Ke Wang

Ke Wang, Houxing Ren, Aojun Zhou et al.

The recently released GPT-4 Code Interpreter has demonstrated remarkable proficiency in solving challenging math problems, primarily attributed to its ability to seamlessly reason with natural language, generate code, execute code, and continue reasoning based on the execution output. In this paper, we present a method to fine-tune open-source language models, enabling them to use code for modeling and deriving math equations and, consequently, enhancing their mathematical reasoning abilities. We propose a method of generating novel and high-quality datasets with math problems and their code-based solutions, referred to as MathCodeInstruct. Each solution interleaves natural language, code, and execution results. We also introduce a customized supervised fine-tuning and inference approach. This approach yields the MathCoder models, a family of models capable of generating code-based solutions for solving challenging math problems. Impressively, the MathCoder models achieve state-of-the-art scores among open-source LLMs on the MATH (45.2%) and GSM8K (83.9%) datasets, substantially outperforming other open-source alternatives. Notably, the MathCoder model not only surpasses ChatGPT-3.5 and PaLM-2 on GSM8K and MATH but also outperforms GPT-4 on the competition-level MATH dataset. The dataset and models will be released at https://github.com/mathllm/MathCoder.

Yu Wang, Ke Wang

Study patterns that models have learned has long been a focus of pattern recognition research. Explaining what patterns are discovered from training data, and how patterns are generalized to unseen data are instrumental to understanding and advancing the pattern recognition methods. Unfortunately, the vast majority of the application domains deal with continuous data (i.e. statistical in nature) out of which extracted patterns can not be formally defined. For example, in image classification, there does not exist a principle definition for a label of cat or dog. Even in natural language, the meaning of a word can vary with the context it is surrounded by. Unlike the aforementioned data format, programs are a unique data structure with a well-defined syntax and semantics, which creates a golden opportunity to formalize what models have learned from source code. This paper presents the first formal definition of patterns discovered by code summarization models (i.e. models that predict the name of a method given its body), and gives a sound algorithm to infer a context-free grammar (CFG) that formally describes the learned patterns. We realize our approach in PATIC which produces CFGs for summarizing the patterns discovered by code summarization models. In particular, we pick two prominent instances, code2vec and code2seq, to evaluate PATIC. PATIC shows that the patterns extracted by each model are heavily restricted to local, and syntactic code structures with little to none semantic implication. Based on these findings, we present two example uses of the formal definition of patterns: a new method for evaluating the robustness and a new technique for improving the accuracy of code summarization models. Our work opens up this exciting, new direction of studying what models have learned from source code.

Youssef A. Ait Alama, Sampada Sakpal, Ke Wang et al.

Hardware failures are a growing challenge for machine learning accelerators, many of which are based on systolic arrays. When a permanent hardware failure occurs in a systolic array, existing solutions include localizing and isolating the faulty processing element (PE), using a redundant PE for re-execution, or in some extreme cases decommissioning the entire accelerator for further investigation. In this paper, we propose novel algorithmic approaches that mitigate permanent hardware faults in neural network (NN) accelerators by uniquely integrating the behavior of the faulty component instead of bypassing it. In doing so, we aim for a more sustainable use of the accelerator where faulty hardware is neither bypassed nor discarded, instead being given a second life. We first introduce a CUDA-accelerated systolic array simulator in PyTorch, which enabled us to quantify the impact of permanent faults appearing on links connecting two PEs or in weight registers, where one bit is stuck at 0 or 1 in the float32, float16, or bfloat16 representation. We then propose several algorithmic mitigation techniques for a subset of stuck-at faults, such as Invertible Scaling or Shifting of activations and weights, or fine tuning with the faulty behavior. Notably, the proposed techniques do not require any hardware modification, instead relying on existing components of widely used systolic array based accelerators, such as normalization, activation, and storage units. Extensive experimental evaluations using fully connected and convolutional NNs trained on MNIST, CIFAR-10 and ImageNet show that the proposed fault-tolerant approach matches or gets very close to the original fault-free accuracy.