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In utilizing large language models (LLMs) for mathematical reasoning, addressing the errors in the reasoning and calculation present in the generated text by LLMs is a crucial challenge. In this paper, we propose a novel framework that integrates the Chain-of-Thought (CoT) method with an external tool (Python REPL). We discovered that by prompting LLMs to generate structured text in XML-like markup language, we could seamlessly integrate CoT and the external tool and control the undesired behaviors of LLMs. With our approach, LLMs can utilize Python computation to rectify errors within CoT. We applied our method to ChatGPT (GPT-3.5) to solve challenging mathematical problems and demonstrated that combining CoT and Python REPL through the markup language enhances the reasoning capability of LLMs. Our approach enables LLMs to write the markup language and perform advanced mathematical reasoning using only zero-shot prompting.

As large language models (LLMs) take on more complex tasks, their inputs incorporate longer contexts to respond to questions that require domain knowledge or user-specific conversational histories. Yet, using long contexts poses a challenge for responsive LLM systems, as nothing can be generated until all the contexts are fetched to and processed by the LLM. Existing systems optimize only the computation delay in context processing (e.g., by caching intermediate key-value features of the text context) but often cause longer network delays in context fetching (e.g., key-value features consume orders of magnitude larger bandwidth than the text context). This paper presents CacheGen to minimize the delays in fetching and processing contexts for LLMs. CacheGen reduces the bandwidth needed for transmitting long contexts' key-value (KV) features through a novel encoder that compresses KV features into more compact bitstream representations. The encoder combines adaptive quantization with a tailored arithmetic coder, taking advantage of the KV features' distributional properties, such as locality across tokens. Furthermore, CacheGen minimizes the total delay in fetching and processing a context by using a controller that determines when to load the context as compressed KV features or raw text and picks the appropriate compression level if loaded as KV features. We test CacheGen on three models of various sizes and three datasets of different context lengths. Compared to recent methods that handle long contexts, CacheGen reduces bandwidth usage by 3.7-4.3x and the total delay in fetching and processing contexts by 2.7-3x while maintaining similar LLM performance on various tasks as loading the text contexts.

The success of language models has inspired the NLP community to attend to tasks that require implicit and complex reasoning, relying on human-like commonsense mechanisms. While such vertical thinking tasks have been relatively popular, lateral thinking puzzles have received little attention. To bridge this gap, we devise BRAINTEASER: a multiple-choice Question Answering task designed to test the model's ability to exhibit lateral thinking and defy default commonsense associations. We design a three-step procedure for creating the first lateral thinking benchmark, consisting of data collection, distractor generation, and generation of adversarial examples, leading to 1,100 puzzles with high-quality annotations. To assess the consistency of lateral reasoning by models, we enrich BRAINTEASER based on a semantic and contextual reconstruction of its questions. Our experiments with state-of-the-art instruction- and commonsense language models reveal a significant gap between human and model performance, which is further widened when consistency across adversarial formats is considered. We make all of our code and data available to stimulate work on developing and evaluating lateral thinking models.

With the increasing capabilities of large language models (LLMs), these high-performance models have achieved state-of-the-art results on a wide range of natural language processing (NLP) tasks. However, the models' performance on commonly-used benchmark datasets often fails to accurately reflect their reliability and robustness when applied to real-world noisy data. To address these challenges, we propose a unified robustness evaluation framework based on the slot-filling task to systematically evaluate the dialogue understanding capability of LLMs in diverse input perturbation scenarios. Specifically, we construct a input perturbation evaluation dataset, Noise-LLM, which contains five types of single perturbation and four types of mixed perturbation data. Furthermore, we utilize a multi-level data augmentation method (character, word, and sentence levels) to construct a candidate data pool, and carefully design two ways of automatic task demonstration construction strategies (instance-level and entity-level) with various prompt templates. Our aim is to assess how well various robustness methods of LLMs perform in real-world noisy scenarios. The experiments have demonstrated that the current open-source LLMs generally achieve limited perturbation robustness performance. Based on these experimental observations, we make some forward-looking suggestions to fuel the research in this direction.

Large language models (LLMs) have pushed the limits of natural language understanding and exhibited excellent problem-solving ability. Despite the great success, most existing open-source LLMs (e.g., LLaMA-2) are still far away from satisfactory for solving mathematical problem due to the complex reasoning procedures. To bridge this gap, we propose MetaMath, a fine-tuned language model that specializes in mathematical reasoning. Specifically, we start by bootstrapping mathematical questions by rewriting the question from multiple perspectives without extra knowledge, which results in a new dataset called MetaMathQA. Then we fine-tune the LLaMA-2 models on MetaMathQA. Experimental results on two popular benchmarks (i.e., GSM8K and MATH) for mathematical reasoning demonstrate that MetaMath outperforms a suite of open-source LLMs by a significant margin. Our MetaMath-7B model achieves 66.4% on GSM8K and 19.4% on MATH, exceeding the state-of-the-art models of the same size by 11.5% and 8.7%. Particularly, MetaMath-70B achieves an accuracy of 82.3% on GSM8K, slightly better than GPT-3.5-Turbo. We release all the MetaMathQA dataset, the MetaMath models with different model sizes and the training code for public use.

This paper pursues the insight that language models naturally enable an intelligent variation operator similar in spirit to evolutionary crossover. In particular, language models of sufficient scale demonstrate in-context learning, i.e. they can learn from associations between a small number of input patterns to generate outputs incorporating such associations (also called few-shot prompting). This ability can be leveraged to form a simple but powerful variation operator, i.e. to prompt a language model with a few text-based genotypes (such as code, plain-text sentences, or equations), and to parse its corresponding output as those genotypes' offspring. The promise of such language model crossover (which is simple to implement and can leverage many different open-source language models) is that it enables a simple mechanism to evolve semantically-rich text representations (with few domain-specific tweaks), and naturally benefits from current progress in language models. Experiments in this paper highlight the versatility of language-model crossover, through evolving binary bit-strings, sentences, equations, text-to-image prompts, and Python code. The conclusion is that language model crossover is a promising method for evolving genomes representable as text.

Existing regression models tend to fall short in both accuracy and uncertainty estimation when the label distribution is imbalanced. In this paper, we propose a probabilistic deep learning model, dubbed variational imbalanced regression (VIR), which not only performs well in imbalanced regression but naturally produces reasonable uncertainty estimation as a byproduct. Different from typical variational autoencoders assuming I.I.D. representations (a data point's representation is not directly affected by other data points), our VIR borrows data with similar regression labels to compute the latent representation's variational distribution; furthermore, different from deterministic regression models producing point estimates, VIR predicts the entire normal-inverse-gamma distributions and modulates the associated conjugate distributions to impose probabilistic reweighting on the imbalanced data, thereby providing better uncertainty estimation. Experiments in several real-world datasets show that our VIR can outperform state-of-the-art imbalanced regression models in terms of both accuracy and uncertainty estimation. Code will soon be available at \url{//github.com/Wang-ML-Lab/variational-imbalanced-regression}.

Retrieving documents and prepending them in-context at inference time improves performance of language model (LMs) on a wide range of tasks. However, these documents, often spanning hundreds of words, make inference substantially more expensive. We propose compressing the retrieved documents into textual summaries prior to in-context integration. This not only reduces the computational costs but also relieves the burden of LMs to identify relevant information in long retrieved documents. We present two compressors -- an extractive compressor which selects useful sentences from retrieved documents and an abstractive compressor which generates summaries by synthesizing information from multiple documents. Both compressors are trained to improve LMs' performance on end tasks when the generated summaries are prepended to the LMs' input, while keeping the summary concise.If the retrieved documents are irrelevant to the input or offer no additional information to LM, our compressor can return an empty string, implementing selective augmentation.We evaluate our approach on language modeling task and open domain question answering task. We achieve a compression rate of as low as 6% with minimal loss in performance for both tasks, significantly outperforming the off-the-shelf summarization models. We show that our compressors trained for one LM can transfer to other LMs on the language modeling task and provide summaries largely faithful to the retrieved documents.

The emergence of large language models (LLMs) has substantially influenced natural language processing, demonstrating exceptional results across various tasks. In this study, we employ ``Introspective Tips" to facilitate LLMs in self-optimizing their decision-making. By introspectively examining trajectories, LLM refines its policy by generating succinct and valuable tips. Our method enhances the agent's performance in both few-shot and zero-shot learning situations by considering three essential scenarios: learning from the agent's past experiences, integrating expert demonstrations, and generalizing across diverse games. Importantly, we accomplish these improvements without fine-tuning the LLM parameters; rather, we adjust the prompt to generalize insights from the three aforementioned situations. Our framework not only supports but also emphasizes the advantage of employing LLM in in-contxt decision-making. Experiments involving over 100 games in TextWorld illustrate the superior performance of our approach.

Pre-trained language representation models, such as BERT, capture a general language representation from large-scale corpora, but lack domain-specific knowledge. When reading a domain text, experts make inferences with relevant knowledge. For machines to achieve this capability, we propose a knowledge-enabled language representation model (K-BERT) with knowledge graphs (KGs), in which triples are injected into the sentences as domain knowledge. However, too much knowledge incorporation may divert the sentence from its correct meaning, which is called knowledge noise (KN) issue. To overcome KN, K-BERT introduces soft-position and visible matrix to limit the impact of knowledge. K-BERT can easily inject domain knowledge into the models by equipped with a KG without pre-training by-self because it is capable of loading model parameters from the pre-trained BERT. Our investigation reveals promising results in twelve NLP tasks. Especially in domain-specific tasks (including finance, law, and medicine), K-BERT significantly outperforms BERT, which demonstrates that K-BERT is an excellent choice for solving the knowledge-driven problems that require experts.