Jingqi Sun | Searcharxiv

arXiv2026

Representation theory of inhomogeneous Gaussian unitaries

Gaussian unitaries, generated by quadratic Hamiltonians, are fundamental in quantum optics and continuous-variable computing. Their structures correspond to symplectic (bosons) and orthogonal (fermions) groups, but physical realizations give rise to their respective double covers, introducing phase and sign ambiguities. The homogeneous (quadratic-only) case has been resolved through a parameterization constructed in a recent work [arXiv:2409.11628]. We extend the previous framework to inhomogeneous Gaussian unitaries parameterized by $(M,z,\Psi)$. The Baker-Campbel-Hausdorff formula allows us then to factor any Gaussian unitary into a squeezing and a displacement transformation, from which we derive the group multiplication law.

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arXiv2025

Neural Forward Filtering for Speaker-Image Separation

We address monaural multi-speaker-image separation in reverberant conditions, aiming at separating mixed speakers but preserving the reverberation of each speaker. A straightforward approach for this task is to directly train end-to-end DNN systems to predict the reverberant speech of each speaker based on the input mixture. Although effective, this approach does not explicitly exploit the physical constraint that reverberant speech can be reproduced by convolving the direct-path signal with a linear filter. To address this, we propose CxNet, a two-DNN system with a neural forward filtering module in between. The first DNN is trained to jointly predict the direct-path signal and reverberant speech. Based on the direct-path estimate, the neural forward filtering module estimates the linear filter, and the estimated filter is then convolved with the direct-path estimate to obtain another estimate of reverberant speech, which is utilized as a discriminative feature to help the second DNN better estimate the reverberant speech. By explicitly modeling the linear filter, CxNet could leverage the physical constraint between the direct-path signal and reverberant speech to capture crucial information about reverberation tails. Evaluation results on the SMS-WSJ dataset show the effectiveness of the proposed algorithms.

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