Related papers: Effective Versions of Strong Measure Zero

The problem of deciding whether a set of quantum measurements is jointly measurable is known to be equivalent to determining whether a quantum assemblage is unsteerable. This problem can be formulated as a semidefinite program (SDP).…

Large Deep Learning models are often compressed before being deployed in a resource-constrained environment. Can we trust the prediction of compressed models just as we trust the prediction of the original large model? Existing work has…

Neural networks achieve outstanding accuracy in classification and regression tasks. However, understanding their behavior still remains an open challenge that requires questions to be addressed on the robustness, explainability and…

As an alternative to the well-known methods of "chaining" and "bracketing" that have been developed in the study of random fields, a new method, which is based on a {\em stochastic maximal inequality} derived by using the formula for…

Measurement incompatibility is one of the basic aspects of quantum theory. Here we study the structure of the set of compatible -- i.e. jointly measurable -- measurements. We are interested in whether or not there exist compatible…

Reliable evaluation protocols are of utmost importance for reproducible NLP research. In this work, we show that sometimes neither metric nor conventional human evaluation is sufficient to draw conclusions about system performance. Using…

A sequence $x_1,\dots,x_n,\dots$ of discrete-valued observations is generated according to some unknown probabilistic law (measure) $\mu$. After observing each outcome, one is required to give conditional probabilities of the next…

A strong submeasure on a compact metric space X is a sub-linear and bounded operator on the space of continuous functions on X. A strong submeasure is positive if it is non-decreasing. By Hahn-Banach theorem, a positive strong submeasure is…

For any continuous map f on a compact manifold M, we define the SRB-like (or observable) probabilities as a generalization of Sinai-Ruelle-Bowen (i.e. physical) measures. We prove that f has observable measures, even if SRB measures do not…

For partial, nondeterministic, finite state machines, a new conformance relation called strong reduction is presented. It complements other existing conformance relations in the sense that the new relation is well-suited for model-based…

We consider the numbers of positive and negative eigenvalues of matrices of squared distances between randomly sampled i.i.d. points in a given metric measure space. These numbers and their limits, as the number of points grows, in fact…

Previous studies have used a specific success metric within an algorithmic search framework to prove machine learning impossibility results. However, this specific success metric prevents us from applying these results on other forms of…

Quantifying robustness in a single measure for the purposes of model selection, development of adversarial training methods, and anticipating trends has so far been elusive. The simplest metric to consider is the number of trainable…

We analyze the degree-structure induced by large reducibilities under the Axiom of Determinacy. This generalizes the analysis of Borel reducibilities given in references [1], [6] and [5] e.g. to the projective levels.

We are concerned with the problem of witnessing the Baire property of the Borel and the projective sets (assuming determinacy) through a sufficiently definable function in the codes. We prove that in the case of projective sets it is…

Machine learning has demonstrated remarkable performance over finite datasets, yet whether the scores over the fixed benchmarks can sufficiently indicate the model's performance in the real world is still in discussion. In reality, an ideal…

The ability to post-select the outcomes of an experiment is a useful theoretical concept and experimental tool. In the context of weak measurements post-selection can lead to surprising results such as complex weak values outside the range…

Building on recent results regarding symmetric probabilistic constructions of countable structures, we provide a method for constructing probability measures, concentrated on certain classes of countably infinite structures, that are…

Model evaluation is a critical component in supervised machine learning classification analyses. Traditional metrics do not currently incorporate case difficulty. This renders the classification results unbenchmarked for generalization.…

Effectively inseparable pairs and their properties play an important role in the meta-mathematics of arithmetic and incompleteness. Different notions are introduced and shown in the literature to be equivalent to effective inseparability.…