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.
New knots found with specific slope properties.
Derives new orthogonal coordinates for evolving surfaces and curves.
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…
A new runtime for AI agents calculates risks in real-time.
Smectic liquid crystals are materials formed by stacking deformable, fluid layers. Though smectics prefer to have flat, uniformly-spaced layers, boundary conditions can impose curvature on the layers. Since the layer spacing and curvature are intertwined, the problem of finding minimal configurations for the layers bec…
In this paper, a new algorithm based on differential geometry viewpoint to solve the 3D rotating Navier-Stokes equations with complex Boundary is proposed, which is called Bi-parallel algorithm. For xample, it can be applied to passage flow between two blades in impeller and circulation flow through aircrafts with comp…
A new method for imbalanced binary classification without resampling.
We use layer potential to establish that the boundary biharmonic Steklov operators are elliptic pseudo-differential operators. Thus we are able to establish lower bounds on both the measure of boundary nodal sets and interior nodal sets for biharmonic Steklov eigenfunctions.
Deep generative neural networks (DGNNs) have achieved realistic and high-quality data generation. In particular, the adversarial training scheme has been applied to many DGNNs and has exhibited powerful performance. Despite of recent advances in generative networks, identifying the image generation mechanism still rema…
Large twist-angle grain boundaries in layered structures are often described by Scherk's first surface whereas small twist-angle grain boundaries are usually described in terms of an array of screw dislocations. We show that there is no essential distinction between these two descriptions and that, in particular, their…
LGAC enhances heat transfer in turbulent boundary layers using slot jets.
BEKAN uses RBFs and evolutionary methods to solve PDEs with boundary conditions.
We construct and analyze minimal disc stackings with bounds on their Morse index.
We build polyhedral complexes in Rn that coincide with dyadic grids with different orientations, while keeping uniform lower bounds (depending only on n) on the flatness of the added polyhedrons including their subfaces in all dimensions. After the definitions and first properties of compact Euclidean polyhedrons and c…
Soft-Radial Projection solves gradient saturation in constrained deep learning.
We introduce a technique based on the singular vector canonical correlation analysis (SVCCA) for measuring the generality of neural network layers across a continuously-parametrized set of tasks. We illustrate this method by studying generality in neural networks trained to solve parametrized boundary value problems ba…
Local invertibility of ray transforms on convex manifolds.
Paper proves convergence of MDL to Einstein-Hilbert with boundary term.
New method initializes sigmoidal MLPs for interpretable shapes.
A new tensor network method for image classification reduces computation cost.
Outlier detection has received special attention in various fields, mainly for those dealing with machine learning and artificial intelligence. As strong outliers, anomalies are divided into the point, contextual and collective outliers. The most important challenges in outlier detection include the thin boundary betwe…
Neural networks compress uninformative input directions, improving test error.
We present a formulation of deep learning that aims at producing a large margin classifier. The notion of margin, minimum distance to a decision boundary, has served as the foundation of several theoretically profound and empirically successful results for both classification and regression tasks. However, most large m…
The paper explores transferability of adversarial examples between convex and 01 loss models, finding non-transferability due to different decision boundaries caused by outliers.
We provide a theoretical explanation of the role of the number of nodes at each layer in deep neural networks. We prove that the largest variation of a deep neural network with ReLU activation function arises when the layer with the fewest nodes changes its activation pattern. An important implication is that deep neur…
Reduces nonlinear electromechanical dynamics through quasi-steady state hypothesis.
We prove that a potential can be reconstructed from the Dirichlet-to-Neumann map for the Schrodinger operator in a fixed admissible 3-dimensional Riemannian manifold . We also show that an admissible metric in a fixed conformal class can be constructed from the Dirichlet-to-Neumann map for $Δ_…
Novel boundary integral equations for Dirac operators in 3D Lipschitz domains.
A family of one-vertex triangulations of 3-manifolds, layered-triangulations, is defined. Layered-triangulations are first described for handlebodies and then extended to all 3-manifolds via Heegaard splittings. A complete and detailed analysis of layered-triangulations is given in the cases of the solid torus and lens…
Combining Bayesian nonparametrics and a forward model selection strategy, we construct parsimonious Bayesian deep networks (PBDNs) that infer capacity-regularized network architectures from the data and require neither cross-validation nor fine-tuning when training the model. One of the two essential components of a PB…
We develop a statistical mechanical approach based on the replica method to study the design space of deep and wide neural networks constrained to meet a large number of training data. Specifically, we analyze the configuration space of the synaptic weights and neurons in the hidden layers in a simple feed-forward perc…
Prominently used in support vector machines and logistic regressions, kernel functions (kernels) can implicitly map data points into high dimensional spaces and make it easier to learn complex decision boundaries. In this work, by replacing the inner product function in the softmax layer, we explore the use of kernels …
In order to classify linearly non-separable data, neurons are typically organized into multi-layer neural networks that are equipped with at least one hidden layer. Inspired by some recent discoveries in neuroscience, we propose a new model of artificial neuron along with a novel activation function enabling the learni…
Study well-posedness of generalized Stokes operator on cylindrical domains.
ManifoldFlow relaxes fixed-spectrum Stiefel layers to learn a positive spectrum.
New neural network approach solves Poisson equations efficiently.
A classification of spanning surfaces for alternating links is provided up to genus, orientability, and a new invariant that we call aggregate slope. That is, given an alternating link, we determine all possible combinations of genus, orientability, and aggregate slope that a surface spanning that link can have. To thi…
Study proves rigidity results for analytic spacetimes without boundary or timelike boundary.
In this paper, we propose a capsule-based neural network model to solve the semantic segmentation problem. By taking advantage of the extractable part-whole dependencies available in capsule layers, we derive the probabilities of the class labels for individual capsules through a recursive, layer-by-layer procedure. We…
Dropout training, originally designed for deep neural networks, has been successful on high-dimensional single-layer natural language tasks. This paper proposes a theoretical explanation for this phenomenon: we show that, under a generative Poisson topic model with long documents, dropout training improves the exponent…
It is shown that given any link-manifold, there is an algorithm to decide if the manifold contains an embedded, essential planar surface; if it does, the algorithm will construct one. If a slope on the boundary of the link-manifold is given, there is an algorithm to determine if the slope bounds an embedded punctured-d…
A major challenge in Bayesian Optimization is the boundary issue (Swersky, 2017) where an algorithm spends too many evaluations near the boundary of its search space. In this paper, we propose BOCK, Bayesian Optimization with Cylindrical Kernels, whose basic idea is to transform the ball geometry of the search space us…
Semantic boundary and edge detection aims at simultaneously detecting object edge pixels in images and assigning class labels to them. Systematic training of predictors for this task requires the labeling of edges in images which is a particularly tedious task. We propose a novel strategy for solving this task, when pi…
We propose a multi-label multi-task framework based on a convolutional recurrent neural network to unify detection of isolated and overlapping audio events. The framework leverages the power of convolutional recurrent neural network architectures; convolutional layers learn effective features over which higher recurren…
Agol recently introduced the notion of a veering triangulation, and showed that such triangulations naturally arise as layered triangulations of fibered hyperbolic 3-manifolds. We prove, by a constructive argument, that every veering triangulation admits positive angle structures, recovering a result of Hodgson, Rubins…
We study the geometry of deep (neural) networks (DNs) with piecewise affine and convex nonlinearities. The layers of such DNs have been shown to be {\em max-affine spline operators} (MASOs) that partition their input space and apply a region-dependent affine mapping to their input to produce their output. We demonstrat…
Deep NURBS improves PINNs for solving PDEs on arbitrary geometries.
We study the interplay between memorization and generalization of overparameterized networks in the extreme case of a single training example and an identity-mapping task. We examine fully-connected and convolutional networks (FCN and CNN), both linear and nonlinear, initialized randomly and then trained to minimize th…