Reinforcement Learning for Reasoning in Small LLMs: What Works and What Doesn't

Enhancing the reasoning capabilities of large language models (LLMs) typically relies on massive computational resources and extensive datasets, limiting accessibility for resource-constrained settings. Our study investigates the potential of reinforcement learning (RL) to improve reasoning in small LLMs, focusing on a 1.5-billion-parameter model, DeepSeek-R1-Distill-Qwen-1.5B, under strict constraints: training on 4 NVIDIA A40 GPUs (48 GB VRAM each) within 24 hours. Adapting the Group Relative Policy Optimization (GRPO) algorithm and curating a compact, high-quality mathematical reasoning dataset, we conducted three experiments to explore model behavior and performance. Our results demonstrate rapid reasoning gains - e.g., AMC23 accuracy rising from 63% to 80% and AIME24 reaching 46.7%, surpassing o1-preview - using only 7,000 samples and a $42 training cost, compared to thousands of dollars for baseline models. However, challenges such as optimization instability and length constraints emerged with prolonged training. These findings highlight the efficacy of RL-based fine-tuning for small LLMs, offering a cost-effective alternative to large-scale approaches. We release our code and datasets as open-source resources, providing insights into trade-offs and laying a foundation for scalable, reasoning-capable LLMs in resource-limited environments. All are available at https://github.com/knoveleng/open-rs.

MoD: A Distribution-Based Approach for Merging Large Language Models

Large language models (LLMs) have enabled the development of numerous specialized, task-specific variants. However, the maintenance and deployment of these individual models present substantial challenges in terms of resource utilization and operational efficiency. In this work, we propose the \textit{Mixture of Distributions (MoD)} framework, a novel approach for merging LLMs that operates directly on their output probability distributions, rather than on model weights. Unlike traditional weight-averaging methods, MoD effectively preserves the specialized capabilities of individual models while enabling efficient knowledge sharing across tasks. Through extensive experimentation on mathematical reasoning benchmarks using Qwen2.5 models, we demonstrate that MoD significantly outperforms existing model merging techniques across multiple benchmarks. All code, data, and experimental materials are published at https://github.com/knovel-eng/mod.

wav2graph: A Framework for Supervised Learning Knowledge Graph from Speech

Knowledge graphs (KGs) enhance the performance of large language models (LLMs) and search engines by providing structured, interconnected data that improves reasoning and context-awareness. However, KGs only focus on text data, thereby neglecting other modalities such as speech. In this work, we introduce wav2graph, the first framework for supervised learning knowledge graph from speech data. Our pipeline are straightforward: (1) constructing a KG based on transcribed spoken utterances and a named entity database, (2) converting KG into embedding vectors, and (3) training graph neural networks (GNNs) for node classification and link prediction tasks. Through extensive experiments conducted in inductive and transductive learning contexts using state-of-the-art GNN models, we provide baseline results and error analysis for node classification and link prediction tasks on human transcripts and automatic speech recognition (ASR) transcripts, including evaluations using both encoder-based and decoder-based node embeddings, as well as monolingual and multilingual acoustic pre-trained models. All related code, data, and models are published online.