PolySim: Deterministic Polynomial Surrogates for Cross-Modal Retrieval on CiM

Xinzhao Li, Charles Power, Pengyu Ren, Jongun Won, Likai Pei, Yuting Hu, Jinjun Xiong, Alptekin Vardar, Ningyuan Cao, Xiaobo Sharon Hu, Thomas Kämpfe, Kai Ni, Ruiyang Qin

Cross-modal retrieval on edge devices benefits from probabilistic embeddings that capture semantic uncertainty, but deploying them on compute-in-memory (CiM) hardware remains an open problem. The core difficulty is a sampling gap: probabilistic methods such as PCME rely on Monte Carlo sampling and nonlinear distance evaluation at inference, which are fundamentally incompatible with CiM crossbar arrays that support only deterministic, single-step matrix-vector multiplication. Few existing probabilistic retrieval methods can be executed on a conventional crossbar. To bridge this gap, we propose PolySim, a framework that reformulates probabilistic retrieval into a fully deterministic pipeline. PolySim approximates each Gaussian embedding dimension using low-order polynomial bases and computes similarity via a learnable order-bilinear kernel, eliminating stochastic sampling while preserving distributional information. In experiments on six benchmarks spanning video, image, and audio retrieval, PolySim improves R@1 over deterministic baselines by up to 10.3\% and matches or exceeds PCME, while reducing inference to a single crossbar-compatible matrix-vector multiplication. CrossSim evaluation under realistic device non-idealities confirms robust deployment on conventional crossbar arrays. To the best of our knowledge, PolySim is the first method to enable probabilistic cross-modal retrieval on CiM hardware.