Implementing engrams from a machine learning perspective: XOR as a basic motif

TL;DR

This work tackles how a biological system could implement a loss-like learning signal by using a homeostatic XOR motif as a comparator between incoming and learned signals. It combines a minimal, biologically plausible circuit modeled with excitatory and inhibitory neurons and demonstrates feasibility in the C. elegans connectome, as well as in LTC/NCP-based recurrent networks trained on binary sequences and melodies. A key contribution is the MULTIXOR architecture, which embeds the XOR motif into an autoencoder-like scheme and shows that simple inhibitory feedback can drive convergence and enable basic Boolean operations. The findings propose a bridge between biological circuit motifs and computational learning, with potential implications for rapid convergence, memory processing, and the design of bio-inspired learning blocks.

Abstract

We have previously presented the idea of how complex multimodal information could be represented in our brains in a compressed form, following mechanisms similar to those employed in machine learning tools, like autoencoders. In this short comment note we reflect, mainly with a didactical purpose, upon the basic question for a biological implementation: what could be the mechanism working as a loss function, and how it could be connected to a neuronal network providing the required feedback to build a simple training configuration. We present our initial ideas based on a basic motif that implements an XOR switch, using few excitatory and inhibitory neurons. Such motif is guided by a principle of homeostasis, and it implements a loss function that could provide feedback to other neuronal structures, establishing a control system. We analyse the presence of this XOR motif in the connectome of C.Elegans, and indicate the relationship with the well-known lateral inhibition motif. We then explore how to build a basic biological neuronal structure with learning capacity integrating this XOR motif. Guided by the computational analogy, we show an initial example that indicates the feasibility of this approach, applied to learning binary sequences, like it is the case for simple melodies. In summary, we provide didactical examples exploring the parallelism between biological and computational learning mechanisms, identifying basic motifs and training procedures, and how an engram encoding a melody could be built using a simple recurrent network involving both excitatory and inhibitory neurons.

Figures (9)

• Figure 1: Scheme of the XOR motif implemented using neurons. Arrows indicate the signal flow through excitatory (green) or inhibitory (red) synaptic connections
• Figure 2: XOR comparator scheme implemented in SIMULINK using as components the neurons from the simulation of C.Elegans neurons.
• Figure 3: Example of XOR circuit voltage output (yellow line) with two input signal pulses (red and blue lines). Notice that the coincidence of both input signals results in a null output, as expected.
• Figure 4: Example of XOR circuit as in figure 3, in this case the synaptic connections strengths started at a minimum value and were reinforced with each new pulse, until saturation. The saturation values were chosen to be those used in the previous basic XOR model.
• Figure 5: Graph showing the implementation of an XOR motif based on LTC and using the NCP framework.