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Paper · 2603.10624 · 2026

Reinforcement Learning with Conditional Expectation Reward

Yixin Cao, Changyi Xiao, Caijun Xu

arXiv · PDF · Open in the Atlas

Code that ran

We lifted 13 functions out of this paper's own repositories and ran 6 of them in a sandbox. "Ran" means the function executed on a synthesized input and returned a value. It is not a reproduction of the paper's results.

RepositoryRoleRan
changyi7231/CER canonical 6 of 13
FunctionStatusWhere it lives
exact_match Ran changyi7231/CER/recipe/cer/src/reward_manager.py
code served (permissive licence) · get_code("bacda3216fdce102")
extract_boxed_answer Ran changyi7231/CER/recipe/cer/src/data_preparation.py
code served (permissive licence) · get_code("904946a1f147981f")
extract_solution_answer Ran changyi7231/CER/recipe/cer/src/cer_ray_trainer.py
code served (permissive licence) · get_code("5285b1569c3d6597")
get_prompt Ran changyi7231/CER/recipe/cer/src/data_preparation.py
code served (permissive licence) · get_code("a6f637988f82514b")
is_ipv4 Ran changyi7231/CER/verl/utils/net_utils.py
code served (permissive licence) · get_code("735e93af30b15fa9")
unpad_dataproto Ran changyi7231/CER/verl/protocol.py
code served (permissive licence) · get_code("25f0ea3f460f6ce1")
get_generation_config Not yet run changyi7231/CER/verl/utils/model.py
code served (permissive licence) · get_code("c9d58036da0286f2")
get_huggingface_actor_config Not yet run changyi7231/CER/verl/utils/model.py
code served (permissive licence) · get_code("59904a8955b34252")
get_weight_loader Not yet run changyi7231/CER/verl/models/weight_loader_registry.py
code served (permissive licence) · get_code("acf240079d434746")
get_weight_saver Not yet run changyi7231/CER/verl/models/weight_loader_registry.py
code served (permissive licence) · get_code("55f217ce71432b58")
is_ipv6 Not yet run changyi7231/CER/verl/utils/net_utils.py
code served (permissive licence) · get_code("705afe175ad8e404")
load_state_dict_to_megatron_gptmodel Not yet run changyi7231/CER/verl/models/mcore/loader.py
code served (permissive licence) · get_code("1853101234cf952e")
squeeze Not yet run changyi7231/CER/verl/utils/model.py
code served (permissive licence) · get_code("3b15e2ac7497c441")

Repositories linked to this paper

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Abstract

Reinforcement Learning with Verifiable Rewards (RLVR) has proven effective in enhancing the reasoning capabilities of large language models, particularly in domains such as mathematics where reliable rule-based verifiers can be constructed. However, the reliance on handcrafted, domainspecific verification rules substantially limits the applicability of RLVR to general reasoning domains with free-form answers, where valid answers often exhibit significant variability, making it difficult to establish complete and accurate rules. To address this limitation, we propose Conditional Expectation Reward (CER), which leverages the large language model itself as an implicit verifier, and is therefore applicable to general domains and eliminates the need for external verifiers or auxiliary models. CER is defined as the expected likelihood of generating the reference answer conditioned on the generated answer. In contrast to rule-based verifiers that yield binary feedback, CER provides a soft, graded reward signal that reflects varying degrees of correctness, making it better suited to tasks where answers vary in correctness. Experimental results demonstrate that CER is effective across a wide range of reasoning tasks, spanning both mathematical and general domains, indicating that CER serves as a flexible and general verification mechanism. The code is available at https: //github.com/changyi7231/CER.

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