Sharper Reasoning: Guiding Language Models with Semantic Focus

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Author: Denis Avetisyan

A new reinforcement learning framework leverages semantic curriculum learning and token entropy to improve the reasoning abilities of large language models.

The system employs a curriculum learning strategy guided by semantic entropy, progressively refining performance while optimization focuses on low-entropy tokens to encourage stable and predictable behavior-a process acknowledging that all systems inevitably degrade, and graceful aging relies on minimizing disruptive fluctuations.
The system employs a curriculum learning strategy guided by semantic entropy, progressively refining performance while optimization focuses on low-entropy tokens to encourage stable and predictable behavior-a process acknowledging that all systems inevitably degrade, and graceful aging relies on minimizing disruptive fluctuations.

This research introduces SENT, a method for mitigating entropy collapse and optimizing token-level performance in LLM reasoning tasks.

While reinforcement learning has proven effective for enhancing the reasoning abilities of large language models, a critical limitation-entropy collapse-often hinders policy exploration and ultimately restricts performance. This paper, ‘Efficient Reinforcement Learning with Semantic and Token Entropy for LLM Reasoning’, addresses this challenge by introducing a novel framework that strategically leverages both semantic and token-level entropy signals. Specifically, the authors combine entropy-guided curriculum learning with targeted KL regularization to mitigate entropy collapse and improve reasoning across diverse benchmarks. Could this approach unlock more robust and adaptable reasoning capabilities in future large language models?

The Inevitable Narrowing: Entropy and the Limits of Efficiency

Despite their demonstrated successes, contemporary reinforcement learning policies are increasingly vulnerable to a phenomenon termed ‘Entropy Collapse’. This occurs when an agent prematurely converges on a limited set of actions, effectively curtailing its exploratory behavior. Initially, focusing on high-probability actions appears efficient, yielding quick rewards; however, this prioritization inadvertently restricts the agent’s capacity to discover potentially superior, yet less obvious, strategies. The result is a policy that performs well within a narrow scope but lacks the adaptability necessary to thrive in complex or changing environments, ultimately hindering the pursuit of truly optimal solutions. This collapse isn’t a failure of learning, but rather a consequence of an overly efficient algorithm becoming trapped in a local maximum, sacrificing long-term potential for immediate gains.

The pursuit of efficiency in reinforcement learning can paradoxically hinder long-term success through a phenomenon where agents prematurely converge on suboptimal solutions. As an agent repeatedly chooses actions perceived as highly probable, its exploration of alternative strategies diminishes, creating a self-limiting cycle. This over-reliance on high-probability actions-driven by algorithms optimizing for immediate reward-effectively narrows the agent’s search space. Consequently, even if a more advantageous, yet initially less probable, strategy exists, the agent may never discover it, becoming trapped in a local optimum. This ‘entropy collapse’ underscores the critical balance between exploitation of known rewards and continued exploration of the unknown, highlighting that maximizing immediate gains can inadvertently preclude the discovery of truly optimal policies.

The tendency of reinforcement learning agents to prematurely converge on suboptimal solutions is often driven by a prioritization of ‘low-entropy tokens’ – predictable elements within the decision-making process. These tokens, representing actions or states with high initial probabilities, offer immediate rewards and thus become favored by the agent. However, this preference inadvertently narrows the scope of exploration, as the agent dedicates increasing resources to exploiting known, high-probability paths while neglecting potentially superior, yet less predictable, alternatives. This creates a feedback loop where the agent becomes increasingly confident in its limited knowledge, effectively ‘collapsing’ its entropy and hindering the discovery of genuinely optimal strategies. Consequently, the initial efficiency gained from exploiting low-entropy tokens is ultimately offset by the long-term cost of a restricted and potentially flawed policy.

Learning curves demonstrate that both 1.5B and 7B models decrease entropy during training, with the GRPO method employing a mask on low-entropy tokens consistently improving performance as indicated by the shaded standard error.
Learning curves demonstrate that both 1.5B and 7B models decrease entropy during training, with the GRPO method employing a mask on low-entropy tokens consistently improving performance as indicated by the shaded standard error.

Restoring the Spectrum: Regularization as a Countermeasure

KL Regularization is implemented as a targeted intervention to mitigate Entropy Collapse during reinforcement learning. This technique introduces a penalty term to the policy update step, directly proportional to the Kullback-Leibler divergence $D_{KL}(π(a|s) || π_{old}(a|s))$. By quantifying the difference between the current policy $π$ and a prior policy $π_{old}$, KL Regularization discourages substantial shifts in the agent’s behavior. The strength of this penalty is controlled by a hyperparameter, $\beta$, allowing for tunable constraint of policy updates and preventing overconfidence in potentially limited action spaces.

KL Regularization functions by adding a penalty term to the policy update step, proportional to the Kullback-Leibler divergence between the new policy and a reference or prior policy distribution. This divergence, $D_{KL}(π_{θ}(a|s) || π_{θ_{old}}(a|s))$, quantifies the information lost when approximating the prior distribution with the updated policy. By penalizing substantial deviations – large KL divergence values – the regularization prevents the policy from converging too quickly on a narrow set of actions, even if those actions initially yield high rewards. This is particularly effective in scenarios where the action space is limited or contains easily exploitable elements, thereby mitigating the risk of over-optimization and promoting more robust and generalizable behavior.

KL Regularization mitigates the impact of low-entropy tokens by introducing a penalty proportional to the Kullback-Leibler divergence between the current policy and a reference policy. This discourages the agent from converging to solutions heavily dependent on predictable, low-entropy actions. Specifically, the penalty term forces the policy to maintain a degree of distributional similarity to the prior, preventing excessive confidence in a limited set of actions and promoting exploration of the broader action space, even if those actions initially appear less optimal. The strength of this regularization is controlled by a hyperparameter, allowing for a tunable trade-off between maximizing reward and maintaining distributional robustness.

Learning curves demonstrate that incorporating entropy regularization (w/ En) and masking low-entropy tokens (w/ Mask) into the GRPO method improves learning stability, as indicated by the reduced standard error shown in the shaded regions.
Learning curves demonstrate that incorporating entropy regularization (w/ En) and masking low-entropy tokens (w/ Mask) into the GRPO method improves learning stability, as indicated by the reduced standard error shown in the shaded regions.

Evidence of Resilience: Sustained Exploration and Performance Gains

KL Regularization functions as a method for preventing Entropy Collapse in reinforcement learning by penalizing significant deviations of the policy from a prior distribution. Empirical evaluations across multiple challenging benchmarks indicate that implementation of KL Regularization consistently maintains higher entropy levels during training compared to methods lacking this regularization. This stabilization is achieved by adding a term to the loss function proportional to the Kullback-Leibler divergence between the current policy and a reference policy, effectively discouraging overly confident or deterministic behavior that leads to premature convergence and reduced exploration. The result is improved generalization and robustness, particularly in environments with sparse rewards or complex state spaces, as the agent retains the capacity to explore a wider range of actions throughout the learning process.

The SENT framework demonstrably achieves state-of-the-art performance in benchmark evaluations. Specifically, utilizing a 1.5B parameter model, SENT attained a ‘Pass@32’ score of 68.57. This metric quantifies the proportion of tasks successfully completed within 32 attempts. Importantly, this result represents a 3.26-point improvement over the performance of the next best-performing method on the same benchmarks, indicating a statistically significant advancement in task completion rates.

The proposed method achieved an average score of 44.01 (‘Avg@32’) when evaluated across a diverse set of 1818 reinforcement learning tasks. Critically, this performance was sustained by maintaining stable entropy levels throughout the training process. Unlike baseline methods which exhibited entropy collapse – a phenomenon leading to diminished exploration and suboptimal policy learning – our approach consistently preserved entropy, indicating robust and continued exploration across all evaluated tasks. This stability directly correlates with the improved average performance observed and suggests a mitigation of the issues associated with premature convergence to local optima.

Evaluations conducted using the Qwen3-14B model yielded a ‘Pass@16’ score of 100, indicating successful completion of all sixteen test cases within the evaluation suite. This represents optimal performance on this specific model size. Furthermore, performance metrics on the AIME2024 and AIME2025 benchmarks demonstrate a statistically significant improvement over existing methods, suggesting enhanced generalization capabilities and robustness of the implemented approach on these challenging datasets.

Semantic entropy data from the training set and its token entropy frequency distribution reveal the characteristics of the learned representations.
Semantic entropy data from the training set and its token entropy frequency distribution reveal the characteristics of the learned representations.

The pursuit of efficient reinforcement learning, as detailed in this work, inherently acknowledges the transient nature of even the most sophisticated systems. The framework, SENT, attempts to navigate the challenge of entropy collapse – a form of decay within the model’s reasoning process – through semantic curriculum learning and token-level optimization. This echoes a core principle: any simplification, such as reducing entropy to accelerate learning, carries a future cost. Ada Lovelace observed, “The Analytical Engine has no pretensions whatever to originate anything. It can do whatever we know how to order it to perform.” This sentiment resonates deeply; SENT doesn’t create reasoning ability, but meticulously structures the learning process to coax it forth, understanding that the order of operations – the curriculum – is paramount in delaying the inevitable system decay and maximizing performance over time.

The Long Refactor

The pursuit of efficient reinforcement learning for large language models, as exemplified by this work, isn’t about achieving a final state-it’s simply delaying the inevitable. Entropy collapse, a fundamental decay in model exploration, is addressed here with semantic curriculum learning and token-level optimization, but it’s a local fix within a larger system relentlessly tending toward uniformity. Versioning, in essence, is a form of memory, a recording of states before the arrow of time points toward further refactoring. The true challenge lies not in minimizing entropy now, but in building systems robust enough to anticipate and gracefully accommodate its eventual return.

Future iterations will likely focus on dynamic curricula-systems capable of self-assessment and adjustment. However, the temptation to chase ever-increasing scale must be tempered with a recognition that complexity itself breeds fragility. A more fruitful avenue might be exploring intrinsic motivation-designing models that want to explore, not merely those incentivized to do so. This shifts the focus from extrinsic reward to the inherent properties of the system itself-a subtle but vital distinction.

Ultimately, the field must acknowledge that reasoning isn’t a feature to be added to a language model, but an emergent property of a sufficiently complex, and fundamentally unstable, system. The goal isn’t perfection, but resilience-the ability to maintain functionality even as the system inevitably degrades. The long refactor never truly ends; it merely enters new phases.

Original article: https://arxiv.org/pdf/2512.04359.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/

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2025-12-07 22:13