Symbolic systems are powerful frameworks for modeling cognitive processes as they encapsulate the rules and relationships fundamental to many aspects of human reasoning and behavior. Central to these models are systematicity, compositionality, and productivity, making them invaluable in both cognitive science and artificial intelligence. However, certain limitations remain. For instance, the integration of structured symbolic processes and latent sub-symbolic processes has been implemented at the computational level through fiat methods such as quantization or softmax sampling, which assume, rather than derive, the operations underpinning discretization and symbolicization. In this work, we introduce a novel neural stochastic dynamical systems model that integrates attractor dynamics with symbolic representations to model cognitive processes akin to the probabilistic language of thought (PLoT). Our model segments the continuous representational space into discrete basins, with attractor states corresponding to symbolic sequences, that reflect the semanticity and compositionality characteristic of symbolic systems through unsupervised learning, rather than relying on pre-defined primitives. Moreover, like PLoT, our model learns to sample a diverse distribution of attractor states that reflect the mutual information between the input data and the symbolic encodings. This approach establishes a unified framework that integrates both symbolic and sub-symbolic processing through neural dynamics, a neuro-plausible substrate with proven expressivity in AI, offering a more comprehensive model that mirrors the complex duality of cognitive operations.

翻译：符号系统是建模认知过程的强大框架，因其封装了人类推理与行为诸多方面的基本规则与关系。这些模型的核心在于系统性、组合性与生成性，使其在认知科学与人工智能领域均具有重要价值。然而，现有模型仍存在一定局限。例如，结构化符号过程与潜在亚符号过程的整合，在计算层面通常通过量化或softmax采样等强制方法实现，这些方法假设而非推导出离散化与符号化背后的操作机制。本研究提出一种新颖的神经随机动力学系统模型，将吸引子动力学与符号表征相结合，用于建模类似于概率思维语言（PLoT）的认知过程。该模型通过无监督学习将连续表征空间分割为离散吸引域，其吸引子状态对应符号序列，从而反映符号系统特有的语义性与组合性，而无需依赖预定义基元。此外，与PLoT类似，本模型能够学习采样多样化的吸引子状态分布，这些分布反映了输入数据与符号编码之间的互信息。该方法通过神经动力学——一种在人工智能中已被证明具有强表达能力的神经可塑性基质——建立了融合符号与亚符号处理的统一框架，提供了一个更全面模拟认知操作复杂双重性的模型。