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.
This thesis explores GNNs, categorizing them into local and global approaches.
New perspective on federated learning as posterior inference, improving optimization.
Global and local blowups of manifolds are proven equivalent.
A note on learning with agents having global perspectives and a principal optimizing their performance.
P3I learns holistic scene representations from a single image.
Paper examines global Covid-19 data complexity and finds low intrinsic dimensions.
For a strict Lie 2-group, we develop a notion of Lie 2-algebra-valued differential forms on Lie groupoids, furnishing a differential graded-commutative Lie algebra equipped with an adjoint action of the Lie 2-group and a pullback operation along Morita equivalences between Lie groupoids. Using this notion, we define co…
We consider the problem of minimizing a sum of clipped convex functions; applications include clipped empirical risk minimization and clipped control. While the problem of minimizing the sum of clipped convex functions is NP-hard, we present some heuristics for approximately solving instances of these problems. These h…
The fragmentation of production across countries has become an important feature of the globalization in recent decades and is often conceptualized by the term, global value chains (GVCs). When empirically investigating the GVCs, previous studies are mainly interested in knowing how global the GVCs are rather than how …
SogCLR uses small batch sizes for global contrastive learning, achieving similar performance to SimCLR.
We review some recent results on the mean curvature flows of Lagrangian submanifolds from the perspective of geometric partial differential equations. These include global existence and convergence results, characterizations of first-time singularities, and constructions of self-similar solutions.
The paper constructs Levi flat structures using structure sheaves and differential complexes.
Theoretical study explains why federated optimization fails to achieve perfect fitting.
We derive a representation formula for the tensorial wave equation $\Box_\bg φ^I=F^I$ in globally hyperbolic Lorentzian spacetimes $(\M^{2+1}, \bg)$ by giving a geometric formulation of the method of descent which is applicable for any dimension.
New framework for DNN training guarantees convergence to global minimum.
This work analyzes tree-based methods from a ranking perspective, providing insights and new statistics.
Deep neural networks perform well on local tasks but struggle with global tasks.
This paper is motivated by recent developments of higher gauge theory. Different from its style of using higher category theory, we try to describe the concept of higher parallel transport within setting of classical principal bundle theory. From this perspective, we obtain a global geometric proof on a generalized 3-d…
Framework for analyzing dynamic topological changes in point clouds using persistent homology and dynamic optimal transport.
Model strategic interactions between market makers and traders to optimize execution.
Throughout economic history, the global economy has experienced recurring crises. The persistent recurrence of such economic crises calls for an understanding of their generic features rather than treating them as singular events. The global economic system is a highly complex system and can best be viewed in terms of …
Survey of global geometry for double field theory.
The abstract introduces golden Finsler structures and explores their local and global properties.
Study explores embedding signature-changing manifolds into higher-dimensional spaces.
Local mass perspective on Bayesian inference
Multivariate time series (MTS) forecasting is widely used in various domains, such as meteorology and traffic. Due to limitations on data collection, transmission, and storage, real-world MTS data usually contains missing values, making it infeasible to apply existing MTS forecasting models such as linear regression an…
Study fragility in global financial indices using network analysis.
Global Autoregressive Models (GAMs) are a recent proposal [Parshakova et al., CoNLL 2019] for exploiting global properties of sequences for data-efficient learning of seq2seq models. In the first phase of training, an Energy-Based model (EBM) over sequences is derived. This EBM has high representational power, but is u…
In this paper, we provide an integrated systems modeling approach to analyzing global externalities from a microeconomic perspective. Various forms of policy (fiscal, monetary, etc.) have addressed flaws and market failures in models, but few have been able to successfully eliminate modern externalities that remain an …
The marriage of wireless big data and machine learning techniques revolutionizes the wireless system by the data-driven philosophy. However, the ever exploding data volume and model complexity will limit centralized solutions to learn and respond within a reasonable time. Therefore, scalability becomes a critical issue…
We introduce an equivariant Pontrjagin-Thom construction which identifies equivariant cohomotopy classes with certain fixed point bordism classes. This provides a concrete geometric model for equivariant cohomotopy which works for any compact Lie group G. In the special case when G is finite or a torus, we show that ou…
We study a class of nonlocal, energy-driven dynamical models that govern the motion of closed, embedded curves from both an energetic and dynamical perspective. Our energetic results provide a variety of ways to understand physically motivated energetic models in terms of more classical, combinatorial measures of compl…
Replica exchange Langevin diffusion accelerates nonconvex optimization.
Empirical evidence suggests that neural networks with ReLU activations generalize better with over-parameterization. However, there is currently no theoretical analysis that explains this observation. In this work, we provide theoretical and empirical evidence that, in certain cases, overparameterized convolutional net…
QP perspective on Poisson-Lie T-duality topology changes.
New approach to principal groupoid bundles with connections using dg-Lie groupoids.
Correlation Networks (CNs) inherently suffer from redundant information in their network topology. Bayesian Networks (BNs), on the other hand, include only non-redundant information (from a probabilistic perspective) resulting in a sparse topology from which generalizable physical features can be extracted. We advocate…
We establish that first-order methods avoid saddle points for almost all initializations. Our results apply to a wide variety of first-order methods, including gradient descent, block coordinate descent, mirror descent and variants thereof. The connecting thread is that such algorithms can be studied from a dynamical s…
FedBE aggregates local models into a robust global model via Bayesian inference.
SAGE quantifies feature importance in machine learning models.
New method improves MMD estimation without convexity assumptions.
Mercat preserves angles to create accurate low-dimensional embeddings.
We solve the optimization of two-layer ReLU networks using convex math.
Max-Pooling operations are a core component of deep learning architectures. In particular, they are part of most convolutional architectures used in machine vision, since pooling is a natural approach to pattern detection problems. However, these architectures are not well understood from a theoretical perspective. For…
Paper analyzes SHB method for neural networks, proving stability, connectivity, and global convergence.
The paper explores how topology affects the solvability of first-order differential equations.
In this paper we establish a constructive method in order to show global existence and regularity for a class of degenerate parabolic Cauchy problems which satisfy a weak Hoermander condition on a subset of the domain where the data are measurable and which have regular data on the complementary set of the domain. This…
OceanForecastBench offers a comprehensive benchmark for data-driven ocean forecasting models.