We present a framework for chemical learning based on competitive dimerization networks (CDNs)—systems in which multiple molecular species, e.g., proteins or DNA-RNA oligomers, reversibly bind to form dimers. We show numerically that these networks can, in principle, be trained in vitro through directed evolution, enabling the implementation of complex learning tasks such as multiclass classification without digital hardware or prior knowledge of all microscopic association constants. Each molecular species functions analogously to a neuron, with binding affinities acting as tunable synaptic weights. A training protocol involving mutation, selection, and amplification of DNA-based components allows CDNs to robustly discriminate among noisy input patterns. The resulting classifiers exhibit strong output contrast and high mutual information between input and output, especially when guided by a contrast-enhancing loss function. Comparative analysis with in silico gradient descent training reveals closely correlated performance. These results establish CDNs as a promising platform for analog physical computation, bridging synthetic biology and machine learning, and advancing the development of adaptive, energy-efficient molecular computing systems.

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• Analog computation
• Biological neural networks
• Collective behavior in networks
• Fitness
• Information & communication theory
• Molecular networks
• Network evolution
• Neural mechanisms of decision making
• Nucleic acid replication & information processes
• Physics of computation