Large Language Models (LLMs) are widely used for knowledge-seeking yet suffer from hallucinations. The knowledge boundary (KB) of an LLM limits its factual understanding, beyond which it may begin to hallucinate. Investigating the perception of LLMs' KB is crucial for detecting hallucinations and LLMs' reliable generation. Current studies perceive LLMs' KB on questions with a concrete answer (close-ended questions) while paying limited attention to semi-open-ended questions (SoeQ) that correspond to many potential answers. Some researchers achieve it by judging whether the question is answerable or not. However, this paradigm is unsuitable for SoeQ, which are usually partially answerable, containing both answerable and ambiguous (unanswerable) answers. Ambiguous answers are essential for knowledge-seeking, but they may go beyond the KB of LLMs. In this paper, we perceive the LLMs' KB with SoeQ by discovering more ambiguous answers. First, we apply an LLM-based approach to construct SoeQ and obtain answers from a target LLM. Unfortunately, the output probabilities of mainstream black-box LLMs are inaccessible to sample for low-probability ambiguous answers. Therefore, we apply an open-sourced auxiliary model to explore ambiguous answers for the target LLM. We calculate the nearest semantic representation for existing answers to estimate their probabilities, with which we reduce the generation probability of high-probability answers to achieve a more effective generation. Finally, we compare the results from the RAG-based evaluation and LLM self-evaluation to categorize four types of ambiguous answers that are beyond the KB of the target LLM. Following our method, we construct a dataset to perceive the KB for GPT-4. We find that GPT-4 performs poorly on SoeQ and is often unaware of its KB. Besides, our auxiliary model, LLaMA-2-13B, is effective in discovering more ambiguous answers.

Vector Quantized Variational AutoEncoder (VQ-VAE) is an established technique in machine learning for learning discrete representations across various modalities. However, its scalability and applicability are limited by the need to retrain the model to adjust the codebook for different data or model scales. We introduce the Rate-Adaptive VQ-VAE (RAQ-VAE) framework, which addresses this challenge with two novel codebook representation methods: a model-based approach using a clustering-based technique on an existing well-trained VQ-VAE model, and a data-driven approach utilizing a sequence-to-sequence (Seq2Seq) model for variable-rate codebook generation. Our experiments demonstrate that RAQ-VAE achieves effective reconstruction performance across multiple rates, often outperforming conventional fixed-rate VQ-VAE models. This work enhances the adaptability and performance of VQ-VAEs, with broad applications in data reconstruction, generation, and computer vision tasks.

Gloss-free sign language translation (SLT) aims to develop well-performing SLT systems with no requirement for the costly gloss annotations, but currently still lags behind gloss-based approaches significantly. In this paper, we identify a representation density problem that could be a bottleneck in restricting the performance of gloss-free SLT. Specifically, the representation density problem describes that the visual representations of semantically distinct sign gestures tend to be closely packed together in feature space, which makes gloss-free methods struggle with distinguishing different sign gestures and suffer from a sharp performance drop. To address the representation density problem, we introduce a simple but effective contrastive learning strategy, namely SignCL, which encourages gloss-free models to learn more discriminative feature representation in a self-supervised manner. Our experiments demonstrate that the proposed SignCL can significantly reduce the representation density and improve performance across various translation frameworks. Specifically, SignCL achieves a significant improvement in BLEU score for the Sign Language Transformer and GFSLT-VLP on the CSL-Daily dataset by 39% and 46%, respectively, without any increase of model parameters. Compared to Sign2GPT, a state-of-the-art method based on large-scale pre-trained vision and language models, SignCL achieves better performance with only 35% of its parameters.

Proof assistants like Lean have revolutionized mathematical proof verification, ensuring high accuracy and reliability. Although large language models (LLMs) show promise in mathematical reasoning, their advancement in formal theorem proving is hindered by a lack of training data. To address this issue, we introduce an approach to generate extensive Lean 4 proof data derived from high-school and undergraduate-level mathematical competition problems. This approach involves translating natural language problems into formal statements, filtering out low-quality statements, and generating proofs to create synthetic data. After fine-tuning the DeepSeekMath 7B model on this synthetic dataset, which comprises 8 million formal statements with proofs, our model achieved whole-proof generation accuracies of 46.3% with 64 samples and 52% cumulatively on the Lean 4 miniF2F test, surpassing the baseline GPT-4 at 23.0% with 64 samples and a tree search reinforcement learning method at 41.0%. Additionally, our model successfully proved 5 out of 148 problems in the Lean 4 Formalized International Mathematical Olympiad (FIMO) benchmark, while GPT-4 failed to prove any. These results demonstrate the potential of leveraging large-scale synthetic data to enhance theorem-proving capabilities in LLMs. Both the synthetic dataset and the model will be made available to facilitate further research in this promising field.

As Large Language Models (LLMs) and Retrieval Augmentation Generation (RAG) techniques have evolved, query rewriting has been widely incorporated into the RAG system for downstream tasks like open-domain QA. Many works have attempted to utilize small models with reinforcement learning rather than costly LLMs to improve query rewriting. However, current methods require annotations (e.g., labeled relevant documents or downstream answers) or predesigned rewards for feedback, which lack generalization, and fail to utilize signals tailored for query rewriting. In this paper, we propose ours, a framework for training query rewriting models free of annotations. By leveraging a publicly available reranker, ours~provides feedback aligned well with the rewriting objectives. Experimental results demonstrate that ours~can obtain better performance than baselines.

Continual learning, also known as lifelong learning or incremental learning, refers to the process by which a model learns from a stream of incoming data over time. A common problem in continual learning is the classification layer's bias towards the most recent task. Traditionally, methods have relied on incorporating data from past tasks during training to mitigate this issue. However, the recent shift in continual learning to memory-free environments has rendered these approaches infeasible. In this study, we propose a solution focused on the testing phase. We first introduce a simple Out-of-Task Detection method, OTD, designed to accurately identify samples from past tasks during testing. Leveraging OTD, we then propose: (1) an Adaptive Retention mechanism for dynamically tuning the classifier layer on past task data; (2) an Adaptive Correction mechanism for revising predictions when the model classifies data from previous tasks into classes from the current task. We name our approach Adaptive Retention & Correction (ARC). While designed for memory-free environments, ARC also proves effective in memory-based settings. Extensive experiments show that our proposed method can be plugged in to virtually any existing continual learning approach without requiring any modifications to its training procedure. Specifically, when integrated with state-of-the-art approaches, ARC achieves an average performance increase of 2.7% and 2.6% on the CIFAR-100 and Imagenet-R datasets, respectively.

Multiple-choice questions (MCQs) are widely used in the evaluation of large language models (LLMs) due to their simplicity and efficiency. However, there are concerns about whether MCQs can truly measure LLM's capabilities, particularly in knowledge-intensive scenarios where long-form generation (LFG) answers are required. The misalignment between the task and the evaluation method demands a thoughtful analysis of MCQ's efficacy, which we undertake in this paper by evaluating nine LLMs on four question-answering (QA) datasets in two languages: Chinese and English. We identify a significant issue: LLMs exhibit an order sensitivity in bilingual MCQs, favoring answers located at specific positions, i.e., the first position. We further quantify the gap between MCQs and long-form generation questions (LFGQs) by comparing their direct outputs, token logits, and embeddings. Our results reveal a relatively low correlation between answers from MCQs and LFGQs for identical questions. Additionally, we propose two methods to quantify the consistency and confidence of LLMs' output, which can be generalized to other QA evaluation benchmarks. Notably, our analysis challenges the idea that the higher the consistency, the greater the accuracy. We also find MCQs to be less reliable than LFGQs in terms of expected calibration error. Finally, the misalignment between MCQs and LFGQs is not only reflected in the evaluation performance but also in the embedding space. Our code and models can be accessed at https://github.com/Meetyou-AI-Lab/Can-MC-Evaluate-LLMs.

In constrained Markov decision processes (CMDPs) with adversarial rewards and constraints, a well-known impossibility result prevents any algorithm from attaining both sublinear regret and sublinear constraint violation, when competing against a best-in-hindsight policy that satisfies constraints on average. In this paper, we show that this negative result can be eased in CMDPs with non-stationary rewards and constraints, by providing algorithms whose performances smoothly degrade as non-stationarity increases. Specifically, we propose algorithms attaining $\tilde{\mathcal{O}} (\sqrt{T} + C)$ regret and positive constraint violation under bandit feedback, where $C$ is a corruption value measuring the environment non-stationarity. This can be $\Theta(T)$ in the worst case, coherently with the impossibility result for adversarial CMDPs. First, we design an algorithm with the desired guarantees when $C$ is known. Then, in the case $C$ is unknown, we show how to obtain the same results by embedding such an algorithm in a general meta-procedure. This is of independent interest, as it can be applied to any non-stationary constrained online learning setting.

Solving partial differential equations (PDEs) in Euclidean space with closed-form symbolic solutions has long been a dream for mathematicians. Inspired by deep learning, Physics-Informed Neural Networks (PINNs) have shown great promise in numerically solving PDEs. However, since PINNs essentially approximate solutions within the continuous function space, their numerical solutions fall short in both precision and interpretability compared to symbolic solutions. This paper proposes a novel framework: a closed-form \textbf{Sym}bolic framework for \textbf{PDE}s (SymPDE), exploring the use of deep reinforcement learning to directly obtain symbolic solutions for PDEs. SymPDE alleviates the challenges PINNs face in fitting high-frequency and steeply changing functions. To our knowledge, no prior work has implemented this approach. Experiments on solving the Poisson's equation and heat equation in time-independent and spatiotemporal dynamical systems respectively demonstrate that SymPDE can provide accurate closed-form symbolic solutions for various types of PDEs.

Intelligent Tutoring Systems (ITSs) have shown great potential in delivering personalized and adaptive education, but their widespread adoption has been hindered by the need for specialized programming and design skills. Existing approaches overcome the programming limitations with no-code authoring through drag and drop, however they assume that educators possess the necessary skills to design effective and engaging tutor interfaces. To address this assumption we introduce generative AI capabilities to assist educators in creating tutor interfaces that meet their needs while adhering to design principles. Our approach leverages Large Language Models (LLMs) and prompt engineering to generate tutor layout and contents based on high-level requirements provided by educators as inputs. However, to allow them to actively participate in the design process, rather than relying entirely on AI-generated solutions, we allow generation both at the entire interface level and at the individual component level. The former provides educators with a complete interface that can be refined using direct manipulation, while the latter offers the ability to create specific elements to be added to the tutor interface. A small-scale comparison shows the potential of our approach to enhance the efficiency of tutor interface design. Moving forward, we raise critical questions for assisting educators with generative AI capabilities to create personalized, effective, and engaging tutors, ultimately enhancing their adoption.