Related papers: The Sparse Manifold Transform
Sparse coding networks, which utilize unsupervised learning to maximize coding efficiency, have successfully reproduced response properties found in primary visual cortex \cite{AN:OlshausenField96}. However, conventional sparse coding…
This paper describes a hierarchical learning strategy for generating sparse representations of multivariate datasets. The hierarchy arises from approximation spaces considered at successively finer scales. A detailed analysis of stability,…
We establish exact asymptotic expressions for the normalized mutual information and minimum mean-square-error (MMSE) of sparse linear regression in the sub-linear sparsity regime. Our result is achieved by a generalization of the adaptive…
We introduce a framework for designing multi-scale, adaptive, shift-invariant frames and bi-frames for representing signals. The new framework, called AdaFrame, improves over dictionary learning-based techniques in terms of computational…
Low-resolution image representation is a special form of sparse representation that retains only low-frequency information while discarding high-frequency components. This property reduces storage and transmission costs and benefits various…
In compressed sensing one measures sparse signals directly in a compressed form via a linear transform and then reconstructs the original signal. However, it is often the case that the linear transform itself is known only approximately, a…
This work proposes an algorithm for explicitly constructing a pair of neural networks that linearize and reconstruct an embedded submanifold, from finite samples of this manifold. Our such-generated neural networks, called Flattening…
Large language models (LLMs) encode a diverse range of linguistic features within their latent representations, which can be harnessed to steer their output toward specific target characteristics. In this paper, we modify the internal…
Diffusion magnetic resonance imaging (dMRI) is an important tool in characterizing tissue microstructure based on biophysical models, which are complex and highly non-linear. Resolving microstructures with optimization techniques is prone…
The growing environmental footprint of artificial intelligence (AI), especially in terms of storage and computation, calls for more frugal and interpretable models. Sparse models (e.g., linear, neural networks) offer a promising solution by…
We apply recent advances in machine learning and computer vision to a central problem in materials informatics: The statistical representation of microstructural images. We use activations in a pre-trained convolutional neural network to…
In linear inverse problems, the goal is to recover a target signal from undersampled, incomplete or noisy linear measurements. Typically, the recovery relies on complex numerical optimization methods; recent approaches perform an unfolding…
Vision foundation models (FMs) achieve state-of-the-art performance in medical imaging. However, they encode information in abstract latent representations that clinicians cannot interrogate or verify. The goal of this study is to…
Many transformations in deep learning architectures are sparsely connected. When such transformations cannot be designed by hand, they can be learned, even through plain backpropagation, for instance in attention mechanisms. However, during…
Understanding 3D object shapes necessitates shape representation by object parts abstracted from results of instance and semantic segmentation. Promising shape representations enable computers to interpret a shape with meaningful parts and…
Compressed sensing is a signal processing technique that allows for the reconstruction of a signal from a small set of measurements. The key idea behind compressed sensing is that many real-world signals are inherently sparse, meaning that…
Modern visual generative models acquire rich visual knowledge through large-scale training, yet existing visual representations (such as pixels, latents, or tokens) remain external to the model and cannot directly exploit this knowledge for…
The objective of this paper is audio-visual synchronisation of general videos 'in the wild'. For such videos, the events that may be harnessed for synchronisation cues may be spatially small and may occur only infrequently during a many…
To gain insight into the mechanisms behind machine learning methods, it is crucial to establish connections among the features describing data points. However, these correlations often exhibit a high-dimensional and strongly nonlinear…
Data is said to follow the transform (or analysis) sparsity model if it becomes sparse when acted on by a linear operator called a sparsifying transform. Several algorithms have been designed to learn such a transform directly from data,…