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.
Shallow nonlinear networks can separate classes linearly with polynomially scaling width.
New constructions from non-separating planar graphs improve understanding of graph linkability and knotability.
Modern large-scale datasets are frequently said to be high-dimensional. However, their data point clouds frequently possess structures, significantly decreasing their intrinsic dimensionality (ID) due to the presence of clusters, points being located close to low-dimensional varieties or fine-grained lumping. We test a…
New framework links fractal complexity to separation dimension.
New proof shows no flat embedding for Petersen family graphs.
The complement of a non-separating planar graph contains a K_n minor.
Exploration in sparse reward reinforcement learning remains an open challenge. Many state-of-the-art methods use intrinsic motivation to complement the sparse extrinsic reward signal, giving the agent more opportunities to receive feedback during exploration. Commonly these signals are added as bonus rewards, which res…
We bound the locations of outermost minimal surfaces in geometrostatic manifolds whose ADM mass is small relative to the separation between the black holes and prove the Intrinsic Flat Stability of the Positive Mass Theorem in this setting.
Minimal simplicial complexes in high dimensions always contain complex links.
Scattering networks maximize separation on low-dimensional data.
A new measure of causal influence quantifies intrinsic contributions in DAGs.
A new multi-objective RL framework improves intrinsic exploration performance.
EOI enhances individuality in multi-agent systems.
Characterizes minor-minimal separating projective planar graphs and their generalizations.
The paper analyzes the intrinsic exploration terms in policy-gradient algorithms.
Theoretical and empirical taxonomy of imbalance in binary classification.
The focus of this paper is on intrinsic methods to detect overfitting. By intrinsic methods, we mean methods that rely only on the model and the training data, as opposed to traditional methods (we call them extrinsic methods) that rely on performance on a test set or on bounds from model complexity. We propose a famil…
We provide the proof that the space of time series data is a Kolmogorov space with -separation axiom using the loop space of time series data. In our approach we define a cyclic coordinate of intrinsic time scale of time series data after empirical mode decomposition. A spinor field of time series data comes fro…
New curvature bounds defined for Lorentzian spaces.
Intrinsic dimensionality (ID) is one of the most fundamental characteristics of multi-dimensional data point clouds. Knowing ID is crucial to choose the appropriate machine learning approach as well as to understand its behavior and validate it. ID can be computed globally for the whole data point distribution, or comp…
New saliency evaluations focus on completeness and soundness, improving explanations.
TOFU-POV tackles partially observed linear bandits, achieving sublinear regret with low-dimensional action vectors.
Measures mode separation in high-dimensional densities via a reversible diffusion process.
We propose a data-driven approach to solve multiscale elliptic PDEs with random coefficients based on the intrinsic low dimension structure of the underlying elliptic differential operators. Our method consists of offline and online stages. At the offline stage, a low dimension space and its basis are extracted from th…
Unsupervised mesh disentanglement separates identity and pose.
Functional Magnetic Resonance Imaging (fMRI) is a powerful non-invasive tool for localizing and analyzing brain activity. This study focuses on one very important aspect of the functional properties of human brain, specifically the estimation of the level of parallelism when performing complex cognitive tasks. Using fM…
The paper optimizes RV estimation by efficient sampling in time-changed diffusion models.
In many situations, classes of data points of primary interest also happen to be those that are least numerous. A well-known example is detection of fraudulent transactions among the collection of all financial transactions, the vast majority of which are legitimate. These types of problems fall under the label of `rar…
Disentangled representation learning finds compact, independent and easy-to-interpret factors of the data. Learning such has been shown to require an inductive bias, which we explicitly encode in a generative model of images. Specifically, we propose a model with two latent spaces: one that represents spatial transform…
High-dimensional models trained on smooth manifolds achieve optimal rates in Wasserstein metrics.
Study local exploration on dynamic graphs with time-varying edges.
The classification of multi-class microarray datasets is a hard task because of the small samples size in each class and the heavy overlaps among classes. To effectively solve these problems, we propose novel Error Correcting Output Code (ECOC) algorithm by Enhance Class Separability related Data Complexity measures du…
Differential privacy of Gaussian process posterior sampling
Curiosity-Critic improves world model training by focusing on cumulative prediction error.
We analyze the spectral clustering procedure for identifying coarse structure in a data set , and in particular study the geometry of graph Laplacian embeddings which form the basis for spectral clustering algorithms. More precisely, we assume that the data is sampled from a mixture model supported on …
Analysis of 'big data' characterized by high-dimensionality such as word vectors and complex networks requires often their representation in a geometrical space by embedding. Recent developments in machine learning and network geometry have pointed out the hyperbolic space as a useful framework for the representation o…
The goal of the present paper is to investigate the algebraic structure of global conformal invariants of submanifolds. These are defined to be conformally invariant integrals of geometric scalars of the tangent and normal bundle. A famous example of a global conformal invariant is the Willmore energy of a surface. In …
This work proposes external correctors for quick AI error corrections without system modification.
Introduces intrinsic Hopf-Lax semigroup linking to intrinsic slope.
Infants are experts at playing, with an amazing ability to generate novel structured behaviors in unstructured environments that lack clear extrinsic reward signals. We seek to mathematically formalize these abilities using a neural network that implements curiosity-driven intrinsic motivation. Using a simple but ecolo…
This paper has two main goals. First, we give a complete, explicit, and computable solution to the problem of when two simple closed curves on a surface are equivalent under the Johnson kernel. Second, we show that the Johnson filtration and the Johnson homomorphism can be defined intrinsically on subsurfaces and prove…
Robustly detects jumps in high-frequency CIR and CKLS models.
Develops a new tensor model for clustering with degree correction.
We propose new symplectic networks (SympNets) for identifying Hamiltonian systems from data based on a composition of linear, activation and gradient modules. In particular, we define two classes of SympNets: the LA-SympNets composed of linear and activation modules, and the G-SympNets composed of gradient modules. Cor…
Survey of intrinsically linked or knotted graphs.
The paper studies properties of intrinsically Lipschitz constants in metric spaces.
We introduce new sufficient conditions for intrinsic knotting and linking. A graph on n vertices with at least 4n-9 edges is intrinsically linked. A graph on n vertices with at least 5n-14 edges is intrinsically knotted. We also classify graphs that are 0, 1, or 2 edges short of being complete partite graphs with respe…
The paper tackles transfer learning for growing matrix representations, improving estimation accuracy.