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The quantum probabilistic convergence in measurement, distinct from mathematical convergence, is derived for indeterminate probabilities from the weak quantum law of large numbers. This is presented in three theorems. The first establishes…
In image compression, with recent advances in generative modeling, the existence of a trade-off between the rate and the perceptual quality (realism) has been brought to light, where the realism is measured by the closeness of the output…
First we consider pair-wise distances for literal objects consisting of finite binary files. These files are taken to contain all of their meaning, like genomes or books. The distances are based on compression of the objects concerned,…
Neural-based image and video codecs are significantly more power-efficient when weights and activations are quantized to low-precision integers. While there are general-purpose techniques for reducing quantization effects, large losses can…
We compute, for a compact set $K\subset\mathbb R^d$, the value of the upper and of the lower $L^q$-dimension of a typical probability measure with support contained in $K$, for any $q\in\mathbb R$. Different definitions of the "dimension"…
A large amount of literature in social choice theory deals with quantifying the probability of certain election outcomes. One way of computing the probability of a specific voting situation under the Impartial Anonymous Culture assumption…
Probabilities for observations in cosmology are conditioned both on the universe's quantum state and on local data specifying the observational situation. We show the quantum state defines a measure for prediction through such conditional…
Approximate Counting refers to the problem where we are given query access to a function $f : [N] \to \{0,1\}$, and we wish to estimate $K = #\{x : f(x) = 1\}$ to within a factor of $1+\epsilon$ (with high probability), while minimizing the…
We extend our work for compression of currents and varifolds to a compression algorithm for the embedded normal cycles representation of shape, restricted to the constant normal kernel case, using the Nystrom approximation in Reproducing…
In this paper, a new probability density function (pdf) is proposed to model the statistics of wavelet coefficients, and a simple Kalman's filter is derived from the new pdf using Bayesian estimation theory. Specifically, we decompose the…
Probability calibration for deep models is highly desirable in safety-critical applications such as medical imaging. It makes output probabilities of deep networks interpretable, by aligning prediction probability with the actual accuracy…
Could we compress images via standard codecs while avoiding visible artifacts? The answer is obvious -- this is doable as long as the bit budget is generous enough. What if the allocated bit-rate for compression is insufficient? Then…
We introduce $k$-variance, a generalization of variance built on the machinery of random bipartite matchings. $K$-variance measures the expected cost of matching two sets of $k$ samples from a distribution to each other, capturing local…
A new approach for estimating the Decoding Error-Probability (DEP) of LT codes with dense rows is derived by using the conditional Kovalenko's rank distribution. The estimate by the proposed approach is very close to the DEP approximated by…
We define a new notion of compressibility of a set of numbers through the dynamics of a polynomial function. We provide approaches to solve the problem by reducing it to the multi-criteria traveling salesman problem through a series of…
When a logical qubit is protected using a quantum error-correcting code, the net effect of coding, decoherence (a physical channel acting on qubits in the codeword) and recovery can be represented exactly by an effective channel acting…
In Image Compression, the researchers' aim is to reduce the number of bits required to represent an image by removing the spatial and spectral redundancies. Recently discrete wavelet transform and wavelet packet has emerged as popular…
Approximation theory is concerned with the ability to approximate functions by simpler and more easily calculated functions. The first question we ask in approximation theory concerns the {\it possibility of approximation}. Is the given…
CLIP is a widely used foundational vision-language model that is used for zero-shot image recognition and other image-text alignment tasks. We demonstrate that CLIP is vulnerable to change in image quality under compression. This surprising…
We show that real-value approximations of Kolmogorov-Chaitin (K_m) using the algorithmic Coding theorem as calculated from the output frequency of a large set of small deterministic Turing machines with up to 5 states (and 2 symbols), is in…