Text watermarking has emerged as a pivotal technique for identifying machine-generated text. However, existing methods often rely on arbitrary vocabulary partitioning during decoding to embed watermarks, which compromises the availability of suitable tokens and significantly degrades the quality of responses. This study assesses the impact of watermarking on different capabilities of large language models (LLMs) from a cognitive science lens. Our finding highlights a significant disparity; knowledge recall and logical reasoning are more adversely affected than language generation. These results suggest a more profound effect of watermarking on LLMs than previously understood. To address these challenges, we introduce Watermarking with Mutual Exclusion (WatME), a novel approach leveraging linguistic prior knowledge of inherent lexical redundancy in LLM vocabularies to seamlessly integrate watermarks. Specifically, WatME dynamically optimizes token usage during the decoding process by applying a mutually exclusive rule to the identified lexical redundancies. This strategy effectively prevents the unavailability of appropriate tokens and preserves the expressive power of LLMs. We provide both theoretical analysis and empirical evidence showing that WatME effectively preserves the diverse capabilities of LLMs while ensuring watermark detectability.

Spatial reasoning in text plays a crucial role in various real-world applications. Existing approaches for spatial reasoning typically infer spatial relations from pure text, which overlook the gap between natural language and symbolic structures. Graph neural networks (GNNs) have showcased exceptional proficiency in inducing and aggregating symbolic structures. However, classical GNNs face challenges in handling multi-hop spatial reasoning due to the over-smoothing issue, i.e., the performance decreases substantially as the number of graph layers increases. To cope with these challenges, we propose a novel Depth-Wise Graph Neural Network (DepWiGNN). Specifically, we design a novel node memory scheme and aggregate the information over the depth dimension instead of the breadth dimension of the graph, which empowers the ability to collect long dependencies without stacking multiple layers. Experimental results on two challenging multi-hop spatial reasoning datasets show that DepWiGNN outperforms existing spatial reasoning methods. The comparisons with the other three GNNs further demonstrate its superiority in capturing long dependency in the graph.