ModNet-Flat: A Self-Growing Layer-Free Recurrent Network for Universal Computation An evolutionary framework that discovers structure from first principles

# ModNet-Flat A Self-Growing Layer-Free Recurrent Network for Universal Computation An evolutionary framework that discovers structure from first principles We present ModNet, a self-growing layer-free recurrent network whose topology is discovered through evolution rather than imposed by a designer. The architecture has no predefined layers and no modular grouping: every node is a general-purpose threshold unit that may receive input from any other node, including itself, and the first nout nodes of the network are designated as outputs. Starting from a minimal random topology, the network grows, prunes, and reorganizes itself through a compact evolutionary loop. We evaluate ModNet on a suite of sixteen benchmark problems spanning Boolean logic, digital arithmetic, sorting networks, and continuous regression. The network solves fourteen of the sixteen tasks, including full adder, 2-bit adder, comparator, 4-to-1 multiplexer, and 4-bit sorting network, all with exact 100% accuracy using no more than 27 nodes. On continuous targets, ModNet achieves root-mean-square errors as low as 0.0143 on the x2 + y2 surface and 0.0254 on the multiplication task with only 13 nodes. We observe that recurrence emerges spontaneously and scales with task complexity: XOR-2 requires one self-loop, while Gaussian and multiplication require 10 to 14 self-loops, indicating that temporal memory is a structural necessity, not an imposed design. Our results suggest that a fully layer-free architecture driven by a minimal evolutionary process can rediscover structural principles — non-linearity, recurrence, sparsity — that are typically imposed by human designers. We provide a complete open-source implementation and a reproducible benchmark suite. Keywords: neuroevolution, layer-free architectures, self-growing networks, recurrent networks, Boolean function learning, digital circuits, sparse connectivity.