Related papers: Entropy Encoding, Hilbert Space and Karhunen-Loeve…
Learned image compression methods have attracted great research interest and exhibited superior rate-distortion performance to the best classical image compression standards of the present. The entropy model plays a key role in learned…
A definition of entropy via the Kolmogorov algorithmic complexity is discussed. As examples, we show how the meanfield theory for the Ising model, and the entropy of a perfect gas can be recovered. The connection with computations are…
Entropy estimation is of practical importance in information theory and statistical science. Many existing entropy estimators suffer from fast growing estimation bias with respect to dimensionality, rendering them unsuitable for…
Entropy coding is the backbone data compression. Novel machine-learning based compression methods often use a new entropy coder called Asymmetric Numeral Systems (ANS) [Duda et al., 2015], which provides very close to optimal bitrates and…
Approaches to signal representation and coding theory have traditionally focused on how to best represent signals using parsimonious representations that incur the lowest possible distortion. Classical examples include linear and non-linear…
The concept of refinement from probability elicitation is considered for proper scoring rules. Taking directions from the axioms of probability, refinement is further clarified using a Hilbert space interpretation and reformulated into the…
We investigate the following generalisation of the entropy of quantum measurement. Let H be an infinite-dimensional separable Hilbert space with a 'density' operator {\rho}, tr {\rho}=1. Let I(P)\in R be defined for any partition P =…
The time evolution of complex systems usually can be described through stochastic processes. These processes are measured at finite resolution, what necessarily reduces them to finite sequences of real numbers. In order to relate these data…
The translation of an operator is defined by using conjugation with time-frequency shifts. Thus, one can define $\Lambda$-shift-invariant subspaces of Hilbert-Schmidt operators, finitely generated, with respect to a lattice $\Lambda$ in…
A double-atom partitioning of the molecular one-electron density matrix is used to describe atoms and bonds. All calculations are performed in Hilbert space. The concept of atomic weight functions (familiar from Hirshfeld analysis of the…
Configurational entropy is an important factor in the free energy change of many macromolecular recognition and binding processes, and has been intensively studied. Despite great progresses that have been made, the global sampling remains…
Convolutional autoencoders are now at the forefront of image compression research. To improve their entropy coding, encoder output is typically analyzed with a second autoencoder to generate per-variable parametrized prior probability…
In the last years several estimation strategies have been formulated to determine the value of an unknown parameter in the most precise way, taking into account the presence of noise. These strategies typically rely on the use of quantum…
Looped Transformers provide advantages in parameter efficiency, computational capabilities, and generalization for reasoning tasks. However, their expressive power regarding function approximation remains underexplored. In this paper, we…
Modern scientific instruments produce vast amounts of data, which can overwhelm the processing ability of computer systems. Lossy compression of data is an intriguing solution, but comes with its own drawbacks, such as potential signal…
This work studies the entropic regularization formulation of the 2-Wasserstein distance on an infinite-dimensional Hilbert space, in particular for the Gaussian setting. We first present the Minimum Mutual Information property, namely the…
We extend the operator preconditioning framework [R. Hiptmair, Comput. Math. with Appl. 52 (2006), pp.~699--706] to Petrov-Galerkin methods while accounting for parameter-dependent perturbations of both variational forms and their…
In this paper we obtain order estimates for entropy numbers of embeddings of weighted Sobolev spaces into weighted Lebesgue spaces and of weighted summation operators on trees. Here we consider some critical conditions on the parameters.
Encoding in a high-dimensional Hilbert space improves noise resilience in quantum information processing. This approach, however, may result in cross-mode coupling and detection complexities, thereby reducing quantum cryptography…
There has been recent interest in identifying entanglement as the fundamental concept from which space may emerge. We note that the particular way that a Hilbert space is decomposed into tensor factors is important in what the resulting…