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.
The paper introduces a new FOR framework using Huber and ε-insensitive losses.
We establish linear regret bounds for convex smooth losses using Fenchel-Young losses.
Optimal risk sharing found for heterogeneous risk attitudes using distortion risk measures.
Deep neural networks solve optimal risk sharing problems.
This paper finds bounds on the ribbonlength of knots and links with up to 9 crossings.
The infimal Heegaard gradient of a compact 3-manifold was defined and studied by Marc Lackenby in an approach toward the well-known virtually Haken conjecture. As instructive examples, we consider Seifert fibered 3-manifolds, and show that a Seifert fibered 3-manifold has zero infimal Heegaard gradient if and only if i…
Observations depending on sums of random variables are common throughout many fields; however, no efficient solution is currently known for performing max-product inference on these sums of general discrete distributions (max-product inference can be used to obtain maximum a posteriori estimates). The limiting step to …
Paper shows how to embed Möbius bands with many twists and small aspect ratios.
New algorithm for safer machine learning with different testing and training distributions.
New principle controls graph-informed adversarial discrepancies.
We establish general versions of a variety of results for quasiconvex, lower-semicontinuous, and law-invariant functionals. Our results extend well-known results from the literature to a large class of spaces of random variables. We sometimes obtain sharper versions, even for the well-studied case of bounded random var…
The purpose of this work is to develop and study a distributed strategy for Pareto optimization of an aggregate cost consisting of regularized risks. Each risk is modeled as the expectation of some loss function with unknown probability distribution while the regularizers are assumed deterministic, but are not required…
Generalizes Fenchel conjugation to nonlinear functions on arbitrary sets.
We investigate the effects of the social interactions of a finite set of agents on an equilibrium pricing mechanism. A derivative written on non-tradable underlyings is introduced to the market and priced in an equilibrium framework by agents who assess risk using convex dynamic risk measures expressed by Backward Stoc…
New gradient flows for non-negative and probability measures combining optimal transport and interaction forces.
We show that any finitely generated non-elementary Kleinian group has a co-final family of finite index normal subgroups with respect to which it has Property . As a consequence, any closed hyperbolic 3-manifold has a co-final family of finite index normal subgroups for which the infimal Heegaard gradient is positiv…
Introduces a new divergence measure for optimal transport.
New divergences improve estimation and GAN training performance.
We study the SL(2,R)-infimal lengths of simple closed curves on half-translation surfaces. Our main result is a characterization of Veech surfaces in terms of these lengths. We also revisit the "no small virtual triangles" theorem of Smillie and Weiss and establish the following dichotomy: the virtual triangle area spe…
In this second part of a series of papers on the long-time behavior of Ricci flows with surgery, we establish a bound on the evolution of the infimal area of simplicial complexes inside a 3-manifold under the Ricci flow. This estimate generalizes an area estimate of Hamilton, which we will recall in the first part of t…
Optimizes energy of mappings from complex projective spaces.
New method enhances adversarial robustness of deep learning models.
Upper bound on 3-manifold volumes from surface homeomorphisms.
The aims of this study are twofold. First, we consider an optimal risk allocation problem with non-convex preferences. By establishing an infimal representation for distortion risk measures, we give some necessary and sufficient conditions for the existence of optimal and asymptotic optimal allocations. We will show th…
Two trees in the boundary of outer space are said to be \emph{primitive-equivalent} whenever their translation length functions are equal in restriction to the set of primitive elements of . We give an explicit description of this equivalence relation, showing in particular that it is nontrivial. This question is …
Study on the ribbonlength of knots and links, improving upper bounds.
Proves bounds on ribbonlength for various knot types.
DeepCAM learns convolutional dictionaries for image processing.
Introduces Finslerian convolution metrics and their properties.
Spectral graph convolutional neural networks (CNNs) require approximation to the convolution to alleviate the computational complexity, resulting in performance loss. This paper proposes the topology adaptive graph convolutional network (TAGCN), a novel graph convolutional network defined in the vertex domain. We provi…
Generative flows are attractive because they admit exact likelihood optimization and efficient image synthesis. Recently, Kingma & Dhariwal (2018) demonstrated with Glow that generative flows are capable of generating high quality images. We generalize the 1 x 1 convolutions proposed in Glow to invertible d x d convolu…
VC dimensions of group CNNs are infinite for certain kernels and groups.
We introduce a guide to help deep learning practitioners understand and manipulate convolutional neural network architectures. The guide clarifies the relationship between various properties (input shape, kernel shape, zero padding, strides and output shape) of convolutional, pooling and transposed convolutional layers…
Enhances group convolutional networks with attention to learn meaningful relationships.
Convolution Neural Network (CNN) has gained tremendous success in computer vision tasks with its outstanding ability to capture the local latent features. Recently, there has been an increasing interest in extending convolution operations to the non-Euclidean geometry. Although various types of convolution operations h…
We introduce Group equivariant Convolutional Neural Networks (G-CNNs), a natural generalization of convolutional neural networks that reduces sample complexity by exploiting symmetries. G-CNNs use G-convolutions, a new type of layer that enjoys a substantially higher degree of weight sharing than regular convolution la…
In recent times, the use of separable convolutions in deep convolutional neural network architectures has been explored. Several researchers, most notably (Chollet, 2016) and (Ghosh, 2017) have used separable convolutions in their deep architectures and have demonstrated state of the art or close to state of the art pe…
Proves DCNNs with expansive convolution are strongly universally consistent.
New framework for manifold convolutions using toric embeddings.
Functor connects Lie groupoid algebras to bornological structures.
Convolution has been playing a prominent role in various applications in science and engineering for many years. It is the most important operation in convolutional neural networks. There has been a recent growth of interests of research in generalizing convolutions on curved domains such as manifolds and graphs. Howev…
Convolutional Neural Networks, as most artificial neural networks, are commonly viewed as methods different in essence from kernel-based methods. We provide a systematic translation of Convolutional Neural Networks (ConvNets) into their kernel-based counterparts, Convolutional Kernel Networks (CKNs), and demonstrate th…
New method enforces orthogonality in convolutional layers for improved robustness.
New method improves grouped convolutions on edge devices.
GCNs improve regression tasks by aggregating neighbor signals.
Convolution and pooling improve kernel methods in image classification.
Convolutional networks outperform fully-connected ones in certain tasks.
Proposes a fixed smooth convolutional layer to reduce checkerboard artifacts in CNNs.