Numerical reasoning is a vital capability for natural language processing models to understand and process numerical information in real-world scenarios. Most current methods first generate the Intermediate Meaning Representations (IMRs) of questions and then generate answers. Current SOTA methods generate programs as IMRs with large language models (LLMs). Intuitively, equations have fewer restrictions and closer semantics to the question than programs, leading to higher generation accuracy. However, current LLMs generate equations worse than programs, where we assume that the equation data is rare in pre-training data compared to programs. So in this paper, we try to use equations as IMRs to solve the numerical reasoning task by addressing two problems: (1) Theoretically, how to prove that the equation is an IMR with higher generation accuracy than programs; (2) Empirically, how to improve the generation accuracy of equations with LLMs. For the first problem, we propose and prove a proposition to theoretically compare the generation accuracy of different IMRs. For the second problem, we present a method called Boosting Numerical ReasonIng by Decomposing the Generation of Equations Bridge, which can improve the accuracy of LLMs in generating equations as IMRs by reducing the tendency of generating constant expressions and programs. Our method improves the performance by 2.2%, 0.9%, and 1.7% on GSM8K, SVAMP, and Algebra datasets compared to the previous state-of-the-art methods under the single reasoning path setting. Our code and prompts are available at https://github.com/zirui-HIT/Bridge_for_Numerical_Reasoning}.

With the popularization of consortium blockchain, how to supervise numerous business chains has become a problem. Recently, some researchers have proposed the concept of ‘governing chain by chain’, which means that multiple organizations deploy a consortium blockchain to supervise many business chains in the industry. However, as the number of business chains increases, a performance bottleneck occurs on the supervision chain. Sharding is a promising direction to improve scalability, but existing studies focus on public chains. If transplanted to the supervision chain, these solutions will bring two challenges. Firstly, data from multiple business chains will cause storage conflicts and unbalanced sharding. Secondly, sharding makes it difficult for inter-shard transaction validation. Aiming at the challenges, we propose $\mathcal{S}$-chain, a shard-based supervision chain scheme. The contribution of our work lies in three points. Firstly, we design a unified label-based data sharding method that can evenly map data from different business chains to all shards without conflict. Secondly, we propose a mechanism to validate general smart-contract-based inter-shard transactions. At first, we design a smart contract splitting algorithm that splits one inter-shard smart contract into multiple sub-contracts and depicts their dependencies via a Directed Acyclic Graph(DAG). Then, we design an inter-shard transaction validation method by analyzing the dependencies of all sub-contracts. Finally, we implement a prototype system of $\mathcal{S}$-chain and test its performance. The results show that our $\mathcal{S}$-chain outperforms the scheme without sharding on throughput and storage overhead.

In this paper, we propose a new variant of supervised Latent Dirichlet Allocation(sLDA): mixture of soft max sLDA, for image classification. Ensemble classification methods can combine multiple weak classifiers to construct a strong classifier. Inspired by the ensemble idea, we try to improve sLDA model using the idea. The mixture of soft max model is a probabilistic ensemble classification model, it can fit the training data and class label well. We embed the mixture of soft max model into LDA model under the framwork of sLDA, and construct an ensemble supervised topic model for image classification. Meanwhile, we derive an elegant parameters estimation algorithm based on variational EM method, and give a simple and efficient approximation method for classifying a new image. Finally, we demonstrate the effectiveness of our model by comparing with some existing approaches on two real world datasets. The results show that our model enhances classification accuracy by 7% on the 1600-image Label Me dataset and 9% on the 1791-image UIUC-Sport dataset.