Spectral dynamics reservoir computing for high-speed hardware-efficient neuromorphic processing

Abstract

Physical reservoir computing (PRC) is a promising brain-inspired computing architecture for overcoming the von Neumann bottleneck by utilizing the intrinsic dynamics of physical systems. However, a major obstacle to its real-world implementation lies in the tension between extracting sufficient information for high computational performance and maintaining a hardware-feasible, high-speed architecture. Here, we report spectral dynamics reservoir computing (SDRC), a broadly applicable framework based on analogue filtering and envelope detection that bridges this gap. SDRC effectively exploits the fast spectral dynamics embedded in short-time, coarse spectra of material responses to attain strong computational capability while maintaining high-speed processing and minimal hardware overhead. This approach circumvents the need for implementation-intensive, precision-sensitive integrated circuits required in high-speed time-multiplexing measurements, while enabling real-time use of the material's spectral manifold as a high-dimensional computational resource. We implement and experimentally demonstrate SDRC applied to spin waves that achieves state-of-the-art-level performance with only 56 nodes on benchmark tasks of parity-check and second-order nonlinear autoregressive moving average, as well as high accuracy of 98.0% on a real-world problem of speech recognition.

Figures (6)

• Figure 1: | PRC architecture and different information-extraction schemes.a, Typical architecture of a PRC system capable of performing various information processing tasks. A node-extraction layer is employed to extract high-dimensional information for effective computation. b, A typical scheme of temporal information extraction, where a pulse generator first produces narrow time pulses, which are distributed to multiple multivibrator ICs to introduce high-precision temporal delays, thereby forming time-multiplexing sampling references. Multiple sampling ICs are then used to sample and hold the temporal evolution of a physical response according to the time-multiplexing pulses as clock signals. c, A typical scheme of spectral information extraction, where a finely resolved frequency spectrum is obtained through the Fourier transform (FT), necessitating a long integration time window that inherently introduces computational overhead and operation latency that hinder true real-time processing. Increasing processing speed results in a coarse spectrum where distinctive peaks are blurred. Whether such a spectrum retains sufficiently rich latent information for complex neuromorphic computation remains a question. d, A scheme of spectral dynamics extraction, where multiple analogue filters extract short-time, coarse spectral dynamics of the physical response with power detectors for envelope detection, providing a high-speed and hardware-efficient implementation for real-time computation.
• Figure 2: | The SDRC system using spin-wave dynamics. An analogue pulse train that encodes the input data through pulse modulation is fed into a spin-wave reservoir made by a YIG single crystal to excite spin-wave propagation. The resulting spin-wave responses are subsequently processed to extract parallel spectral dynamics as reservoir states from their coarse spectra through analogue filtering and envelope detection. These high-dimensional reservoir states are then combined through a linear readout with trainable weights to generate output signals for information processing tasks.
• Figure 3: | Benchmark performance of the SDRC system on parity check and NARMA-$2$.a, b, Example time-domain waveforms for the parity-check task at a memory depth $K = 3$, showing the target signal (black) and the predicted signals obtained using time multiplexing (brown) and spectral dynamics extraction (green), respectively, with $20$ nodes per detector. c, Corresponding coefficients of determination plotted against memory depth $K$, where the enclosed area indicates the parity-check capacity for each approach. d, Parity-check capacity in relation to the number of nodes per detector for both approaches, showing their maximum (circles) and minimum (triangles) values obtained from random node selections. e, Comparison of SDRC performance on parity check in terms of capacity and node number with other PRC tanaka2022selflee2023physicaltoprasertpong2022reservoirrajib2025magnetoheins2025benchmarkingnagase2024spintsunegi2019physical. f, g, Example time-domain waveforms for the NARMA-$2$ task, showing the target signal (black) and the predicted signals obtained using time multiplexing (brown) and spectral dynamics extraction (green), respectively, with $20$ nodes per detector. h, NMSE in relation to the number of nodes per detector for both approaches, showing their minimum (circles) and maximum (triangles) values from random node selections. e, Comparison of SDRC performance on NARMA-$2$ in terms of NMSE and node number with other PRC nishioka2025twonamiki2024optoakashi2020inputkan2021simpleakai2022performanceyamada2024physicalkan2022physical.
• Figure 4: | Spectral distributions of information-effective spectral nodes.a, c, Occurrence distributions of spectral nodes in relation to the bias magnetic field for the parity-check and NARMA-$2$ tasks, respectively. Occurrence counts are accumulated over the top $20$ performing node combinations obtained from random node selections with $5$ nodes per detector. The colormap jointly encodes the occurrence count by saturation and computational performance (capacity and NMSE, respectively) by brightness. b, d, Bias-field-dependent capacity and NMSE for parity check and NARMA-$2$, respectively, averaged over the top $20$ node selections.
• Figure 5: | Hardware demonstration of SDRC.a, Experimental setup for spectral dynamics extraction, where the spin-wave response from a detector is split into eight channels, each filtered by a BPF with a distinct spectral band. The filtered responses are then rectified and detected using diodes, with waveforms recorded in an oscilloscope. b, Circuit diagram of the spectral dynamics extraction setup for each detector. c, d, Computational performance of the SDRC system with hardware-implemented spectral nodes for the parity-check and NARMA-$2$ tasks, respectively, showing the capacity and NMSE in relation to the bias field. Both a coarse sweep (black) from $149.8$ mT to $299.8$ mT in steps of $10$ mT and a fine sweep (green) from $169.8$ mT to $199.8$ mT in steps of $1$ mT are performed. e, f, g, Example operation flow of the spectral-node extraction process, showing the spectral ranges of the BPFs, the corresponding filtered responses, and the detected responses, respectively.