Fully Analog Resonant Recurrent Neural Network via Metacircuit

Always-on AI applications, from environmental sensors to biomedical implants, require ultra-low power consumption. Analog circuits offer a path to sub-microwatt inference, yet existing analog implementations are limited to feedforward architectures: extending them to recurrent dynamics has been considered impractical due to noise accumulation through temporal feedback. We demonstrate that this barrier can be overcome through hardware-software co-design. Specifically, we identify that Bistable Memory Recurrent Units (BMRUs), a class of Recurrent Neural Networks (RNNs) with discrete-valued outputs and hysteretic dynamics, admit an ultra-low power current-mode analog implementation which we design from first principles. The resulting circuit establishes a one-to-one correspondence between each learned parameter and a circuit element. The discrete outputs suppress analog noise by at least 20-fold at each cell boundary, breaking the noise accumulation that prevents analog recurrence. We reformulate BMRUs for first-quadrant operation with fixed thresholds, enabling the direct correspondence while preserving expressivity and trainability. Transistor-level simulations in 180 nm Complementary Metal-Oxide-Semiconductor (CMOS) show near-perfect agreement between software predictions and circuit-level behavior, with the software model thereby serving as a high-fidelity simulator of the physical hardware at low computational cost. We leverage this fidelity to conduct large-scale noise immunity and power scaling analyses: the power cost of adding recurrence scales linearly with state dimension, while the feedforward layers dominating total power scale quadratically, meaning recurrence is added at linear marginal cost relative to the feedforward backbone. End-to-end keyword spotting achieves sub-microwatt inference at the RNN core.

Kolmogorov-Arnold Networks (KANs) shift neural computation from linear layers to learnable nonlinear edge functions, but implementing these nonlinearities efficiently in hardware remains an open challenge. Here we introduce a physical analogue KAN architecture in which edge functions are realized in materia using reconfigurable nonlinear-processing units (RNPUs): multi-terminal nanoscale silicon devices whose input-output characteristics are tuned via control voltages. By combining multiple RNPUs into an edge processor and assembling these blocks into a reconfigurable analogue KAN (aKAN) architecture with integrated mixed-signal interfacing, we establish a realistic system-level hardware implementation that enables compact KAN-style regression and classification with programmable nonlinear transformations. Using experimentally calibrated RNPU models and hardware measurements, we demonstrate accurate function approximation across increasing task complexity while requiring fewer or comparable trainable parameters than multilayer perceptrons (MLPs). System-level estimates indicate an energy per inference of roughly 200 pJ and an end-to-end inference latency of roughly 0.6 $μ$s for a representative workload, corresponding to over 100$\times$ reduction in energy accompanied by $>$10$\times$ reduction in area compared to a digital fixed-point MLP at similar approximation error. These results establish RNPUs as scalable, hardware-native nonlinear computing primitives and identify analogue KAN architectures as a realistic silicon-based pathway toward energy-, latency-, and footprint-efficient analogue neural-network hardware, particularly for edge inference.

Building on resistive communication, this paper presents a physics-based design of an on-chip neural network with multi-level memristive synapses supporting a dense spectrum of conductance states. Derived from ionic transport physics, we develop a state-variable model and quantify storable sub-levels under thermal noise, drift, and quantized conductance. We assemble these devices into a 1T1R crossbar fabric, derive the linear algebra of analog vector-matrix multiplication (VMM) under wire resistance, and design a differential synapse for signed weights. A multilayer pipeline executes inference, backpropagation, and weight updates physically in the analog domain. We derive the in-situ outer-product learning rule, its discretization onto the conductance lattice, and the resulting quantization noise. We provide energy, area, capacity, and inter-tile models, showing this substrate is ideally suited for large language models (LLMs). Our design eliminates weight movement, surpassing binary ReRAM and traditional CMOS. We detail the material stack (HfO_2-based), the FEOL/BEOL CMOS foundry-integration flow, a self-contained SPICE model, the complete memristive-FPGA neuromorphic system, and an in-memory self-attention engine with current-mode translinear softmax. Finally, a ternary BitNet datapath shows projected per-token efficiency orders of magnitude better than advanced CPUs or GPUs. The result is a self-contained hardware-native blueprint for a high-density, analog, in-memory neural processor.