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.
Proves DCNNs with expansive convolution are strongly universally consistent.
This work proposes hyperbolic deep convolutional neural networks for better pattern recognition.
Filters in a Convolutional Neural Network (CNN) contain model parameters learned from enormous amounts of data. In this paper, we suggest to decompose convolutional filters in CNN as a truncated expansion with pre-fixed bases, namely the Decomposed Convolutional Filters network (DCFNet), where the expansion coefficient…
Encoding the scale information explicitly into the representation learned by a convolutional neural network (CNN) is beneficial for many computer vision tasks especially when dealing with multiscale inputs. We study, in this paper, a scaling-translation-equivariant (ST-equivariant) CNN with joint convolutions across th…
We give a short proof of a strong version of the short time asymptotic expansion of heat kernels associated to Laplace type operators acting on sections of vector bundles over compact Riemannian manifolds, including exponential decay of the difference of the approximate heat kernel and the true heat kernel. We use this…
Recently, graph neural networks have been adopted in a wide variety of applications ranging from relational representations to modeling irregular data domains such as point clouds and social graphs. However, the space of graph neural network architectures remains highly fragmented impeding the development of optimized …
Explicit encoding of group actions in deep features makes it possible for convolutional neural networks (CNNs) to handle global deformations of images, which is critical to success in many vision tasks. This paper proposes to decompose the convolutional filters over joint steerable bases across the space and the group …
Paper defines mathematical framework for neural network explainability.
The aim of this paper is to provide a general mathematical framework for group equivariance in the machine learning context. The framework builds on a synergy between persistent homology and the theory of group actions. We define group-equivariant non-expansive operators (GENEOs), which are maps between function spaces…
We propose a new formulation for pruning convolutional kernels in neural networks to enable efficient inference. We interleave greedy criteria-based pruning with fine-tuning by backpropagation - a computationally efficient procedure that maintains good generalization in the pruned network. We propose a new criterion ba…
New methods improve translation-equivariant neural processes for modeling unknown functions.
Group convolutional neural networks (G-CNNs) can be used to improve classical CNNs by equipping them with the geometric structure of groups. Central in the success of G-CNNs is the lifting of feature maps to higher dimensional disentangled representations, in which data characteristics are effectively learned, geometri…
With the rapid expansion of mobile phone networks in developing countries, large-scale graph machine learning has gained sudden relevance in the study of global poverty. Recent applications range from humanitarian response and poverty estimation to urban planning and epidemic containment. Yet the vast majority of compu…
The remarkable development of deep learning in medicine and healthcare domain presents obvious privacy issues, when deep neural networks are built on users' personal and highly sensitive data, e.g., clinical records, user profiles, biomedical images, etc. However, only a few scientific studies on preserving privacy in …
The fruit fly Drosophila's olfactory circuit has inspired a new locality sensitive hashing (LSH) algorithm, FlyHash. In contrast with classical LSH algorithms that produce low dimensional hash codes, FlyHash produces sparse high-dimensional hash codes and has also been shown to have superior empirical performance compa…
Rescaling expansiveness proven for k*-expansive vector fields.
During the past decade, with the significant progress of computational power as well as ever-rising data availability, deep learning techniques became increasingly popular due to their excellent performance on computer vision problems. The size of the Protein Data Bank has increased more than 15 fold since 1999, which …
Injectivity of ReLU networks is characterized for generative models and inverse problems.
The paper derives expansions for Green's operators and resolvents using Hadamard methods.
Develops a martingale expansion for stochastic volatility models.
Taylor expansions improve reinforcement learning policies.
Analytic torsion expansions for symmetric and complex homogeneous spaces.
Proved cyclotomic expansion for double twist knots' HOMFLY-PT invariants.
Study of hypersurfaces with specific expansion properties.
A new hypergraph expansion method treats vertices and hyperedges equally, improving node classification.
New method speeds up neural kernel computations for various activations.
The paper calculates asymptotic expansions for specific types of oscillatory integrals.
Dropout increases the generalization of neural networks by expanding the weight space.
New derivation of knot invariants from universal invariant.
This work explores functional expansions to handle path dependence in various fields.
In the planar limit of the 't Hooft expansion, the Wilson-loop average in 3d Chern-Simons theory (i.e. the HOMFLY polynomial) depends in a very simple way on representation (the Young diagram), so that the (knot-dependent) Ooguri-Vafa partition function becomes a trivial KP tau-function. We study higher genus correctio…
Paper calculates third coefficient in Kaehler-Einstein metric expansion.
We describe the first known mean-field study of landing probabilities for random walks on hypergraphs. In particular, we examine clique-expansion and tensor methods and evaluate their mean-field characteristics over a class of random hypergraph models for the purpose of seed-set community expansion. We describe paramet…
Study on heat trace expansion for thermoelastic Dirichlet-to-Neumann map.
The paper proposes and proves asymptotic expansions for quantum invariants.
New method models portfolios with leptokurtic risk factors using Gram-Charlier expansions.
Develops AMITE for analyzing neural network nonlinearities.
We survey recent results about the asymptotic expansion of Toeplitz operators and their kernels, as well as Berezin-Toeplitz quantization. We deal in particular with calculation of the first coefficients of these expansions.
Paper presents new expansions for option pricing with cash dividends.
The validity of an approximation formula for European option prices under a general stochastic volatility model is proved in the light of the Edgeworth expansion for ergodic diffusions. The asymptotic expansion is around the Black-Scholes price and is uniform in bounded payoff func- tions. The result provides a validat…
The paper uses polyhedral expansions to capture the shape of compact metric spaces.
We prove a local index theorem of Atiyah-Singer type for Dirac operators on manifolds with a Lie structure at infinity (Lie manifolds for short). With the help of a renormalized supertrace, defined on a suitable class of regularizing operators, the proof of the index theorem relies on a rescaling technique similar in s…
We provide a general method to compute a Taylor expansion in time of implied volatility for stochastic volatility models, using a heat kernel expansion. Beyond the order 0 implied volatility which is already known, we compute the first order correction exactly at all strikes from the scalar coefficient of the heat kern…
We quantify predictive uncertainty using the posterior predictive variance.
The study improves volatility model pricing accuracy with new statistical expansions.
The notion of a symplectic expansion directly relates the topology of a surface to formal symplectic geometry. We give a method to construct a symplectic expansion by solving a recurrence formula given in terms of the Baker-Campbell-Hausdorff series.
For any strictly positive martingale for which has a characteristic function, we provide an expansion for the implied volatility. This expansion is explicit in the sense that it involves no integrals, but only polynomials in the log strike. We illustrate the versatility of our expansion by computing t…
Researchers calculate the second coefficient in the expansion of a Toeplitz operator.