New training method improves model performance across various tasks.
problem Training deep neural networks using only the ground-truth class information.
method Maximizes likelihood of ground-truth classes while neutralizing complement classes.
result Training with both primary and complement objectives improves model performance across multiple tasks.
The paper connects quivers to knot complements and studies their BPS states and 3d N=2 theories.
problem Understanding the relationship between quivers and knot complements.
method Assigning quivers to knot complements and exploring their physical interpretation.
result Proposed a physical interpretation of quivers in terms of BPS states and 3d N=2 theories.
The complement of a complex hyperplane arrangement is known to be homotopic to a minimal CW complex. There are several approaches to the minimality. In this paper, we restrict our attention to real two dimensional cases, and introduce the "dual" objects so called minimal stratifications. The strata are explicitly descr…
Let g be a Leibniz algebra and E a vector space containing g as a subspace. All Leibniz algebra structures on E containing g as a subalgebra are explicitly described and classified by two non-abelian cohomological type objects: ${\mathcal H}{\mathcal L}^{2}_{\mathfrak{g}} \, (…
Spatial statisticians and quantitative investors use the same mathematical object: a Schur complement, damped by one parameter.
problem The Schur complement is used in both spatial modeling and portfolio allocation, but the parameters are different.
method The Schur complement is interpreted as reliability shrinkage of a conditional Gaussian.
result The Schur complement is the same in both applications.
The paper studies posets from decompositions in symmetric monoidal categories.
problem Understanding posets from decompositions in symmetric monoidal categories.
method Defining decompositions and partial decompositions, complexes of frames, partial bases, and ordered versions.
result Unified approach to combinatorics and homotopy type of posets and complexes.
A new gradient boosting method improves interpretability of probabilistic models.
problem Learning interpretable yet accurate probabilistic models with limited rule complexity.
method A new objective function that measures the angle between risk gradient and condition output vector projection.
result Significantly improves comprehensibility/accuracy trade-off of fitted ensemble.
A database of objects discovered in houses in the Roman city of Pompeii provides a unique view of ordinary life in an ancient city. Experts have used this collection to study the structure of Roman households, exploring the distribution and variability of tasks in architectural spaces, but such approaches are necessari…
We consider braids on m+n strands, such that the first m strands are trivially fixed. We denote the set of all such braids by Bm,n. Via concatenation Bm,n acquires a group structure. The objective of this paper is to find a presentation for Bm,n using the structure of its corresponding pure braid sub…
Consider a number of workers running SGD independently on the same pool of data and averaging the models every once in a while -- a common but not well understood practice. We study model averaging as a variance-reducing mechanism and describe two ways in which the frequency of averaging affects convergence. For convex…
Optimizes functions on manifolds using Gaussian processes and graph models.
problem Optimizing functions on unknown manifolds with limited data.
method Graph Gaussian process surrogate model for sequential optimization.
result Established regret bounds for the proposed algorithm.
Within the unmanageably large class of nonconvex optimization, we consider the rich subclass of nonsmooth problems that have composite objectives---this already includes the extensively studied convex, composite objective problems as a special case. For this subclass, we introduce a powerful, new framework that permits…
Soft geometric bias improves physical dynamics predictions.
problem Learning physical dynamics with exact group equivariance can degrade performance.
method Object-centric world models using geometric algebra neural networks.
result Soft geometric inductive bias leads to better physical fidelity predictions.
Given a heterogeneous time-series sample, the objective is to find points in time (called change points) where the probability distribution generating the data has changed. The data are assumed to have been generated by arbitrary unknown stationary ergodic distributions. No modelling, independence or mixing assumptions…
Researchers create a Fukaya category for knot complements using specific metrics.
problem Constructing a Fukaya category for knot complements.
method Using cylindrical adjustments and wrapping, they construct the Fukaya category and its wrapped Floer complex.
result The quasi-equivalence and quasi-isomorphism classes are independent of the choice of metrics.
This paper's theme is the relation between several classical and well-known objects: triangle Fuchsian groups, quasi-homogeneous singularities of plane curves, torus knot complements in the 3-sphere. Torus knots are the only nontrivial knots whose complements admit transitive Lie group actions. In fact S^3\K_{p,q} is d…
The paper studies symmetries and hidden symmetries of twisted knot complements.
problem Analyzing symmetries and hidden symmetries of (ε,dL)-twisted knot complements. method Analysis via long Dehn fillings on fully augmented links complements.
result No hidden symmetries in (ε,dL)-twisted knot complements, implying at most two commensurability classes. The paper proves limitations on hyperbolic knot complements with hidden symmetries.
problem Identifying hyperbolic knot complements with hidden symmetries.
method Obstructions to infinitely many fillings producing knot complements with hidden symmetries.
result The figure-eight knot complement is the only hyperbolic knot complement with hidden symmetries.
We show that a hyperbolic 2-bridge knot complement is the unique knot complement in its commensurability class. We also discuss constructions of commensurable hyperbolic knot complements and put forth a conjecture on the number of hyperbolic knot complements in a commensurability class.
The paper classifies cusp types in hyperbolic knot complements.
problem Classifying cusp types in hyperbolic knot complements.
method Analyzing quotients of hyperbolic knot complements.
result All cusp types arise in the quotients of link complements.
CRAUM-Net improves salient object detection with context and uncertainty modeling.
problem Accurate salient object detection with precise boundary delineation.
method Contextual Recursive Attention with Uncertainty Modeling, multi-scale context aggregation, attention mechanisms, edge-aware decoder, Monte Carlo Dropout.
result Superior performance in producing accurate and reliable saliency maps.
Study shows most hyperbolic knot complements lack hidden symmetries.
problem Proving most knot complements lack hidden symmetries.
method Using rational functions on varieties associated to a link.
result Most knot complements lack hidden symmetries.
New algorithms identify Pareto optimal sets in multi-objective bandit problems.
problem Identifying Pareto optimal sets in multi-objective bandit problems.
method Empirical Gap Elimination (EGE) algorithms combining hardness estimation and elimination schemes.
result Two EGE algorithms have exponentially decaying error probabilities with budget.
Flat fully augmented links with homeomorphic complements are equivalent.
problem Determining equivalence of flat fully augmented links based on their complements.
method Careful analysis of totally geodesic surfaces and cusps in link complements and their behavior under homeomorphism.
result Complete classification of flat fully augmented link complements with multiple reflection surfaces and symmetries.
The complement of a non-separating planar graph contains a K_n minor.
problem Characterizing the structure of complements of planar graphs.
method Analyzing the structure of complements of non-separating planar graphs and using examples to illustrate hypotheses.
result The order 2n-3 is the lowest possible for a non-separating planar graph whose complement contains a K_n minor.
Upper and lower bounds for hyperbolic rod complements in 3-torus volumes.
problem Understanding geometric properties of hyperbolic rod complements in 3-torus.
method Provided upper and lower bounds for volumes in terms of rod parameters.
result Volume bounds for hyperbolic rod complements in 3-torus depend on rod parameters.
Knots in circle bundles are uniquely identified by their complements.
problem Determining knots in circle bundles based on their complements.
method Analyzing the complements of knots in orientable circle bundles over surfaces.
result Knots in circle bundles are determined by their complements.
We show that all two-bridge knot and link complements are virtually fibered. We also show that spherical Montesinos knot and link complements are virtually fibered. This is accomplished by showing that such knot complements are finitely covered by great circle link complements.
In this paper, we show that any non-arithmetic hyperbolic 2-bridge link complement admits no hidden symmetries. As a corollary, we conclude that a hyperbolic 2-bridge link complement cannot irregularly cover a hyperbolic 3-manifold. By combining this corollary with the work of Boileau and Weidmann, we obtain a ch…
Topology-enhanced loss improves 3D object reconstruction from 2D images.
problem Challenges in reconstructing 3D objects from 2D images, especially capturing shape information.
method Integrates multi-scale topological features into the reconstruction loss using cubical complexes and optimal transport distance.
result Topology-aware loss substantially improves 3D reconstruction quality.
This paper exhibits an infinite family of hyperbolic knot complements that have three knot complements in their respective commensurability classes.
Aitchison and Rubinstein constructed two knot complements that can be decomposed into two regular ideal dodecahedra. This paper shows that these knot complements are the only knot complements that decompose into n regular ideal dodecahedra, providing a partial solution to a conjecture of Neumann and Reid.
The study examines the topology of complements of polytopal skeletons.
problem Characterizing topological properties of polytopal complexes and their skeletons.
method Constructing a long exact sequence relating homologies of skeleton complements and links of faces.
result Characterizations of Cohen-Macaulay and Leray complexes, stacked balls, and neighbourly spheres in terms of skeleton complements.
Study on colored Jones polynomial and link complements.
problem Understanding the structure of link complements with arbitrary colors.
method Investigated the potential function of the colored Jones polynomial and established a relationship with hyperbolicity.
result Evidence supports the Chen-Yang conjecture on link complements.
Formula connects knot complements' invariants.
problem Understanding invariants of knot complements.
method Proposed a connect sum formula for two-variable series invariants.
result Numerical evidence supports the formula for various torus knots.
We give examples of non-fibered hyperbolic knot complements in homology spheres that are not commensurable to fibered knot complements in homology spheres. In fact, we give many examples of knot complements in homology spheres with the property that every commensurable knot complement in a homology sphere has non-monic…
Study Lagrangian Floer theory in smooth divisor complements.
problem Intersection Floer theory of Lagrangians in smooth divisor complements.
method Complete construction of Floer homology.
result Floer homology for Lagrangians in smooth divisor complements constructed.
New bounds on Heegaard distance for link complements in 3D space.
problem Finding bounds on Heegaard distance for link complements.
method Constructing specific links with given properties.
result Existence of links with specific Heegaard distances.
For graphs with 13 or more vertices, either the graph or its complement is intrinsically linked.
problem Identifying graphs with 13 or more vertices that are intrinsically linked or their complements.
method Analyzing properties of graphs and their complements to determine if either is intrinsically linked.
result For graphs with 13 or more vertices, either the graph or its complement is intrinsically linked.
Paper computes hyperbolic structure of Borromean rings complement.
problem Computing hyperbolic structures for link complements.
method Classical construction of Thurston's sense.
result Exact computation of hyperbolic structure for Borromean rings.
Preserves hyperbolicity in link complements with two moves.
problem Maintaining hyperbolicity in link complements.
method Chain move and switch move to preserve hyperbolicity.
result Preserves hyperbolicity in a substantial number of links.
The purpose of this note is to announce complete answers to the following questions. (1) For an essential simple loop on a 2-bridge sphere in a 2-bridge link complement, when is it null-homotopic in the link complement? (2) For two distinct essential simple loops on a 2-bridge sphere in a 2-bridge link complement, when…
New link types derived from old links.
problem Understanding the structure of modular links.
method Analyzing the complements of arithmetic modular links and comparing them to augmented chainlinks.
result Arithmetic modular links are homeomorphic to augmented chainlinks.
We show that every hyperbolic link complement contains closed quasi-Fuchsian surfaces. As a consequence, we obtain the result that on a hyperbolic link complement, if we remove from each cusp of the manifold a certain finite set of slopes, then all remaining Dehn fillings on the link complement yield manifolds with clo…
We prove that there are compact submanifolds of the 3-sphere whose interiors are not homeomorphic to any geometric limit of hyperbolic knot complements.
Study on the existence of Dirac complements for Dirac structures.
problem Existence of Dirac complements for Dirac structures.
method Cohomological techniques and Lie-theoretical methods.
result Non-existence of Dirac complements for certain Lie algebras.
Distillation improves simple models by approximating complex labels.
problem Why does distillation improve simple models?
method Statistical perspective on distillation, connecting to extreme multiclass retrieval.
result Distillation helps by approximating underlying class-probabilities, reducing bias and variance.
Complete classification of rod complements in 3-torus using topology.
problem Classifying rod complements in the 3-torus.
method Topological arguments.
result Complete classification of all rod complements in the 3-torus.