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.
Machine learning simplifies spectroscopy equipment, making it cheaper and easier.
A branched covering surface-knot over an oriented surface-knot is a surface-knot in the form of a branched covering over . A branched covering surface-knot over is presented by a graph called a chart on a surface diagram of . For a branched covering surface-knot, an addition of 1-handles equipped with cha…
This note has an experimental nature and contains no new theorems. We introduce certain moves for classical knot diagrams that for all the very many examples we have tested them on give a monotonic complete simplification. A complete simplification of a knot diagram D is a sequence of moves that transform D into a diag…
We establish a full principle (close, relative, parametric) for the simplification of singularities of Lagrangian and Legendrian fronts. More precisely, we prove that if there is no homotopy theoretic obstruction to simplifying the singularities of tangency of a Lagrangian or Legendrian submanifold with respe…
We prove that any arc-presentation of the unknot admits a monotonic simplification by elementary moves; this yields a simple algorithm for recognizing the unknot. We obtain similar results for split links and composite links.
Natural gradient simplification for deep learning networks.
It is generally accepted that all models are wrong -- the difficulty is determining which are useful. Here, a useful model is considered as one that is capable of combining data and expert knowledge, through an inversion or calibration process, to adequately characterize the uncertainty in predictions of interest. This…
In the present paper a criteria for a rectangular diagram to admit a simplification is given in terms of Legendrian knots. It is shown that there are two types of simplifications which are mutually independent in a sense. A new proof of the monotonic simplification theorem for the unknot is given. It is shown that a mi…
Recent work on stable minimal hypersurface singularities.
This paper simplifies deep ReLU networks into local linear models for better interpretability.
Simplifies residual flows to make flow-based modeling more practical.
The second author previously discussed how classical complexity separation conjectures, we call them "axioms", have implications in three manifold topology: polynomial length stings of operations which preserve certain Jones polynomial evaluations cannot produce exponential simplifications of link diagrams. In this pap…
In a recent work "Arc-presentation of links: Monotonic simplification" Ivan Dynnikov showed that each rectangular diagram of the unknot, composite link, or split link can be monotonically simplified into a trivial, composite, or split diagram, respectively. The following natural question arises: Is it always possible t…
New method simplifies data analysis.
AST provides a method to validate safe autonomy without unsafe simplifications.
NeuRewriter learns to choose and rewrite heuristics in combinatorial problems.
Two smooth manifolds M and N are called R-diffeomorphic if their product with the real line are diffeomorphic. We consider the following simplification problem: does R-diffeomorphism imply diffeomorphism or homeomorphism? For compact manifolds, analysis of this problem relies on some of the main achievements of the the…
Simplifies RF predictions by focusing on a subset of nearest neighbors.
Stochastic gradient descent (SGD) still is the workhorse for many practical problems. However, it converges slow, and can be difficult to tune. It is possible to precondition SGD to accelerate its convergence remarkably. But many attempts in this direction either aim at solving specialized problems, or result in signif…
We define a new combinatorial complex computing the hat version of link Floer homology over Z/2Z, which turns out to be significantly smaller than the Manolescu-Ozsvath-Sarkar one.
Both classical and virtual knots arise as formal Gauss diagrams modulo some abstract moves corresponding to Reidemeister moves. If we forget about both over/under crossings structure and writhe numbers of knots modulo the same Reidemeister moves, we get a dramatic simplification of virtual knots, which kills all classi…
Abstract: From complex financial models to simpler Hamilton-Jacobi equations.
We propose a simple yet effective technique to simplify the training and the resulting model of neural networks. In back propagation, only a small subset of the full gradient is computed to update the model parameters. The gradient vectors are sparsified in such a way that only the top-k elements (in terms of magnitude…
We give a new algorithm to simplify a given triangulation with respect to a given curve. The simplification uses flips together with powers of Dehn twists in order to complete in polynomial time in the bit-size of the curve.
Eliashberg simplifies singularities in geometry.
We describe a simplification of Donaldson's arguments for the construction of symplectic hypersurfaces or Lefschetz pencils that makes it possible to avoid any reference to Yomdin's work on the complexity of real algebraic sets.
Simplified Khovanov-Rozansky calculus for bipartite knots.
The traditional Sznajd model, as well as its Ochrombel simplification for opinion spreading, are applied to marketing with the help of advertising. The larger the lattice is the smaller is the amount of advertising needed to convince the whole market
Morphology in unbalanced languages remains a big challenge in the context of machine translation. In this paper, we propose to de-couple machine translation from morphology generation in order to better deal with the problem. We investigate the morphology simplification with a reasonable trade-off between expected gain…
Paper proposes a classifier using fuzzy sets for data simplification.
We present a simplification of Neumann's formula for the universal Cheeger-Chern-Simons class of the second Chern polynomial. Our approach is completely algebraic, and the final formula can be applied directly on a homology class in the bar complex.
This is a survey of some of the recent developments in the theory of complex Monge-Ampere equations. The topics discussed include refinements and simplifications of classical a priori estimates, methods from pluripotential theory, variational methods for big cohomology classes, semiclassical constructions of solutions …
We give a proof that the geometric K-homology theory for finite CW-complexes defined by Baum and Douglas is isomorphic to Kasparov's K-homology. The proof is a simplification of more elaborate arguments which deal with the geometric formulation of equivariant K-homology theory.
A method to improve LLMs by automating the construction of a mixture of expert prompts.
Simplified proofs and new distributions on anti-quasi-Sasakian manifolds.
The purpose of this short note is to relate a representation formula due to the Author and P. Romon for Lagrangian surfaces (see math.DG/0009202) to a more general Weierstrass representation type formula found by Konopelchenko for surfaces in 4-dimensional space (see math.DG/9807129). Simplifications are pointed out.
Deep RL predicts equipment maintenance from sensor data.
Simplified proof of gluing formula for analytic torsion forms.
Simplified presentations for non-orientable surface mapping class groups.
New method calculates credit exposures for complex options efficiently.
We describe the Polyak-Viro arrow diagram formulas for the coefficients of the Conway polynomial. As a consequence, we obtain the Conway polynomial as a state sum over some subsets of the crossings of the knot diagram. It turns out to be a simplification of a special case of Jaeger's state model for the HOMFLY polynomi…
The paper examines how depth and width affect local minima in neural networks.
Explains partial duality for ribbon graphs in simple terms.
This is an exposition of a proof of the Madsen-Weiss Theorem, which asserts that the homology of mapping class groups of surfaces, in a stable dimension range, is isomorphic to the homology of a certain infinite loopspace that arises naturally when one applies the "scanning method". The proof given here utilizes simpli…
Unified geometric flows improve deep learning efficiency and simplify neural network topologies.
AR algorithm simplifies backpropagation with improved scalability and biological plausibility.
A new, simplified form of 10D supergravity action is derived up to all fermion orders.
In this paper, a survey of the recent results about the classification of the connected holonomy groups of the Lorentzian manifolds is given. A simplification of the construction of the Lorentzian metrics with all possible connected holonomy groups is obtained. As the applications, the Einstein equation, Lorentzian man…