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.
Formula proves invariant matches for smooth and orbifold test configurations.
Any solvency regime for financial institutions should be aligned with the fundamental objectives of regulation: protecting liability holders and securing the stability of the financial system. The first objective leads to consider surplus-invariant capital adequacy tests, i.e. tests that do not depend on the surplus of…
Develops tests for conditional symmetry under group actions.
Randomization tests rely on simple data transformations and possess an appealing robustness property. In addition to being finite-sample valid if the data distribution is invariant under the transformation, these tests can be asymptotically valid under a suitable studentization of the test statistic, even if the invari…
The paper extends hypothesis testing to non-diagonalizable matrices, improving network statistics inference.
Paper introduces effect-invariance for better policy generalization.
The regulator is interested in proposing a capital adequacy test by specifying an acceptance set for firms' capital positions at the end of a given period. This set needs to be surplus-invariant, i.e., not to depend on the surplus of firms' shareholders, because the test means to protect firms' liability holders. We pr…
For smooth test configurations, there always exist C^{1,1} geodesic rays in Kahler metric space parallel to the algebraic ray. The invariant agrees with Futaki invariant, at least under nice assumptions. Explicit examples in Toric cases are calculated. On simple test configurations, Donaldson's correspondence be…
Develops non-parametric tests for group symmetry in data.
The theory of acceptance sets and their associated risk measures plays a key role in the design of capital adequacy tests. The objective of this paper is to investigate, in the context of bounded financial positions, the class of surplus-invariant acceptance sets. These are characterized by the fact that acceptability …
In this paper, we give a new version of the modified Futaki invariant for a test configuration associated to the soliton action on a Fano manifold. Our version will naturally come from toric test configurations defined by Donaldson for toric manifolds. As an application, we show that the modified -energy is proper f…
The paper tackles spurious correlations in machine learning models and introduces counterfactual invariance.
New framework learns sufficient invariant features robustly across distribution shifts.
In this note, we consider a sequence of test configurations compatible with a Kaehler metric in on a polarized algebraic manifold . Then an explicit formula for the Donaldson-Futaki invariant for the sequence will be given.
Tests for equivariance in non-parametric regression models.
New method uses MMD estimators to enforce model invariance with missing data.
Kernel embeddings of distributions and the Maximum Mean Discrepancy (MMD), the resulting distance between distributions, are useful tools for fully nonparametric two-sample testing and learning on distributions. However, it is rarely that all possible differences between samples are of interest -- discovered difference…
New method learns models to adapt to domain shifts at test time.
New approach to -stability and critical metrics on Kähler manifolds.
Paper computes stability of Q-Fano spherical varieties using test configurations and Futaki invariants.
Proposes a measure to predict generalization in non-matching environments.
Hotelling's -test for the mean of a multivariate normal distribution is one of the triumphs of classical multivariate analysis. It is uniformly most powerful among invariant tests, and admissible, proper Bayes, and locally and asymptotically minimax among all tests. Nonetheless, investigators often prefer non-inva…
Paper tests if beta coefficients in AMF model are consistent over time.
New method selects causal features from diverse data types.
New test uncovers causal links in rare event dynamics.
The study connects K-stability and large complex structure limits in mirror symmetry.
Introduces valuative stability for polarised varieties, equivalent to K-stability.
This note improves correlation stress tests using geodesic distance.
In this note, given a polarized algebraic manifold , we define the Donaldson-Futaki invariant for a sequence of test configurations for with exponents tending to infinity. This then allows us to define a strong version of K-stability or K-semistability for . In particular, will be shown to…
Chern-Simons theory in the 1/N expansion has been conjectured to be equivalent to a topological string theory. This conjecture predicts a remarkable relationship between knot invariants and Gromov-Witten theory. We review some basic aspects of this relationship, as well as the tests of this conjecture performed over th…
Enhances GNNs by capturing node relationships, outperforming 2-WL test.
Improves contrastive learning invariance with novel training objectives and feature averaging.
This paper develops methods for obtaining distribution-free prediction regions for invariant representations.
The paper classifies test configurations and derives a criterion for uniform K-stability of certain algebraic varieties.
SFB uses stable features to adapt unstable ones for better performance.
Study shows IRM framework can be unstable with small changes, leading to worse generalization.
In recent years, convolutional neural networks (CNN) have played an important role in the field of deep learning. Variants of CNN's have proven to be very successful in classification tasks across different domains. However, there are two big drawbacks to CNN's: their failure to take into account of important spatial h…
We compute the vacuum expectation values of torus knot operators in Chern-Simons theory, and we obtain explicit formulae for all classical gauge groups and for arbitrary representations. We reproduce a known formula for the HOMFLY invariants of torus links and we obtain an analogous formula for Kauffman invariants. We …
We consider the problem of undirected graphical model inference. In many applications, instead of perfectly recovering the unknown graph structure, a more realistic goal is to infer some graph invariants (e.g., the maximum degree, the number of connected subgraphs, the number of isolated nodes). In this paper, we propo…
For test configurations, the Donaldson-Futaki invariant F_1 is well-known. In this note, its refinement will be discussed. Then we see that Li-Xu's pathology doesn't occur, since their example of a non-normal test configuration, with trivial normalization, actually has non-vanishing F_1 in this refined sense.
New models exploit invariance to reduce model complexity.
We propose a new algorithm for Dehn surgery problem, finding exceptional Dehn filling slopes for a given hyperbolic 3-manifold with a torus boundary, using a quantum invariant called "3D index". The invariant is defined using an ideal triangulation of the cusped 3-manifold. We test the algorithm for many examples.
Bayesian Hierarchical Invariant Prediction refines ICP for better scalability and prior integration.
New framework detects directional influence in multivariate time series.
Domain generalization aims to apply knowledge gained from multiple labeled source domains to unseen target domains. The main difficulty comes from the dataset bias: training data and test data have different distributions, and the training set contains heterogeneous samples from different distributions. Let denote …
For any flat projective family $(\mX,\mL)\rightarrow C$ such that the generic fibre $\mX_η$ is a klt Q-Fano variety and $\mL|_{\mX_η}\sim_{Q}-K_{X_η}$, we use the techniques from the minimal model program (MMP) to modify the total family. The end product is a family such that every fiber is a klt Q-Fano variety. Moreov…
We focus on two supervised visual reasoning tasks whose labels encode a semantic relational rule between two or more objects in an image: the MNIST Parity task and the colorized Pentomino task. The objects in the images undergo random translation, scaling, rotation and coloring transformations. Thus these tasks involve…
The paper introduces a test to distinguish spatial graphs based on their knot diagrams.