Fault-Free Analog Computing with Imperfect Hardware

The growing demand for edge computing and AI drives research into analog in-memory computing using memristors, which overcome data movement bottlenecks by computing directly within memory. However, device failures and variations critically limit analog systems' precision and reliability. Existing fault-tolerance techniques, such as redundancy and retraining, are often inadequate for high-precision applications or scenarios requiring fixed matrices and privacy preservation. Here, we introduce and experimentally demonstrate a fault-free matrix representation where target matrices are decomposed into products of two adjustable sub-matrices programmed onto analog hardware. This indirect, adaptive representation enables mathematical optimization to bypass faulty devices and eliminate differential pairs, significantly enhancing computational density. Our memristor-based system achieved >99.999% cosine similarity for a Discrete Fourier Transform matrix despite 39% device fault rate, a fidelity unattainable with conventional direct representation, which fails with single device faults (0.01% rate). We demonstrated 56-fold bit-error-rate reduction in wireless communication and >196% density with 179% energy efficiency improvements compared to state-of-the-art techniques. This method, validated on memristors, applies broadly to emerging memories and non-electrical computing substrates, showing that device yield is no longer the primary bottleneck in analog computing hardware.