arXiv research

Researchers identify valid auxiliary functions for extreme value distributions and their max-domains of attraction.

Proposes a new method to learn representations directly optimized for a task.

We define the representation ring of a saturated fusion system $\mathcal F$ as the Grothendieck ring of the semiring of $\mathcal F$-stable representations, and study the dimension functions of $\mathcal F$-stable representations using the transfer map induced by the characteristic idempotent of $\mathcal F$. We find a…

Study feature representations induced by dependence between variables.

In this effort, we derive a formula for the integral representation of a shallow neural network with the ReLU activation function. We assume that the outer weighs admit a finite $L_1$-norm with respect to Lebesgue measure on the sphere. For univariate target functions we further provide a closed-form formula for all po…

Proposes a neural network autoencoder for smoothing and representation learning of functional data.

We show how Conway's multivariable potential function can be constructed using braids and the reduced Gassner representation. The resulting formula is a multivariable generalization of a construction, due to Kassel-Turaev, of the Alexander-Conway polynomial in terms of the Burau representation. Apart from providing an …

Sharp lower bound on GHHs' representation power of CPWL functions.

The paper computes characteristic classes for Lie group representations.

Revisits the connection between neural networks and the Kolmogorov-Arnold theorem.

New method learns robust meta-representations for fast task adaptation.

Generalized matrix-fractional (GMF) functions are a class of matrix support functions introduced by Burke and Hoheisel as a tool for unifying a range of seemingly divergent matrix optimization problems associated with inverse problems, regularization and learning. In this paper we dramatically simplify the support func…

Unified framework for learning function representations using INRs and Transformers.

Proposes FunNoL for better curve classification and reconstruction in multivariate functional data.

We develop a functional encoder-decoder approach to supervised meta-learning, where labeled data is encoded into an infinite-dimensional functional representation rather than a finite-dimensional one. Furthermore, rather than directly producing the representation, we learn a neural update rule resembling functional gra…

We study Hitchin representations and maximal symplectic representations of surface groups, which can be both thought of as generalisations of Fuchsian representations. We show that the corresponding energy functionals are proper on Teichmuller space. We also prove that the mapping class group acts properly on the corre…

Defines spherical type surfaces via support function and classifies them.

Simplified proof of Gaussian concentration inequality using covariance.

We consider the representation space of a compact surface, that is the space of morphisms from the fundamental group to SU(2) up to conjugation. We show that the trace functions associated to multicurves on the surface are linearly independent as functions on the representation space. The proof relies on the Fourier de…

In this paper we study a class of functions that appear naturally in some equidistribution problems and that we call $F$-harmonic. These are functions of the universal cover of a closed and negatively curved which possess an integral representation analogous to the Poisson representation of harmonic functions, where th…

Study non-acyclic SL2-representations of twist knots and their L-functions.

Study multiplicity of non-acyclic SL2-representations and L-functions of Whitehead links.

FairNN learns fair representations and decisions by optimizing a multi-objective loss function.

Riemannian Geometry, Topology and Dynamics permit to introduce partially defined holomorphic functions on the variety of representations of the fundamental group of a manifold. The functions we consider are the complex valued Ray-Singer torsion, the Milnor-Turaev torsion, and the dynamical torsion. They are associated …

New method tightens variational representations of divergences for faster learning.

Researchers develop multi-utility representations for incomplete preferences linked to risk measures.

Sharp representation theorems show depth benefits for ReLU networks.

In this work, we study value function approximation in reinforcement learning (RL) problems with high dimensional state or action spaces via a generalized version of representation policy iteration (RPI). We consider the limitations of proto-value functions (PVFs) at accurately approximating the value function in low d…

Relation between generalized Weierstrass representation for conformal immersion of generic surfaces into three-dimensional space and Lax-Phillips scattering theory for automorphic functions is considered.

We provide a dual representation of quasiconvex maps between two lattices of random variables in terms of conditional expectations. This generalizes the dual representation of quasiconvex real valued functions and the dual representation of conditional convex maps.

Representation costs in data science: Unifying function-space views of parametric methods

SOC-ICNN expands neural network representational capacity by using conic optimization.

Spherical representations and functions are the building blocks for harmonic analysis on riemannian symmetric spaces. In this paper we consider spherical functions and spherical representations related to certain infinite dimensional symmetric spaces $G_\infty/K_\infty = \varinjlim G_n/K_n$. We use the representation t…

This paper presents a novel deep learning-based method for learning a functional representation of mammalian neural images. The method uses a deep convolutional denoising autoencoder (CDAE) for generating an invariant, compact representation of in situ hybridization (ISH) images. While most existing methods for bio-ima…

Many theories of deep learning have shown that a deep network can require dramatically fewer resources to represent a given function compared to a shallow network. But a question remains: can these efficient representations be learned using current deep learning techniques? In this work, we test whether standard deep l…

Unified theory for representation learning using learnable functions.

For an oriented diagram of a link $L$ in the 3-sphere, Cho and Murakami defined the potential function whose critical point, slightly different from the usual sense, corresponds to a boundary parabolic $\mathrm{PSL}(2,\mathbb{C})$-representation of $π_1(S^3 \setminus L)$. They also showed that the volume and Chern-Simo…

Two-layer neural networks can approximate functions with fractal singularities.

Improved AutoDML estimator for causal inference using outcome-adapted shared covariate representation.

Paper finds sparse representation of functions using inverse scale space flow.

Researchers generalize Ribaucour-type surfaces with new mathematical representation.

We study the character of the infinite wedge projective representation of the algebra of differential operators on the circle. We prove quasi-modularity of this character and also compute certain generating functions for traces of differential operators which we call correlation functions. These correlation functions a…

Proposes adversarial method to estimate Riesz representer.

The paper shows how to stabilize off-policy reinforcement learning using specific state representations.

Extends Fried's result to arbitrary representations of compact hyperbolic manifolds.

New method learns stochastic process representations without exact reconstruction.

The paper proves positivity of a $L^2$-torsion function for certain 3-manifolds.

In this paper, we aim at introducing a new machine learning model, namely reconciled polynomial machine, which can provide a unified representation of existing shallow and deep machine learning models. Reconciled polynomial machine predicts the output by computing the inner product of the feature kernel function and va…