Proposes α-integration pooling for CNNs to improve performance.
problem Finding optimal pooling method for CNNs is challenging.
method Introduces α-integration pooling with a trainable parameter α. result Demonstrates α-integration pooling outperforms other pooling methods in image recognition. A new spectral pooling method reduces loss in CNNs for better performance.
problem Lossy downsampling in CNNs reduces discriminability.
method Hartley Spectral Pooling using Hartley Transform.
result Hartley Spectral Pooling preserves more structure features than max/average pooling.
Convolutional neural networks converge quickly with gradient descent.
problem Learning efficient image classifiers with over-parameterized networks.
method Gradient descent for training over-parametrized CNNs with global average-pooling.
result Gradient descent quickly reduces the misclassification risk of CNNs.
GSP improves global average pooling for deep metric learning by learning weights and selecting semantic entities.
problem Improving global average pooling for deep metric learning.
method Generalized Sum Pooling (GSP) method that learns weights and selects semantic entities.
result GSP improves metric learning performance on 4 popular benchmarks.
A modified VDCNN model reduces size and latency for mobile platforms.
problem Memory and processing constraints on mobile platforms.
method Temporal Depthwise Separable Convolutions and Global Average Pooling.
result The squeezed model (SVDCNN) is 10x-20x smaller with minimal accuracy loss.
Tensor regression networks achieve high compression rate of neural networks while having slight impact on performances. They do so by imposing low tensor rank structure on the weight matrices of fully connected layers. In recent years, tensor regression networks have been investigated from the perspective of their comp…
Enhanced CNN kernels improve image classification accuracy.
problem Improving classification accuracy of CNNs.
method Local Average Pooling and random image patch representation.
result 89% accuracy on CIFAR-10, matching AlexNet performance.
The paper reformulates U-Nets as wavelet-based models and applies this to hierarchical VAEs.
problem Theoretical understanding and regularization properties of U-Nets and their relationship to wavelets.
method Formulating a multi-resolution framework to identify U-Nets as finite-dimensional truncations of infinite-dimensional models, proving average pooling corresponds to projection, and identifying HVAEs as discretizations of multi-resolution diffusion processes.
result HVAEs learn a time representation allowing for improved parameter efficiency through weight-sharing.
Faces of quasi-arithmetic Coxeter polytopes are also quasi-arithmetic.
problem Characterizing faces of quasi-arithmetic Coxeter polytopes.
method Proof of quasi-arithmetic property of faces and sufficient condition for arithmetic faces.
result Lower-dimensional faces of quasi-arithmetic Coxeter polytopes are quasi-arithmetic.
In this article, we investigate when the set of primitive geodesic lengths on a Riemannian manifold have arbitrarily long arithmetic progressions. We prove that in the space of negatively curved metrics, a metric having such arithmetic progressions is quite rare. We introduce almost arithmetic progressions, a coarsific…
XceptionTime improves hand gesture recognition accuracy using novel deep learning.
problem Improving hand gesture recognition from sparse sEMG signals.
method Depthwise separable convolutions, adaptive pooling, non-linear normalization.
result Significantly improved accuracy (5.71% improvement) in hand gesture recognition.
Develops arithmetic PDE geometry concepts like curvature and cohomology.
problem Creating a geometry framework for arithmetic PDEs.
method Introducing arithmetic analogues of Levi-Civita and Chern connections, then developing curvature and characteristic classes.
result Arithmetic analogues of curvature and characteristic classes have been developed.
New geometric invariant limits the number of semi-arithmetic groups.
problem Understanding the structure of semi-arithmetic Fuchsian groups.
method Introducing a new geometric invariant called stretch and using the arithmetic Margulis lemma.
result There exist only finitely many conjugacy classes of semi-arithmetic groups with bounded arithmetic dimension, stretch, and coarea.
Course on arithmetic lattices at EPFL.
problem Understanding arithmetic lattices.
method Introductory course on arithmetic lattices.
result Introduction to arithmetic lattices.
Hybrid subgroups found in non-arithmetic PU(2,1) lattices.
problem Exploring hybrid subgroups in non-arithmetic PU(2,1) lattices.
method Exploring hybrid subgroups of certain non-arithmetic lattices in PU(2,1). Showing that Mostow's lattices are virtually hybrids and some are hybrids of two non-commensurable arithmetic lattices in PU(1,1).
result Mostow's lattices are virtually hybrids and some are hybrids of two non-commensurable arithmetic lattices in PU(1,1).
Paper shows non-arithmetic surface with unique geometric property.
problem Non-arithmetic surfaces with unique geometric properties.
method Example of a non-arithmetic surface with marked length variety rigidity.
result Found a non-arithmetic surface with marked length variety rigidity.
New classification of hyperbolic Coxeter prisms.
problem Classifying hyperbolic Coxeter prisms.
method Determine which prisms are quasi-arithmetic or arithmetic.
result New insights into commensurability and systoles of associated orbifolds.
Arithmetic Dijkgraaf-Witten theory constructs analogues in Chern-Simons TQFT.
problem Developing arithmetic analogues in Chern-Simons TQFT.
method Constructing arithmetic analogues of Chern-Simons 1-cocycle, prequantization bundle, and Chern-Simons functional.
result Decomposition and gluing formulas for arithmetic Chern-Simons invariants and arithmetic Dijkgraaf-Witten partition functions.
In this article, we prove that every arithmetic locally symmetric orbifold of classical type without Euclidean or compact factors has arbitrarily long arithmetic progressions in its primitive length spectrum. Moreover, we show the stronger property that every primitive length occurs in arbitrarily long arithmetic progr…
Improves text-dependent speaker verification using neural network supervectors and AUC optimization.
problem Enhance performance in text-dependent speaker verification systems.
method Proposes a supervector generation method and AUC optimization for neural networks.
result Improves system performance through novel alignment techniques and AUC optimization.
New method constructs non-arithmetic hyperbolic orbifolds from complex arithmetic ball quotients.
problem Creating non-arithmetic lattices in projective orthogonal groups.
method Using anti-holomorphic involutions on complex arithmetic ball quotients, gluing fixed loci along geodesic subspaces.
result Explicit calculation of the volume of constructed non-arithmetic orbifolds.
We show that the non-arithmetic lattices in PO(n,1) of Belolipetsky and Thomson (2011), obtained as fundamental groups of closed hyperbolic manifolds with short systole, are quasi-arithmetic in the sense of Vinberg, and, by contrast, the well-known non-arithmetic lattices of Gromov and Piatetski-Shapiro are not quasi-a…
The paper explores subspaces in hyperbolic lattices and their arithmetic properties.
problem Arithmeticity criterion for hyperbolic lattices and suborbifolds.
method Analysis of totally geodesic suborbifolds and Vinberg's commensurability invariants.
result Arithmeticity of hyperbolic orbifolds is linked to the existence of infinitely many fc-subspaces.
Define an arithmetic variety to be the quotient of a bounded symmetric domain by an arithmetic group. An arithmetic variety is algebraic, and the theorem in question states that when one applies an automorphism of the field of complex numbers to the coefficients of an arithmetic variety the resulting variety is again a…
Geodesics on modular surface yield arithmetic 3-manifolds.
problem Understanding arithmetic properties of modular surfaces.
method Constructing geodesics and analyzing their lifts.
result Complements of canonical lifts are arithmetic 3-manifolds.
New property identifies arithmetic lattices from nonuniform lattices.
problem Characterizing arithmetic lattices among nonuniform lattices.
method Introduced Bounded Clustering (B-C) property.
result B-C property uniquely identifies arithmetic lattices.
Arithmetic 3-manifolds with infinite geodesics are proven.
problem Arithmeticity of 3-manifolds with infinitely many geodesics.
method Analysis of totally geodesic surfaces in hyperbolic 3-manifolds.
result Arithmetic 3-manifolds with infinite geodesics are proven.
New proof shows maximal arithmetic groups are finite.
problem Finiteness of maximal arithmetic reflection groups.
method Arithmetic Margulis lemma without automorphic forms.
result Finiteness of maximal arithmetic reflection groups proven.
Develops arithmetic PDE geometry using Fermat quotients.
problem Creating an arithmetic PDE analogue of Riemannian geometry.
method Using Fermat quotients and Frobenius elements in the absolute Galois group of a p-adic field. result Existence and uniqueness of geodesics and connections proved.
We study the arithmeticity of the Couwenberg-Heckman-Looijenga lattices in PU(n,1), and show that they contain a non-arithmetic lattice in PU(3,1) which is not commensurable to the non-arithmetic Deligne-Mostow lattice in PU(3,1).
Study general hyperbolic gluings, proving quasi-arithmeticity of building blocks.
problem Proving quasi-arithmeticity of building blocks in hyperbolic gluings.
method Generalized gluings of hyperbolic orbifolds, proving quasi-arithmeticity.
result Building blocks of quasi-arithmetic gluings must also be quasi-arithmetic.
The study of systoles in arithmetic hyperbolic manifolds.
problem Understanding the systoles of arithmetic hyperbolic manifolds.
method Construction and analysis of arithmetic hyperbolic manifolds.
result Explicit bounds on volumes and systoles of arithmetic hyperbolic manifolds.
New research shows certain arithmetic lattices can't be LERF.
problem Determining if arithmetic lattices are LERF.
method Analyzing trialitarian arithmetic lattices in PSO7,1(R). result Trialitarian arithmetic lattices in PSO7,1(R) are not LERF. Arithmetic spaces' thin parts are negligible, impacting Betti numbers.
problem Understanding the structure of arithmetic locally symmetric spaces.
method Analyzing thin parts and deducing asymptotic results on Betti numbers.
result Arithmetic spaces' thin parts are negligible, impacting Betti numbers.
We apply G. Prasad's volume formula for the arithmetic quotients of semi-simple groups and Bruhat-Tits theory to study the covolumes of arithmetic subgroups of SO(1,n). As a result we prove that for any even dimension n there exists a unique compact arithmetic hyperbolic n-orbifold of the smallest volume. We give a for…
Develops Kleinian Sphere Packings and Bugs, proving their arithmetic origins.
problem Understanding sphere packings and their arithmetic origins in various dimensions.
method Introduces Kleinian Sphere Packings and Bugs, extending Arithmeticity Theorem.
result Kleinian packings and Bugs come from Q-arithmetic lattices of simplest type.
Conditions for flat manifolds as cusp cross-sections in arithmetic hyperbolic manifolds.
problem Determining when a flat manifold can be a cusp cross-section in arithmetic hyperbolic manifolds.
method Analyzing rational representations of holonomy groups and quasi-arithmetic manifolds.
result Conditions for a flat manifold to appear as a cusp cross-section in every commensurability class of arithmetic hyperbolic manifolds.
Study on Alexander polynomials in braids, linking number theory and topology.
problem Distribution of Alexander polynomials in specific families of braids.
method Exploration of arithmetic invariants and analogies with number theory.
result New directions in arithmetic topology and statistics.
Study finds bounds for systole length on arithmetic punctured spheres.
problem Finding the shortest essential curve on arithmetic punctured spheres.
method Correspondence between surfaces and planar triangulations to bound systole length.
result Arithmetic surfaces do not achieve maximal systole length for n=7,10,11. The study finds infinitely many semi-arithmetic Riemann surfaces with dense systoles and distinct invariant trace fields.
problem Existence and properties of semi-arithmetic Riemann surfaces.
method Combining number theory and hyperbolic geometry to prove existence and properties of semi-arithmetic Riemann surfaces.
result Existence of infinitely many semi-arithmetic Riemann surfaces with dense systoles and distinct invariant trace fields.
Neural Power Unit (NPU) learns arbitrary power functions on real numbers.
problem Neural Networks struggle with generalizing beyond seen data and arithmetic operations.
method Introduces Neural Power Unit (NPU) that operates on real numbers and learns arbitrary power functions.
result NPU outperforms competitors in accuracy and sparsity on arithmetic datasets and discovers governing equations from data.
We prove that any arithmetic hyperbolic n-manifold of simplest type can either be geodesically embedded into an arithmetic hyperbolic (n+1)-manifold or its universal mod 2 Abelian cover can.
The paper characterizes arithmetic metrics in coarsely geometric settings.
problem Characterizing arithmetic metrics in coarsely geometric settings.
method Using coarse-geometric commensurators and under the Hilbert-Smith conjecture.
result Positive answer in general and unconditional for specific cases.
We prove, under the assumption of the virtual fibration conjecture for arithmetic hyperbolic 3-manifolds, that all arithmetic lattices in O(n,1), n> 4, and different from 7, are non-coherent. We also establish noncoherence of uniform arithmetic lattices of the simplest type in SU(n,1), n> 1, and of uniform lattices in …
Study C-Fuchsian subgroups of non-arithmetic lattices.
problem Understand structure and fundamental domains of C-Fuchsian subgroups. method General procedure to analyze structure and show fundamental domains lie on a complex geodesic.
result Fundamental domains of C-Fuchsian subgroups lie on a complex geodesic homeomorphic to the unit disk. Explains how arithmetic manifolds solve geometric questions about systole and kissing number.
problem Geometric questions about systole and kissing number in hyperbolic manifolds.
method Use of arithmetic manifolds to solve geometric questions.
result Answers geometric questions about systole and kissing number for dimension 2 and higher dimensions.
We extend the Faltings modular heights of abelian varieties to general arithmetic varieties and show direct relations with the Kahler-Einstein geometry, the Minimal Model Program, heights of Bost and Zhang, and give some applications. Along the way, we propose arithmetic Yau-Tian-Donaldson conjecture, an equivalence of…
The paper studies arithmeticity and hidden symmetries in fully augmented pretzel link complements.
problem Determining arithmeticity and commensurability of fully augmented pretzel link complements.
method Careful analysis of geometry, including cusp shapes and totally geodesic surfaces.
result Construction of two infinite families of non-arithmetic fully augmented link complements.