Markov Chain of Thought for Efficient Mathematical Reasoning

Chain of Thought (CoT) of multi-step benefits from the logical structure of the reasoning steps and task-specific actions, significantly enhancing the mathematical reasoning capabilities of large language models. As the prevalence of long CoT, the number of reasoning steps exceeds manageable token limits and leads to higher computational demands. Inspired by the fundamental logic of human cognition, ``derive, then reduce'', we conceptualize the standard multi-step CoT as a novel Markov Chain of Thought (MCoT). In this study, we consider the mathematical reasoning task, defining each reasoning step as text accompanied by a Python code snippet. To facilitate a longer reasoning path, self-correction is enabled through interactions with the code interpreter. Our MCoT aims to compress previous reasoning steps into a simplified question, enabling efficient next-step inference without relying on a lengthy KV cache. In our experiments, we curate the \texttt{MCoTInstruct} dataset, and the empirical results indicate that MCoT not only significantly enhances efficiency but also maintains comparable accuracy. While much remains to be explored, this work paves the way for exploring the long CoT reasoning abilities of LLMs.

AnyTrans: Translate AnyText in the Image with Large Scale Models

This paper introduces AnyTrans, an all-encompassing framework for the task-Translate AnyText in the Image (TATI), which includes multilingual text translation and text fusion within images. Our framework leverages the strengths of large-scale models, such as Large Language Models (LLMs) and text-guided diffusion models, to incorporate contextual cues from both textual and visual elements during translation. The few-shot learning capability of LLMs allows for the translation of fragmented texts by considering the overall context. Meanwhile, the advanced inpainting and editing abilities of diffusion models make it possible to fuse translated text seamlessly into the original image while preserving its style and realism. Additionally, our framework can be constructed entirely using open-source models and requires no training, making it highly accessible and easily expandable. To encourage advancement in the TATI task, we have meticulously compiled a test dataset called MTIT6, which consists of multilingual text image translation data from six language pairs.

Step-level Value Preference Optimization for Mathematical Reasoning

Direct Preference Optimization (DPO) using an implicit reward model has proven to be an effective alternative to reinforcement learning from human feedback (RLHF) for fine-tuning preference aligned large language models (LLMs). However, the overall preference annotations of responses do not fully capture the fine-grained quality of model outputs in complex multi-step reasoning tasks, such as mathematical reasoning. To address this limitation, we introduce a novel algorithm called Step-level Value Preference Optimization (SVPO). Our approach employs Monte Carlo Tree Search (MCTS) to automatically annotate step-level preferences for multi-step reasoning. Furthermore, from the perspective of learning-to-rank, we train an explicit value model to replicate the behavior of the implicit reward model, complementing standard preference optimization. This value model enables the LLM to generate higher reward responses with minimal cost during inference. Experimental results demonstrate that our method achieves state-of-the-art performance on both in-domain and out-of-domain mathematical reasoning benchmarks.

Enhancing Security and Privacy in Federated Learning using Update Digests and Voting-Based Defense

Federated Learning (FL) is a promising privacy-preserving machine learning paradigm that allows data owners to collaboratively train models while keeping their data localized. Despite its potential, FL faces challenges related to the trustworthiness of both clients and servers, especially in the presence of curious or malicious adversaries. In this paper, we introduce a novel framework named \underline{\textbf{F}}ederated \underline{\textbf{L}}earning with \underline{\textbf{U}}pdate \underline{\textbf{D}}igest (FLUD), which addresses the critical issues of privacy preservation and resistance to Byzantine attacks within distributed learning environments. FLUD utilizes an innovative approach, the $\mathsf{LinfSample}$ method, allowing clients to compute the $l_{\infty}$ norm across sliding windows of updates as an update digest. This digest enables the server to calculate a shared distance matrix, significantly reducing the overhead associated with Secure Multi-Party Computation (SMPC) by three orders of magnitude while effectively distinguishing between benign and malicious updates. Additionally, FLUD integrates a privacy-preserving, voting-based defense mechanism that employs optimized SMPC protocols to minimize communication rounds. Our comprehensive experiments demonstrate FLUD's effectiveness in countering Byzantine adversaries while incurring low communication and runtime overhead. FLUD offers a scalable framework for secure and reliable FL in distributed environments, facilitating its application in scenarios requiring robust data management and security.

AlphaMath Almost Zero: process Supervision without process

Recent advancements in large language models (LLMs) have substantially enhanced their mathematical reasoning abilities. However, these models still struggle with complex problems that require multiple reasoning steps, frequently leading to logical or numerical errors. While numerical mistakes can largely be addressed by integrating a code interpreter, identifying logical errors within intermediate steps is more challenging. Moreover, manually annotating these steps for training is not only expensive but also demands specialized expertise. In this study, we introduce an innovative approach that eliminates the need for manual annotation by leveraging the Monte Carlo Tree Search (MCTS) framework to generate both the process supervision and evaluation signals automatically. Essentially, when a LLM is well pre-trained, only the mathematical questions and their final answers are required to generate our training data, without requiring the solutions. We proceed to train a step-level value model designed to improve the LLM's inference process in mathematical domains. Our experiments indicate that using automatically generated solutions by LLMs enhanced with MCTS significantly improves the model's proficiency in dealing with intricate mathematical reasoning tasks.

MARIO Eval: Evaluate Your Math LLM with your Math LLM--A mathematical dataset evaluation toolkit

Large language models (LLMs) have been explored in a variety of reasoning tasks including solving of mathematical problems. Each math dataset typically includes its own specially designed evaluation script, which, while suitable for its intended use, lacks generalizability across different datasets. Consequently, updates and adaptations to these evaluation tools tend to occur without being systematically reported, leading to inconsistencies and obstacles to fair comparison across studies. To bridge this gap, we introduce a comprehensive mathematical evaluation toolkit that not only utilizes a python computer algebra system (CAS) for its numerical accuracy, but also integrates an optional LLM, known for its considerable natural language processing capabilities. To validate the effectiveness of our toolkit, we manually annotated two distinct datasets. Our experiments demonstrate that the toolkit yields more robust evaluation results compared to prior works, even without an LLM. Furthermore, when an LLM is incorporated, there is a notable enhancement. The code for our method will be made available at \url{https://github.com/MARIO-Math-Reasoning/math_evaluation}.

MARIO: MAth Reasoning with code Interpreter Output -- A Reproducible Pipeline

Large language models (LLMs) have seen considerable advancements in natural language understanding tasks, yet there remains a gap to bridge before attaining true artificial general intelligence, especially concerning shortcomings in mathematical reasoning capabilities. We postulate that the inherent nature of LLM training, which focuses on predicting probabilities of next token, presents challenges in effectively modeling mathematical reasoning that demands exact calculations, both from data-driven and theoretical standpoints. In this paper, we address this challenge by enriching the data landscape and introducing a novel math dataset, enhanced with a capability to utilize a Python code interpreter. This dataset is derived from GSM8K and MATH and has been further refined through a combination of GPT-4 annotations, human review, and self-training processes, where the errors in the original GSM8K training set have been fixed. Additionally, we propose a tentative, easily replicable protocol for the fine-tuning of math-specific LLMs, which has led to a significant improvement in the performance of a 7B-parameter LLM on the GSM8K and MATH datasets. We are committed to advancing the field of mathematical reasoning in LLMs and, to that end, we have made the model checkpoints and will make the dataset publicly available. We hope this will facilitate further research and development within the community.

Adaptive Policy with Wait-$k$ Model for Simultaneous Translation

Simultaneous machine translation (SiMT) requires a robust read/write policy in conjunction with a high-quality translation model. Traditional methods rely on either a fixed wait-$k$ policy coupled with a standalone wait-$k$ translation model, or an adaptive policy jointly trained with the translation model. In this study, we propose a more flexible approach by decoupling the adaptive policy model from the translation model. Our motivation stems from the observation that a standalone multi-path wait-$k$ model performs competitively with adaptive policies utilized in state-of-the-art SiMT approaches. Specifically, we introduce DaP, a divergence-based adaptive policy, that makes read/write decisions for any translation model based on the potential divergence in translation distributions resulting from future information. DaP extends a frozen wait-$k$ model with lightweight parameters, and is both memory and computation efficient. Experimental results across various benchmarks demonstrate that our approach offers an improved trade-off between translation accuracy and latency, outperforming strong baselines.

Neural Machine Translation with Dynamic Graph Convolutional Decoder

Existing wisdom demonstrates the significance of syntactic knowledge for the improvement of neural machine translation models. However, most previous works merely focus on leveraging the source syntax in the well-known encoder-decoder framework. In sharp contrast, this paper proposes an end-to-end translation architecture from the (graph \& sequence) structural inputs to the (graph \& sequence) outputs, where the target translation and its corresponding syntactic graph are jointly modeled and generated. We propose a customized Dynamic Spatial-Temporal Graph Convolutional Decoder (Dyn-STGCD), which is designed for consuming source feature representations and their syntactic graph, and auto-regressively generating the target syntactic graph and tokens simultaneously. We conduct extensive experiments on five widely acknowledged translation benchmarks, verifying that our proposal achieves consistent improvements over baselines and other syntax-aware variants.

Translate the Beauty in Songs: Jointly Learning to Align Melody and Translate Lyrics

Song translation requires both translation of lyrics and alignment of music notes so that the resulting verse can be sung to the accompanying melody, which is a challenging problem that has attracted some interests in different aspects of the translation process. In this paper, we propose Lyrics-Melody Translation with Adaptive Grouping (LTAG), a holistic solution to automatic song translation by jointly modeling lyrics translation and lyrics-melody alignment. It is a novel encoder-decoder framework that can simultaneously translate the source lyrics and determine the number of aligned notes at each decoding step through an adaptive note grouping module. To address data scarcity, we commissioned a small amount of training data annotated specifically for this task and used large amounts of augmented data through back-translation. Experiments conducted on an English-Chinese song translation data set show the effectiveness of our model in both automatic and human evaluation.