ActPC-Geom: Towards Scalable Online Neural-Symbolic Learning via Accelerating Active Predictive Coding with Information Geometry & Diverse Cognitive Mechanisms (2501.04832v1)

Abstract: This paper introduces ActPC-Geom, an approach to accelerate Active Predictive Coding (ActPC) in neural networks by integrating information geometry, specifically using Wasserstein-metric-based methods for measure-dependent gradient flows. We propose replacing KL-divergence in ActPC's predictive error assessment with the Wasserstein metric, suggesting this may enhance network robustness. To make this computationally feasible, we present strategies including: (1) neural approximators for inverse measure-dependent Laplacians, (2) approximate kernel PCA embeddings for low-rank approximations feeding into these approximators, and (3) compositional hypervector embeddings derived from kPCA outputs, with algebra optimized for fuzzy FCA lattices learned through neural architectures analyzing network states. This results in an ActPC architecture capable of real-time online learning and integrating continuous (e.g., transformer-like or Hopfield-net-like) and discrete symbolic ActPC networks, including frameworks like OpenCog Hyperon or ActPC-Chem for algorithmic chemistry evolution. Shared probabilistic, concept-lattice, and hypervector models enable symbolic-subsymbolic integration. Key features include (1) compositional reasoning via hypervector embeddings in transformer-like architectures for tasks like commonsense reasoning, and (2) Hopfield-net dynamics enabling associative long-term memory and attractor-driven cognitive features. We outline how ActPC-Geom combines few-shot learning with online weight updates, enabling deliberative thinking and seamless symbolic-subsymbolic reasoning. Ideas from Galois connections are explored for efficient hybrid ActPC/ActPC-Chem processing. Finally, we propose a specialized HPC design optimized for real-time focused attention and deliberative reasoning tailored to ActPC-Geom's demands.

• The paper introduces ActPC-Geom, which accelerates neural learning by integrating active predictive coding with Wasserstein-based information geometry.
• It employs neural approximations, kernel PCA embeddings, and compositional hypervector embeddings to enable efficient real-time integration of neural and symbolic processes.
• The approach marks a paradigm shift by replacing KL divergence with the Wasserstein metric, laying the groundwork for scalable, hybrid neural-symbolic architectures.

Analyzing "ActPC-Geom: Towards Scalable Online Neural-Symbolic Learning via Accelerating Active Predictive Coding with Information Geometry Diverse Cognitive Mechanisms"

The paper introduces "ActPC-Geom," a speculative approach designed to enhance Active Predictive Coding (ActPC) through integration with information geometry, specifically leveraging the Wasserstein metric for optimizing learning in neural networks. This exploration aims to address issues in real-time and large-scale neural learning through a new synthesis of predictive coding and information geometric principles, while also highlighting significant architectural and algorithmic developments that promise to accelerate neural-symbolic convergence.

Core Concepts and Contributions

ActPC is built on reducing prediction errors within neural networks, emphasizing local updates over global backpropagation. This has been posited as a more effective approach for real-time online learning, specifically for contexts requiring rapid integration of symbolic reasoning and learning dynamics.

The paper proposes integrating this with information geometry, focusing on the Wasserstein metric as a replacement for KL divergence in measuring predictive error. This shift is motivated by the Wasserstein distance's continuous and computable nature over non-overlapping distributions, potentially yielding more robust network behaviors in terms of corresponding probability distributions and cognitive tasks.

To make the Wasserstein metric computationally efficient, ActPC-Geom advocates for:

1. Neural approximators for inverse measure-dependent Laplacians.
2. Kernel PCA (kPCA) embeddings to facilitate low-rank approximations.
3. Compositional hypervector embeddings derived from neural architecture-analyzed fuzzy FCA lattices to supplement kPCA vectors.

This results in a neural architecture potentially capable of real-time online integration between continuous ActPC neural networks and discrete symbolic networks, promising enhanced robustness and efficiency.

Architectural Exploration and Cognitive Synergy

The paper also embarks on the architectural possibilities of hybrid ActPC systems, specifically focusing on transformers. It elucidates how transformer-like architectures with integrated compositional hypervector embeddings could perform sophisticated compositional reasoning and facilitate associative long-term memory dynamics. This is notable as the architecture could engage in effective real-time processing, benefiting from:

• Compositional reasoning, aiding question-answering and commonsense reasoning tasks.
• Dynamics akin to Hopfield networks, bolstering associative memory and cognitive functions.

Moreover, the emergent potential for blending few-shot learning with continuous and incremental online learning processes is underscored as a promising direction for AGI architectures.

Theoretical Implications and Future Directions

Significantly, the paper suggests a paradigm shift from traditional divergence measures to Wasserstein-based metrics for system-level error assessment in neural networks. This conceptual transition aligns the predictive coding theory more harmoniously with efficient and stable learning dynamics in high-dimensional probability spaces, providing a novel basis for deriving cognitive processes and learning algorithms.

The potential application of Galois connections is highlighted to optimize hybrid ActPC implementations, ensuring efficient concurrency across neural-symbolic operations. Additionally, a proposed HPC architecture embodies specialized subsystems to manage discrete symbolic processing, continuous neural processing, and a unified Wasserstein metric, demonstrating feasibility for large-scale implementations.

Concluding Remarks

The paper ambitiously reimagines Active Predictive Coding through the lens of information geometry and novel cognitive mechanisms. By proposing aggressive theoretical and architectural unifications, it suggests pathways that transform neural-symbolic integration into a reality with substantial efficiency and learning advantages. While still speculative, ActPC-Geom lays a compelling groundwork for extensive experimentation and subsequent development, potentially reshaping the landscape of neural network learning dynamics and their applications to artificial general intelligence.