Large Language Models (LLMs) have demonstrated strong mathematical reasoning abilities through supervised fine-tuning and reinforcement learning. However, existing Process Reward Models (PRMs) are vulnerable to reward hacking and require expensive, large-scale annotation of reasoning steps, limiting their reliability and scalability. To address the first problem, we propose a novel reward model approach, Hierarchical Reward Model (HRM), which evaluates both individual and consecutive reasoning steps from fine-grained and coarse-grained level. HRM excels at assessing multi-step mathematical reasoning coherence, particularly in cases where a flawed step is later corrected through self-reflection. Furthermore, to address the inefficiency of autonomously annotating PRM training data via Monte Carlo Tree Search (MCTS), we propose a lightweight data augmentation strategy, Hierarchical Node Compression (HNC), which merges consecutive reasoning steps within the tree structure. Applying HNC to MCTS-generated reasoning trajectories increases the diversity and robustness of HRM training data, while introducing controlled noise with minimal computational overhead. Empirical results on the PRM800K dataset demonstrate that HRM, in conjunction with HNC, achieves superior stability and reliability in evaluation compared to PRM. Furthermore, cross-domain evaluations on MATH500 and GSM8K dataset confirm HRM’s superior generalization and robustness across diverse mathematical reasoning tasks.

Transformer-based large language models (LLM) have been widely used in language processing applications. However, due to the memory constraints of the devices, most of them restrict the context window. Even though recurrent models in previous works can memorize past tokens to enable unlimited context and maintain effectiveness, they have “flat” memory architectures. Such architectures have limitations in selecting and filtering information. Since humans are good at learning and self-adjustment, we believe that imitating brain memory hierarchy is beneficial for model memorization. Thus, we propose the Hierarchical Memory Transformer (HMT), a novel framework that facilitates a model’s long-context processing ability by imitating human memorization behavior. Leveraging memory-augmented segment-level recurrence, we organize the memory hierarchy by preserving tokens from early input segments, passing memory embeddings along the sequence, and recalling relevant information from history. Evaluating general language modeling, question-answering tasks, and the summarization task, we show that HMT consistently improves the long-context processing ability of existing models. Furthermore, HMT achieves a comparable or superior generation quality to long-context LLMs with 2 ∼ 57× fewer parameters and 2.5 ∼ 116× less inference memory, significantly outperforming previous memory-augmented models.