Related papers: No-Free-Lunch Theorems in the continuum
In this short paper, I recall the history of dealing with the lack of compactness of a sequence in the case of an unbounded domain and prove the vanishing Lions-type result for a sequence of Lebesgue-measurable functions. This lemma…
We study the classic online learning problem of predicting with expert advice, and propose a truly parameter-free and adaptive algorithm that achieves several objectives simultaneously without using any prior information. The main component…
Within the framework of generalized noncontextuality, we introduce a general technique for systematically deriving noncontextuality inequalities for any experiment involving finitely many preparations and finitely many measurements, each of…
We address the following question of neural network identifiability: Suppose we are given a function $f:\mathbb{R}^m\to\mathbb{R}^n$ and a nonlinearity $\rho$. Can we specify the architecture, weights, and biases of all feed-forward neural…
No-Signalling is a fundamental constraint on the probabilistic predictions made by physical theories. It is usually justified in terms of the constraints imposed by special relativity. However, this justification is not as clear-cut as is…
To support people trying to lose weight and stay healthy, more and more fitness apps have sprung up including the ability to track both calories intake and expenditure. Users of such apps are part of a wider ``quantified self'' movement and…
A method for machine learning and serving of discrete field theories in physics is developed. The learning algorithm trains a discrete field theory from a set of observational data on a spacetime lattice, and the serving algorithm uses the…
Many software systems offer configuration options to tailor their functionality and non-functional properties (e.g., performance). Often, users are interested in the (performance-)optimal configuration, but struggle to find it, due to…
We introduce the concept of topological finite-determinacy for germs of analytic functions within a fixed ideal $I$, which provides a notion of topological finite-determinacy of functions with non-isolated singularities. We prove the…
Private inference (PI) enables inference directly on cryptographically secure data.While promising to address many privacy issues, it has seen limited use due to extreme runtimes. Unlike plaintext inference, where latency is dominated by…
We review and develop a mathematical framework for nonlocal quantum field theory (QFT) with a fundamental length. As an instructive example, we reexamine the normal ordered Gaussian function of a free field and find the primitive…
For any quantity of interest in a system governed by ordinary differential equations, it is natural to seek the largest (or smallest) long-time average among solution trajectories, as well as the extremal trajectories themselves. Upper…
We establish new upper and lower bounds on the number of queries required to test convexity of functions over various discrete domains. 1. We provide a simplified version of the non-adaptive convexity tester on the line. We re-prove the…
This paper, and its companion [BCV24], are devoted to a negative resolution of the Aldous--Lyons Conjecture [AL07, Ald07]. This conjecture, originated in probability theory, is well known (cf. [Gel18]) to be equivalent to the statement that…
The free central-limit theorem, a fundamental theorem in free probability, states that empirical averages of freely independent random variables are asymptotically semi-circular. We extend this theorem to general dynamical systems of…
The study of non-linearity (linearity) of Boolean function was initiated by Rothaus in 1976. The classical non-linearity of a Boolean function is the minimum Hamming distance of its truth table to that of affine functions. In this note we…
It is often hypothesized that a crucial role for recurrent connections in the brain is to constrain the set of possible response patterns, thereby shaping the neural code. This implies the existence of neural codes that cannot arise solely…
The algorithmic theory of randomness is well developed when the underlying space is the set of finite or infinite sequences and the underlying probability distribution is the uniform distribution or a computable distribution. These…
A linear functional of an object from a convex symmetric set can be optimally estimated, in a worst-case sense, by a linear functional of observations made on the object. This well-known fact is extended here to a nonlinear setting: other…
There is no general existence theorem for solutions for nonlinear difference equations, so we must prove the existence of solutions in accordance with models one by one. In our work, we found theorems for the existence of analytic solutions…