This preprint presents the Neural Genome Hypothesis, a speculative framework proposing that genomes exhibit functional properties akin to distributed, memory-bearing neural networks, including attractors, latent representations, and context-dependent activation. Drawing on empirical examples such as precise ancestral reversions in plant secondary metabolism (e.g., Galápagos wild tomatoes), abrupt emergence of de novo genes via regulatory gating in humans, convergent evolution in echolocating mammals, and the success of genomic language models like Evo 1.5 in generating functional proteins from context alone, the paper argues that regulatory and developmental architectures encode evolutionary memory of past successful configurations. This hypothesis complements neo-Darwinian principles by providing a theory of the structured fitness landscape upon which mutation and selection operate. It formalizes genomic elements as network components (e.g., genes as nodes, regulatory interactions as edges) and discusses mechanisms like pleiotropic locking and epistatic ratcheting that preserve latent attractors. The framework explains phenomena like "reverse evolution" and convergence not as coincidences but as recalls from preserved network structures. While metaphorical, the hypothesis yields five testable predictions, including that ancestral reversions require fewer genetic changes than novel adaptations, and that evolvability correlates with regulatory complexity. Broader implications frame biodiversity as a planetary memory system, where extinction represents irreplaceable loss of evolutionary solutions. This is a theoretical manuscript aimed at evolutionary biologists, geneticists, and AI researchers interested in biological analogies. It is not peer-reviewed and invites empirical testing. Version 1.0 (November 27, 2025).