Reservoir expansion can improve online independent component analysis (ICA) under nonlinear mixing, yet top-$n$ whitening may discard injected features. We formalize this bottleneck as \emph{reservoir subspace injection} (RSI): injected features help only if they enter the retained eigenspace without displacing passthrough directions. RSI diagnostics (IER, SSO, $ρ_x$) identify a failure mode in our top-$n$ setting: stronger injection increases IER but crowds out passthrough energy ($ρ_x: 1.00\!\rightarrow\!0.77$), degrading SI-SDR by up to $2.2$\,dB. A guarded RSI controller preserves passthrough retention and recovers mean performance to within $0.1$\,dB of baseline $1/N$ scaling. With passthrough preserved, RE-OICA improves over vanilla online ICA by $+1.7$\,dB under nonlinear mixing and achieves positive SI-SDR$_{\mathrm{sc}}$ on the tested super-Gaussian benchmark ($+0.6$\,dB).

Abstract--Kurtosis-based Independent Component Analysis (ICA) weakens in wide, balanced mixtures. We also show that purification--selecting m R sign-consistent sources--restores R-independent contrast Ω(1/m), with a simple data-driven heuristic. Synthetic experiments validate the predicted decay, the T crossover, and contrast recovery. Independent Component Analysis (ICA) recovers statistically independent latent sources from linear mixtures and is identifiable whenever at most one source is Gaussian [1]. Excess kurtosis--the standardized fourth cumulant--is a central contrast function [9], and kurtosis-type nonlinearities remain standard in FastICA.

Independent Component Analysis (ICA) was introduced in the 1980's as a model

Blind source separation, particularly through independent component analysis (ICA), is widely utilized across various signal processing domains for disentangling underlying components from observed mixed signals, owing to its fully data-driven nature that minimizes reliance on prior assumptions. However, conventional ICA methods rely on an assumption of linear mixing, limiting their ability to capture complex nonlinear relationships and to maintain robustness in noisy environments. In this work, we present deep deterministic nonlinear independent component analysis (DDICA), a novel deep neural network-based framework designed to address these limitations. DDICA leverages a matrix-based entropy function to directly optimize the independence criterion via stochastic gradient descent, bypassing the need for variational approximations or adversarial schemes. This results in a streamlined training process and improved resilience to noise. We validated the effectiveness and generalizability of DDICA across a range of applications, including simulated signal mixtures, hyperspectral image unmixing, modeling of primary visual receptive fields, and resting-state functional magnetic resonance imaging (fMRI) data analysis. Experimental results demonstrate that DDICA effectively separates independent components with high accuracy across a range of applications. These findings suggest that DDICA offers a robust and versatile solution for blind source separation in diverse signal processing tasks.

Diffusion models (Sohl-Dickstein et al., 2015; Ho et al., 2020; Song et al., 2020) have emerged as one of the most powerful classes of generative models for high-dimensional data, achieving state-of-the-art performance in image synthesis (Dhariwal and Nichol, 2021; Rombach et al., 2022) and other tasks such as action generation in robotic or protein design (Watson et al., 2023; Chi et al., 2025). However, sampling from these models is typically slow: many reverse-time steps are required to transform an initial Gaussian sample into a high-quality sample in data space (Ho et al., 2020; Song et al., 2020). This computational cost is especially problematic, and it restricts the practical deployment of diffusion models in real-time or resource-constrained settings (Salimans and Ho, 2022; Lu et al., 2022). Recent theoretical and empirical studies suggest that this inefficiency is closely related to a dynamical phase transition (bifurcation) that occurs during the reverse process (Raya and Ambrogioni, 2024; Biroli et al., 2024; Ambrogioni, 2025). In the early reverse steps, the trajectories stay near a stable fixed point whose distribution is close to the initial independent Gaussian, and little structure is present in the samples.

We study the problem of learning disentangled signals from data using non-linear Independent Component Analysis (ICA). Motivated by advances in self-supervised learning, we propose to learn self-sufficient signals: A recovered signal should be able to reconstruct a missing value of its own from all remaining components without relying on any other signals. We formulate this problem as the minimization of a conditional KL divergence. Compared to traditional maximum likelihood estimation, our algorithm is prior-free and likelihood-free, meaning that we do not need to impose any prior on the original signals or any observational model, which often restricts the model's flexibility. To tackle the KL divergence minimization problem, we propose a sequential algorithm that reduces the KL divergence and learns an optimal de-mixing flow model at each iteration. This approach completely avoids the unstable adversarial training, a common issue in minimizing the KL divergence. Experiments on toy and real-world datasets show the effectiveness of our method.

Nonlinear independent component analysis (ICA) provides an appealing framework for unsupervised feature learning, but the models proposed so far are not identifiable.

These solutions provide detailed information about the performance of the ICA algorithm, as many practical performance metrics are functionals of the joint empirical measures.

Non-intrusive load monitoring (NILM) is an advanced load monitoring technique that uses data-driven algorithms to disaggregate the total power consumption of a household into the consumption of individual appliances. However, real-world NILM deployment still faces major challenges, including overfitting, low model generalization, and disaggregating a large number of appliances operating at the same time. To address these challenges, this work proposes an end-to-end framework for the NILM classification task, which consists of high-frequency labeled data, a feature extraction method, and a lightweight neural network. Within this framework, we introduce a novel feature extraction method that fuses Independent Component Analysis (ICA) and Principal Component Analysis (PCA) features. Moreover, we propose a lightweight architecture for multi-label NILM classification (Fusion-ResNet). The proposed feature-based model achieves a higher $F1$ score on average and across different appliances compared to state-of-the-art NILM classifiers while minimizing the training and inference time. Finally, we assessed the performance of our model against baselines with a varying number of simultaneously active devices. Results demonstrate that Fusion-ResNet is relatively robust to stress conditions with up to 15 concurrently active appliances.