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 ONNX for quantized neural networks with new formats and operators.
Existence proof of noncompact self-shrinkers with arbitrary genus.
We give a precise and general description of gerbes valued in arbitrary crossed module and over an arbitrary differential stack. We do it using only Lie groupoids, hence ordinary differential geometry. We prove the coincidence with the existing notions by comparing our construction with non-Abelian cohomology.
The paper shows how to infer conditional independence from non-Gaussian data.
New forms calibrate minimal graphs in arbitrary dimensions.
Geodesic algorithms extended to arbitrary ellipsoids.
This paper numerically computes the topological and smooth invariants of Eschenburg spaces with small fourth cohomology group, following Kruggel's determination of the Kreck-Stolz invariants of Eschenburg spaces that satisfy condition C. The GNU GMP arbitrary-precision library is utilised.
We solve the Fu-Yau equation for arbitrary dimension and arbitrary slope . Actually we obtain at the same time a solution of the open case , an improved solution of the known case , and solutions for a family of Hessian equations which includes the Fu-Yau equation as a special case. The method is based …
Proves existence of minimal surfaces of arbitrary genus with two ends.
In this article we revisit the definition of Precision-Recall (PR) curves for generative models proposed by Sajjadi et al. (arXiv:1806.00035). Rather than providing a scalar for generative quality, PR curves distinguish mode-collapse (poor recall) and bad quality (poor precision). We first generalize their formulation …
New method for triclustering with reduced arbitrariness.
Reduced numerical precision is a common technique to reduce computational cost in many Deep Neural Networks (DNNs). While it has been observed that DNNs are resilient to small errors and noise, no general result exists that is capable of predicting a given DNN system architecture's sensitivity to reduced precision. In …
We construct, for a homogeneous Lagrangian of arbitrary order in two independent variables, a differential 2-form with the property that it is closed precisely when the Lagrangian is null. This is similar to the property of the `fundamental Lepage equivalent' associated with first-order Lagrangians defined on jets of s…
We develop a spinorial description of CR structures of arbitrary codimension. More precisely, we characterize almost CR structures of arbitrary codimension on (Riemannian) manifolds by the existence of a Spin structure carrying a partially pure spinor field. We study various integrability conditions of the alm…
New symmetries found for scalar and vector ODEs of arbitrary dimensions.
In this paper we offer a novel type of network model which can capture the precise structure of a financial market based, for example, on empirical findings. With the attached stochastic framework it is further possible to study how an arbitrary network structure and its expected counterparty credit risk are analytical…
We investigate whether a robot arm can learn to pick and throw arbitrary objects into selected boxes quickly and accurately. Throwing has the potential to increase the physical reachability and picking speed of a robot arm. However, precisely throwing arbitrary objects in unstructured settings presents many challenges:…
Deep NURBS improves PINNs for solving PDEs on arbitrary geometries.
We consider the robust phase retrieval problem of recovering the unknown signal from the magnitude-only measurements, where the measurements can be contaminated by both sparse arbitrary corruption and bounded random noise. We propose a new nonconvex algorithm for robust phase retrieval, namely Robust Wirtinger Flow to …
State of the art deep learning models have made steady progress in the fields of computer vision and natural language processing, at the expense of growing model sizes and computational complexity. Deploying these models on low power and mobile devices poses a challenge due to their limited compute capabilities and str…
Rex solves the inverse problem for ODE/SDE solvers, improving precision and stability.
Let S be a closed oriented surface of genus g > 1, and let T denote its Torelli group. First, given a set E of homotopically nontrivial, pairwise disjoint, pairwise nonisotopic simple closed curves on S, we determine precisely when a multitwist on E is an element of T by defining an equivalence relation on E and then a…
We give some concrete examples of moduli spaces of connections. Precisely, we explain how to explicitly construct the moduli spaces of rank 2 fuchsian systems and logarithmic connections on the Riemann sphere with 4 poles. The former ones are affine cubic surfaces; the latter ones are analytically isomorphic to affine …
StatQAT optimizes quantization for deep networks, reducing computational cost and memory usage.
Transformers can predict new tokens based on any number of context tokens, approximating continuous mappings with fixed resources.
We present a training system, which can provably defend significantly larger neural networks than previously possible, including ResNet-34 and DenseNet-100. Our approach is based on differentiable abstract interpretation and introduces two novel concepts: (i) abstract layers for fine-tuning the precision and scalabilit…
This paper introduces Graph Convolutional Recurrent Network (GCRN), a deep learning model able to predict structured sequences of data. Precisely, GCRN is a generalization of classical recurrent neural networks (RNN) to data structured by an arbitrary graph. Such structured sequences can represent series of frames in v…
This paper addresses the following question of neural network identifiability: Does the input-output map realized by a feed-forward neural network with respect to a given nonlinearity uniquely specify the network architecture, weights, and biases? Existing literature on the subject Sussman 1992, Albertini, Sontag et al…
Constructs hyperbolic reflection groups with 3D limit sets.
There is a significant literature on methods for incorporating knowledge into multiple testing procedures so as to improve their power and precision. Some common forms of prior knowledge include (a) beliefs about which hypotheses are null, modeled by non-uniform prior weights; (b) differing importances of hypotheses, m…
In this paper we generalize special geometry to arbitrary signatures in target space. We formulate the definitions in a precise mathematical setting and give a translation to the coordinate formalism used in physics. For the projective case, we first discuss in detail projective Kaehler manifolds, appearing in N=1 supe…
In recent literature, a general two step procedure has been formulated for solving the problem of phase retrieval. First, a spectral technique is used to obtain a constant-error initial estimate, following which, the estimate is refined to arbitrary precision by first-order optimization of a non-convex loss function. N…
We present here a possible generalisation of the Poincaré-Cartan form in classical field theory in the most general case: arbitrary dimension, arbitrary order of the theory and in the absence of a fibre bundle structure. We use for the kinematical description of the system the -Grassmann manifold associated to a…
The classical Universal Approximation Theorem holds for neural networks of arbitrary width and bounded depth. Here we consider the natural `dual' scenario for networks of bounded width and arbitrary depth. Precisely, let be the number of inputs neurons, be the number of output neurons, and let be any nonaff…
Paper calculates braid indices for reverse parallel links of alternating knots.
Counting meanders on surfaces of arbitrary genus, with precise asymptotics.
The study of invariant SKT structures on nilmanifolds, focusing on 2-step cases.
We introduce a faithful representation of the heavy tail multivariate distribution of asset returns, as parsimonous as the Gaussian framework. Using calculation techniques of functional integration and Feynman diagrams borrowed from particle physics, we characterize precisely, through its cumulants of high order, the d…
We show that the topological charge of the n-soliton solution of the sine-Gordon equation n is related to the genus g > 1 of a constant negative curvature compact surface described by this configuration. The relation is n=2(g-1), where n is even. The moduli space of complex dimension B(g)=3(g-1) corresponds precisely t…
Recent research has considered the stochastic thermodynamics of multiple interacting systems, representing the overall system as a Bayes net. I derive fluctuation theorems governing the entropy production (EP)of arbitrary sets of the systems in such a Bayes net. I also derive ``conditional'' fluctuation theorems, gover…
Sharp bounds for eigenfunctions on product spaces restricted to submanifolds.
New RBF networks can approximate any continuous function.
Generalizes Riemann's results on flat coordinates for non-symmetric bilinear forms.
New bounds on inscribed triangles in arbitrary planar domains.
We propose a new \cu{class-optimal} algorithm for the distributed computation of Wasserstein Barycenters over networks. Assuming that each node in a graph has a probability distribution, we prove that every node can reach the barycenter of all distributions held in the network by using local interactions compliant with…
Let X be a smooth manifold of dimension 1+n endowed with a lorentzian metric g, and let T be the electromagnetic energy tensor associated to a 2-form F. In this paper we characterize this tensor T as the only 2-covariant natural tensor associated to a lorentzian metric and a 2-form that is independent of the unit of sc…
The paper proves stability of critical points for conformally invariant Lagrangians.
Extends elliptic operator regularity to maximally hypoelliptic operators.