This raises a fundamental dilemma of statistical-computational tradeoffs: removing all samples from an unwanted domain may be computationally prohibitive, while randomly removing a subset may not provide distribution-level statistical guarantees. We propose a statistical framework for distributional unlearning, in which domains are modeled as probability distributions, and the goal is to remove a carefully chosen subset of samples that reduces the effect of an unwanted distribution while preserving performance on a desired one. We formalize this using a hypothesis test of the edited data with the desired and unwanted domains, leading to an interpretable and robust criterion for selecting samples to remove. Within this statistical framework, we characterize the fundamental region of the allowable edited data distributions and the removal-preservation Pareto frontier for a broad class of distribution families. This includes parametric families such as shifted Gaussians of arbitrary dimension, a one-dimensional location family with log-concave noise, and the one-dimensional Poisson family. It also includes nonparametric families such as the Gaussian white noise model, a canonical model for nonparametric regression. We prove composition rules that describe how distributional unlearning behaves across multimodal unwanted domains, and introduce a central-limit behavior for the removal-preservation baselines when composing a large number of such families. Finally, we provide finite sample guarantees by providing Pareto frontiers for some selection algorithms, and observe an information-computation gap.

Spectral graph sparsification is a classical tool for reducing graph complexity while preserving Laplacian quadratic forms. In graph neural networks (GNNs), sparsification is often used to accelerate computation while maintaining predictive performance. In this work, we study a complementary representation-level question: does sparsification preserve the geometry of learned embeddings? For polynomial-filter GNNs, we prove that any $ε$-spectral sparsifier induces $O(ε)$ perturbations in polynomial graph filters, multilayer hidden representations, and their Gram matrices. These guarantees imply stability of squared pairwise distances, class means, and covariance structure in embedding space. We further establish finite-time training stability: under smoothness and boundedness assumptions, gradient descent on dense and sparsified graphs produces weight trajectories whose separation grows at most proportionally to the sparsification distortion. Empirically, effective-resistance sparsification validates the predicted perturbation chain on synthetic graphs and preserves hidden representation geometry on real datasets. In our experiments, the gram matrix and training dynamics show low divergence even under substantial sparsification, consistent with the predicted stability under spectral sparsification. Hidden Gram preservation strongly predicts neighborhood preservation and class-centroid stability across FashionMNIST, Cora, and Paul15. Together, these results show that spectral sparsification preserves not only graph operators, but also the representation geometry that supports downstream use of GNN embeddings for interpretability.

Discovering cause and effect variables from observational data is an important but challenging problem in science and engineering. In this work, a recently proposed brain inspired learning algorithm namely-Neurochaos Learning (NL) is used for the classification of cause and effect time series generated using coupled autoregressive processes, coupled 1D chaotic skew tent maps, coupled 1D chaotic logistic maps and a real-world prey-predator system. In the case of coupled skew tent maps, the proposed method consistently outperforms a five layer Deep Neural Network (DNN) and Long Short Term Memory (LSTM) architecture for unidirectional coupling coefficient values ranging from 0.1 to 0.7. Further, we investigate the preservation of causality in the feature extracted space of NL using Granger Causality for coupled autoregressive processes and Compression-Complexity Causality for coupled chaotic systems and real-world prey-predator dataset. Unlike DNN, LSTM and 1DConvolutional Neural Network, it is found that NL preserves the inherent causal structures present in the input timeseries data. These findings are promising for the theory and applications of causal machine learning and open up the possibility to explore the potential of NL for more sophisticated causal learning tasks.

Autoencoders are widely used for dimensionality reduction, based on the assumption that high-dimensional data lies on low-dimensional manifolds. Regularized autoencoders aim to preserve manifold geometry during dimensionality reduction, but existing approaches often suffer from non-injective mappings and overly rigid constraints that limit their effectiveness and robustness. In this work, we identify encoder non-injectivity as a core bottleneck that leads to poor convergence and distorted latent representations. To ensure robustness across data distributions, we formalize the concept of admissible regularization and provide sufficient conditions for its satisfaction. In this work, we propose the Bi-Lipschitz Autoencoder (BLAE), which introduces two key innovations: (1) an injective regularization scheme based on a separation criterion to eliminate pathological local minima, and (2) a bi-Lipschitz relaxation that preserves geometry and exhibits robustness to data distribution drift. Empirical results on diverse datasets show that BLAE consistently outperforms existing methods in preserving manifold structure while remaining resilient to sampling sparsity and distribution shifts. Code is available at https://github.com/qipengz/BLAE.

Major leap towards reanimation after death as mammal's brain preserved A pig's brain has been frozen with its cellular activity locked in place and minimal damage. Could our brains one day be preserved in a way that locks in our thoughts, feelings and perceptions? An entire mammalian brain has been successfully preserved using a technique that will now be offered to people who are terminally ill. The intention is to preserve all the neural information thought necessary to one day reconstruct the mind of the person it once belonged to. "They would need to donate their brain and body for scientific research," says Borys Wróbel at Nectome in San Francisco, California, a research company focused on memory preservation.

Hair editing is a critical image synthesis task that aims to edit hair color and hairstyle using textdescriptions orreference images, while preserving irrelevant attributes(e.g.,identity,background,cloth).

Photoswap is able to maintain the same pose with a decent style preservation.

One of core differences among various deep GCP methods is post-normalization for covariance representations, which plays a crucial role in final performance.