arXiv research

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

Causalfe estimates treatment effects in panel data with fixed effects.

Deviance-style normalization for sparse, jointly overdispersed count matrices

MLP residual networks implement a selective coarse-graining procedure governed by the spectral structure of the input distribution.

This is the second of a series of papers dealing with an analog in Arakelov geometry of the holomorphic Lefschetz fixed point formula. We use the main result of the first paper to prove a residue formula "`a la Bott" for arithmetic characteristic classes living on arithmetic varieties acted upon by a diagonalisable tor…

New diagnostic method detects misspecified models in inverse PDE problems.

REMAL: Residual Equilibrium Manifold Active Learning for Surrogate-Based Multidisciplinary Design Analysis

Using the notion of equivariant Kirwan map, as defined by Goldin, we prove that -- in the case of Hamiltonian torus actions with isolated fixed points -- Tolman and Weitsman's description of the kernel of the Kirwan map can be deduced directly from the residue theorem of Jeffrey and Kirwan. A characterization of the ke…

Study conjugacy classes of parabolic diffeomorphisms fixing the origin.

We give an effective upper bound, for certain arithmetic hyperbolic 3-manifold groups obtained from a quadratic form construction, on the minimal index of a subgroup that embeds in a fixed 6-dimensional right-angled reflection group, stabilizing a totally geodesic subspace. In particular, for manifold groups in any fix…

The paper establishes principles for initializing and designing GNNs with ReLU activations to avoid oversmoothing and correlation collapse.

Improved stochastic approximation method reduces residual error.

Predicting diagnoses from Electronic Health Records (EHRs) is an important medical application of multi-label learning. We propose a convolutional residual model for multi-label classification from doctor notes in EHR data. A given patient may have multiple diagnoses, and therefore multi-label learning is required. We …

Consider the space $R_Δ$ of rational functions of several variables with poles on a fixed arrangement $Δ$ of hyperplanes. We obtain a decomposition of $R_Δ$ as a module over the ring of differential operators with constant coefficients. We generalize to the space $R_Δ$ the notions of principal part and of residue, and …

TRA detects causal direction from bivariate data using geometric shapes.

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…

Jointly trains images and videos using residual vectors.

In this effort, we propose a new deep architecture utilizing residual blocks inspired by implicit discretization schemes. As opposed to the standard feed-forward networks, the outputs of the proposed implicit residual blocks are defined as the fixed points of the appropriately chosen nonlinear transformations. We show …

Normalization layers are a staple in state-of-the-art deep neural network architectures. They are widely believed to stabilize training, enable higher learning rate, accelerate convergence and improve generalization, though the reason for their effectiveness is still an active research topic. In this work, we challenge…

Proves a stack of G-bundles with logarithmic connections is finite type.

An automorphism $α$ of a group $G$ is normal if it fixes every normal subgroup of $G$ setwise. We give an algebraic description of normal automorphisms of relatively hyperbolic groups. In particular, we prove that for any relatively hyperbolic group $G$, $Inn(G)$ has finite index in the subgroup $Aut_n(G)$ of normal au…

CRC improves multivariate forecasting accuracy without risking performance degradation.

Study infinite-depth limits of neural networks with fixed width.

The paper introduces a diagnostic method to detect grokking transitions in models before test accuracy improves.

We study the growth of the rank of subgroups of finite index in residually finite groups, by relating it to the notion of cost. As a by-product, we show that the `Rank vs. Heegaard genus' conjecture on hyperbolic 3-manifolds is incompatible with the `Fixed Price problem' in topological dynamics.

A meromorphic quadratic differential with poles of order two, on a compact Riemann surface, induces a measured foliation on the surface, with a spiralling structure at any pole that is determined by the complex residue of the differential at the pole. We introduce the space of such measured foliations, and prove that f…

MGDL refines deep neural networks by training grades sequentially, improving stability.

Study Transformer layers under cross-entropy training using mean field control.

This paper improves bond market making by adjusting hit-ratios for client flow quality.

Momentum ResNets improve ResNets' memory efficiency.

We show that any smooth bi-Lipschitz $h$ can be represented exactly as a composition $h_m \circ ... \circ h_1$ of functions $h_1,...,h_m$ that are close to the identity in the sense that each $\left(h_i-\mathrm{Id}\right)$ is Lipschitz, and the Lipschitz constant decreases inversely with the number $m$ of functions com…

On a complex curve, we establish a correspondence between integrable connections with irregular singularities, and Higgs bundles such that the Higgs field is meromorphic with poles of any order. The moduli spaces of these objects are obtained by fixing at each singularity the polar part of the connection. We prove that…

Unified learning-rate scale for CNNs and ResNets, avoiding depth imbalance.

In this paper we investigate panel regression models with interactive fixed effects. We propose two new estimation methods that are based on minimizing convex objective functions. The first method minimizes the sum of squared residuals with a nuclear (trace) norm regularization. The second method minimizes the nuclear …

VR-GHAL method solves stochastic fixed-point equations with high probability.

Proposes RaT to mitigate bias in student-teacher estimation.

We present in this article a family of new combinatorial identities via purely differential/complex geometry methods, which include as a speical case a unified and explicit formula for Chern numbers of all complex flag manifolds. Our strategy is to construct concrete circle actions with isolated fixed points on these m…

Deep linear ResNets converge globally with certain transformations.

We prove a functorial correspondence between a category of logarithmic $\mathfrak{sl}_2$-connections on a curve $X$ with fixed generic residues and a category of abelian logarithmic connections on an appropriate spectral double cover $π: Σ\to X$. The proof is by constructing a pair of inverse functors $π^{\text{ab}}, π…

Improved stochastic Halpern iteration for fixed-point approximation in normed spaces.

We present DeepFPC, a novel deep neural network designed by unfolding the iterations of the fixed-point continuation algorithm with one-sided l1-norm (FPC-l1), which has been proposed for solving the 1-bit compressed sensing problem. The network architecture resembles that of deep residual learning and incorporates pri…

Let $M$ be a compact, connected symplectic manifold with a Hamiltonian action of a compact $n$-dimensional torus $G=T^n$. Suppose that $σ$ is an anti-symplectic involution compatible with the $G$-action. The real locus of $M$ is $X$, the fixed point set of $σ$. Duistermaat uses Morse theory to give a description of the…

PROBE optimizes best-arm identification with cheap proxies, improving sample complexity.

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

SA-PEF improves federated learning efficiency by correcting gradient mismatches.

A method for finding most influential sets reduces a complex problem to a sequence of simpler top-$k$ problems.

This paper contains several results concerning circle action on almost-complex and smooth manifolds. More precisely, we show that, for an almost-complex manifold $M^{2mn}$(resp. a smooth manifold $N^{4mn}$), if there exists a partition $λ=(λ_{1},...,λ_{u})$ of weight $m$ such that the Chern number $(c_{λ_{1}}... c_{λ_{…

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…