Significant strides have been made in artificial intelligence and mathematical problem-solving, especially with the arrival of huge language models. Nevertheless, these models still grapple with complex mathematical challenges. Microsoft and Tsinghua University researchers introduce TORA, a groundbreaking approach referred to as Tool-integrated Reasoning Agents, designed to tackle intricate mathematical problems by mixing natural language reasoning with external computational tools.

Researchers have turned to integrating external tools like calculators, code interpreters, and symbolic solvers to handle these challenges. While program-based methods have effectively transformed reasoning tasks into program synthesis tasks, they face nuanced reasoning, planning, and error-handling issues. Augmenting Large language models (LLMs) with these tools has significantly improved reasoning and generation performance. Knowledge distillation techniques, like LLM-generated trajectories for fine-tuning, have also played a job in transferring knowledge from teacher models to student models. 

LLMs have made notable strides in language tasks, including mathematical reasoning, yet complex mathematics stays difficult. Current strategies for enhancing mathematical prowess in LLMs involve step-by-step natural language reasoning and program synthesis. While the previous excels in semantic and abstract reasoning, the latter thrives in rigorous operations and might tap into specialized tools like equation solvers. Their approach outperforms open-source models on mathematical reasoning datasets, achieving high accuracy, particularly on the competition-level MATHS dataset. Their method also offers insights into tool interaction’s benefits and unresolved challenges in mathematical reasoning, guiding future research on this domain.

TORA models were trained using interactive tool-use trajectories on mathematical datasets, applying imitation learning on the annotations and refining reasoning behavior with output space shaping. GPT-4 generated diverse reasoning patterns on training sets. Instructions and few-shot examples were composed in an interleaved format for prompt curation, and TORA’s effectiveness, which integrates rationales with programs, was evaluated. It achieved significant reasoning performance improvements. The challenges identified included a deeper understanding of geometric space and addressing complex symbolic reasoning in Intermediate Algebra and Precalculus problems.

TORA enhances mathematical reasoning by integrating natural language reasoning with external tools. TORA models excel on ten mathematical reasoning datasets, outperforming open-source models with 13%-19% absolute improvements on average and in program-based problem-solving. Their approach analyses tool interaction advantages and challenges, highlighting the effectiveness of TORA’s Tool-integrated Reasoning format, which interweaves rationales and program execution.

TORA represents a major mathematical problem-solving advancement by seamlessly integrating natural language rationale with program-based tool use. It achieves state-of-the-art performance across various mathematical reasoning tasks, surpassing existing rationale and program-based approaches. The great evaluation of tool interaction advantages and challenges offers critical insights for future research, promising to develop more advanced and adaptable reasoning agents.

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