A Closer Look at the Self-Verification Abilities of Large Language Models in Logical Reasoning

Logical reasoning has been an ongoing pursuit in the field of AI. Despite significant advancements made by large language models (LLMs), they still struggle with complex logical reasoning problems. To enhance reasoning performance, one promising direction is scalable oversight, which requires LLMs to identify their own errors and then improve by themselves. Various self-verification methods have been proposed in pursuit of this goal. Nevertheless, whether existing models understand their own errors well is still under investigation. In this paper, we take a closer look at the self-verification abilities of LLMs in the context of logical reasoning, focusing on their ability to identify logical fallacies accurately. We introduce a dataset, FALLACIES, containing 232 types of reasoning fallacies categorized in a hierarchical taxonomy. By conducting exhaustive experiments on FALLACIES, we obtain comprehensive and detailed analyses of a series of models on their verification abilities. Our main findings suggest that existing LLMs could struggle to identify fallacious reasoning steps accurately and may fall short of guaranteeing the validity of self-verification methods. Drawing from these observations, we offer suggestions for future research and practical applications of self-verification methods.

Sub-Sentence Encoder: Contrastive Learning of Propositional Semantic Representations

We introduce sub-sentence encoder, a contrastively-learned contextual embedding model for fine-grained semantic representation of text. In contrast to the standard practice with sentence embeddings, where the meaning of an entire sequence of text is encoded into a fixed-length vector, the sub-sentence encoder learns to produce distinct contextual embeddings corresponding to different atomic propositions, i.e. atomic units of meaning expressed within a text sequence. The sub-sentence embeddings are contrastively learned to recognize (inferred) semantic equivalence between propositions across different text sequences. Our experiments show the effectiveness of sub-sentence encoders in applications, such as retrieving supporting facts for fine-grained text attribution or recognizing the conditional semantic similarity between texts. In practice, we demonstrate that sub-sentence encoders keep the same level of inference cost and space complexity compared to sentence encoders.

StoryAnalogy: Deriving Story-level Analogies from Large Language Models to Unlock Analogical Understanding

Analogy-making between narratives is crucial for human reasoning. In this paper, we evaluate the ability to identify and generate analogies by constructing a first-of-its-kind large-scale story-level analogy corpus, \textsc{StoryAnalogy}, which contains 24K story pairs from diverse domains with human annotations on two similarities from the extended Structure-Mapping Theory. We design a set of tests on \textsc{StoryAnalogy}, presenting the first evaluation of story-level analogy identification and generation. Interestingly, we find that the analogy identification tasks are incredibly difficult not only for sentence embedding models but also for the recent large language models (LLMs) such as ChatGPT and LLaMa. ChatGPT, for example, only achieved around 30% accuracy in multiple-choice questions (compared to over 85% accuracy for humans). Furthermore, we observe that the data in \textsc{StoryAnalogy} can improve the quality of analogy generation in LLMs, where a fine-tuned FlanT5-xxl model achieves comparable performance to zero-shot ChatGPT.

On the Dimensionality of Sentence Embeddings

Learning sentence embeddings is a fundamental problem in natural language processing. While existing research primarily focuses on enhancing the quality of sentence embeddings, the exploration of sentence embedding dimensions is limited. Here we present a comprehensive and empirical analysis of the dimensionality of sentence embeddings. First, we demonstrate that the optimal dimension of sentence embeddings is usually smaller than the default value. Subsequently, to compress the dimension of sentence embeddings with minimum performance degradation, we identify two components contributing to the overall performance loss: the encoder's performance loss and the pooler's performance loss. Therefore, we propose a two-step training method for sentence representation learning models, wherein the encoder and the pooler are optimized separately to mitigate the overall performance loss in low-dimension scenarios. Experimental results on seven STS tasks and seven sentence classification tasks demonstrate that our method significantly improves the performance of low-dimensional sentence embeddings.

SocREval: Large Language Models with the Socratic Method for Reference-Free Reasoning Evaluation

To comprehensively assess the capacity of current models for complex reasoning, it is crucial to assess their step-by-step reasoning in a scalable manner. Established reference-based evaluation metrics rely on human-annotated reasoning chains to assess the model-derived chains. However, such ``gold-standard'' human-written reasoning chains may not be unique and their acquisition is often labor-intensive. Existing reference-free reasoning metrics eliminate the need for human-crafted reasoning chains as references, but they typically require fine-tuning on datasets with human-derived reasoning chains, which complicates the process and raises concerns regarding generalizability across diverse datasets. To address these challenges, we harness GPT-4 to automatically evaluate reasoning chain quality, obviating the need for human-crafted references. Leveraging the Socratic method, we devise tailored prompts to enhance reference-free reasoning evaluation, which we term SocREval (Socratic method for Reasoning Evaluation). Empirical results from four human annotated datasets reveal that SocREval significantly improves GPT-4's performance, surpassing existing reference-free and reference-based reasoning evaluation metrics. Beyond its demonstrated efficacy, our proposed framework, large language models (LLMs) with the Socratic method, proves to be both cost-efficient and robust to prompt writing and example selection, as substantiated by our in-depth analysis.

LASER: LLM Agent with State-Space Exploration for Web Navigation

Large language models (LLMs) have been successfully adapted for interactive decision-making tasks like web navigation. While achieving decent performance, previous methods implicitly assume a forward-only execution mode for the model, where they only provide oracle trajectories as in-context examples to teach the model how to reason in the interactive environment. Consequently, the model could not handle more challenging scenarios not covered in the in-context examples, e.g., mistakes, leading to sub-optimal performance. To address this issue, we propose to model the interactive task as state space exploration, where the LLM agent transitions among a pre-defined set of states by performing actions to complete the task. This formulation enables flexible back-tracking, allowing the model to easily recover from errors. We evaluate our proposed LLM Agent with State-Space ExploRation (LASER) on the WebShop task. Experimental results show that our LASER agent significantly outperforms previous methods and closes the gap with human performance on the web navigation task.

Space-Time Shift Keying Aided OTFS Modulation for Orthogonal Multiple Access

Space-time shift keying-aided orthogonal time frequency space modulation-based multiple access (STSK-OTFS-MA) is proposed for reliable uplink transmission in high-Doppler scenarios. As a beneficial feature of our STSK-OTFS-MA system, extra information bits are mapped onto the indices of the active dispersion matrices, which allows the system to enjoy the joint benefits of both STSK and OTFS signalling. Due to the fact that both the time-, space- and DD-domain degrees of freedom are jointly exploited, our STSK-OTFS-MA achieves increased diversity and coding gains. To mitigate the potentially excessive detection complexity, the sparse structure of the equivalent transmitted symbol vector is exploited, resulting in a pair of low-complexity near-maximum likelihood (ML) multiuser detection algorithms. Explicitly, we conceive a progressive residual check-based greedy detector (PRCGD) and an iterative reduced-space check-based detector (IRCD). Then, we derive both the unconditional single-user pairwise error probability (SU-UPEP) and a tight bit error ratio (BER) union-bound for our single-user STSK-OTFS-MA system employing the ML detector. Furthermore, the discrete-input continuous-output memoryless channel (DCMC) capacity of the proposed system is derived. The optimal dispersion matrices (DMs) are designed based on the maximum attainable diversity and coding gain metrics. Finally, it is demonstrated that our STSK-OTFS-MA system achieves both a lower BER and a higher DCMC capacity than its conventional spatial modulation (SM) {and its orthogonal frequency-division multiplexing (OFDM) counterparts. As a benefit, the proposed system strikes a compelling BER vs. system complexity as well as BER vs. detection complexity trade-offs.

Thrust: Adaptively Propels Large Language Models with External Knowledge

Although large-scale pre-trained language models (PTLMs) are shown to encode rich knowledge in their model parameters, the inherent knowledge in PTLMs can be opaque or static, making external knowledge necessary. However, the existing information retrieval techniques could be costly and may even introduce noisy and sometimes misleading knowledge. To address these challenges, we propose the instance-level adaptive propulsion of external knowledge (IAPEK), where we only conduct the retrieval when necessary. To achieve this goal, we propose measuring whether a PTLM contains enough knowledge to solve an instance with a novel metric, Thrust, which leverages the representation distribution of a small number of seen instances. Extensive experiments demonstrate that thrust is a good measurement of PTLM models' instance-level knowledgeability. Moreover, we can achieve significantly higher cost-efficiency with the Thrust score as the retrieval indicator than the naive usage of external knowledge on 88% of the evaluated tasks with 26% average performance improvement. Such findings shed light on the real-world practice of knowledge-enhanced LMs with a limited knowledge-seeking budget due to computation latency or costs.

A Stitch in Time Saves Nine: Detecting and Mitigating Hallucinations of LLMs by Validating Low-Confidence Generation

Recently developed large language models have achieved remarkable success in generating fluent and coherent text. However, these models often tend to 'hallucinate' which critically hampers their reliability. In this work, we address this crucial problem and propose an approach that actively detects and mitigates hallucinations during the generation process. Specifically, we first identify the candidates of potential hallucination leveraging the model's logit output values, check their correctness through a validation procedure, mitigate the detected hallucinations, and then continue with the generation process. Through extensive experiments with the 'article generation task', we first demonstrate the individual efficacy of our detection and mitigation techniques. Specifically, the detection technique achieves a recall of 88% and the mitigation technique successfully mitigates 57.6% of the correctly detected hallucinations. Importantly, our mitigation technique does not introduce new hallucinations even in the case of incorrectly detected hallucinations, i.e., false positives. Then, we show that the proposed active detection and mitigation approach successfully reduces the hallucinations of the GPT-3 model from 47.5% to 14.5% on average. In summary, our work contributes to improving the reliability and trustworthiness of large language models, a crucial step en route to enabling their widespread adoption in real-world applications.

Performance Analysis and Approximate Message Passing Detection of Orthogonal Time Sequency Multiplexing Modulation

In orthogonal time sequency multiplexing (OTSM) modulation, the information symbols are conveyed in the delay-sequency domain upon exploiting the inverse Walsh Hadamard transform (IWHT). It has been shown that OTSM is capable of attaining a bit error ratio (BER) similar to that of orthogonal time-frequency space (OTFS) modulation at a lower complexity, since the saving of multiplication operations in the IWHT. Hence we provide its BER performance analysis and characterize its detection complexity. We commence by deriving its generalized input-output relationship and its unconditional pairwise error probability (UPEP). Then, its BER upper bound is derived in closed form under both ideal and imperfect channel estimation conditions, which is shown to be tight at moderate to high signal-to-noise ratios (SNRs). Moreover, a novel approximate message passing (AMP) aided OTSM detection framework is proposed. Specifically, to circumvent the high residual BER of the conventional AMP detector, we proposed a vector AMP-based expectation-maximization (VAMP-EM) detector for performing joint data detection and noise variance estimation. The variance auto-tuning algorithm based on the EM algorithm is designed for the VAMP-EM detector to further improve the convergence performance. The simulation results illustrate that the VAMP-EM detector is capable of striking an attractive BER vs. complexity trade-off than the state-of-the-art schemes as well as providing a better convergence. Finally, we propose AMP and VAMP-EM turbo receivers for low-density parity-check (LDPC)-coded OTSM systems. It is demonstrated that our proposed VAMP-EM turbo receiver is capable of providing both BER and convergence performance improvements over the conventional AMP solution.