Mathematical reasoning remains a challenging area for large language models (LLMs), prompting the development of math-specific LLMs such as LLEMMA, DeepSeekMath, and Qwen2-Math, among others. These models typically follow a two-stage training paradigm: pre-training with math-related corpora and posttraining with problem datasets for supervised fine-tuning (SFT). Despite these efforts, the improvements in mathematical reasoning achieved through continued pre-training (CPT) are often less significant compared to those obtained via SFT. We investigate three primary research questions: (1) Can problem-solving data enhance the model's mathematical reasoning capabilities more effectively than general mathematical corpora during CPT? (2) Are synthetic data from the same source equally effective, and which synthesis methods are most efficient? Our findings indicate that problem-solving data significantly enhances the model's mathematical capabilities compared to general mathematical corpora. We also identify effective data synthesis methods, demonstrating that the tutorship amplification synthesis method achieves the best performance. Furthermore, while SFT facilitates instruction-following abilities, it underperforms compared to CPT with the same data, which can be partially attributed to its poor learning capacity for more challenging problem-solving data. To address the challenge of insufficient mathematical reasoning capabilities in large language models (LLMs), various math-specific LLMs are developed. These models generally follow a common training paradigm. During the pre-training stage, math-related corpora are filtered from extensive internet data to augment the model's mathematical knowledge. Work done during Zui Chen's internship at Guangdong Institute of Smart Education, Jinan University, Guangzhou, China. Model is available at https://huggingface.co/ai4ed/MathGPT-8B This enables the models to follow instructions and produce outputs in the desired format. Recently, there is a growing focus on constructing preference datasets for the solution process to perform Step-DPO (Lai et al., 2024) or online-RLHF (Dong et al., 2024). These approaches aim to obtain more accurate reasoning pathways, thereby significantly enhancing the mathematical reasoning capabilities of the models.

Step-level reward models (SRMs) can significantly enhance mathematical reasoning performance through process supervision or step-level preference alignment based on reinforcement learning. The performance of SRMs is pivotal, as they serve as critical guidelines, ensuring that each step in the reasoning process is aligned with desired outcomes. Recently, AlphaZero-like methods, where Monte Carlo Tree Search (MCTS) is employed for automatic step-level preference annotation, have proven particularly effective. However, the precise mechanisms behind the success of SRMs remain largely unexplored. To address this gap, this study delves into the counterintuitive aspects of SRMs, particularly focusing on MCTS-based approaches. Our findings reveal that the removal of natural language descriptions of thought processes has minimal impact on the efficacy of SRMs. Furthermore, we demonstrate that SRMs are adept at assessing the complex logical coherence present in mathematical language while having difficulty in natural language. These insights provide a nuanced understanding of the core elements that drive effective step-level reward modeling in mathematical reasoning. By shedding light on these mechanisms, this study offers valuable guidance for developing more efficient and streamlined SRMs, which can be achieved by focusing on the crucial parts of mathematical reasoning.

A long-standing goal of data management systems has been to build systems which can compute quantitative insights over large corpora of unstructured data in a cost-effective manner. Until recently, it was difficult and expensive to extract facts from company documents, data from scientific papers, or metrics from image and video corpora. Today's models can accomplish these tasks with high accuracy. However, a programmer who wants to answer a substantive AI-powered query must orchestrate large numbers of models, prompts, and data operations. For even a single query, the programmer has to make a vast number of decisions such as the choice of model, the right inference method, the most cost-effective inference hardware, the ideal prompt design, and so on. The optimal set of decisions can change as the query changes and as the rapidly-evolving technical landscape shifts. In this paper we present Palimpzest, a system that enables anyone to process AI-powered analytical queries simply by defining them in a declarative language. The system uses its cost optimization framework to implement the query plan with the best trade-offs between runtime, financial cost, and output data quality. We describe the workload of AI-powered analytics tasks, the optimization methods that Palimpzest uses, and the prototype system itself. We evaluate Palimpzest on tasks in Legal Discovery, Real Estate Search, and Medical Schema Matching. We show that even our simple prototype offers a range of appealing plans, including one that is 3.3x faster and 2.9x cheaper than the baseline method, while also offering better data quality. With parallelism enabled, Palimpzest can produce plans with up to a 90.3x speedup at 9.1x lower cost relative to a single-threaded GPT-4 baseline, while obtaining an F1-score within 83.5% of the baseline. These require no additional work by the user.

Large language models (LLMs) are displaying emergent abilities for math reasoning tasks,and there is a growing attention on enhancing the ability of open-source LLMs through supervised fine-tuning (SFT).In this paper, we aim to explore a general data strategy for supervised data to help optimize and expand math reasoning ability.Firstly, we determine the ability boundary of reasoning paths augmentation by identifying these paths' minimal optimal set.Secondly, we validate that different abilities of the model can be cumulatively enhanced by Mix of Minimal Optimal Sets of corresponding types of data, while our models MMOS achieve SOTA performance on series base models under much lower construction costs.Besides, we point out GSM-HARD is not really hard and today's LLMs no longer lack numerical robustness.Also, we provide an Auto Problem Generator for robustness testing and educational applications.Our code and data are publicly available at https://github.com/cyzhh/MMOS.

Although large language models demonstrate emergent abilities in solving math word problems, there is a challenging task in complex multi-step mathematical reasoning tasks. To improve model performance on mathematical reasoning tasks, previous work has conducted supervised fine-tuning on open-source models by improving the quality and quantity of data. In this paper, we propose a novel approach, named Brain, to imitate human thought processes to enhance mathematical reasoning abilities, using the Frontal Lobe Model to generate plans, and then employing the Parietal Lobe Model to generate code and execute to obtain answers. First, we achieve SOTA performance in comparison with Code LLaMA 7B based models through this method. Secondly, we find that plans can be explicitly extracted from natural language, code, or formal language. Our code and data are publicly available at https://github.com/cyzhh/Brain.

Data curation tasks that prepare data for analytics are critical for turning data into actionable insights. However, due to the diverse requirements of applications in different domains, generic off-the-shelf tools are typically insufficient. As a result, data scientists often have to develop domain-specific solutions tailored to both the dataset and the task, e.g. writing domain-specific code or training machine learning models on a sufficient number of annotated examples. This process is notoriously difficult and time-consuming. We present SEED, an LLM-as-compiler approach that automatically generates domain-specific data curation solutions via Large Language Models (LLMs). Once the user describes a task, input data, and expected output, the SEED compiler produces an executable pipeline composed of LLM-generated code, small model, and data access modules. SEED uses these generated modules to process most of the data records and dynamically decides when the LLM should step in to directly process some individual records, possibly using the data-access modules to retrieve relevant information from the data sources to assist the LLM in solving the task. To validate this new, revolutionary approach, we conducted experiments on 9 datasets spanning over 5 data curation tasks. The results show that SEED generates domain-specific solutions that significantly outperform their generic counterparts, often approaching the performance of the manually curated solutions that use thousands of labeled training examples. Moreover, in comparison to solutions that use the LLM on every data record, SEED achieves state-of-the-art or comparable few-shot performance, while significantly reducing the number of LLM calls.

Data curation is a wide-ranging area which contains many critical but time-consuming data processing tasks. However, the diversity of such tasks makes it challenging to develop a general-purpose data curation system. To address this issue, we present Lingua Manga, a user-friendly and versatile system that utilizes pre-trained large language models. Lingua Manga offers automatic optimization for achieving high performance and label efficiency while facilitating flexible and rapid development. Through three example applications with distinct objectives and users of varying levels of technical proficiency, we demonstrate that Lingua Manga can effectively assist both skilled programmers and low-code or even no-code users in addressing data curation challenges.

We propose RoTaR, a row-based table representation learning method, to address the efficiency and scalability issues faced by existing table representation learning methods. The key idea of RoTaR is to generate query-agnostic row representations that could be re-used via query-specific aggregation. In addition to the row-based architecture, we introduce several techniques: cell-aware position embedding, teacher-student training paradigm, and selective backward to improve the performance of RoTaR model.

Zero-shot NL2SQL is crucial in achieving natural language to SQL that is adaptive to new environments (e.g., new databases, new linguistic phenomena or SQL structures) with zero annotated NL2SQL samples from such environments. Existing approaches either fine-tune pre-trained language models (PLMs) based on annotated data or use prompts to guide fixed large language models (LLMs) such as ChatGPT. PLMs can perform well in schema alignment but struggle to achieve complex reasoning, while LLMs is superior in complex reasoning tasks but cannot achieve precise schema alignment. In this paper, we propose a ZeroNL2SQL framework that combines the complementary advantages of PLMs and LLMs for supporting zero-shot NL2SQL. ZeroNL2SQL first uses PLMs to generate an SQL sketch via schema alignment, then uses LLMs to fill the missing information via complex reasoning. Moreover, in order to better align the generated SQL queries with values in the given database instances, we design a predicate calibration method to guide the LLM in completing the SQL sketches based on the database instances and select the optimal SQL query via an execution-based strategy. Comprehensive experiments show that ZeroNL2SQL can achieve the best zero-shot NL2SQL performance on real-world benchmarks. Specifically, ZeroNL2SQL outperforms the state-of-the-art PLM-based methods by 3.2% to 13% and exceeds LLM-based methods by 10% to 20% on execution accuracy.

We introduce a method for improving the structural understanding abilities of language models. Unlike previous approaches that finetune the models with task-specific augmentation, we pretrain language models on a collection of task-agnostic corpora to generate structures from text. Our structure pretraining enables zero-shot transfer of the learned knowledge that models have about the structure tasks. We study the performance of this approach on 28 datasets, spanning 10 structure prediction tasks including open information extraction, joint entity and relation extraction, named entity recognition, relation classification, semantic role labeling, event extraction, coreference resolution, factual probe, intent detection, and dialogue state tracking. We further enhance the pretraining with the task-specific training sets. We show that a 10B parameter language model transfers non-trivially to most tasks and obtains state-of-the-art performance on 21 of 28 datasets that we evaluate.