EngramNCA: Dual-Channel Memory in NCAs

• EngramNCA is a neural cellular automata model that integrates dual channels to separate public state communication from private intracellular memory storage.
• Its dual-module design combines GeneCA for public state updates that generate primitive morphologies and GenePropCA for exclusive modulation of gene memory channels.
• Inspired by biological processes like RNA transfer and regeneration, EngramNCA enables decentralized memory dynamics and hierarchical, self-organizing morphogenesis.

EngramNCA denotes a class of neural cellular automaton (NCA) models in which each individual cell possesses both publicly visible states and private, cell-internal memory channels. This architecture draws inspiration from biological research indicating that memory storage encompasses not just synaptic modifications, but also intracellular biochemical mechanisms. EngramNCA integrates two complementary modules—GeneCA and GenePropCA—allowing for the encoding, propagation, and hierarchical combination of complex morphologies. Its dual-channel design enables decentralized memory transfer among synthetic agents or patterns and provides a computational abstraction of biological memory phenomena, including regenerative behavior and RNA-based memory transfer.

1. Dual-Module Model Architecture

EngramNCA is constructed as an ensemble of two distinct neural cellular automata:

• GeneCA is responsible for developing primitive morphologies from initial seed cells encoded with immutable “gene” vectors. At each update, GeneCA applies a perception function (composed of convolutional filters such as identity, Sobel, and Laplacian) to the local cell neighborhood and processes both public channels and the cell’s gene encoding through a neural network-based update rule. Crucially, the gene channels remain constant during GeneCA updates, enforcing the primacy of the seed’s genetic information.
• GenePropCA exclusively modulates the private gene (memory) channels. Unlike GeneCA, it does not update the public visible state, focusing instead on propagating and transforming the latent gene information that determines subsequent morphological development.

Interaction between the two occurs via sequential application: GeneCA updates public states while maintaining gene channels, followed by GenePropCA, which refines the gene channels based on the latest public state context. This division allows the memory (gene encoding) to influence the emergent morphology while remaining shielded from direct public state updates.

2. Memory Channel Representation and Information Flow

Each cell in EngramNCA maintains a state: $c_{(i,j)} = [v_{(i,j)}, h_{(i,j)}, g_{(i,j)}]$ where

• $v_{(i,j)} \in \mathbb{R}^4$ are RGBA visible channels,
• $h_{(i,j)} \in \mathbb{R}^{n_h}$ are public hidden channels,
• $g_{(i,j)} \in \mathbb{R}^{n_g}$ are private gene channels.
• Public channels serve as the "communicative" interface of the cell—detectable by neighbors and altered by GeneCA.
• Private gene channels act as intracellular, latent memory stores, directly inspired by documented biological substrates such as RNA. These channels maintain persistent information that can later be activated to drive further development (e.g., limb formation after torso growth).

This dual-channel system enables separation of short-term intercellular communication and long-term memory encoding. Only GenePropCA can modify the gene channels, and GeneCA consults but does not change them.

3. Biological Motivation and Experimental Parallels

EngramNCA was motivated by experimental findings that challenge the exclusive “synaptic dogma” of memory storage:

• Aplysia RNA transfer experiments: RNA from trained specimens transfers associative memory capabilities to untrained specimens.
• Planaria regeneration: Decapitated specimens retain behavioral memory after head regeneration.

These results imply that memory can exist independently of synaptic connectivity, being stored and transferred via intracellular means. EngramNCA’s gene channels serve as a computational abstraction of these mechanisms, offering a model of memory that is both synaptic (public channels) and intracellular (private gene channels).

4. Morphogenesis and Hierarchical Pattern Encoding

EngramNCA supports the growth and combination of complex morphologies from shared genetic substrates through two key processes:

• Immutable gene encodings: Seed cells are initialized with binary (or discrete) gene codes corresponding to primitive shapes. With $n_g$ gene channels, the system can encode up to $2^{n_g}$ distinct primitives. These codes remain unchanged during the GeneCA-driven growth phase, resulting in robust primitive reproduction across the grid.
• GenePropCA-driven hierarchical development: After primitive expansion, GenePropCA can induce transitions in gene encodings—enabling one region to switch from growing a torso to a head or limb, for example. Cells can also combine multiple gene codes, permitting hierarchical and multi-part structures with coexisting morphologies on the same grid.

This two-stage system allows for rich pattern synthesis and regeneration, akin to biological morphogenesis, where both stable templates and dynamic reprogramming are essential.

5. Mathematical Foundations

The model’s update rules formalize the interplay between channels:

GeneCA update (public channels only): $$[v_{(i,j)}^{t+1}, h_{(i,j)}^{t+1}] = [v_{(i,j)}^{t}, h_{(i,j)}^{t}] + \phi_{\text{GeneCA}}(\mathcal{P}(c_{(i,j)}^{t}), g_{(i,j)}^{t})$$

$g_{(i,j)}^{t+1} = g_{(i,j)}^{t}$

where $\phi_{\text{GeneCA}}$ is a neural network updating public states based on local perception $\mathcal{P}(c^{t})$ and gene encoding.

GenePropCA update (gene channels only): $$g_{(i,j)}^{t+1} = g_{(i,j)}^{t} + \psi_{\text{GenePropCA}}(\mathcal{P}(c_{(i,j)}^{t}), g_{(i,j)}^{t})$$

$$[v_{(i,j)}^{t+1}, h_{(i,j)}^{t+1}] = [v_{(i,j)}^{t}, h_{(i,j)}^{t}]$$

Together, the two-phase update for each time step alternates between public state growth and private gene modulation.

6. Implications for Decentralized Memory Storage and Self-Organizing Systems

EngramNCA’s architecture enables several key properties relevant for both biological and synthetic systems:

• Decentralized memory transfer: By embedding durable information at the cell level, memory can be propagated independently of network connectivity—analogous to the transfer of RNA-based memory signals.
• Robust self-organization: Separation of channels allows for self-healing, adaptive behavior, and repair of complex structures from “genetic” seeds.
• Hierarchical and coexisting morphologies: Multiple gene codes can coexist and interact, allowing simultaneous development of distinct structures without interference—an essential feature for modular synthetic organisms or generative models.
• Generative modeling and abstractions: This approach generalizes to developmental problem solving, as demonstrated in applications such as the Abstraction and Reasoning Corpus, where developmental cellular automata enhanced with hidden memories outperform large-scale LLMs in computational efficiency and solve rates (Guichard et al., 13 May 2025).

7. Relationship to Wider Engram and NCA Research

EngramNCA synthesizes concepts from both neurobiological engram theory and computational cellular automata:

• From neuroscience: Adopts the notion that memory traces are encoded both synaptically and intracellularly, integrating principles of structural plasticity, sparse memory assignment, and homeostatic equilibrium.
• From NCA advances: Builds on differentiable neural CA models optimized via local convolutional rules and deep learning, extending them with persistent, private cell-internal channels that store and regulate developmental instructions.

The model provides a developmental and decentralized memory mechanism relevant to ongoing efforts in artificial general intelligence, synthetic biology, and theoretical neuroscience.

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EngramNCA constitutes a rigorous computational model that integrates both synaptic-like and intracellular memory mechanisms in the context of cellular automata. Its dual-channel, two-module design enables robust morphology growth, decentralized memory transfer, and hierarchical pattern synthesis, with mathematical formulations directly paralleling experimental findings and advancing self-organizing systems across biological and synthetic domains (Guichard et al., 16 Apr 2025).