Zhejian Zhou

Though Large Language Models (LLMs) have shown remarkable abilities in mathematics reasoning, they are still struggling with performing numeric operations accurately, such as addition and multiplication. Numbers can be tokenized into tokens in various ways by different LLMs and affect the numeric operations performance. Currently, there are two representatives: 1) Tokenize into 1-digit, and 2) Tokenize into 1∼3 digit. The difference is roughly equivalent to using different numeral systems (namely base 10 or base 10^3). In light of this, we study the scaling behavior of different numeral systems in the context of transformer-based large language models. We empirically show that a base 10 system is consistently more data-efficient than a base 10^2 or 10^3 system across training data scale, model sizes under from-scratch training settings, while different number systems have very similar fine-tuning performances. We attribute this to higher token frequencies of a base 10 system. Additionally, we reveal extrapolation behavior patterns on addition and multiplication. We identify that base 100 and base 1000 systems struggle on token-level discernment and token-level operations. We also sheds light on the mechanism learnt by the models.

The math abilities of large language models can represent their abstract reasoning ability. In this paper, we introduce and open-source our math reasoning LLMs InternLM-Math which is continue pre-trained from InternLM2. We unify chain-of-thought reasoning, reward modeling, formal reasoning, data augmentation, and code interpreter in a unified seq2seq format and supervise our model to be a versatile math reasoner, verifier, prover, and augmenter. These abilities can be used to develop the next math LLMs or self-iteration. InternLM-Math obtains open-sourced state-of-the-art performance under the setting of in-context learning, supervised fine-tuning, and code-assisted reasoning in various informal and formal benchmarks including GSM8K, MATH, Hungary math exam, MathBench-ZH, and MiniF2F. Our pre-trained model achieves 30.3 on the MiniF2F test set without fine-tuning. We further explore how to use LEAN to solve math problems and study its performance under the setting of multi-task learning which shows the possibility of using LEAN as a unified platform for solving and proving in math. Our models, codes, and data are released at https://github.com/InternLM/InternLM-Math.

WebAssembly enables near-native execution in web applications and is increasingly adopted for tasks that demand high performance and robust security. However, its assembly-like syntax, implicit stack machine, and low-level data types make it extremely difficult for human developers to understand, spurring the need for effective WebAssembly reverse engineering techniques. In this paper, we propose StackSight, a novel neurosymbolic approach that combines Large Language Models (LLMs) with advanced program analysis to decompile complex WebAssembly code into readable C++ snippets. StackSight visualizes and tracks virtual stack alterations via a static analysis algorithm and then applies chain-of-thought prompting to harness LLM’s complex reasoning capabilities. Evaluation results show that StackSight significantly improves WebAssembly decompilation. Our user study also demonstrates that code snippets generated by StackSight have significantly higher win rates and enable a better grasp of code semantics.

Conversational large language models (LLMs) such as ChatGPT and GPT-4 have recently exhibited remarkable capabilities across various domains, capturing widespread attention from the public. To facilitate this line of research, in this paper, we report the development of MOSS, an open-sourced conversational LLM that contains 16 B parameters and can perform a variety of instructions in multi-turn interactions with humans. The base model of MOSS is pre-trained on large-scale unlabeled English, Chinese, and code data. To optimize the model for dialogue, we generate 1.1 M synthetic conversations based on user prompts collected through our earlier versions of the model API. We then perform preference-aware training on preference data annotated from AI feedback. Evaluation results on real-world use cases and academic benchmarks demonstrate the effectiveness of the proposed approaches. In addition, we present an effective practice to augment MOSS with several external tools. Through the development of MOSS, we have established a complete technical roadmap for large language models from pre-training, supervised fine-tuning to alignment, verifying the feasibility of chatGPT under resource-limited conditions and providing a reference for both the academic and industrial communities. Model weights and code are publicly available at https://github.com/OpenMOSS/MOSS.