# Convolutive Transfer Function Invariant SDR training criteria for Multi-Channel Reverberant Speech Separation

arXiv: https://arxiv.org/abs/2011.15003 · HTML: https://mlsanity.com/paper/2011.15003/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Nov 2020.

## Built on by (most cited first, 6 of 6)

- [ESPnet-SE++: Speech Enhancement for Robust Speech Recognition, Translation, and Understanding](https://mlsanity.com/paper/2207.09514/) (2022)
- [Implicit Acoustic Echo Cancellation for Keyword Spotting and Device-Directed Speech Detection](https://mlsanity.com/paper/2111.10639/) (2021)
- [Reverberation as Supervision for Speech Separation](https://mlsanity.com/paper/2211.08303/) (2022)
- [Do Neural Codecs Generalize? A Controlled Study Across Unseen Languages and Non-Speech Tasks](https://mlsanity.com/paper/2601.12205/) (2026)
- [Exploring the Integration of Speech Separation and Recognition with Self-Supervised Learning Representation](https://mlsanity.com/paper/2307.12231/) (2023)
- [Weakly Guided and Autoregressive Beamformer Parameterization for Generalizable Moving Speaker Extraction in Higher-Order Ambisonics](https://mlsanity.com/paper/2607.04471/) (2026)

## Abstract (arXiv)

Time-domain training criteria have proven to be very effective for the separation of single-channel non-reverberant speech mixtures. Likewise, mask-based beamforming has shown impressive performance in multi-channel reverberant speech enhancement and source separation. Here, we propose to combine neural network supported multi-channel source separation with a time-domain training objective function. For the objective we propose to use a convolutive transfer function invariant Signal-to-Distortion Ratio (CI-SDR) based loss. While this is a well-known evaluation metric (BSS Eval), it has not been used as a training objective before. To show the effectiveness, we demonstrate the performance on LibriSpeech based reverberant mixtures. On this task, the proposed system approaches the error rate obtained on single-source non-reverberant input, i.e., LibriSpeech test_clean, with a difference of only 1.2 percentage points, thus outperforming a conventional permutation invariant training based system and alternative objectives like Scale Invariant Signal-to-Distortion Ratio by a large margin.