Xunyu Zhu

Xunyu Zhu, Jian Li, Yong Liu et al.

Differentiable Neural Architecture Search (DARTS) is becoming more and more popular among Neural Architecture Search (NAS) methods because of its high search efficiency and low compute cost. However, the stability of DARTS is very inferior, especially skip connections aggregation that leads to performance collapse. Though existing methods leverage Hessian eigenvalues to alleviate skip connections aggregation, they make DARTS unable to explore architectures with better performance. In the paper, we propose operation-level progressive differentiable neural architecture search (OPP-DARTS) to avoid skip connections aggregation and explore better architectures simultaneously. We first divide the search process into several stages during the search phase and increase candidate operations into the search space progressively at the beginning of each stage. It can effectively alleviate the unfair competition between operations during the search phase of DARTS by offsetting the inherent unfair advantage of the skip connection over other operations. Besides, to keep the competition between operations relatively fair and select the operation from the candidate operations set that makes training loss of the supernet largest. The experiment results indicate that our method is effective and efficient. Our method's performance on CIFAR-10 is superior to the architecture found by standard DARTS, and the transferability of our method also surpasses standard DARTS. We further demonstrate the robustness of our method on three simple search spaces, i.e., S2, S3, S4, and the results show us that our method is more robust than standard DARTS. Our code is available at https://github.com/zxunyu/OPP-DARTS.

Xunyu Zhu, Jian Li, Can Ma et al.

Large Language Models (LLMs) have demonstrated exceptional proficiency in mathematical reasoning tasks due to their extensive parameter counts and training on vast datasets. Despite these capabilities, deploying LLMs is hindered by their computational demands. Distilling LLM mathematical reasoning into Smaller Language Models (SLMs) has emerged as a solution to this challenge, although these smaller models often suffer from errors in calculation and semantic understanding. Prior work has proposed Program-of-Thought Distillation (PoTD) to avoid calculation error. To further address semantic understanding errors, we propose Key-Point-Driven Mathematical Reasoning Distillation (KPDD). KPDD enhances the reasoning performance of SLMs by breaking down the problem-solving process into three stages: Core Question Extraction, Problem-Solving Information Extraction, and Step-by-Step Solution. This method is further divided into KPDD-CoT, which generates Chain-of-Thought rationales, and KPDD-PoT, which creates Program-of-Thought rationales. The experiment results show that KPDD-CoT significantly improves reasoning abilities, while KPDD-PoT achieves state-of-the-art performance in mathematical reasoning tasks. Our approach effectively mitigates misunderstanding errors, advancing the deployment of efficient and capable SLMs.

Xunyu Zhu, Jian Li, Yong Liu et al.

This work addresses the challenge of democratizing advanced Large Language Models (LLMs) by compressing their mathematical reasoning capabilities into sub-billion parameter Small Language Models (SLMs) without compromising performance. We introduce Equation-of-Thought Distillation (EoTD), a novel technique that encapsulates the reasoning process into equation-based representations to construct an EoTD dataset for fine-tuning SLMs. Additionally, we propose the Ensemble Thoughts Distillation (ETD) framework to enhance the reasoning performance of SLMs. This involves creating a reasoning dataset with multiple thought processes, including Chain-of-Thought (CoT), Program-of-Thought (PoT), and Equation-of-Thought (EoT), and using it for fine-tuning. Our experimental performance demonstrates that EoTD significantly boosts the reasoning abilities of SLMs, while ETD enables these models to achieve state-of-the-art reasoning performance.

Xunyu Zhu, Jian Li, Can Ma et al.

Large Language Models (LLMs) demonstrate exceptional reasoning capabilities, often achieving state-of-the-art performance in various tasks. However, their substantial computational and memory demands, due to billions of parameters, hinder deployment in resource-constrained environments. A promising solution is knowledge distillation, where LLMs transfer reasoning capabilities to Small Language Models (SLMs, $\le$ 1B parameters), enabling wider deployment on low-resource devices. Existing methods primarily focus on generating high-quality reasoning rationales for distillation datasets but often neglect the critical role of data quantity and quality. To address these challenges, we propose a Feedback-Driven Distillation (FDD) framework to enhance SLMs' mathematical reasoning capabilities. In the initialization stage, a distillation dataset is constructed by prompting LLMs to pair mathematical problems with corresponding reasoning rationales. We classify problems into easy and hard categories based on SLM performance. For easy problems, LLMs generate more complex variations, while for hard problems, new questions of similar complexity are synthesized. In addition, we propose a multi-round distillation paradigm to iteratively enrich the distillation datasets, thereby progressively improving the mathematical reasoning abilities of SLMs. Experimental results demonstrate that our method can make SLMs achieve SOTA mathematical reasoning performance.