Artificial neural networks have revolutionized electronic computing. Similarly, molecular networks with neuromorphic architectures may enable molecular decision-making on a level comparable to gene regulatory networks [1][2][3][4] . Nonenzymatic networks could in principle support neuromorphic architectures, and seminal proof-of-principles have been reported 5,6 . However, leakages, as well as issues with sensitivity, speed, nonlinearities and preparation, make the composition of layers delicate, and molecular classifications equivalent to a multilayer neural network (e.g. nonlinear partitioning of a concentration space) remain elusive. Here we introduce DNA-encoded enzymatic neurons with tunable weights and biases, and which are assembled in multilayer architectures to classify nonlinearly separable regions. We first leverage the sharp decision margin of the neurons to compute various majority functions on 10 bits. We then compose neurons into a twolayer network, and synthetize a parametric family of rectangular functions on a microRNA input. Finally, we connect neural and logical computations into a hybrid circuit that recursively partitions a concentration plane according to a decision tree in cell-sized droplets. This computational power and extreme miniaturization open avenues to query and manage molecular systems with complex contents, such as liquid biopsies or DNA databases.Synthetic DNA has emerged as a versatile polymer to store and process information at the molecular scale. It has powered a rich library of computational molecular devices ranging from logic circuits 7-10 to self-assembling automata 11 . Departing from the biological model of computation, most DNA computing devices imitate the Boolean paradigm of electronics. However, their computing power has fallen short of the exponential growth of Moore's law: their size has been plateauing at ~5-10 logic gates for a decade 8 . In parallel, various groups have started looking at the brain, rather than the CPU, as an inspiration for computing with molecules 2,12,3-6 . This is because neuronal and chemical networks share striking similarities: massively parallel and recurrent architectures, analog and asynchronous operation, fault-tolerant and redundant computations (Figure S12)In 2018, Lopez et al. reported a DNA-based linear classifier 6 that performs all of its computations with a nonenzymatic mechanism: toehold-mediated strand displacement 13 . Using similar DNA-only mechanisms on many more inputs and taking inspiration from competitive neural networks 2,3 , Cherry and Qian reported in a tour de force a DNA classifier for the MNIST database 5 . Together, these molecular classifiers showcased the benefits of neuromorphic networks over Boolean circuits: massive parallelism, handling of analog inputs, and tolerance to corrupted patterns. However, these nonenzymatic classifiers had limited decision margins, i.e. they could not discriminate between two similar inputs belonging to different classes. They also suffered from leaks that made the compositio...

Droplet microfluidics has become a powerful tool in life sciences, underlying digital assays, single- cell sequencing or directed evolution, and it is making foray in physical sciences as well. Imaging and incubation of droplets are crucial, yet they are encumbered by the poor optical, thermal and mechanical properties of PDMS - the de facto material for microfluidics. Here we show that silicon is an ideal material for droplet chambers. Si chambers pack droplets in a crystalline and immobile monolayer, are immune to evaporation or sagging, boost the number of collected photons, and tightly control the temperature field sensed by droplets. We use the mechanical and optical benefits of Si chambers to image ~1 million of droplets from a multiplexed digital assay - with an acquisition rate similar to the best in-line methods. Lastly, we demonstrate their applicability with a demanding assay that maps the thermal dependence of Michaelis-Menten constants with an array of ~150,000. The design of the Si chambers is streamlined to avoid complicated fabrication and improve reproducibility, which makes Silicon a complementary material to PDMS in the toolbox of droplet microfluidics.

We introduce Si chambers that pack microfluidic droplets in a crystalline and immobile monolayer, are immune to evaporation or sagging, boost the number of collected photons, and tightly control the temperature field sensed by droplets.