Photonic Exponential Approximation via Cascaded TFLN Microring Resonators toward Softmax

TL;DR

This paper introduces a cascaded TFLN micro-ring resonator architecture that efficiently synthesizes the exponential function for softmax in photonic AI accelerators, reducing electronic bottlenecks.

Contribution

It presents a novel cascaded micro-ring resonator design that approximates the exponential function needed for softmax entirely in photonics, enabling faster and more energy-efficient AI inference.

Findings

Validated with FDTD simulations of TFLN micro-ring resonators.

Achieved agreement between theory and simulation for cascades up to five rings.

Proposed a WDM-parallel chip architecture for complete photonic softmax implementation.

Abstract

The rapid growth of large-scale AI models has intensified energy consumption and data-movement challenges in modern datacenters. Photonic accelerators offer a promising path by executing the linear matrix multiplications of transformer inference at high throughput and low energy. However, the softmax attention layer, which requires element-wise exponentiation followed by normalization, still relies on electronic post-processing, creating an electro-optic conversion bottleneck that negates much of the potential photonic advantage. We present a cascaded micro-ring resonator (MRR) architecture that synthesizes the per-channel exponential function required by softmax, e^{x_n - max(x)}, over a finite interval with tunable worst-case relative error. A control signal detunes each ring via an electro-optic mechanism; a weak probe at fixed frequency experiences Lorentzian transmission, and cascading N identical stages yields a multiplicative transfer function whose logarithm is approximately linear. We derive mapping rules, depth-scaling estimates, and a minimax fitting formulation, and validate the framework with three-dimensional FDTD simulations of X-cut thin-film lithium niobate (TFLN) add-drop micro-ring resonators. Direct multi-ring FDTD validation extends to a five-ring cascade and confirms agreement with theory primarily over the upper operating range; deeper cascades and higher quality factors are assessed analytically. The cascade implements the per-channel exponential block, the key missing nonlinearity for photonic softmax. We further present a WDM-parallel chip architecture with closed-loop PI feedback that completes the full softmax-exponentiation, summation, and normalization-on a single photonic chip without per-channel normalization circuitry.