Reinforcement Learning with Process-Level Feedback for Efficient Mathematical Reasoning in Small Language Models

Abstract

Mathematical reasoning remains one of the most demanding capabilities for language models because it requires multi-step inference, intermediate validation, and resistance to superficial pattern matching. Although large models have achieved notable gains through scale and reinforcement learning, their computational, financial, and environmental costs limit broad deployment. Small language models offer advantages in latency, privacy, and local execution, but they often lack the representational capacity and training signal efficiency required for robust mathematical reasoning. This paper examines reinforcement learning with process-level feedback as a system-level strategy for improving mathematical reasoning in small language models. Rather than treating reinforcement learning as a monolithic optimization procedure, the analysis emphasizes feedback acquisition, verifier reliability, trajectory filtering, reward aggregation, curriculum design, deployment infrastructure, and governance. Process-level feedback can provide denser credit assignment than outcome-only rewards, but it introduces annotation cost, verifier latency, reward hacking risk, and new accountability burdens. The paper argues that efficient reasoning improvement depends less on a single algorithm and more on the alignment of feedback granularity, model capacity, data provenance, evaluation protocols, and deployment constraints. It also considers fairness, robustness, sustainability, and policy implications for educational, scientific, and professional settings. The conclusion recommends hybrid outcome and process supervision, auditable verification layers, adaptive compute budgeting, staged deployment, and human oversight. These measures can make reinforcement learning with process-level feedback a practical pathway for small language models without reproducing the scale-dependent pathologies of larger systems.