Multi-Level Resistive Synapses for On-Chip Neural Networks: A Physics-Based Design of a Memristive Crossbar Fabric with Quasi-Continuous Conductance States

Abstract

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.