and integration (86.7%, +18.5%). Theoretical safety guarantees include bounds on capability preservation and clinical accuracy. Real-world deployment yields 78% cost reduction, 23% improved diagnostic accuracy, and 89% clinician acceptance. This work provides a principled methodology for biomedical AI alignment, enabling efficient reasoning with essential safety and reliability, with the 0.5B model version to be released.

Supervised Fine-Tuning (SFT) is the standard paradigm for domain adaptation, yet it frequently incurs the cost of catastrophic forgetting. In sharp contrast, on-policy Reinforcement Learning (RL) effectively preserves general capabilities. We investigate this discrepancy and identify a fundamental distributional gap: while RL aligns with the model's internal belief, SFT forces the model to fit external supervision. This mismatch often manifests as "Confident Conflicts" tokens characterized by low probability but low entropy. In these instances, the model is highly confident in its own prediction but is forced to learn a divergent ground truth, triggering destructive gradient updates. To address this, we propose Entropy-Adaptive Fine-Tuning (EAFT). Unlike methods relying solely on prediction probability, EAFT utilizes token-level entropy as a gating mechanism to distinguish between epistemic uncertainty and knowledge conflict. This allows the model to learn from uncertain samples while suppressing gradients on conflicting data. Extensive experiments on Qwen and GLM series (ranging from 4B to 32B parameters) across mathematical, medical, and agentic domains confirm our hypothesis. EAFT consistently matches the downstream performance of standard SFT while significantly mitigating the degradation of general capabilities.

Mixture of Experts models are widely assumed to achieve domain specialization through sparse routing. In this work, we question this assumption by introducing COMMITTEEAUDIT, a post hoc framework that analyzes routing behavior at the level of expert groups rather than individual experts. Across three representative models and the MMLU benchmark, we uncover a domain-invariant Standing Committee. This is a compact coalition of routed experts that consistently captures the majority of routing mass across domains, layers, and routing budgets, even when architectures already include shared experts. Qualitative analysis further shows that Standing Committees anchor reasoning structure and syntax, while peripheral experts handle domain-specific knowledge. These findings reveal a strong structural bias toward centralized computation, suggesting that specialization in Mixture of Experts models is far less pervasive than commonly believed. This inherent bias also indicates that current training objectives, such as load-balancing losses that enforce uniform expert utilization, may be working against the model's natural optimization path, thereby limiting training efficiency and performance.

Parliamentary proceedings are a primary record of democratic deliberation, yet their volume and fragmentation make multi-perspective access difficult for citizens, journalists, and researchers. Applying Retrieval-Augmented Generation (RAG) to parliamentary transcripts introduces three specific risks: dominance of the most frequent speakers, inability to weight speakers according to topical expertise, and citation misattribution in politically sensitive text. We present ParliamentRAG, a RAG system for the Italian Chamber of Deputies that addresses these risks jointly. Its core contribution is a topic-dependent authority model that estimates each speaker's authority as a function of the current query, combining interpretable components such as profession, education, and previous interventions. Given a user query, the system retrieves relevant speech chunks, identifies topic-relevant experts across parliamentary groups, and generates a summary synthesizing their perspectives, accompanied by supporting quotations. ParliamentRAG is evaluated against Google NotebookLM on 15 policy topics via a two-level protocol combining automated metrics and blind A/B human evaluation by six domain experts. The system achieves higher coverage across political groups (0.97 vs. 0.95), perfect quotation faithfulness (1.00 vs. 0.95), and stronger expert preferences on source-related dimensions, while NotebookLM remains stronger on prose-oriented dimensions.

RLVR and OPD have become standard paradigms for post-training. We provide a unified analysis of these two paradigms in consolidating multiple expert capabilities into a single model, identifying capability loss in different ways: mixed RLVR suffers from inter-capability divergence cost, while the pipeline of first training experts and then performing OPD, though avoiding divergence, fails to fully absorb teacher capabilities due to large behavioral pattern gaps between teacher and student. We propose Co-Evolving Policy Distillation (CoPD), which encourages parallel training of experts and introduces OPD during each expert's ongoing RLVR training rather than after complete expert training, with experts serving as mutual teachers (making OPD bidirectional) to co-evolve. This enables more consistent behavioral patterns among experts while maintaining sufficient complementary knowledge throughout. Experiments validate that CoPD achieves all-in-one integration of text, image, and video reasoning capabilities, significantly outperforming strong baselines such as mixed RLVR and MOPD, and even surpassing domain-specific experts. The model parallel training pattern offered by CoPD may inspire a novel training scaling paradigm.

Multi-teacher on-policy distillation (M-OPD) has emerged as a promising paradigm for consolidating domain-specialized reinforcement learning (RL) experts into a single generalist student via dense, token-level reward supervision. Despite its practical success, the optimization dynamics governing multi-teacher capability integration remain poorly understood, and open, rigorously reproducible recipes are conspicuously lacking. In this work, we establish a controlled M-OPD benchmark on SmolLM3-3B-Base with oracle routing, isolating capability integration from routing ambiguity. Our investigation reveals a pronounced capability integration gap: standard M-OPD captures only 35.6% of the available headroom relative to a domain-routed oracle ensemble, with concise tasks such as instruction following suffering severe degradation and premature stagnation. Crucially, we show that this failure stems not from gradient conflict, but from a severe misallocation of the token-level optimization budget. This pathology is driven by three orthogonal factors: structural sequence-length disparities across domains, dynamic convergence drift due to non-uniform learning rates, and multi-step reward staleness from asynchronous policy updates. To resolve these imbalances, we introduce Open-MOPD, a principled framework incorporating token-share balancing, gap-aware dynamic budget allocation, and student reward refresh. Together, these mechanisms systematically restore cross-domain balance, elevating headroom recovery from 35.6% to 83.4% in a single deployable student. We fully open-source our end-to-end post-training recipe, training trajectories, and evaluation suites on an academically accessible hardware budget.

While Large Language Models (LLMs) have emerged with remarkable capabilities in complex tasks through Chain-of-Thought reasoning, practical resource constraints have sparked interest in transferring these abilities to smaller models. However, achieving both domain performance and cross-domain generalization remains challenging. Existing approaches typically restrict students to following a single golden rationale and treat different reasoning paths independently. Due to distinct inductive biases and intrinsic preferences, alongside the student's evolving capacity and reasoning preferences during training, a teacher's "optimal" rationale could act as out-of-distribution noise. This misalignment leads to a degeneration of the student's latent reasoning distribution, causing suboptimal performance. To bridge this gap, we propose MIND, a capability-adaptive framework that transitions distillation from passive mimicry to active cognitive construction. We synthesize diverse teacher perspectives through a novel "Teaching Assistant" network. By employing a Feedback-Driven Inertia Calibration mechanism, this network utilizes inertia-filtered training loss to align supervision with the student's current adaptability, effectively enhancing performance while mitigating catastrophic forgetting. Extensive experiments demonstrate that MIND achieves state-of-the-art performance on both in-distribution and out-of-distribution benchmarks, and our sophisticated latent space analysis further confirms the mechanism of reasoning ability internalization.