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 methods prune unpromising rules from KGs, improving scalability and runtime.
A new hierarchy quantifies agency in systems based on information processing.
Mixed superposition rules, i.e., functions describing the general solution of a system of first-order differential equations in terms of a generic family of particular solutions of first-order systems and some constants, are studied. The main achievement is a generalization of the celebrated Lie-Scheffers Theorem, char…
Generates infinite-depth hierarchical clusters from few examples.
This work proposes optimal decision rules for hierarchical classifiers to better align with evaluation metrics.
It is proved that the members of the Riccati hierarchy, the so-called Riccati chain equations, can be considered as particular cases of projective Riccati equations, which greatly simplifies the study of the Riccati hierarchy. This also allows us to characterize Riccati chain equations geometrically in terms of the pro…
Paper addresses limitations of traditional hierarchical clustering methods.
New method controls false discoveries in structured hypothesis spaces.
Polynomial inequalities lie at the heart of many mathematical disciplines. In this paper, we consider the fundamental computational task of automatically searching for proofs of polynomial inequalities. We adopt the framework of semi-algebraic proof systems that manipulate polynomial inequalities via elementary inferen…
We demonstrate that SDYM equations for the Lie algebra of one-dimensional vector fields represent a natural reduction in the framework of general linearly degenerate dispersionless hierarchy. We define the reduction in terms of wave functions, introduce generating relation, Lax-Sato equations and the dressing scheme fo…
Solves the challenge of retrieving item-specific financial information from Form 10-Q filings.
In many learning settings, it is beneficial to augment the main features with pairwise interactions. Such interaction models can be often enhanced by performing variable selection under the so-called strong hierarchy constraint: an interaction is non-zero only if its associated main features are non-zero. Existing conv…
Unified theory for neural scaling laws in hierarchically compositional data.
Hierarchical clustering has been shown to be valuable in many scenarios. Despite its usefulness to many situations, there is no agreed methodology on how to properly evaluate the hierarchies produced from different techniques, particularly in the case where ground-truth labels are unavailable. This motivates us to prop…
Develops a multilevel Monte Carlo framework with dropout for efficient uncertainty quantification.
When related learning tasks are naturally arranged in a hierarchy, an appealing approach for coping with scarcity of instances is that of transfer learning using a hierarchical Bayes framework. As fully Bayesian computations can be difficult and computationally demanding, it is often desirable to use posterior point es…
Deep networks learn hierarchical data by invariant representations.
ProHOC detects OOD samples in class hierarchies, predicting them to correct internal nodes.
The problem of community detection in networks is usually formulated as finding a single partition of the network into some "correct" number of communities. We argue that it is more interpretable and in some regimes more accurate to construct a hierarchical tree of communities instead. This can be done with a simple to…
NeurT-FDR controls FDR by incorporating feature hierarchy.
This is the third in a series of papers attempting to describe a uniform geometric framework in which many integrable systems can be placed. A soliton hierarchy can be constructed from a splitting of an infinite dimensional group as positive and negative subgroups L_+, L_- and a commuting sequence in the Lie algebr…
The seemingly infinite diversity of the natural world arises from a relatively small set of coherent rules, such as the laws of physics or chemistry. We conjecture that these rules give rise to regularities that can be discovered through primarily unsupervised experiences and represented as abstract concepts. If such r…
We study an economic model where agents trade a variety of products by using one of three competing rules: "need", "greed" and "noise". We find that the optimal strategy for any agent depends on both product composition in the overall market and composition of strategies in the market. In particular, a strategy that do…
In this short note we show how Dubrovin's integrable hierarchies, defined using the Gromov-Witten theory of a closed symplectic manifold, generalizes to Hamiltonian Floer theory. In particular, we show how the required generalization of the PSS isomorphism, relating Gromov-Witten theory and Hamiltonian Floer theory, ca…
We prove that the Kupershmidt deformation of a bi-Hamiltonian system is itself bi-Hamiltonian. Moreover, Magri hierarchies of the initial system give rise to Magri hierarchies of Kupershmidt deformations as well. Since Kupershmidt deformations are not written in evolution form, we start with an outline a geometric fram…
This work proposes a new method to train models with deep latent hierarchies using Optimal Transport.
New method generates critical points for complex functionals.
Spinor fields on surfaces of revolution conformally immersed into 3-dimensional space are considered in the framework of the spinor representations of surfaces. It is shown that a linear problem (a 2-dimensional Dirac equation) related with a modified Veselov- Novikov hierarchy in the case of the surface of revolution …
We describe the combinatorial stochastic process underlying a sequence of conditionally independent Bernoulli processes with a shared beta process hazard measure. As shown by Thibaux and Jordan [TJ07], in the special case when the underlying beta process has a constant concentration function and a finite and nonatomic …
Constructs integrable hierarchies for generalized Frobenius manifolds with non-flat unity.
Solving different types of optimization models (including parameters fitting) for support vector machines on large-scale training data is often an expensive computational task. This paper proposes a multilevel algorithmic framework that scales efficiently to very large data sets. Instead of solving the whole training s…
New method improves blackbox attack transferability by perturbing feature hierarchy.
Building systems that autonomously create temporal abstractions from data is a key challenge in scaling learning and planning in reinforcement learning. One popular approach for addressing this challenge is the options framework (Sutton et al., 1999). However, only recently in (Bacon et al., 2017) was a policy gradient…
Study identifies pitfalls in assessing hierarchies for multi-class classification.
Super tau-covers extend bihamiltonian hierarchies' symmetries.
Hydrodynamic hierarchy deformed using conservation laws.
MOSS optimizes decision rules for accuracy and stability.
A network supporting deep unsupervised learning is presented. The network is an autoencoder with lateral shortcut connections from the encoder to decoder at each level of the hierarchy. The lateral shortcut connections allow the higher levels of the hierarchy to focus on abstract invariant features. While standard auto…
Legendre transformations link related integrable hierarchies.
Twisted - and twisted -hierarchies are soliton hierarchies introduced by Terng to find higher flows of the generalized sine-Gordon equation. Twisted -hierarchies are among the most important classes of twisted hierarchies. In this paper, interesting first and higher flows of twi…
Proposes DCV-ROOD framework for robust OOD detection evaluation.
Unified quadrature framework for large-scale kernel machines.
Derive bihamiltonian structure for rational reduction of 2D-Toda hierarchy
New framework learns interpretable rule ensembles without sacrificing accuracy.
We propose a formally completely integrable extension of heat hierarchy based on the space of symmetries isomorphic to the Weyl algebra . The extended heat hierarchy will be the basic model for the analysis of the extension of KP hierarchy, and other integrable equations.
Wise's Quasiconvex Hierarchy Theorem classifying hyperbolic virtually compact special groups in terms of quasiconvex hierarchies played an essential role in Agol's proof of the Virtual Haken Conjecture. Answering a question of Wise, we construct a new virtual quasiconvex hierarchy for relatively hyperbolic virtually co…
Loss assigns examples to classes and superclasses in hierarchical data.
New hierarchies derived from KP hierarchy using non-formal operators and Yang-Mills action.