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A definition of the nonadditive (nonextensive) conditional entropy indexed by q is presented. Based on the composition law in terms of it, the Shannon-Khinchin axioms are generalized and the uniqueness theorem is established for the Tsallis…
Humans have a remarkable ability to disentangle complex sensory inputs (e.g., image, text) into simple factors of variation (e.g., shape, color) without much supervision. This ability has inspired many works that attempt to solve the…
This paper presents an unsupervised method that trains neural source separation by using only multichannel mixture signals. Conventional neural separation methods require a lot of supervised data to achieve excellent performance. Although…
Many training data attribution (TDA) methods aim to estimate how a model's behavior would change if one or more data points were removed from the training set. Methods based on implicit differentiation, such as influence functions, can be…
Nowadays, deep learning methods, especially the convolutional neural networks (CNNs), have shown impressive performance on extracting abstract and high-level features from the hyperspectral image. However, general training process of CNNs…
We examine a class of deep learning models with a tractable method to compute information-theoretic quantities. Our contributions are three-fold: (i) We show how entropies and mutual informations can be derived from heuristic statistical…
We develop variational representations for the deformed logarithmic and exponential functions and use them to obtain variational representations related to the quantum Tsallis relative entropy. We extend Golden-Thompson's trace inequality…
We develop a variational thermodynamic framework for statistical systems governed by a self-referential nonlinear operator Omega characterized by structural exponents alpha > 0, beta >= 0, a symmetric kernel K, and a self-coupling constant…
Separability conditions for a bipartite quantum system of finite-dimensional subsystems are formulated in terms of R\'{e}nyi and Tsallis entropies. Entropic uncertainty relations often lead to entanglement criteria. We propose new approach…
It is shown that the distribution derived from the principle of maximum Tsallis entropy is a superposable Levy-type distribution. Concomitantly, the leading order correction to the limit distribution is also deduced. This demonstration…
In this paper, inspired from our previous algorithm, which was based on the theory of Tsallis statistical mechanics, we develop a new evolving stochastic learning algorithm for neural networks. The new algorithm combines deterministic and…
This paper deals with rate distortion or source coding with fidelity criterion, in measure spaces, for a class of source distributions. The class of source distributions is described by a relative entropy constraint set between the true and…
A field theory is built for self-similar statistical systems with both generating functional being the Mellin transform of the Tsallis exponential and generator of the scale transformation that is reduced to the Jackson derivative. With…
This work is focussed on the inversion task of inferring the distribution over parameters of interest leading to multiple sets of observations. The potential to solve such distributional inversion problems is driven by increasing…
Quasi-power law ensembles are discussed from the perspective of nonextensive Tsallis distributions characterized by a nonextensive parameter $q$. A number of possible sources of such distributions are presented in more detail. It is further…
Unsupervised contrastive learning has shown significant performance improvements in recent years, often approaching or even rivaling supervised learning in various tasks. However, its learning mechanism is fundamentally different from…
Universal source separation targets at separating the audio sources of an arbitrary mix, removing the constraint to operate on a specific domain like speech or music. Yet, the potential of universal source separation is limited because most…
We discuss the entropic criterion for separability of compound quantum systems for general non-additive entropic forms based on arbitrary concave functions $f$. For any separable state, the generalized entropy of the whole system is shown…
We prove a large deviation principle for the finite dimensional marginals of the Gibbs distribution of the macroscopic `overlap'-parameters in the Hopfield model in the case where the number of random patterns, $M$, as a function of the…
We study counting statistics of number of transitions in a stochastic process. For mesoscopic systems, a path integral formulation for the counting statistics has already been derived. We here show that it is also possible to derive the…