Case2Code: Learning Inductive Reasoning with Synthetic Data

Complex reasoning is an impressive ability shown by large language models (LLMs). Most LLMs are skilled in deductive reasoning, such as chain-of-thought prompting or iterative tool-using to solve challenging tasks step-by-step. In this paper, we hope to focus on evaluating and teaching LLMs to conduct inductive reasoning, that is, LLMs are supposed to infer underlying rules by observing examples or sequential transformations. However, collecting large-scale and diverse human-generated inductive data is challenging. We focus on data synthesis in the code domain and propose a \textbf{Case2Code} task by exploiting the expressiveness and correctness of programs. Specifically, we collect a diverse set of executable programs, synthesize input-output transformations for each program, and force LLMs to infer the underlying code implementations based on the synthetic I/O cases. We first evaluate representative LLMs on the synthesized Case2Code task and demonstrate that the Case-to-code induction is challenging for LLMs. Then, we synthesize large-scale Case2Code training samples to train LLMs to perform inductive reasoning. Experimental results show that such induction training benefits not only in distribution Case2Code performance but also enhances various coding abilities of trained LLMs, demonstrating the great potential of learning inductive reasoning via synthetic data.

Scaling Laws for Fact Memorization of Large Language Models

Fact knowledge memorization is crucial for Large Language Models (LLM) to generate factual and reliable responses. However, the behaviors of LLM fact memorization remain under-explored. In this paper, we analyze the scaling laws for LLM's fact knowledge and LLMs' behaviors of memorizing different types of facts. We find that LLMs' fact knowledge capacity has a linear and negative exponential law relationship with model size and training epochs, respectively. Estimated by the built scaling law, memorizing the whole Wikidata's facts requires training an LLM with 1000B non-embed parameters for 100 epochs, suggesting that using LLMs to memorize all public facts is almost implausible for a general pre-training setting. Meanwhile, we find that LLMs can generalize on unseen fact knowledge and its scaling law is similar to general pre-training. Additionally, we analyze the compatibility and preference of LLMs' fact memorization. For compatibility, we find LLMs struggle with memorizing redundant facts in a unified way. Only when correlated facts have the same direction and structure, the LLM can compatibly memorize them. This shows the inefficiency of LLM memorization for redundant facts. For preference, the LLM pays more attention to memorizing more frequent and difficult facts, and the subsequent facts can overwrite prior facts' memorization, which significantly hinders low-frequency facts memorization. Our findings reveal the capacity and characteristics of LLMs' fact knowledge learning, which provide directions for LLMs' fact knowledge augmentation.

Inference-Time Decontamination: Reusing Leaked Benchmarks for Large Language Model Evaluation

The training process of large language models (LLMs) often involves varying degrees of test data contamination. Although current LLMs are achieving increasingly better performance on various benchmarks, their performance in practical applications does not always match their benchmark results. Leakage of benchmarks can prevent the accurate assessment of LLMs' true performance. However, constructing new benchmarks is costly, labor-intensive and still carries the risk of leakage. Therefore, in this paper, we ask the question, Can we reuse these leaked benchmarks for LLM evaluation? We propose Inference-Time Decontamination (ITD) to address this issue by detecting and rewriting leaked samples without altering their difficulties. ITD can mitigate performance inflation caused by memorizing leaked benchmarks. Our proof-of-concept experiments demonstrate that ITD reduces inflated accuracy by 22.9% on GSM8K and 19.0% on MMLU. On MMLU, using Inference-time Decontamination can lead to a decrease in the results of Phi3 and Mistral by 6.7% and 3.6% respectively. We hope that ITD can provide more truthful evaluation results for large language models.

Unified Active Retrieval for Retrieval Augmented Generation

In Retrieval-Augmented Generation (RAG), retrieval is not always helpful and applying it to every instruction is sub-optimal. Therefore, determining whether to retrieve is crucial for RAG, which is usually referred to as Active Retrieval. However, existing active retrieval methods face two challenges: 1. They usually rely on a single criterion, which struggles with handling various types of instructions. 2. They depend on specialized and highly differentiated procedures, and thus combining them makes the RAG system more complicated and leads to higher response latency. To address these challenges, we propose Unified Active Retrieval (UAR). UAR contains four orthogonal criteria and casts them into plug-and-play classification tasks, which achieves multifaceted retrieval timing judgements with negligible extra inference cost. We further introduce the Unified Active Retrieval Criteria (UAR-Criteria), designed to process diverse active retrieval scenarios through a standardized procedure. Experiments on four representative types of user instructions show that UAR significantly outperforms existing work on the retrieval timing judgement and the performance of downstream tasks, which shows the effectiveness of UAR and its helpfulness to downstream tasks.

Aggregation of Reasoning: A Hierarchical Framework for Enhancing Answer Selection in Large Language Models

Recent advancements in Chain-of-Thought prompting have facilitated significant breakthroughs for Large Language Models (LLMs) in complex reasoning tasks. Current research enhances the reasoning performance of LLMs by sampling multiple reasoning chains and ensembling based on the answer frequency. However, this approach fails in scenarios where the correct answers are in the minority. We identify this as a primary factor constraining the reasoning capabilities of LLMs, a limitation that cannot be resolved solely based on the predicted answers. To address this shortcoming, we introduce a hierarchical reasoning aggregation framework AoR (Aggregation of Reasoning), which selects answers based on the evaluation of reasoning chains. Additionally, AoR incorporates dynamic sampling, adjusting the number of reasoning chains in accordance with the complexity of the task. Experimental results on a series of complex reasoning tasks show that AoR outperforms prominent ensemble methods. Further analysis reveals that AoR not only adapts various LLMs but also achieves a superior performance ceiling when compared to current methods.

LLatrieval: LLM-Verified Retrieval for Verifiable Generation

Verifiable generation aims to let the large language model (LLM) generate text with corresponding supporting documents, which enables the user to flexibly verify the answer and makes it more trustworthy. Its evaluation not only measures the correctness of the answer, but also the answer's verifiability, i.e., how well the answer is supported by the corresponding documents. In typical, verifiable generation adopts the retrieval-read pipeline, which is divided into two stages: 1) retrieve relevant documents of the question. 2) according to the documents, generate the corresponding answer. Since the retrieved documents can supplement knowledge for the LLM to generate the answer and serve as evidence, the retrieval stage is essential for the correctness and verifiability of the answer. However, the widely used retrievers become the bottleneck of the entire pipeline and limit the overall performance. They often have fewer parameters than the large language model and have not been proven to scale well to the size of LLMs. Since the LLM passively receives the retrieval result, if the retriever does not correctly find the supporting documents, the LLM can not generate the correct and verifiable answer, which overshadows the LLM's remarkable abilities. In this paper, we propose LLatrieval (Large Language Model Verified Retrieval), where the LLM updates the retrieval result until it verifies that the retrieved documents can support answering the question. Thus, the LLM can iteratively provide feedback to retrieval and facilitate the retrieval result to sufficiently support verifiable generation. Experimental results show that our method significantly outperforms extensive baselines and achieves new state-of-the-art results.

Unified Demonstration Retriever for In-Context Learning

In-context learning is a new learning paradigm where a language model conditions on a few input-output pairs (demonstrations) and a test input, and directly outputs the prediction. It has been shown highly dependent on the provided demonstrations and thus promotes the research of demonstration retrieval: given a test input, relevant examples are retrieved from the training set to serve as informative demonstrations for in-context learning. While previous works focus on training task-specific retrievers for several tasks separately, these methods are often hard to transfer and scale on various tasks, and separately trained retrievers incur a lot of parameter storage and deployment cost. In this paper, we propose Unified Demonstration Retriever (\textbf{UDR}), a single model to retrieve demonstrations for a wide range of tasks. To train UDR, we cast various tasks' training signals into a unified list-wise ranking formulation by language model's feedback. Then we propose a multi-task list-wise ranking training framework, with an iterative mining strategy to find high-quality candidates, which can help UDR fully incorporate various tasks' signals. Experiments on 30+ tasks across 13 task families and multiple data domains show that UDR significantly outperforms baselines. Further analyses show the effectiveness of each proposed component and UDR's strong ability in various scenarios including different LMs (1.3B - 175B), unseen datasets, varying demonstration quantities, etc.

MoT: Pre-thinking and Recalling Enable ChatGPT to Self-Improve with Memory-of-Thoughts

Large Language Models have shown impressive abilities on various tasks. However, fundamentally improving them depends on high-quality datasets or computationally expensive fine-tuning. On the contrary, human can easily improve themselves by thinking and memory, without external resources. In this paper, we propose a framework, MoT, to let the LLM self-improve through Memory of Thoughts, without annotated datasets and parameter updates. Specifically, the framework is divided into two stages: 1. before the test stage, we let the LLM pre-think on the unlabeled dataset and save the high-confidence thoughts as external memory; 2. during inference, given a test question, we let the LLM recall relevant memory to help itself reason and answer it. Experimental results show that the proposed framework can help ChatGPT significantly improve its abilities in math reasoning, commonsense reasoning, factual reasoning and natural language inference. Further analyses show that each component contributes critically to the improvements.

Finding Supporting Examples for In-Context Learning

In-context learning is a new learning paradigm where a language model observes a few examples and then straightly outputs the test input's prediction. Previous works have shown that in-context learning is sensitive to the provided examples and randomly sampled examples show significantly unstable performance. In this paper, we propose to find ``supporting examples'' for in-context learning: Given the training dataset, we need to select one permutation of a few examples, which are informative for the task's in-context learning and lead to superior performance. Although in traditional gradient-based learning, e.g., fine-tuning, there are numerous methods to find a ``coreset'' from the entire dataset, they are sub-optimal and not suitable for this problem since in-context learning occurs in the language model's inference without gradients or parameter updates. Additionally, the strong dependence among in-context examples makes this problem an NP-hard combinatorial optimization problem and enumerating all possible permutations is infeasible. Hence we propose a two-stage method to tackle this challenge. First we propose a novel metric to select informative examples based on the language model's feedback, with a progressive filtering strategy. And then we propose a diversity-guided beam search method to refine and evaluate the selected examples, iteratively. The experimental results show our method significantly outperforms a wide range of baselines, and further analyses show the effectiveness of our method and shed light on the properties of supporting examples and in-context learning.

Soft-Labeled Contrastive Pre-training for Function-level Code Representation

Code contrastive pre-training has recently achieved significant progress on code-related tasks. In this paper, we present \textbf{SCodeR}, a \textbf{S}oft-labeled contrastive pre-training framework with two positive sample construction methods to learn functional-level \textbf{Code} \textbf{R}epresentation. Considering the relevance between codes in a large-scale code corpus, the soft-labeled contrastive pre-training can obtain fine-grained soft-labels through an iterative adversarial manner and use them to learn better code representation. The positive sample construction is another key for contrastive pre-training. Previous works use transformation-based methods like variable renaming to generate semantically equal positive codes. However, they usually result in the generated code with a highly similar surface form, and thus mislead the model to focus on superficial code structure instead of code semantics. To encourage SCodeR to capture semantic information from the code, we utilize code comments and abstract syntax sub-trees of the code to build positive samples. We conduct experiments on four code-related tasks over seven datasets. Extensive experimental results show that SCodeR achieves new state-of-the-art performance on all of them, which illustrates the effectiveness of the proposed pre-training method.