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.

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}.

Cooperative Gradient Coding for Collaborative Federated Learning

We investigate federated learning (FL) in the presence of stragglers, with emphasis on wireless scenarios where the power-constrained edge devices collaboratively train a global model on their local datasets and transmit local model updates through fading channels. To tackle stragglers resulting from link disruptions without requiring accurate prior information on connectivity or dataset sharing, we propose a gradient coding (GC) scheme based on cooperative communication, which remains valid for general collaborative federated learning. Furthermore, we conduct an outage analysis of the proposed scheme, based on which we conduct the convergence analysis. The simulation results reveal the superiority of the proposed strategy in the presence of stragglers, especially under imbalanced data distribution.

Adaptive Coded Federated Learning: Privacy Preservation and Straggler Mitigation

In this article, we address the problem of federated learning in the presence of stragglers. For this problem, a coded federated learning framework has been proposed, where the central server aggregates gradients received from the non-stragglers and gradient computed from a privacy-preservation global coded dataset to mitigate the negative impact of the stragglers. However, when aggregating these gradients, fixed weights are consistently applied across iterations, neglecting the generation process of the global coded dataset and the dynamic nature of the trained model over iterations. This oversight may result in diminished learning performance. To overcome this drawback, we propose a new method named adaptive coded federated learning (ACFL). In ACFL, before the training, each device uploads a coded local dataset with additive noise to the central server to generate a global coded dataset under privacy preservation requirements. During each iteration of the training, the central server aggregates the gradients received from the non-stragglers and the gradient computed from the global coded dataset, where an adaptive policy for varying the aggregation weights is designed. Under this policy, we optimize the performance in terms of privacy and learning, where the learning performance is analyzed through convergence analysis and the privacy performance is characterized via mutual information differential privacy. Finally, we perform simulations to demonstrate the superiority of ACFL compared with the non-adaptive methods.

Distributed Learning based on 1-Bit Gradient Coding in the Presence of Stragglers

This paper considers the problem of distributed learning (DL) in the presence of stragglers. For this problem, DL methods based on gradient coding have been widely investigated, which redundantly distribute the training data to the workers to guarantee convergence when some workers are stragglers. However, these methods require the workers to transmit real-valued vectors during the process of learning, which induces very high communication burden. To overcome this drawback, we propose a novel DL method based on 1-bit gradient coding (1-bit GCDL), where 1-bit data encoded from the locally computed gradients are transmitted by the workers to reduce the communication overhead. We theoretically provide the convergence guarantees of the proposed method for both the convex loss functions and nonconvex loss functions. It is shown empirically that 1-bit GC-DL outperforms the baseline methods, which attains better learning performance under the same communication overhead.

Gradient Coding in Decentralized Learning for Evading Stragglers

In this paper, we consider a decentralized learning problem in the presence of stragglers. Although gradient coding techniques have been developed for distributed learning to evade stragglers, where the devices send encoded gradients with redundant training data, it is difficult to apply those techniques directly to decentralized learning scenarios. To deal with this problem, we propose a new gossip-based decentralized learning method with gradient coding (GOCO). In the proposed method, to avoid the negative impact of stragglers, the parameter vectors are updated locally using encoded gradients based on the framework of stochastic gradient coding and then averaged in a gossip-based manner. We analyze the convergence performance of GOCO for strongly convex loss functions. And we also provide simulation results to demonstrate the superiority of the proposed method in terms of learning performance compared with the baseline methods.

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.

COMIC: An Unsupervised Change Detection Method for Heterogeneous Remote Sensing Images Based on Copula Mixtures and Cycle-Consistent Adversarial Networks

In this paper, we consider the problem of change detection (CD) with two heterogeneous remote sensing (RS) images. For this problem, an unsupervised change detection method has been proposed recently based on the image translation technique of Cycle-Consistent Adversarial Networks (CycleGANs), where one image is translated from its original modality to the modality of the other image so that the difference map can be obtained by performing arithmetical subtraction. However, the difference map derived from subtraction is susceptible to image translation errors, in which case the changed area and the unchanged area are less distinguishable. To overcome the above shortcoming, we propose a new unsupervised copula mixture and CycleGAN-based CD method (COMIC), which combines the advantages of copula mixtures on statistical modeling and the advantages of CycleGANs on data mining. In COMIC, the pre-event image is first translated from its original modality to the post-event image modality. After that, by constructing a copula mixture, the joint distribution of the features from the heterogeneous images can be learnt according to quantitive analysis of the dependence structure based on the translated image and the original pre-event image, which are of the same modality and contain totally the same objects. Then, we model the CD problem as a binary hypothesis testing problem and derive its test statistics based on the constructed copula mixture. Finally, the difference map can be obtained from the test statistics and the binary change map (BCM) is generated by K-means clustering. We perform experiments on real RS datasets, which demonstrate the superiority of COMIC over the state-of-the-art methods.

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.