High-Speed Image Encoding in Chaotic Neural Maps Using Circulant Topology and Fast Convolution

<title>Abstract</title> <p> Recent studies have shown that images can be stored and recalled inside the chaotic bursts of simulated neural networks such as Coupled Map Lattices - CML. However, the standard industry baseline method uses dense coupling matrices to maintain mathematical stability. For an image of size <italic>N</italic> , this traditional approach requires <italic>O</italic> ( <italic>N</italic> ³ ) setup time and <italic>O</italic> ( <italic>N</italic> ² ) memory. This leads to the crashing of standard computers for normal sized images and making IoT deployment impossible. In this paper, we introduce FC-CML (Fast Circulant-Convolutional Coupled Map Lattice) algorithm. We replace the unstructured matrix padding with a Circulant Array Topology and utilizing OpenCV Morton(Z-order) spatial curves. Through this, we transform the network state update from a dense 2D matrix multiplication into a 1D Fast Convolution. This allows us to use the Fast Fourier Transform (FFT) for chaotic image recall. This approach drops the time complexity to <italic>O</italic> ( <italic>N</italic> log <italic>N</italic> ) and space complexity to <italic>O</italic> ( <italic>N</italic> ). As demonstrated by our empirical performance benchmarks, the standard industry method exhibits unpredictable spikes and severe latency under workload, whereas FC-CML maintains high rock-solid stability. This reduced the memory footprint drastically and allows complex brain-inspired image encoding to run locally on low cost edge devices like the ESP32. </p>