Chia-Yu Chang

Chia-Yu Chang, Fulvio Gesmundo, Jeroen Zuiddam

We determine the border subrank of higher order structure tensors of several families of algebras, and in particular obtain the following results. (1) We determine tight bounds on the border subrank of $k$-fold matrix multiplication and $k$-fold upper triangular matrix multiplication for all $k$. (2) We determine the border subrank of the higher order structure tensors of truncated polynomial algebras, null algebras, and apolar algebras of a quadric. (3) We determine the border subrank of the higher order structure tensors of the Lie algebra $\mathfrak{sl}_2$ for all orders. (4) We prove that degeneration of structure tensors of algebras propagates from higher to lower order. Along the way, we investigate which upper bound methods (geometric rank, $G$-stable rank, socle degree) are effective in which settings, and how they relate. Our work extends the results of Strassen (J.~Reine Angew.~Math., 1987, 1991), who determined the asymptotic subrank of these algebras for tensors of order three, in two directions: we determine the border subrank itself rather than its asymptotic version, and we consider higher order structure tensors.

Yen-Ju Lu, Chia-Yu Chang, Cheng Yu et al.

Previous studies have confirmed that by augmenting acoustic features with the place/manner of articulatory features, the speech enhancement (SE) process can be guided to consider the broad phonetic properties of the input speech when performing enhancement to attain performance improvements. In this paper, we explore the contextual information of articulatory attributes as additional information to further benefit SE. More specifically, we propose to improve the SE performance by leveraging losses from an end-to-end automatic speech recognition (E2E-ASR) model that predicts the sequence of broad phonetic classes (BPCs). We also developed multi-objective training with ASR and perceptual losses to train the SE system based on a BPC-based E2E-ASR. Experimental results from speech denoising, speech dereverberation, and impaired speech enhancement tasks confirmed that contextual BPC information improves SE performance. Moreover, the SE model trained with the BPC-based E2E-ASR outperforms that with the phoneme-based E2E-ASR. The results suggest that objectives with misclassification of phonemes by the ASR system may lead to imperfect feedback, and BPC could be a potentially better choice. Finally, it is noted that combining the most-confusable phonetic targets into the same BPC when calculating the additional objective can effectively improve the SE performance.