Using Single-Neuron Representations for Hierarchical Concepts as Abstractions of Multi-Neuron Representations

TL;DR

This paper demonstrates that multi-neuron hierarchical concept models can be effectively abstracted by simpler single-neuron models, facilitating easier analysis of complex brain network behaviors.

Contribution

It introduces a formal framework linking multi-neuron and single-neuron models, enabling hierarchical concept recognition analysis through abstraction.

Findings

Single-neuron models can accurately represent multi-neuron hierarchical concepts.

Abstract models simplify analysis of complex brain network behaviors.

The approach decomposes complex network analysis into manageable parts.

Abstract

Brain networks exhibit complications such as noise, neuron failures, and partial synaptic connectivity. These can make it difficult to model and analyze their behavior. This paper describes a way to address this difficulty, namely, breaking down the models and analysis using levels of abstraction. We describe the approach for the problem of recognizing hierarchically-structured concepts. Realistic models for representing hierarchical concepts use multiple neurons to represent each concept [10,1,7,3]. These models are intended to capture some behaviors of actual brains; however, their analysis can be complicated. Mechanisms based on single-neuron representations can be easier to understand and analyze [2,4], but are less realistic. Here we show that these two types of models are compatible, and in fact, networks with single-neuron representations can be regarded as formal abstractions of networks with multi-neuron representations. We do this by relating networks with multi-neuron representations like those in [3] to networks with single-neuron representations like those in [2]. Specifically, we consider two networks, H and L, with multi-neuron representations, one with high connectivity and one with low connectivity. We define two abstract networks, A1 and A2, with single-neuron representations, and prove that they recognize concepts correctly. Then we prove correctness of H and L by relating them to A1 and A2. In this way, we decompose the analysis of each multi-neuron network into two parts: analysis of abstract, single-neuron networks, and proofs of formal relationships between the multi-neuron network and single-neuron networks. These examples illustrate what we consider to be a promising, tractable approach to analyzing other complex brain mechanisms.