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From Worms to Mice: Homeostasis Maybe All You Need

Jesus Marco de Lucas

TL;DR

The paper investigates whether a minimal XOR circuit architecture can support homeostatic regulation and learning across biological connectomes. It implements a four-excitatory, one-inhibitory spiking XOR motif and tests its occurrence in C. elegans, Drosophila, and mouse V1 via graph-isomorphism analyses and motif extensions. Findings show abundant strict and virtual XOR motifs across species, with structured layering in mouse V1 and varying sensory-related enrichment in Drosophila neuropils. The work proposes that architecture plus a loss-function–like signal from XOR activity could comprise core components for biologically grounded learning.

Abstract

In this brief and speculative commentary, we explore ideas inspired by neural networks in machine learning, proposing that a simple neural XOR motif, involving both excitatory and inhibitory connections, may provide the basis for a relevant mode of plasticity in neural circuits of living organisms, with homeostasis as the sole guiding principle. This XOR motif simply signals the discrepancy between incoming signals and reference signals, thereby providing a basis for a loss function in learning neural circuits, and at the same time regulating homeostasis by halting the propagation of these incoming signals. The core motif uses a 4:1 ratio of excitatory to inhibitory neurons, and supports broader neural patterns such as the well-known 'winner takes all' (WTA) mechanism. We examined the prevalence of the XOR motif in the published connectomes of various organisms with increasing complexity, and found that it ranges from tens (in C. elegans) to millions (in several Drosophila neuropils) and more than tens of millions (in mouse V1 visual cortex). If validated, our hypothesis identifies two of the three key components in analogy to machine learning models: the architecture and the loss function. And we propose that a relevant type of biological neural plasticity is simply driven by a basic control or regulatory system, which has persisted and adapted despite the increasing complexity of organisms throughout evolution.

From Worms to Mice: Homeostasis Maybe All You Need

TL;DR

The paper investigates whether a minimal XOR circuit architecture can support homeostatic regulation and learning across biological connectomes. It implements a four-excitatory, one-inhibitory spiking XOR motif and tests its occurrence in C. elegans, Drosophila, and mouse V1 via graph-isomorphism analyses and motif extensions. Findings show abundant strict and virtual XOR motifs across species, with structured layering in mouse V1 and varying sensory-related enrichment in Drosophila neuropils. The work proposes that architecture plus a loss-function–like signal from XOR activity could comprise core components for biologically grounded learning.

Abstract

In this brief and speculative commentary, we explore ideas inspired by neural networks in machine learning, proposing that a simple neural XOR motif, involving both excitatory and inhibitory connections, may provide the basis for a relevant mode of plasticity in neural circuits of living organisms, with homeostasis as the sole guiding principle. This XOR motif simply signals the discrepancy between incoming signals and reference signals, thereby providing a basis for a loss function in learning neural circuits, and at the same time regulating homeostasis by halting the propagation of these incoming signals. The core motif uses a 4:1 ratio of excitatory to inhibitory neurons, and supports broader neural patterns such as the well-known 'winner takes all' (WTA) mechanism. We examined the prevalence of the XOR motif in the published connectomes of various organisms with increasing complexity, and found that it ranges from tens (in C. elegans) to millions (in several Drosophila neuropils) and more than tens of millions (in mouse V1 visual cortex). If validated, our hypothesis identifies two of the three key components in analogy to machine learning models: the architecture and the loss function. And we propose that a relevant type of biological neural plasticity is simply driven by a basic control or regulatory system, which has persisted and adapted despite the increasing complexity of organisms throughout evolution.
Paper Structure (8 sections, 6 figures, 5 tables)

This paper contains 8 sections, 6 figures, 5 tables.

Table of Contents

  1. Introduction
  2. The XOR motif in spiking neural networks
  3. XOR Motif in C. Elegans
  4. Identifying XOR Motifs in the C. Elegans Connectome
  5. Virtual XOR Motifs in the Connectome
  6. XOR motif in Drosophila
  7. XOR motifs in mice
  8. Discussion

Figures (6)

  • Figure 1: basic scheme of the neural XOR motif found in C.Elegans.
  • Figure 2: Spiking patterns in the XOR motif neurons (2-7), corresponding to the injection of two pulses (neurons 0 and 1); left: 0-1 / 1-0 pattern, neuron 6 (XOR output) spikes regularly; right: 0-0 / 1-1 pattern, neuron 6 does not spike, as neurons 4 and 5 are inhibited by neuron 7.
  • Figure 3: Comparison of a basic “strict” XOR motif (left) and an example of “virtual” one (right), that includes additional connections among the nodes. Strict motifs are defined as an isomorphism between the motif and a subgraph in the connectome, while virtual motifs are defined as monomorphisms.
  • Figure 4: A different motif with six interconnected neurons, one of them inhibitory, and eight edges. Notice that other configurations may overlap with the strict XOR motif, so it is not obvious what other motifs could be included in the comparison.
  • Figure 5: Two “extended” XOR motifs: left, full feedback; right, asymmetric feedback..
  • ...and 1 more figures