We propose utilizing background operators for mathematical reasoning in large language models (LLMs). To achieve this, we define a set of fundamental mathematical predicates as the basic building blocks. For each mathematical problem, we develop a Prolog solution that includes problem-specific predicates and intermediate predicates derived from these background operators, ensuring that each solution adheres to the defined operator set. We introduce the MATH-Prolog corpus, which is derived from the counting and probability categories of the MATH corpus. For efficient data augmentation, we apply K-fold cross-validated self-training. This method incrementally generates new Prolog solutions for each fold, incorporating those verified as correct into the training set throughout the model training process. Our experimental results demonstrate that 5-fold crossvalidated self-training effectively identifies new, accurate Prolog solutions, achieving an accuracy of 84.6% on the cross-validated set, and 84.8% on the test set during fine-tuning the Meta-Llama-3.1-8B-Instruct model. This approach successfully uncovers new solutions with fully computable inference steps for previously unseen problems. Additionally, incorporating the background mathematical predicates into the prompt enhances solution coverage.

Instructing large language models (LLMs) to solve elementary school math problems has shown great success using Chain of Thought (CoT). However, the CoT approach relies on an LLM to generate a sequence of arithmetic calculations which can be prone to cascaded calculation errors. We hypothesize that an LLM should focus on extracting predicates and generating symbolic formulas from the math problem description so that the underlying calculation can be done via an external code interpreter. We investigate using LLM to generate Prolog programs to solve mathematical questions. Experimental results show that our Prolog-based arithmetic problem-solving outperforms CoT generation in the GSM8K benchmark across three distinct LLMs. In addition, given the insensitive ordering of predicates and symbolic formulas in Prolog, we propose to permute the ground truth predicates for more robust LLM training via data augmentation.

Recently, there has been a surge in interest in NLP driven by ChatGPT. ChatGPT, a transformer-based generative language model of substantial scale, exhibits versatility in performing various tasks based on natural language. Nevertheless, large language models often exhibit poor performance in solving mathematics questions that require reasoning. Prior research has demonstrated the effectiveness of chain-of-thought prompting in enhancing reasoning capabilities. Now, we aim to investigate whether fine-tuning a model for the generation of Prolog codes, a logic language, and subsequently passing these codes to a compiler can further improve accuracy. Consequently, we employ chain-of-thought to fine-tune LLaMA7B as a baseline model and develop other fine-tuned LLaMA7B models for the generation of Prolog code, Prolog code + chain-of-thought, and chain-of-thought + Prolog code, respectively. The results reveal that the Prolog generation model surpasses the baseline in performance, while the combination generation models do not yield significant improvements. The Prolog corpus based on GSM8K and the correspondingly finetuned Prolog generation model based on LLaMA7B are released to the research community.

Causal language modeling (LM) uses word history to predict the next word. BERT, on the other hand, makes use of bi-directional word information in a sentence to predict words at masked positions. While BERT is effective in sequence encoding, it is non-causal by nature and is not designed for sequence generation. In this paper, we propose a novel language model, SUffix REtrieval-Augmented LM (SUREALM), that simulates a bi-directional contextual effect in an autoregressive manner. SUREALM employs an embedding retriever to search for training sentences in a data store that share similar word history during sequence generation. In particular, the suffix portions of the retrieved sentences mimick the "future" context. We evaluated our proposed model on the DSTC9 spoken dialogue corpus and showed promising word perplexity reduction on the validation and test set compared to competitive baselines.

We propose a UNITER(Chen et al. 2020)-based model for The goal of Situated and Interactive Multimodal Conversation SIMMC 2.0. UNITER is proposed in computer vision (CV) (SIMMC) 2.0 (Kottur et al. 2021) is to aid the conversational for universal embeddings for image and text. To achieve this AI community in developing successful multimodal goal, UNITER is pre-trained with masked language modelling, assistant agents capable of handling real-world multimodal masked region modelling and word-region alignment dialog inputs.