Modeling and analyzing long sequences of text is an essential task for Natural Language Processing. Success in capturing long text dynamics using neural language models will facilitate many downstream tasks such as coherence evaluation, text generation, machine translation and so on. This paper presents a novel approach to model sequences through a stochastic process. We introduce a likelihood-based training objective for the text encoder and design a more thorough measurement (score) for long text evaluation compared to the previous approach. The proposed training objective effectively preserves the sequence coherence, while the new score comprehensively captures both temporal and spatial dependencies. Theoretical properties of our new score show its advantages in sequence evaluation. Experimental results show superior performance in various sequence evaluation tasks, including global and local discrimination within and between documents of different lengths. We also demonstrate the encoder achieves competitive results on discriminating human and AI written text.

Measuring the coherence of text is a vital aspect of evaluating the quality of written content. Recent advancements in neural coherence modeling have demonstrated their efficacy in capturing entity coreference and discourse relations, thereby enhancing coherence evaluation. However, many existing methods heavily depend on static embeddings or focus narrowly on nearby context, constraining their capacity to measure the overarching coherence of long texts. In this paper, we posit that coherent texts inherently manifest a sequential and cohesive interplay among sentences, effectively conveying the central theme, purpose, or standpoint. To explore this abstract relationship, we introduce the "BBScore," a novel reference-free metric grounded in Brownian bridge theory for assessing text coherence. Our findings showcase that when synergized with a simple additional classification component, this metric attains a performance level comparable to state-of-the-art techniques on standard artificial discrimination tasks. We also establish in downstream tasks that this metric effectively differentiates between human-written documents and text generated by large language models under a specific domain. Furthermore, we illustrate the efficacy of this approach in detecting written styles attributed to diverse large language models, underscoring its potential for generalizability. In summary, we present a novel Brownian bridge coherence metric capable of measuring both local and global text coherence, while circumventing the need for end-to-end model training. This flexibility allows for its application in various downstream tasks.