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Abstract. We use neuromorphic chips to perform arbitrary mathematical computations for the first time. Static and dynamic computations are realized with heterogeneous spiking silicon neurons by programming their weighted connections. Using 4K neurons with 16M feed-forward or recurrent synaptic connections, formed by 256K local arbors, we communicate a scalar stimulus, quadratically transform its value, and compute its time integral. Our approach provides a promising alternative for extremely power-constrained embedded controllers, such as fully implantable neuroprosthetic decoders. Keywords: Neuromorphic chips, Silicon neurons, Probabilisitic synapses 1 Brain-Inspired Analog-Digital SystemsAnalog computation promises extreme energy-efficiency by operating close to the shot-noise limit [1]. By exploiting physical laws (e.g., conservation of charge for summation), a handful of analog devices is sufficient to perform computation. In contrast, digital computation relies on abstractions that require many more devices to achieve the same function (e.g., hundreds of transistors to add two 8-bit numbers). Furthermore, these abstractions break when noise exceeds a critical level, requiring enormous noise margins to avoid catastrophic failures. In contrast, analog degrades gracefully, allowing for operation at low noise margins, thereby saving power.However, robust and programmable computation using noisy analog circuits is challenging. Robust computation requires a distributed approach, but this is difficult because analog communication is susceptible to heterogeneity and noise. Programmable computation requires flexibility, but this is also difficult because analog computation exploits the underlying devices' fixed physical properties.In this paper, we realize robust and programmable mathematical computations with noisy and heterogeneous components using a framework inspired by the brain [2]. The brain uses graded dendritic potentials (cf. analog computation), all-or-none axonal spikes (cf. digital communication) and probabilistic synapses (cf. weighted connections). Our analog computational units are spiking silicon neurons [5]; our digital communication fabric is a packet-switched

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