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.
Extends branch and bound for probabilistic neural network verification.
New method diagnoses criticality in deep neural networks, improving performance.
Simplified neural network EFTs reveal a single critical condition.
Gaussian processes are ubiquitous in nature and engineering. A case in point is a class of neural networks in the infinite-width limit, whose priors correspond to Gaussian processes. Here we perturbatively extend this correspondence to finite-width neural networks, yielding non-Gaussian processes as priors. The methodo…
Bayesian methods have been successfully applied to sparsify weights of neural networks and to remove structure units from the networks, e. g. neurons. We apply and further develop this approach for gated recurrent architectures. Specifically, in addition to sparsification of individual weights and neurons, we propose t…
New neural network architectures use signed permutation representations for finite groups, improving performance.
Recently, a lot of techniques were developed to sparsify the weights of neural networks and to remove networks' structure units, e.g. neurons. We adjust the existing sparsification approaches to the gated recurrent architectures. Specifically, in addition to the sparsification of weights and neurons, we propose sparsif…
Training avoids edge of stability by aligning Jacobian matrices.
LCW reduces activation shift in neural networks, improving training efficiency and generalization.
REPAIR mitigates variance collapse to enable linear interpolation between SGD solutions.
Paper analyzes infinite-width attention layers using Tensor Programs.
Adaptive kernels from neural networks improve model performance.
SPlit optimizes dataset splitting for better model performance.
The paper extends keenness concept to bridge splittings and finds conditions for existence.
Non-split almost complex supermanifolds and non-split Riemannian supermanifolds are studied. The first obstacle for a splitting is parametrized by group orbits on an infinite dimensional vector space. Further it is shown that non-split structures appear in the first case as deformations of a split reduction and in the …
Study flippable Heegaard splittings in Seifert fibered spaces.
We study the self-dual Yang-Mills equations in split signature. We give a special solution, called the basic split instanton, and describe the ADHM construction in the split signature. Moreover a split version of t'Hooft ansatz is described.
Paper proposes a novel SVM method for creating survival trees.
New methods improve prediction regions for high-dimensional data.
New spheres can split a 4D link in ways not possible in 3D.
This paper studies properties of weak reducing pairs in critical Heegaard splittings.
We show that if a split link is obtained from a split link in by -Dehn surgery along a trivial knot , then the link is splittable. That is to say, it is impossible to obtain a split link from a split link via a non-trivial twisting. As its corollary, we completely determine when a trivial li…
New methods convert complex link presentations to simpler, recognizable forms.
The splitting number of a link is the minimal number of crossing changes between different components required, on any diagram, to convert it to a split link. We introduce new techniques to compute the splitting number, involving covering links and Alexander invariants. As an application, we completely determine the sp…
Deep networks with orthogonal weights show stable fluctuations, improving generalization and training speed.
New proof of Lorentzian splitting theorems using elliptic operators.
Little is known on the classification of Heegaard splittings for hyperbolic 3-manifolds. Although Kobayashi gave a complete classification of Heegaard splittings for the exteriors of 2-bridge knots, our knowledge of other classes is extremely limited. In particular, there are very few hyperbolic manifolds that are know…
New proof of Giroux Correspondence for tight contact 3-manifolds.
Let M_1 and M_2 be compact, orientable 3-manifolds, and M the manifold obtained by gluing some component F of \bdy M_1 to some component of \bdy M_2 by a homeomorphism φ. We show that when φis "sufficiently complicated" then (1) the amalgamation of low genus, unstabilized, boundary-unstabilized Heegaard splittings of M…
Minimal splitting factors help study scalar curvature constraints.
Non-isotopic Heegaard splittings of non-minimal genus were known previously only for very special 3-manifolds. We show in this paper that they are in fact a wide spread phenomenon in 3-manifold theory: We exhibit a large class of knots and manifolds obtained by Dehn surgery on these knots which admit such splittings. M…
Introduces nonlinear splittings on fibre bundles for generalizing connections.
We define a notion of Hempel distance for one-sided Heegaard splittings and show that the existence of alternate surfaces restricts distance for one-sided splittings in a manner similar to Hartshorn's and Scharlemann-Tomova's results for two-sided splittings. We also show that every geometrically compressible one-sided…
New method escapes local optima in neural architecture optimization.
We explicitly compute the lower algebraic K-theory of the split three-dimensional crystallographic groups; i.e., the groups G that act properly and cocompactly on three-dimensional Euclidean space by isometries, such that the natural map from G to O(3) is a split injection onto its image. There are 73 split three-dimen…
We describe an example of a closed orientable 3-manifold with distinct distance three genus two Heegaard splittings. This demonstrates that the constructions of alternate genus two Heegaard splittings of closed orientable 3-manifolds described by Rubinstein and Scharlemann in their 1998 paper Genus Two Heegaard Splitti…
Casson and Gordon gave the rectangle condition for strong irreducibility of Heegaard splittings [1]. We give a parity condition for irreducibility of Heegaard splittings of irreducible manifolds. As an application, we give examples of non-stabilized Heegaard splittings by doing a single Dehn twist.
Using basic properties of one-sided Heegaard splittings, a direct proof that geometrically compressible one-sided splittings of RP^3 are stabilised is given. The argument is modelled on that used by Waldhausen to show that two-sided splittings of S^3 are standard.
New approach connects stochastic gradient descent to ODE splitting schemes.
Let M be a totally orientable graph manifold with characteristic submanifold T and let M = V cup_S W be a Heegaard splitting. We prove that S is standard. In particular, S is the amalgamation of strongly irreducible Heegaard splittings. The splitting surfaces S_i of these strongly irreducible Heegaard splittings have t…
The splitting number of a link is the minimum number of crossing changes between distinct components that is required to convert the link into a split link. We provide a bound on the splitting number in terms of the four-genus of related knots.
Extend Kauffman bracket skein module to homology theory using Heegaard splittings
A new method for kernel tests without data splitting increases power.
This paper studies Heegaard splittings of surface bundles via the curve complex of the fibre. The translation distance of the monodromy is the smallest distance it moves any vertex of the curve complex. We prove that the translation distance is bounded above in terms of the genus of any strongly irreducible Heegaard sp…
We show that if a Heegaard splitting is obtained by gluing a splitting of Hempel distance at least 4 and the genus-1 splitting of , then the Goeritz group of the splitting is finitely generated. To show this, we first provide a sufficient condition for a full subcomplex of the arc complex for a compact …
Twinning splits data into fast, statistically similar sets.
We construct families of manifolds that have pairs of genus Heegaard splittings that must be stabilized roughly times to become equivalent. We also show that when two unstabilized, boundary-unstabilized Heegaard splittings are amalgamated by a "sufficiently complicated" map, the resulting splitting is unstabili…
A Heegaard splitting which admits a unique pair of disjoint compression disks on distinct sides is said to be keen weakly reducible. This paper provides an construction of keen weakly reducible Heegaard splittings of arbitrary genus except 2. Furthermore, critical Heegaard splittings may yield if we change some conditi…