Discrete, compositional, and symbolic representations through attractor dynamics (2310.01807v2)

Abstract: 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.

• The paper introduces an attractor dynamics-based model to partition continuous neural representations into discrete symbolic forms.
• It employs a generative flow network expectation-maximization algorithm to enable the emergence of compositional language from complex inputs.
• Experimental validation on both Gaussian grids and dSprites demonstrates effective mapping of continuous attributes to structured symbolic representations.

Exploring Discrete, Compositional, and Symbolic Representations through Attractor Dynamics

This paper investigates a novel approach to reconciling symbolic and continuous processing within neural networks by leveraging attractor dynamics. Attractor dynamics enable the partitioning of a continuous representation space into discrete symbolic basins, offering a neurally plausible mechanism for implementing discretization without imposing explicit quantization steps.

Core Contributions

The research presents two key contributions:

1. Attractor-Based Discretization: The authors propose a model that bridges continuous high-dimensional neural representations and discrete symbolic thoughts. This is achieved through attractor dynamics that naturally partition the space, allowing the learning of discrete symbolic representations without explicit algorithmic interventions like quantization.
2. Emergent Compositional Language: By employing generative flow network expectation-maximization (GFN-EM) algorithms, the research demonstrates how a compositional language can emerge to encode complex sensory inputs. This addresses the challenge of mapping rich, distributed input information to discrete, symbolic representations.

Methodology

The model operates as a continuous dynamical system, where a stochastic policy samples latent state trajectories, starting with an initial encoding $z_0$ of the input $x$ and converging to terminal points $z_T$ near attractor states $\hat{z}_w$ representing symbol sequences $w$. The training utilizes a generative flow network framework to ensure the terminal distribution is proportional to a target function encoding information similarity and symbolic priors.

Utilizing the dSprites dataset, the research showcases the emergence of compositionality in learned symbolic representations. Through rigorous training regimes, including an expectation-maximization loop, the model learns to discretize input data into symbolic forms, with inherent compositional structure reflecting semantic attributes.

Experimental Validation

Two primary experimental setups validate the model's efficacy:

1. Grid of Gaussians: This experiment serves as an initial validation. Inputs sampled from a grid of Gaussian distributions resulted in attractor dynamics that effectively learned to place symbolic representations at the centers of Gaussians, demonstrating the system's ability to map continuous regions to discrete symbols.
2. dSprites Dataset: In this more complex task, dSprites images with attributes such as color, shape, and position were encoded into compositional sequences. The model successfully predicted attributes like position and color, demonstrating its capability to parse complex sensory inputs into structured and meaningful symbolic representations.

Implications and Future Directions

The implications of this research are substantial for cognitive and artificial intelligence domains. It provides a conceptual and practical framework for symbol grounding in neural networks, offering insights into compositional thought and cognitive representations. The approach bridges the gap between continuous neural processes and discrete symbolic reasoning, which has been a persistent challenge in cognitive modeling.

Theoretically, this model advances understanding of how dynamical systems might underpin symbolic processing, potentially aligning more closely with cognitive processes thought to occur in the human brain. Practically, such models could innovate artificial intelligence systems tasked with understanding and manipulating complex, abstract concepts.

Future research could focus on extending this methodology to broader applications, integrating additional sensory modalities, and refining the training algorithms to eliminate residual reliance on explicitly defined discretizers. Further exploration could also involve the relaxing of structured discretization in favor of learning purely emergent symbolic constructs.

In conclusion, this paper provides an integrated approach to continuous-to-discrete representation transformation within neural systems, using attractor dynamics to balance the demands of cognitive plausibility and computational efficacy.