This work compares three fusion paradigms by the artefacts they reuse and suggests that Merge when experts already exist and cheap fusion is paramount; Mix RL when training a unified model without experts, with domain proportions adjusted for cross-domain transfer; and MOPD when preserving domain-specific gains matters more than surpassing teachers or minimizing end-to-end cost.
Abstract
Reinforcement learning with verifiable rewards (RLVR) improves specific capabilities of large language models, but covering multiple capabilities often involves training separate domain experts and subsequently consolidating them. We organize three fusion paradigms by the artefacts they reuse: Merge combines expert task vectors, Mix RL pools their datasets, and multi-teacher on-policy distillation (MOPD) uses both. Because they have largely been studied in isolation, how they compare and how to choose among them remain unclear. We compare all three using shared experts and data across model scales and a multi-domain benchmark suite. Although their average performance differs by at most 1.4 points, the gap reaches 8.6 points on a single benchmark, with domain-level variation tracking cross-domain relations visible in task-vector geometry. Training dynamics expose distinct constraints: Mix RL depends on domain mixture proportions, MOPD remains bounded by its teachers, and Merge compresses all expert updates into one. All three improve single-sample accuracy without measurable gains in solution coverage or losses in held-out capabilities. These results yield a practical guideline: use Merge when experts already exist and cheap fusion is paramount; Mix RL when training a unified model without experts, with domain proportions adjusted for cross-domain transfer; and MOPD when preserving domain-specific gains matters more than surpassing teachers or minimizing end-to-end cost.
Reinforcement learning with verifiable rewards (RLVR) is rapidly advancing the reasoning capabilities of language models, yet the optimization layer that converts reward feedback into weight-space updates remains poorly understood. Building on our prior analysis (Zhu et al., 2025), we study this missing layer through the singular structure of model weights and identify spectral inheritance: RLVR can reuse the base model's weight spectra while acquiring new behavior through changes in the associated input and output singular frames. We operationalize spectral inheritance as Isospectral Optimization (ISO), an RLVR-native, fixed-spectrum optimization framework with complementary offline and online instantiations. Offline, ISO-Merger combines the frame changes of shared-base specialists into a single fixed-spectrum model, requiring no post-merge data, rollouts, gradient updates, or on-policy distillation (OPD). It recovers complementary specialist capabilities and achieves the strongest aggregate performance among the compared data-free merging methods. Online, ISO-Optimizer applies a chosen base optimizer, including AdamW and Muon, to the frame variables while keeping the base spectra fixed. Across reasoning and coding tasks ranging from 1.5B to 8B parameters, ISO-Optimizer improves accuracy in the reported runs and reaches matched scores with substantially fewer training steps. On Qwen3-8B-Base, AdamW reaches an aggregate accuracy of 0.495 after 270 training steps. ISO-AdamW reaches the same accuracy after only 100 training steps and improves further to 0.509 after 210 training steps. Together, ISO offers a concrete answer to RLVR's missing optimization layer: rather than inheriting pre-training optimization wholesale, design post-training around the structure of reward-driven adaptation: inherit the spectrum, optimize the frames.
Hanqing Zhu, Wenyan Cong, Zhizhou Sha et al.· 0 citations
Reinforcement Learning with Verifiable Rewards (RLVR) makes Multimodal Large Language Models more accurate, but the gains are brittle: simply paraphrasing a question or changing the prompt template can degrade them, which challenges reliable deployment in high-stakes scenarios like medical VQA. We trace this to two issues of the standard RL objective. First, the binary verifier conflates format with content, so the reward signal cannot tell a wrong answer apart from a misformatted one. Second, the training distribution covers only a thin slice of the real-world prompts that the model might meet at deployment, so policies that perform well on the training distribution can behave differently under unseen prompts during test. Both failures call for a robust post-training method that helps the policy cover a broader distribution of semantically equivalent prompts, and we identify two measures that help achieve this objective: separating format from semantics in the reward, and applying policy invariance across perturbed prompts with equivalent semantics. We therefore propose Prompt-Invariant RLVR (PIRL), consisting of a dynamic trinary reward and a consistency regularizer based on an embedding-space adversary. Under stress testing, PIRL's average accuracy on benchmarks drops by only $\le 1\%$, where GRPO drops ~3%. On dynamic evaluation, PIRL also achieves the smallest performance drop.
P. Zhou, Zhiwei Tang, Xiaopeng Peng et al.· 0 citations
Deep neural networks excel in various tasks but struggle to generalize across evolving data distributions, leading to significant performance degradation under domain shifts. Domain incremental learning (DIL) addresses this challenge by enabling models to continuously adapt while retaining prior knowledge. Among existing DIL approaches, the parameter-isolation paradigm achieves state-of-the-art performance. However, these methods often adopt a one-size-fits-all approach to adapt to new domains, resulting in either insufficient learning capacity or redundant parameters. In this work, we propose BPG, a unified framework that addresses both challenges through two complementary components: BPG-Adapter, which dynamically determines each domain's adapter hidden dimension based on domain-specific feature separability, and BPG-Inference, a soft domain mixture strategy that integrates multiple domain-specific models at test time, mitigating domain ID misselection. Experimental results on DomainNet, CDDB, and CORe50 demonstrate that BPG consistently outperforms uniform adapter-based approaches and hard domain selection strategies, achieving state-of-the-art average accuracy while reducing forgetting to as low as 0.22% on DomainNet.
Qiang Wang, Songlin Dong, Shaokun Wang et al.· 0 citations
This thesis proposes a unified two-axis framework that organizes SFT and RL methods along a data axis (off-policy to on-policy) and a loss function axis (positive-only to positive-plus-negative to GRPO) and enables controlled ablations of individual components.
G. Kim, Chair Chenyan Xiong, Aditi Raghunathan· 0 citations
River, a simple training recipe that improves reward quality by filtering low-quality environments and augmenting outcome rewards with process-level behavior regularization is proposed, which achieves the best performance among evaluated open-source RL-trained 8B models across four terminal-agent benchmarks.
Yi-Fan Yao, Bo Pang, Xuan-Phi Nguyen et al.· 0 citations
On-policy distillation (OPD) transfers teacher capabilities by supervising trajectories sampled from the student's own policy, yet its generalization behavior remains poorly understood, as most studies evaluate OPD on a single domain and on benchmarks close to the training data. We present a controlled study that varies one generalization factor at a time, from in-domain distribution shifts to cross-domain transfer and the multi-teacher setting. We find that OPD transfers a teacher's reasoning behavior rather than its answers to particular problems: training difficulty barely matters, and even problems the teacher never solves are useful. Transfer depends strongly on the origin relationship between teacher and student: same-origin pairs bring the student close to the teacher across languages, reasoning horizons, and even other domains, whereas cross-origin pairs mostly fit the trained distribution. This broad reach is a double-edged sword: since routing prompts to domain experts cannot confine each teacher's influence, combining them yields a mixture-dependent seesaw among their capabilities. These results clarify when OPD generalizes and offer a useful perspective for diagnosing multi-teacher OPD.
Zhaoyi Li, Deyang Kong, Yuan Wei et al.· 0 citations