Beyond the Exploration-Exploitation Trade-off: A Hidden State Approach
  for LLM Reasoning in RLVR
A prevailing view in Reinforcement Learning for Verifiable Rewards (RLVR)
interprets recent progress through the lens of an exploration-exploitation
trade-off, a perspective largely shaped by token-level metrics. We re-examine
this perspective, proposing that this perceived trade-off may not be a
fundamental constraint but rather an artifact of the measurement level. To
investigate this, we shift the analysis to the semantically rich hidden-state
space, adopting Effective Rank (ER) to quantify exploration and proposing its
novel first- and second-order derivatives, named Effective Rank Velocity (ERV)
and Effective Rank Acceleration (ERA), to capture exploitation dynamics. Our
analysis reveals that at the hidden-state level, exploration and exploitation
could be decoupled (Sec. 4). This finding reveals an opportunity to enhance
both capacities simultaneously. This insight motivates our method,
Velocity-Exploiting Rank-Learning (VERL), the first to operationalize the
principle of synergistic exploration-exploitation enhancement by directly
shaping the RL advantage function. The key innovation is leveraging the
theoretically stable ERA as a predictive meta-controller to create a
synergistic, dual-channel incentive structure. Instead of forcing a trade-off,
VERL prospectively amplifies rewards for exploration to preempt overconfidence
and reinforces exploitative gains to consolidate reasoning. Experiments across
diverse LLMs and reasoning benchmarks show consistent gains, including up to
21.4% absolute accuracy improvement on the challenging Gaokao 2024 dataset.
68db671fd2bf1f4b15ec762e
Fanding Huang
claimed_verified
2025-09-30T06:29:22.925Z
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Fanding Huang
user
Niugan
68db671fd2bf1f4b15ec762f
Guanbo Huang
claimed_verified
2025-09-30T07:12:27.555Z
68db7b19a72e7113caffb1cb
/avatars/355871f30bdc97141004d15b2dc2378c.svg
Guanbo huang
user
Gambel
68db671fd2bf1f4b15ec7630
Xiao Fan
claimed_verified
2025-09-30T06:29:26.824Z
670bd8e972c44e17cd6900bd
/avatars/898137782df8762e3a6ca4451dd871ea.svg
Fan Xiao
user
AnikiFan
68db671fd2bf1f4b15ec7631
Yi He
68db671fd2bf1f4b15ec7632
Xiao Liang
claimed_verified
2025-09-30T06:00:17.152Z
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https://cdn-avatars.huggingface.co/v1/production/uploads/6560763e152b659e623865ae/cTT2jGnPU_8XMrUTvqZ2h.jpeg
Xiao Liang
user
MasterVito
68db671fd2bf1f4b15ec7633
Xiao Chen
claimed_verified
2025-09-30T06:00:14.332Z
676fcb88f40e1460661f0d9b
https://cdn-avatars.huggingface.co/v1/production/uploads/no-auth/U-npvTTY6ub1bjIHbjVjm.png
Xiao Chen
user
Cevaaa
68db671fd2bf1f4b15ec7634
Qinting Jiang
68db671fd2bf1f4b15ec7635
Faisal Nadeem Khan
68db671fd2bf1f4b15ec7636
Jingyan Jiang
claimed_verified
2025-10-01T10:24:38.274Z
6575a4a6b238c76bbafaae04
/avatars/9efa2509af86346405f4f49235d9d3b6.svg
jingyan
user
ginger0106
68db671fd2bf1f4b15ec7637
Zhi Wang
Beyond the Exploration-Exploitation Trade-off: A Hidden State Approach
  for LLM Reasoning in RLVR
A prevailing view in Reinforcement Learning for Verifiable Rewards (RLVR)
interprets recent progress through the lens of an exploration-exploitation
trade-off, a perspective largely shaped by token-level metrics. We re-examine
this perspective, proposing that this perceived trade-off may not be a
fundamental constraint but rather an artifact of the measurement level. To
investigate this, we shift the analysis to the semantically rich hidden-state
space, adopting Effective Rank (ER) to quantify exploration and proposing its
novel first- and second-order derivatives, named Effective Rank Velocity (ERV)
and Effective Rank Acceleration (ERA), to capture exploitation dynamics. Our
analysis reveals that at the hidden-state level, exploration and exploitation
could be decoupled (Sec. 4). This finding reveals an opportunity to enhance
both capacities simultaneously. This insight motivates our method,
Velocity-Exploiting Rank-Learning (VERL), the first to operationalize the
principle of synergistic exploration-exploitation enhancement by directly
shaping the RL advantage function. The key innovation is leveraging the
theoretically stable ERA as a predictive meta-controller to create a
synergistic, dual-channel incentive structure. Instead of forcing a trade-off,
VERL prospectively amplifies rewards for exploration to preempt overconfidence
and reinforces exploitative gains to consolidate reasoning. Experiments across
diverse LLMs and reasoning benchmarks show consistent gains, including up to
21.4% absolute accuracy improvement on the challenging Gaokao 2024 dataset.
Re-examining the exploration-exploitation trade-off in Reinforcement Learning for Verifiable Rewards through hidden-state analysis reveals opportunities for simultaneous enhancement using Effective Rank and its derivatives, leading to improved performance in diverse benchmarks.
Reinforcement Learning for Verifiable Rewards exploration-exploitation trade-off token-level metrics semantically rich hidden-state space Effective Rank Effective Rank Velocity Effective Rank Acceleration Velocity-Exploiting Rank-Learning RL advantage function predictive meta-controller dual-channel incentive structure Gaokao 2024 dataset