Related papers: Two Decreasing Measures for Simply Typed Lambda-Te…

Given a measure space and a totally ordered ordered collection of measurable sets, called an ordered core, the notion of a core decreasing function is introduced and used to define the down space of a Banach function space. This is done…

We consider a class of sparsity-inducing regularization terms based on submodular functions. While previous work has focused on non-decreasing functions, we explore symmetric submodular functions and their \lova extensions. We show that the…

The precise measurement of spatial attitude parameters is critical for applications in inertial navigation, industrial monitoring, instrument calibration, quantum metrology, etc. In this work, we theoretically investigate and experimentally…

We consider constraints on the measure of the support for integrable functions on arbitrary measure spaces. It is shown that this non-convex and discontinuous constraint can be equivalently reformulated by the difference of two convex and…

Task Arithmetic has emerged as a simple yet effective method to merge models without additional training. However, by treating entire networks as flat parameter vectors, it overlooks key structural information and is susceptible to task…

The pursuit of reducing the memory footprint of the self-attention mechanism in multi-headed self attention (MHA) spawned a rich portfolio of methods, e.g., group-query attention (GQA) and multi-head latent attention (MLA). The methods…

Calculi with control operators have been studied to reason about control in programming languages and to interpret the computational content of classical proofs. To make these calculi into a real programming language, one should also…

Here we study what we call bounded rough Riemannian metrics $(M,g)$, which are positive definite, symmetric tensors on each tangent space, $T_pM$, which are bounded and measurable as functions in coordinates. This is enough structure to…

Scaling describes how a given quantity $Y$ that characterizes a system varies with its size $P$. For most complex systems it is of the form $Y\sim P^\beta$ with a nontrivial value of the exponent $\beta$, usually determined by regression…

Concentration of measure is a phenomenon in which a random variable that depends in a smooth way on a large number of independent random variables is essentially constant. The random variable will "concentrate" around its median or…

We propose a "decomposition method" to prove non-asymptotic bound for the convergence of empirical measures in various dual norms. The main point is to show that if one measures convergence in duality with sufficiently regular observables,…

For a given measure space $(X,{\mathscr B},\mu)$ we construct all measure spaces $(Y,{\mathscr C},\lambda)$ in which $(X,{\mathscr B},\mu)$ is embeddable. The construction is modeled on the ultrafilter construction of the Stone--\v{C}ech…

Tensor decomposition methods are popular tools for learning latent variables given only lower-order moments of the data. However, the standard assumption is that we have sufficient data to estimate these moments to high accuracy. In this…

This paper investigates the predictive performance of model averaging in high-dimensional linear regression where the number of regressors is comparable to the sample size. We demonstrate that the double descent trajectory manifests within…

Standard inference about a scalar parameter estimated via GMM amounts to applying a t-test to a particular set of observations. If the number of observations is not very large, then moderately heavy tails can lead to poor behavior of the…

We consider $C$-pseudo-cones, that is, closed convex sets $K \subset{\mathbb R}^n$ with $o\notin K\subset C$, for which $C$ is the recession cone. Here $C$ is a given closed convex cone in ${\mathbb R}^n$, pointed and with nonempty…

Contrary to several other families of lambda terms, no closed formula or generating function is known and none of the sophisticated techniques devised in analytic combinatorics can currently help with counting or generating the set of {\em…

Tensor-based modulation (TBM) has been proposed in the context of unsourced random access for massive uplink communication. In this modulation, transmitters encode data as rank-1 tensors, with factors from a discrete vector constellation.…

Let $(T,d)$ be a metric space and $\phi:\mathbb{R}_+\to \mathbb{R}$ an increasing, convex function with $\phi(0)=0$. We prove that if $m$ is a probability measure $m$ on $T$ which is majorizing with respect to $d,\phi$, that is,…

A notion of probabilistic lambda-calculus usually comes with a prescribed reduction strategy, typically call-by-name or call-by-value, as the calculus is non-confluent and these strategies yield different results. This is a break with one…