Cajal - Neural-inspired Cellular Automata

Biologically-inspired machine learning models have long captured the interest of researchers seeking alternative approaches to traditional artificial neural networks. Nearly eight years ago, the author embarked on an ambitious project titled “Distributed Neuron,” which aimed to replicate the clustered growth patterns of real neurons. This model incorporated biological concepts such as neurotropic factors and signaling gradients, diverging from the more rigid and simplistic neural network architectures popular at the time. Although the original project has faded into obscurity, with only some archived blog posts and old video recordings remaining, the foundational curiosity about biologically plausible machine learning models has persisted. Recently, the author encountered an intriguing paper about a neural-inspired cellular automaton called CoDi-1Bit. Designed for simplicity, minimalism, and computational efficiency, CoDi-1Bit was built to run effectively on Field Programmable Gate Arrays (FPGAs). The primary objective was to quickly evolve and assess neural networks in silico, forming discrete modules capable of specific functions such as timers, pattern detectors, and Hubel-Wiesel line motion detectors. The ultimate ambition was to apply these evolved neural modules to control a robotic cat in real-time. However, the original research concluded around 2001 without achieving the robotic cat control goal due to the closure of the research division. The CoDi system is a cellular automaton that mimics neuronal growth and signaling within a discrete grid. Initially, a small number of neuron bodies are seeded onto the grid, which undergoes iterative growth phases. Each neuron sprouts axons and dendrites into adjacent cells, spreading across the grid. While the original CoDi system operated in three dimensions, the current focus is on a simplified 2D version. The growth of each grid cell is governed by a chromosome overlaying the entire grid, which encodes simple instructions such as growing straight, turning, or splitting. This chromosome-driven mechanism allows the automaton to grow according to encoded genetic-like rules. A key feature of CoDi’s design is that newly grown cells retain their lineage, ensuring dendrites grow dendritic cells and axons grow axonal cells. Also, each cell stores a pointer back to the cell it originated from, enabling tracing back to the original neuron body. This structure forms the basis for the signaling network. Growth ceases when no empty adjacent cells remain or when active cells cannot grow further. The signaling phase follows growth but is reserved for future discussion. Compared to the author’s earlier Distributed Neuron project, CoDi’s chromosome mechanism uses only 4 bits per cell to dictate growth instructions, reducing memory overhead and enabling local evolutionary changes without destabilizing the entire network. Currently named Cajal, after the pioneering neuroscientist Santiago Ramón y Cajal, the implementation can create arbitrarily sized grids, simulate CoDi-esque network growth, inject signals, and observe neuron firing patterns. The codebase, however, is acknowledged to be a work in progress, requiring refactoring and more comprehensive documentation. At the lowest level, the grid world is organized into vectors of Pages, each containing vectors of Cells. Each Cell is represented internally as a 32-bit unsigned integer (u32), encoding various attributes such as cell type, growth direction (gate), stimulatory or inhibitory properties, chromosomal instructions, firing thresholds, and signal potentials through carefully defined binary masks. This compact encoding reflects the complex yet efficient representation of neuronal properties within the cellular automaton framework.