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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.

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48 results for simplified approach

The Min-Hashing approach to sketching has become an important tool in data analysis, information retrial, and classification. To apply it to real-valued datasets, the ICWS algorithm has become a seminal approach that is widely used, and provides state-of-the-art performance for this problem space. However, ICWS suffers…

2018-03-30abs ↗pdf ↗

Simplified optimization for structured matrices in deep learning.

problem Computational challenges in Riemannian submanifold optimization for structured symmetric positive-definite matrices.
method Proposed a generalized Riemannian normal coordinates that dynamically orthonormalizes the metric and converts the problem into an unconstrained Euclidean space problem.
result Simplified existing approaches for structured covariances and developed matrix-inverse-free 2nd-order optimizers for deep learning with low precision.

Paper studies simplified trisections and their equivalence classes.

problem Understanding right-left equivalence of simplified (2,0)(2, 0)-trisections.
method Analyzes simplified trisection diagrams and upper-triangular handle-slides.
result At least two simplified (2,0)(2, 0)-trisections can be right-left equivalent without being related by automorphisms or handle-slides.

Unified analysis simplifies Johnson-Lindenstrauss lemma for data reduction.

problem Efficiently reducing high-dimensional data while preserving geometry.
method Unified analysis of various JL constructions using probabilistic tools.
result First rigorous proof and extension of spherical construction's effectiveness.

In this paper, we present a deep neural network (DNN) training approach called the "DeepMimic" training method. Enormous amounts of data are available nowadays for training usage. Yet, only a tiny portion of these data is manually labeled, whereas almost all of the data are unlabeled. The training approach presented ut…

2019-11-24abs ↗pdf ↗

In this paper we continue our systematic analysis of the operatorial approach previously proposed in an economical context and we discuss a {\em mixed} toy model of a simplified stock market, i.e. a model in which the price of the shares is given as an input. We deduce the time evolution of the portfolio of the various…

2009-04-21abs ↗pdf ↗

The paper simplifies FLRW photon propagators using geometric embeddings.

problem Understanding Friedmann-Lemaître-Robertson-Walker (FLRW) spaces.
method Differential-geometric methods applied to FLRW spaces as submanifolds in \(\mathbb{R}^{n+2}\).
result New and simplified expressions for the photon propagator in four dimensions.

Deep learning using multi-layer neural networks (NNs) architecture manifests superb power in modern machine learning systems. The trained Deep Neural Networks (DNNs) are typically large. The question we would like to address is whether it is possible to simplify the NN during training process to achieve a reasonable pe…

2016-06-23abs ↗pdf ↗

A simplified trisection is a trisection map on a 4-manifold such that, in its critical value set, there is no double point and cusps only appear in triples on innermost fold circles. We give a necessary and sufficient condition for a 3-tuple of systems of simple closed curves in a surface to be a diagram of a simplifie…

2017-11-08abs ↗pdf ↗

Classifies 3-manifolds from simplified (2,0)-trisections of 4-manifolds.

problem Classifying 3-manifolds from simplified (2,0)-trisections of 4-manifolds.
method Classifies vertical 3-manifolds as preimages of arcs on the plane for simplified (2,0)-trisection maps.
result Each 6-tuple of vertical 3-manifolds determines the source 4-manifold uniquely up to orientation reversing diffeomorphisms.

Simplifies neural network models by explicitly enforcing constraints in Cartesian coordinates.

problem Learning dynamics of complex systems efficiently and accurately.
method Embedding systems into Cartesian coordinates and using Lagrange multipliers to enforce constraints.
result Explicitly enforcing constraints leads to a 100x improvement in accuracy and data efficiency.

In this note we sketch an initial tentative approach to funding costs analysis and management for contracts with bilateral counterparty risk in a simplified setting. We depart from the existing literature by analyzing the issue of funding costs and benefits under the assumption that the associated risks cannot be hedge…

2014-10-08abs ↗pdf ↗

Shapes of four dimensional spaces can be studied effectively via maps to standard surfaces. We explain, and illustrate by quintessential examples, how to simplify such generic maps on 4-manifolds topologically, in order to derive simple decompositions into much better understood manifold pieces. Our methods not only al…

2017-10-17abs ↗pdf ↗

Simplified image clustering achieves competitive results without text-based embeddings.

problem Complexity and resource requirements of state-of-the-art clustering methods.
method SCP: trains a small cluster head using pre-trained vision model features and positive data pairs.
result SCP achieves highly competitive performance on various benchmark datasets.

Simplifies efficient estimation via automatic differentiation and probabilistic programming.

problem Constructing efficient estimators for complex statistical models.
method Automatic differentiation applied to statistical functionals, avoiding the need to derive efficient influence functions.
result Users can generate efficient estimators with minimal code, simplifying the process for non-experts.

Study on nonorientable 4-manifolds using simplified fibrations and trisections.

problem Classify and understand nonorientable 4-manifolds.
method Use simplified broken Lefschetz fibrations and trisections, topological modifications of singularities, handlebody decompositions, and mapping classes of surfaces.
result Classify low genus simplified broken Lefschetz fibrations on nonorientable 4-manifolds.

Proves a conjecture about the maximum tet-volume of triangulations of a 2-sphere.

problem Proving the conjectured maximum tet-volume for all triangulations of a 2-sphere.
method Simplified version of Mathieu and Thurston's combinatorial proof using more general volume notions.
result Proves the full conjecture about the maximum tet-volume for all triangulations of a 2-sphere.

Residual Neural Networks (ResNets) achieve state-of-the-art performance in many computer vision problems. Compared to plain networks without residual connections (PlnNets), ResNets train faster, generalize better, and suffer less from the so-called degradation problem. We introduce simplified (but still nonlinear) vers…

2019-05-27abs ↗pdf ↗

Many real-world engineering problems rely on human preferences to guide their design and optimization. We present PrefOpt, an open source package to simplify sequential optimization tasks that incorporate human preference feedback. Our approach extends an existing latent variable model for binary preferences to allow f…

2018-01-09abs ↗pdf ↗

A time schedule simplifies learning in flow-based models for high-dimensional data.

problem Disappearance of relative probability phase in high-dimensional Gaussian mixture sampling.
method Introduces a time dilation schedule to characterize phases of learning.
result Autoencoder learns to simplify by focusing on relevant parameters for each phase.

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.

2016-04-14abs ↗pdf ↗

Simplified DGPs training by fixing inducing inputs to subset of data.

problem Challenging training of deep Gaussian processes.
method Fixed subset of data for inducing inputs, variational sampling.
result Significant reduction in trainable parameters and computation cost without performance degradation.

We compare two different bilateral counterparty valuation adjustment (BVA) formulas. The first formula is an approximation and is based on subtracting the two unilateral Credit Valuation Adjustment (CVA)'s formulas as seen from the two different parties in the transaction. This formula is only a simplified representati…

2011-06-17abs ↗pdf ↗

We consider a Black-Scholes market in which a number of stocks and an index are traded. The simplified Capital Asset Pricing Model is the conjunction of the usual Capital Asset Pricing Model, or CAPM, and the statement that the appreciation rate of the index is equal to its squared volatility plus the interest rate. (T…

2011-11-11abs ↗pdf ↗

New simulation method simplifies Heston model with Poisson conditioning for better accuracy and efficiency.

problem Computational expense in exact simulation schemes for Heston model.
method Proposes a new exact simulation scheme without modified Bessel function evaluations, leveraging conditional integrated variance simplification.
result Good performance in terms of accuracy, efficiency, and reliability compared to existing methods.

The paper challenges the notion that asset return doesn't affect Black-Scholes-Merton model.

problem The role of asset return in the Black-Scholes-Merton model.
method Refutation of the claim through simplified stochastic calculus approach.
result The expected rate of return of the underlying asset does affect the Black-Scholes-Merton model.

We present a graded-geometric approach to modular classes of Lie algebroids and their generalizations, introducing in this setting an idea of relative modular class of a Dirac structure for a certain type of Courant algebroids, called projectable. This novel approach puts several concepts related to Poisson geometry an…

2013-11-15abs ↗pdf ↗