When is a closed, orientable surface with genus , we show that the automorphism group of the compression body graph is the mapping class group. Here, vertices are compression bodies with exterior boundary , and edges connect pairs of compression bodies where one contains the other.
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,657 papers · 148 categories
Trend · papers per month
48 results for “compressible boundary”
New adapted renormalized volume for hyperbolic 3-manifolds with compressible boundary.
problem Analyzing convex co-compact hyperbolic 3-manifolds with compressible boundaries.
method Defining and analyzing a new version of the renormalized volume.
result The adapted renormalized volume is bounded and has properties analogous to the classical renormalized volume.
If M is a manifold with compressible boundary, we analyze essential disks in M, as well as incompressible, but not necessarily boundary incompressible, surfaces in M. We are most interested in the case where M is a handlebody or compression body. The analysis depends on a new normal surface theory. We hope the normal s…
We analyze the mapping class group of extendible automorphisms of the exterior boundary W of a compression body of dimension 3 or 4, which extend over the compression body (Q,V), where V is the interior boundary. Those that extend as automorphisms of (Q,V) rel V are called discrepant automorphisms, forming the mapping …
New proof of Laudenbach and Poénaru's theorem on 4D 1-handlebodies.
problem Proving diffeomorphisms extend to 4D 1-handlebodies and compression bodies.
method Classification of Heegaard splittings and Cerf's theorem on 3-ball diffeomorphisms.
result Every diffeomorphism of the positive boundary extends to the whole compression body.
Neural networks compress uninformative input directions, improving test error.
problem Data lie in a high-dimensional space but labels vary along a lower-dimensional manifold.
method One-hidden layer network trained with gradient descent, analyzing weight evolution and compression.
result Compression factor λ ∼ √p improves test error, with β Feature > β Lazy.
Let M be a nontrivial compression body without toroidal boundary components. We study the dynamics of the group of outer automorphisms of the fundamental group of M on the PSL(2,C)-character variety of M.
This paper provides a theoretical justification of the superior classification performance of deep rectifier networks over shallow rectifier networks from the geometrical perspective of piecewise linear (PWL) classifier boundaries. We show that, for a given threshold on the approximation error, the required number of b…
We study the problem of inviscid slightly compressible fluids in a bounded domain. We find a unique solution to the initial-boundary value problem and show that it is near the analogous solution for an incompressible fluid provided the initial conditions for the two problems are close. In particular, the divergence of …
We consider hyperbolic structures on the compression body C with genus 2 positive boundary and genus 1 negative boundary. Note that C deformation retracts to the union of the torus boundary and a single arc with its endpoints on the torus. We call this arc the core tunnel of C. We conjecture that, in any geometrically …
Extends characterization of -pairs with aspherical boundaries to those with spherical boundaries.
problem Characterizing fundamental triples of -pairs with boundary components of different types.
method Extends Turaev and Bleile's work by relaxing the -injectivity hypothesis and considering pairs with spherical boundary components.
result Characterization of fundamental triples for -pairs with spherical boundary components and .
We show that a pseudo-Anosov map on a boundary component of an irreducible 3-manifold has a power that partially extends to the interior if and only if its (un)stable lamination is a projective limit of meridians. The proof is through 3-dimensional hyperbolic geometry, and involves an investigation of algebraic limits …
Data compression is a popular technique for improving the efficiency of data processing workloads such as SQL queries and more recently, machine learning (ML) with classical batch gradient methods. But the efficacy of such ideas for mini-batch stochastic gradient descent (MGD), arguably the workhorse algorithm of moder…
We develop an explicit and tractable representation of a twist-grain-boundary phase of a smectic A liquid crystal. This allows us to calculate the interaction energy between grain boundaries and the relative contributions from the bending and compression deformations. We discuss the special stability of the 90 degree g…
Suppose N is a compressible boundary component of a compact orientable irreducible 3-manifold M and Q is an orientable properly embedded essential surface in M in which each component is incident to N and no component is a disk. Let VN and QN denote respectively the sets of vertices in the curve complex for N represent…
A recent paper (\cite{BJM}) by Biringer, Johnson, and Minsky prove that any pseudo-Anosov whose stable lamination is the limit of disks in a compression body has a power which extends over some non-trivial minimal compression body. This paper presents an alternative proof of their theorem, using techniques of Long and …
Let M be a hyperbolizable, nontrivial compression body without toroidal boundary components. In this paper, we characterize which discrete and faithful representations of the fundamental group of M into PSL(2,C) are separable-stable. The set of separable-stable representations forms a domain of discontinuity for the ac…
Various structural properties are developed for non-orientable surfaces in link spaces. The Möbius band tree is described to represent genus growth of one-sided surfaces in solid tori. The structure of the Tree allows various insights into the change of genus under boundary slope, which are not possible using the exist…
Port-Hamiltonian Modeling of Ideal Fluid Flow: Part II. Compressible and Incompressible Flowphysics.flu-dyn
Paper extends port-Hamiltonian model to include internal energy for compressible and incompressible flow.
problem Modeling fluid flow dynamics with internal energy and constraints.
method Derived port-Hamiltonian model using interconnection maps and added internal energy and constraint forces.
result Model accurately represents both compressible and incompressible fluid flow.
CTT compresses samples to test distributions near-linearly, outperforming existing methods.
problem Efficiently testing distributions with high power and near-linear runtime.
method Sample compression followed by permutation testing.
result CTT achieves near-linear runtime while maintaining high statistical power.
We study the existence of incompressible embeddings of surfaces into the genus two handlebody. We show that for every compact surface with boundary, orientable or not, there is an incompressible embedding of the surface into the genus two handlebody. In the orientable case the embedding can be either separating or non-…
We consider a compact orientable hyperbolic 3-manifold with a compressible boundary. Suppose that we are given a sequence of geometrically finite hyperbolic metrics whose conformal boundary structures at infinity diverge to a projective lamination. We prove that if this limit projective lamination is doubly incompressi…
Solving Inverse Problems with Conditional-GAN Prior via Fast Network-Projected Gradient Descentcs.LG
Faster reconstruction of compressed signals using conditional GAN and NPGD.
problem Recovering compressed signals from measurements.
method Network-based projected gradient descent (NPGD) combined with measurement-conditional generative adversarial networks (GANs/BEGANs).
result Significant speed-up in reconstruction (up to 140-175 times faster).
In this article we show that for any given Riemann surface of genus , we can bound (from above) the renormalized volume of a (hyperbolic) Schottky group with boundary at infinity conformal to in terms of the genus and the combined extremal lengths on of disjoint, non-homotopic, simple closed comp…
We study eta-invariants on odd dimensional manifolds with boundary. The dependence on boundary conditions is best summarized by viewing the (exponentiated) eta-invariant as an element of the (inverse) determinant line of the boundary. We prove a gluing law and a variation formula for this invariant. This yields a new, …
Paper develops a new fluid flow model with energy exchange through boundaries.
problem Modeling ideal fluid flow with energy exchange through boundaries.
method Port-Hamiltonian model based on Stokes-Dirac structures.
result Wide range of fluid dynamical systems can be achieved with this model.
We find boundaries of Borel-Serre compactifications of locally symmetric spaces, for which any filling is incompressible. We prove this result by showing that these boundaries have small singular models and using these models to obstruct compressions. We also show that small singular models of boundaries obstruct …
Given a set of simplifying moves on 3-manifolds, we apply them to a given 3-manifold M as long as possible. What we get is a root of M. For us, it makes sense to consider three types of moves: compressions along 2-spheres, proper discs and proper annuli having boundary circles in different components of the boundary of…
FedSGM tackles constrained federated learning with unified framework.
problem Functional constraints, communication bottlenecks, local updates, and partial client participation in federated learning.
method Unified framework based on switching gradient method, incorporating bi-directional error feedback, and soft switching for stability.
result Achieves convergence rate with high-probability bounds decoupling from sampling noise.
We prove that if is a non-trivial alternating link embedded (without crossings) in a closed surface , then has a compressing disk whose boundary intersects in no more than two points. Moreover, whenever the surface is incompressible and -incompressible in the link exterior, it can be…
We show that bordered Heegaard Floer homology detects incompressible surfaces and bordered-sutured Floer homology detects partly boundary parallel tangles and bridges, in natural ways. For example, there is a bimodule Lambda so that the tensor product of CFD(Y) and Lambda is Hom-orthogonal to CFD(Y) if and only if the …
We give the rectangle condition for strong irreducibility of Heegaard splittings of -manifolds with non-empty boundary. We apply this to a generalized Heegaard splitting of a -fold covering of branched along a link. The condition implies that any thin meridional level surface in the link complement is incom…
BMRS offers a Bayesian approach to structured pruning of neural networks.
problem Overparameterized neural networks lead to high compute costs.
method Bayesian Model Reduction for Structured pruning (BMRS) based on two recent methods: Bayesian structured pruning with multiplicative noise and Bayesian model reduction.
result BMRS yields high compression rates and accuracy without tuning thresholds.
Study shows nonextendibility of warped spacelike singularities in specific spacetimes.
problem Nonextendibility of warped spacelike singularities in specific spacetimes.
method Establishes a local obstruction through integrability conditions and radial compression.
result Imply -inextendibility for the one-horizon Birmingham-Kottler family.
Study decision boundaries using heat diffusion and probabilistic techniques.
problem Understanding the geometry of decision boundaries in machine learning.
method Using Brownian motion and probabilistic techniques to analyze decision boundaries.
result Decision boundaries exhibit persistent 'wiggly and fuzzy' regions, even under adversarial attacks.
Let N be a complete hyperbolic 3-manifold that is an algebraic limit of geometrically finite hyperbolic 3-manifolds. We show N is homeomorphic to the interior of a compact 3-manifold, or tame, if one of the following conditions holds: (1) N has non-empty conformal boundary, (2) N is not homotopy equivalent to a compres…
Flexible framework compresses models using LC algorithm.
problem Efficiently compressing neural networks for resource constraints.
method Decouples learning and compression steps with alternating L and C phases.
result Compressed models maintain performance and accuracy.
Reduces multiclass and regression compression schemes to binary ones.
problem Developing efficient learning algorithms for multiclass and regression problems.
method Reduces sample compression schemes for binary classes to multiclass and regression settings.
result Establishes new compression schemes for multiclass and regression problems.
Proposes a link between randomness and compression in deep learning.
problem Improving efficiency in deep learning training.
method Introduces a novel tomographic compression framework called Dual Tomographic Compression (DTC).
result Demonstrates high correlation between learning performance and Gibbs entropy over compression ratios.
Paper introduces a new adaptive gradient method with gradient compression for distributed training.
problem Communication overhead in distributed machine learning systems.
method Adaptive gradient method with gradient compression, scalable system BytePS-Compress.
result Convergence rate of for non-convex problems.
Galen algorithm compresses neural networks for specific hardware with reduced latency.
problem Finding optimal compression policies for neural networks on specific hardware.
method Reinforcement learning using pruning and quantization to optimize inference latency.
result Compressed ResNet18 for ARM processor reduced inference latency by 80%.
The Compressibility of Minimal Lattice Knotscond-mat.soft
The (isothermic) compressibility of lattice knots can be examined as a model of the effects of topology and geometry on the compressibility of ring polymers. In this paper, the compressibility of minimal length lattice knots in the simple cubic, face centered cubic and body centered cubic lattices are determined. Our r…
Neural Normalized Compression Distance and the Disconnect Between Compression and Classificationcs.LG
Neural NCD reveals LLMs don't compress well for classification.
problem The disconnect between compression and classification in neural networks.
method Developed Neural NCD to compare LLMs to classic algorithms, finding classification accuracy not correlated with compression rate.
result Classification accuracy is not predictable by compression rate alone, challenging current understanding.
BDC compresses both sample size and dimensionality of large datasets.
problem Large datasets in both sample size and dimensionality.
method Two-stage framework using Decoded MMD, Reconstruction MMD, and Encoded MMD.
result BDC achieves comparable or superior performance with lower cost and higher compression rates.
We propose a simple but efficient method termed Guided Learning for weakly-labeled semi-supervised sound event detection (SED). There are two sub-targets implied in weakly-labeled SED: audio tagging and boundary detection. Instead of designing a single model by considering a trade-off between the two sub-targets, we de…
DoCoFL compresses model updates for cross-device federated learning.
problem Downlink compression for cross-device federated learning where clients may appear only once.
method Proposes DoCoFL framework for downlink compression in cross-device federated learning.
result Significant bi-directional bandwidth reduction with competitive accuracy.
Compressing neural nets is an active research problem, given the large size of state-of-the-art nets for tasks such as object recognition, and the computational limits imposed by mobile devices. We give a general formulation of model compression as constrained optimization. This includes many types of compression: quan…
Study explores various KD methods to improve model performance.
problem Improving model performance with limited data.
method Nine different KD methods covering various aspects of the teacher.
result KD framework provides generalization gains over standard training.