arXiv research

Wide residual networks generalize well with uniform convergence to RNTK as width increases.

Defines and proves generalized noncommutative residue theorems for specific dimensions.

Given a prime $p$, a group is called residually $p$ if the intersection of its $p$-power index normal subgroups is trivial. A group is called virtually residually $p$ if it has a finite index subgroup which is residually $p$. It is well-known that finitely generated linear groups over fields of characteristic zero are …

Residual flows are shown to approximate MMD well.

Let $p$ be a prime. In this paper, we classify the geometric 3-manifolds whose fundamental groups are virtually residually $p$. Let $M=M^3$ be a virtually fibered 3-manifold. It is well-known that $G=π_1(M)$ is residually solvable and even residually finite solvable. We prove that $G$ is always virtually residually $p$…

We show that Out(G) is residually finite if G is a one-ended group that is hyperbolic relative to virtually polycyclic subgroups. More generally, if G is one-ended and hyperbolic relative to proper residually finite subgroups, the group of outer automorphisms preserving the peripheral structure is residually finite. We…

Study on endomorphism and automorphism groups of specific quandles.

We show a residues formula for maps generically transversal to regular holomorphic distributions.

Generalization bounds derived for neural ODEs and deep residual networks.

The skip-connections used in residual networks have become a standard architecture choice in deep learning due to the increased training stability and generalization performance with this architecture, although there has been limited theoretical understanding for this improvement. In this work, we analyze overparameter…

Proves Singer conjecture for graph manifolds with residually finite groups.

Study of uncountable family of finitely generated groups.

Alpha-based performance evaluation may fail to capture correlated residuals due to model errors. This paper proposes using the Generalized Information Ratio (GIR) to measure performance under misspecified benchmarks. Motivated by the theoretical link between abnormal returns and residual covariance matrix, GIR is deriv…

The paper derives spectral (0,4)-tensor functionals using the noncommutative residue.

Classifies connected components of meromorphic differentials with residue conditions.

Residual connections significantly boost the performance of deep neural networks. However, there are few theoretical results that address the influence of residuals on the hypothesis complexity and the generalization ability of deep neural networks. This paper studies the influence of residual connections on the hypoth…

The paper studies residues of manifolds and their applications in geometry.

We count meromorphic differentials with fixed residues and poles of fixed orders.

The paper develops residue currents for cohesive modules and proves a generalized Poincaré-Lelong formula.

Many 2D Artin groups are residually finite.

Flow-based generative models parameterize probability distributions through an invertible transformation and can be trained by maximum likelihood. Invertible residual networks provide a flexible family of transformations where only Lipschitz conditions rather than strict architectural constraints are needed for enforci…

We generalize Luck's Theorem to show that the L^2-Betti numbers of a residually amenable covering space are the limit of the L^2-Betti numbers of a sequence of amenable covering spaces. We show that any residually amenable covering space of a finite simplicial complex is of determinant class, and that the L^2 torsion i…

A well known result on pseudodifferential operators states that the noncommutative residue (Wodzicki residue) of a pseudodifferential projection vanishes. This statement is non-local and implies the regularity of the eta invariant at zero of Dirac type operators. We prove that in a filtered algebra the value of a proje…

Abstract: Non-residually finite hyperbolic groups imply non-residually finite rigid hyperbolic groups.

ResMem improves model generalization by explicitly memorizing residuals.

In this paper we generalize Leray's calculus of residues in several complex variables, to the situation of an abstract smooth CR manifold M of general type (n,k).

Residual finiteness is known to be an important property of groups appearing in combinatorial group theory and low dimensional topology. In a recent work [2] residual finiteness of quandles was introduced, and it was proved that free quandles and knot quandles are residually finite. In this paper, we extend these resul…

In this note, residual finiteness of quandles is defined and investigated. It is proved that free quandles and knot quandles of tame knots are residually finite and Hopfian. Residual finiteness of quandles arising from residually finite groups (conjugation, core and Alexander quandles) is established. Further, residual…

The fundamental n-quandles of links are residually finite for n ≥ 2.

Groups with similar pro-$p$ completions have two-generated subgroups that are free.

Study on residual Monge-Ampère mass for symmetric plurisubharmonic functions.

The study examines Hopfian properties of conjugation quandles and their underlying groups.

Every non-trivial knot group is fully residually perfect.

The covariance matrix is formulated in the framework of a linear multivariate ARCH process with long memory, where the natural cross product structure of the covariance is generalized by adding two linear terms with their respective parameter. The residuals of the linear ARCH process are computed using historical data …

Residual neural networks don't help overcome sampling complexity issues.

Gaussian Process (GP) regression models typically assume that residuals are Gaussian and have the same variance for all observations. However, applications with input-dependent noise (heteroscedastic residuals) frequently arise in practice, as do applications in which the residuals do not have a Gaussian distribution. …

We show that there is no algorithm deciding whether the maximal residually free quotient of a given finitely presented group is finitely presentable or not. Given a finitely generated subgroup G of a finite product of limit groups, we discuss the possibility of finding an explicit set of defining equations (i.e. of exp…

Extends spectral Einstein functionals computation to 4D spin manifolds with boundary.

Residual Continual Learning prevents forgetting in sequential tasks.

This paper aims at theoretically and empirically comparing two standard optimization criteria for Reinforcement Learning: i) maximization of the mean value and ii) minimization of the Bellman residual. For that purpose, we place ourselves in the framework of policy search algorithms, that are usually designed to maximi…

Researchers identify critical protein residues using advanced graph theory.

Defines Wodzicki residue using groupoids and fibered distributions.

In this work we prove a Baum-Bott type residue theorem for flags of holomorphic foliations. We prove some relations between the residues of the flag and the residues of their correspondent foliations. We define the Nash residue for flags and we give a partial answer to the Baum-Bott type rationality conjecture in this …

The study proves residual finiteness for certain lattice extensions and negatively curved projective varieties.

We revisit residual algorithms in both model-free and model-based reinforcement learning settings. We propose the bidirectional target network technique to stabilize residual algorithms, yielding a residual version of DDPG that significantly outperforms vanilla DDPG in the DeepMind Control Suite benchmark. Moreover, we…

Paper improves bike-sharing demand prediction by adapting to changing patterns.

Simplifies residual flows to make flow-based modeling more practical.

Causality-aware methods outperform linear residualization in confounding adjustment for anticausal prediction.