In this work, we introduce S4M, a new efficient speech separation framework
based on neural state-space models (SSM). Motivated by linear time-invariant
systems for sequence modeling, our SSM-based approach can efficiently model
input signals into a format of linear ordinary differential equations (ODEs)
for representation learning. To extend the SSM technique into speech separation
tasks, we first decompose the input mixture into multi-scale representations
with different resolutions. This mechanism enables S4M to learn globally
coherent separation and reconstruction. The experimental results show that S4M
performs comparably to other separation backbones in terms of SI-SDRi, while
having a much lower model complexity with significantly fewer trainable
parameters. In addition, our S4M-tiny model (1.8M parameters) even surpasses
attention-based Sepformer (26.0M parameters) in noisy conditions with only 9.2
of multiply-accumulate operation (MACs).

提出了一种基于神经状态空间模型的高效音频分离框架 S4M，该模型可以将输入信号建模为线性常微分方程的形式，并在多尺度表示学习中学习全局一致的分离和重构，其模型复杂度显著低于 Attention-based Sepformer。

一种基于神经状态空间模型的高效语音分离方法

A Neural State-Space Model Approach to Efficient Speech Separation

Effective quantification of uncertainty is an essential and still missing
step towards a greater adoption of deep-learning approaches in different
applications, including mission-critical ones. In particular, investigations on
the predictive uncertainty of deep-learning models describing non-linear
dynamical systems are very limited to date. This paper is aimed at filling this
gap and presents preliminary results on uncertainty quantification for system
identification with neural state-space models. We frame the learning problem in
a Bayesian probabilistic setting and obtain posterior distributions for the
neural network's weights and outputs through approximate inference techniques.
Based on the posterior, we construct credible intervals on the outputs and
define a surprise index which can effectively diagnose usage of the model in a
potentially dangerous out-of-distribution regime, where predictions cannot be
trusted.

本研究应用 Bayesian 概率框架和近似推理技术，对神经状态空间模型进行不确定性量化，得出模型输出的可信区间和惊奇指数，以有效诊断模型在潜在危险的分布区域内的使用可能性。

神经状态空间模型：不确定性量化的实证评估

Neural State-Space Models: Empirical Evaluation of Uncertainty  Quantification

In recent years, several algorithms for system identification with neural
state-space models have been introduced. Most of the proposed approaches are
aimed at reducing the computational complexity of the learning problem, by
splitting the optimization over short sub-sequences extracted from a longer
training dataset. Different sequences are then processed simultaneously within
a minibatch, taking advantage of modern parallel hardware for deep learning. An
issue arising in these methods is the need to assign an initial state for each
of the sub-sequences, which is required to run simulations and thus to evaluate
the fitting loss. In this paper, we provide insights for calibration of neural
state-space training algorithms based on extensive experimentation and analyses
performed on two recognized system identification benchmarks. Particular focus
is given to the choice and the role of the initial state estimation. We
demonstrate that advanced initial state estimation techniques are really
required to achieve high performance on certain classes of dynamical systems,
while for asymptotically stable ones basic procedures such as zero or random
initialization already yield competitive performance.

本文对神经状态空间模型的系统识别算法的学习问题进行了深入的研究，探讨了初始状态估计的选择和作用，并在两个系统识别基准测试上进行了大量实验和分析，表明高级初始状态估计技术对于某些类型的动态系统需要实现高性能，而对于渐近稳定的系统，则基本过程，如零或随机初始化，已经具有竞争性能。