LLM Critics Help Catch Bugs in Mathematics: Towards a Better Mathematical Verifier with Natural Language Feedback

Mathematical verfier achieves success in mathematical reasoning tasks by validating the correctness of solutions. However, existing verifiers are trained with binary classification labels, which are not informative enough for the model to accurately assess the solutions. To mitigate the aforementioned insufficiency of binary labels, we introduce step-wise natural language feedbacks as rationale labels (i.e., the correctness of the current step and the explanations). In this paper, we propose \textbf{Math-Minos}, a natural language feedback enhanced verifier by constructing automatically-generated training data and a two-stage training paradigm for effective training and efficient inference. Our experiments reveal that a small set (30k) of natural language feedbacks can significantly boost the performance of the verifier by the accuracy of 1.6\% (86.6\% $\rightarrow$ 88.2\%) on GSM8K and 0.8\% (37.8\% $\rightarrow$ 38.6\%) on MATH. We have released our code and data for further exploration.

The Reason behind Good or Bad: Towards a Better Mathematical Verifier with Natural Language Feedback

Mathematical verfier achieves success in mathematical reasoning tasks by validating the correctness of solutions. However, existing verifiers are trained with binary classification labels, which are not informative enough for the model to accurately assess the solutions. To mitigate the aforementioned insufficiency of binary labels, we introduce step-wise natural language feedbacks as rationale labels (i.e., the correctness of the current step and the explanations). In this paper, we propose \textbf{Math-Minos}, a natural language feedback enhanced verifier by constructing automatically-generated training data and a two-stage training paradigm for effective training and efficient inference. Our experiments reveal that a small set (30k) of natural language feedbacks can significantly boost the performance of the verifier by the accuracy of 1.6\% (86.6\% $\rightarrow$ 88.2\%) on GSM8K and 0.8\% (37.8\% $\rightarrow$ 38.6\%) on MATH. We will release the code, data and model for reproduction soon.

DeepSeek-Coder-V2: Breaking the Barrier of Closed-Source Models in Code Intelligence

We present DeepSeek-Coder-V2, an open-source Mixture-of-Experts (MoE) code language model that achieves performance comparable to GPT4-Turbo in code-specific tasks. Specifically, DeepSeek-Coder-V2 is further pre-trained from an intermediate checkpoint of DeepSeek-V2 with additional 6 trillion tokens. Through this continued pre-training, DeepSeek-Coder-V2 substantially enhances the coding and mathematical reasoning capabilities of DeepSeek-V2, while maintaining comparable performance in general language tasks. Compared to DeepSeek-Coder-33B, DeepSeek-Coder-V2 demonstrates significant advancements in various aspects of code-related tasks, as well as reasoning and general capabilities. Additionally, DeepSeek-Coder-V2 expands its support for programming languages from 86 to 338, while extending the context length from 16K to 128K. In standard benchmark evaluations, DeepSeek-Coder-V2 achieves superior performance compared to closed-source models such as GPT4-Turbo, Claude 3 Opus, and Gemini 1.5 Pro in coding and math benchmarks.

Multimodal ArXiv: A Dataset for Improving Scientific Comprehension of Large Vision-Language Models

Large vision-language models (LVLMs), exemplified by GPT-4V, excel across diverse tasks involving concrete images from natural scenes. However, their ability to interpret abstract figures, such as geometry shapes and scientific plots, remains limited due to a scarcity of training datasets in scientific domains. To fill this gap, we introduce Multimodal ArXiv, consisting of ArXivCap and ArXivQA, for enhancing LVLMs scientific comprehension. ArXivCap is a figure-caption dataset comprising 6.4M images and 3.9M captions sourced from 572K ArXiv papers spanning various scientific domains. Drawing from ArXivCap, we introduce ArXivQA, a question-answering dataset generated by prompting GPT-4V based on scientific figures. ArXivQA greatly enhances LVLMs' mathematical reasoning capabilities, achieving a 10.4% absolute accuracy gain on a multimodal mathematical reasoning benchmark. Furthermore, employing ArXivCap, we devise four vision-to-text tasks for benchmarking LVLMs. Evaluation results with state-of-the-art LVLMs underscore their struggle with the nuanced semantics of academic figures, with domain-specific training yielding substantial performance gains. Our error analysis uncovers misinterpretations of visual context, recognition errors, and the production of overly simplified captions by current LVLMs, shedding light on future improvements.

Utilizing Local Hierarchy with Adversarial Training for Hierarchical Text Classification

Hierarchical text classification (HTC) is a challenging subtask of multi-label classification due to its complex taxonomic structure. Nearly all recent HTC works focus on how the labels are structured but ignore the sub-structure of ground-truth labels according to each input text which contains fruitful label co-occurrence information. In this work, we introduce this local hierarchy with an adversarial framework. We propose a HiAdv framework that can fit in nearly all HTC models and optimize them with the local hierarchy as auxiliary information. We test on two typical HTC models and find that HiAdv is effective in all scenarios and is adept at dealing with complex taxonomic hierarchies. Further experiments demonstrate that the promotion of our framework indeed comes from the local hierarchy and the local hierarchy is beneficial for rare classes which have insufficient training data.

Reducing Hallucinations in Entity Abstract Summarization with Facts-Template Decomposition

Entity abstract summarization aims to generate a coherent description of a given entity based on a set of relevant Internet documents. Pretrained language models (PLMs) have achieved significant success in this task, but they may suffer from hallucinations, i.e. generating non-factual information about the entity. To address this issue, we decompose the summary into two components: Facts that represent the factual information about the given entity, which PLMs are prone to fabricate; and Template that comprises generic content with designated slots for facts, which PLMs can generate competently. Based on the facts-template decomposition, we propose SlotSum, an explainable framework for entity abstract summarization. SlotSum first creates the template and then predicts the fact for each template slot based on the input documents. Benefiting from our facts-template decomposition, SlotSum can easily locate errors and further rectify hallucinated predictions with external knowledge. We construct a new dataset WikiFactSum to evaluate the performance of SlotSum. Experimental results demonstrate that SlotSum could generate summaries that are significantly more factual with credible external knowledge.

PeriodicLoRA: Breaking the Low-Rank Bottleneck in LoRA Optimization

Supervised fine-tuning is the most common method to adapt large language models (LLMs) to downstream tasks, but full fine-tuning LLMs requires massive computational resources. Recently, parameter-efficient fine-tuning (PEFT) methods have been widely studied due to its cost-effectiveness. LoRA is one of the most widely used methods, which assumes that the optimization process is essentially low-dimensional. Although LoRA fine-tuning is effective, there is still a performance gap compared to full fine-tuning, since its weight update is limited to low-rank matrices. In order to break the low-rank bottleneck in LoRA Optimization, we propose PeriodicLoRA (PLoRA), which accumulates low-rank update matrices multiple times to achieve a higher update rank. PLoRA has multiple training stages. During each stage, we still update only the LoRA weights. However, at the end of each stage, we unload the LoRA weights into the backbone parameters and then reinitialize the LoRA states. Experimental results show that PLoRA has stronger learning ability, approximately 1.8 times that of LoRA's learning ability at most, but it does not increase memory usage. Further, we introduce a momentum-based unloading strategy for PLoRA to mitigate the training instability.

PCA-Bench: Evaluating Multimodal Large Language Models in Perception-Cognition-Action Chain

We present PCA-Bench, a multimodal decision-making benchmark for evaluating the integrated capabilities of Multimodal Large Language Models (MLLMs). Departing from previous benchmarks focusing on simplistic tasks and individual model capability, PCA-Bench introduces three complex scenarios: autonomous driving, domestic robotics, and open-world games. Given task instructions and diverse contexts, the model is required to seamlessly integrate multiple capabilities of Perception, Cognition, and Action in a reasoning chain to make accurate decisions. Moreover, PCA-Bench features error localization capabilities, scrutinizing model inaccuracies in areas such as perception, knowledge, or reasoning. This enhances the reliability of deploying MLLMs. To balance accuracy and efficiency in evaluation, we propose PCA-Eval, an automatic evaluation protocol, and assess 10 prevalent MLLMs. The results reveal significant performance disparities between open-source models and powerful proprietary models like GPT-4 Vision. To address this, we introduce Embodied-Instruction-Evolution (EIE), an automatic framework for synthesizing instruction tuning examples in multimodal embodied environments. EIE generates 7,510 training examples in PCA-Bench and enhances the performance of open-source MLLMs, occasionally surpassing GPT-4 Vision (+3\% in decision accuracy), thereby validating the effectiveness of EIE. Our findings suggest that robust MLLMs like GPT4-Vision show promise for decision-making in embodied agents, opening new avenues for MLLM research.

ICDPO: Effectively Borrowing Alignment Capability of Others via In-context Direct Preference Optimization

Large Language Models (LLMs) rely on Human Preference Alignment (HPA) to ensure the generation of safe content. Due to the heavy cost associated with fine-tuning, fine-tuning-free methods have emerged, typically modifying LLM decoding with external auxiliary methods. However, these methods do not essentially enhance the LLM itself. In this paper, we rethink the derivation procedures of DPO, based on which we conversely build an instant scorer using the states of the LLM before and after In-context Learning (ICL). Accordingly, we propose a novel approach called In-Context Direct Preference Optimization (ICDPO). It enables LLMs to borrow the HPA capabilities from superior LLMs with ICL, generating well-aligned responses as estimated by the aforementioned instant scorer, thereby enhancing the final performance. ICDPO can be further enhanced with a two-stage retriever and an upgraded scorer, both offering benefits. Extensive experiments show its effectiveness, particularly in outperforming two fine-tuning-free baselines, and it exhibits competitiveness with SFT + LoRA. We also conduct detailed analyses to offer comprehensive insights into ICDPO.

DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models

Mathematical reasoning poses a significant challenge for language models due to its complex and structured nature. In this paper, we introduce DeepSeekMath 7B, which continues pre-training DeepSeek-Coder-Base-v1.5 7B with 120B math-related tokens sourced from Common Crawl, together with natural language and code data. DeepSeekMath 7B has achieved an impressive score of 51.7% on the competition-level MATH benchmark without relying on external toolkits and voting techniques, approaching the performance level of Gemini-Ultra and GPT-4. Self-consistency over 64 samples from DeepSeekMath 7B achieves 60.9% on MATH. The mathematical reasoning capability of DeepSeekMath is attributed to two key factors: First, we harness the significant potential of publicly available web data through a meticulously engineered data selection pipeline. Second, we introduce Group Relative Policy Optimization (GRPO), a variant of Proximal Policy Optimization (PPO), that enhances mathematical reasoning abilities while concurrently optimizing the memory usage of PPO.