Imagine a corridor where the echo returns with a delay, and that echo suddenly starts answering questions. That is exactly how a reservoir computer works: a single node that receives a signal, delays it, and sends it back, creating a complex network of virtual neurons over time. In the new work, the role of such a corridor is played by a silicon spiral fabricated in a standard factory. It compresses 1.76 meters of optical path into a few square millimeters, forcing light to run in circles and return after 11.63 nanoseconds.
Previously, such a delay was achieved either with coils of optical fiber or with digital buffers. Fiber is bulky, and digital buffers lose the phase of the light wave. The silicon spiral preserves phase and fits on a chip. It was inserted into a feedback loop: a laser shines through a modulator, light passes through the spiral, hits a photodetector, and the electrical signal returns to the modulator. A single nonlinear node unfolds into 50 virtual neurons through time-division multiplexing with a step of 20.48 nanoseconds.
The most surprising part: the phase of the light wave became an additional encoding channel. The researchers deliberately caused aliasing by feeding a 10 MHz signal at a sampling rate of only 976.6 kHz. The phase difference between the spiral and a straight waveguide was 0.232π, and they used it as a computational resource. This allowed them to achieve a prediction error of 0.0767 and zero recognition error without increasing the gain.
Previously, it was unclear whether bulky coils and digital buffers could be replaced with a compact integrated delay line without losing computational power. Now it is clear: a passive silicon spiral with losses of 23.2 dB and a gain of 0.0223 works successfully. It classifies signals without error, predicts chaos with an error of 0.0082, and recognizes nine speakers of Japanese vowels with an error of 0.0898. This is twice as good as the previous speckle processor and only 2.5 percentage points worse than a digital delay line with a gain 23 times higher.
The time spiral on a chip brings us back to the beginning: a corridor that does not just delay the echo but turns it into thought. Already today, one can design compact photonic accelerators for time-series and speech recognition tasks where small size and low power consumption matter. The next step is obvious: reduce losses from 23.2 dB to a few decibels, and then silicon spirals will become the heart of fast and energy-efficient neural networks.
The Archimedean spiral used in the chip is named after the ancient Greek mathematician who described it in the 3rd century BC to solve the problem of trisecting an angle. Now the same geometry compresses 1.76 meters of optical path into a few square millimeters.
The idea of delay-based reservoir computing echoes the 'liquid' neural networks from Greg Egan's novel 'Permutation City', where computational substrates use time delays to process information without traditional logic elements.