Deep CNN learns writer-independent features for signature verification.
problem Building classifiers that can distinguish between genuine and forged signatures.
method Used Deep Convolutional Neural Networks to learn writer-independent features.
result Features learned from one set of users are discriminative for other users, including across different datasets.
The study tackles forgery in machine unlearning, showing that forging is limited and can be detected.
problem Adversarial crafting of data to mimic model behavior without removing information.
method Developed a framework to analyze ε-forging sets and proved their measure decay. result The forging set measure decays as ε(d−r)/2, providing evidence against false unlearning claims. Paper proposes detecting video manipulation using stream descriptors.
problem Misuse of manipulated video content.
method Binary classifiers on multimedia stream descriptors.
result Scalable approach can detect high-quality manipulations.
Interpool solves interoperability issues by minting, exchanging, and burning tokens within a single liquidity pool.
problem Lack of proper interoperability in blockchain use cases.
method Interpool operates as a standalone liquidity pool that mints, exchanges, and burns tokens, optimizing the order of transactions in the mempool.
result Interpool transforms front-running issues into a solution that ensures ultimate liquidity through a burning procedure, enabling trustless design.
The paper constructs homotopically rigid spaces for applications in algebraic topology.
problem Creating highly connected rational spaces with specific symmetries.
method Constructing infinite families of homotopically rigid spaces and using them as building blocks.
result Examples of highly connected inflexible and strongly chiral manifolds.
The paper explains the importance of diffeological groupoids in modern geometry and physics.
problem None explicitly stated, focuses on the concept and applications.
method Expository review of the development and applications of diffeological groupoids.
result The diffeological groupoid serves as a powerful tool in various areas of modern geometry and physics.
Random forests improve probability estimates through kernel regression.
problem Improving the principled approach to random forest probability estimation.
method Forge a connection between random forests and kernel regression, develop a proximity kernel model.
result Improves statistical footing of random forest probability estimation.
The paper revisits expected signatures in semimartingale models, providing new formulae and simplifying complexity.
problem Computing expected signatures in semimartingale models.
method Revisits and provides new formulae for computing expected signatures in a general semimartingale setting.
result Log-transform of expected signatures simplifies complexity, leading to signature cumulants.
Defines knot signature invariant using G-signature theorem.
problem No specific problem stated; focuses on knot theory.
method Uses G-signature theorem to define knot invariant.
result Defines an invariant for strongly invertible knots.
Deep signature/log-signature FBSDE algorithm improves accuracy and training time.
problem Solving FBSDEs with state and path dependent features.
method Incorporates deep signature/log-signature transformation into RNN model.
result Improves accuracy and training time compared to existing methods.
A well-known property of the signature of closed oriented 4n-dimensional manifolds is Novikov additivity, which states that if a manifold is split into two manifolds with boundary along an oriented smooth hypersurface, then the signature of the original manifold equals the sum of the signatures of the resulting manifol…
Maximum Levine-Tristram signature of torus knots follows a reduction formula.
problem Determining the maximum Levine-Tristram signature for torus knots.
method Proved a reduction formula analogous to Gordon-Litherland-Murasugi's classical signature result.
result Maximum Levine-Tristram signature of torus knots satisfies a reduction formula.
New findings on mesh group-planes validate Signature-inverse Theorem under specific conditions.
problem Invalidity of existing inverse theorems for mesh group-planes.
method Classification of three and five point meshes, analysis of joint invariant signatures.
result Valid conditions for the Signature-inverse Theorem in mesh group-planes.
Introduces flat discrete signatures for financial data analysis.
problem Representing financial data for machine learning without continuous transformation.
method Introduced flat discrete signatures and discrete signatures, generalizing flat discrete signatures.
result Flat discrete signatures can represent quadratic variation relevant in finance.
Method extracts cancer signatures from genome data, reducing noise and variability.
problem Identifying stable cancer signatures from noisy genomic data.
method Applied statistical risk models from finance to cancer genome data, using NMF.
result Extracted signatures have lower variability and improved stability.
This is a sequel to the paper "The signature package on Witt spaces, I. Index classes" by the same authors. In the first part we investigated, via a parametrix construction, the regularity properties of the signature operator on a stratified Witt pseudomanifold, proving, in particular, that one can define a K-homology …
We define the Analytical signature, the Hodge signature and the de Rham signature for a foliated manifold with boundary with foliation transverse to the boundary. We show that all these signatures coincide and a Hirzebruch formula is valid.
The paper examines the consistency of Lasso regression applied to signature analysis of time series data.
problem Consistency of Lasso regression in signature analysis of time series data.
method The paper studies the consistency of Lasso regression applied to signature analysis of time series data, both theoretically and numerically.
result The Lasso regression is consistent both asymptotically and in finite sample for certain types of time series and processes.
Study signatures of torus links and their cores using Neumann's equivariant signatures and Hirzebruch's formula.
problem Computing signatures of torus links and their cores.
method Use Neumann's equivariant signatures and rewrite Hirzebruch's formula for torus links (without cores) in terms of integral points in a parallelogram.
result Rewritten Hirzebruch's formula for torus links with cores using integral points in a parallelogram.
New methods price American options in rough volatility models.
problem Pricing American options under rough volatility.
method Integrating deep-signature and signature-kernel learning into optimal stopping problem solutions.
result Performance comparison in rough Heston and rough Bergomi models.
New signatures for knotted graphs linked to classical knot signatures.
problem Defining invariants for knotted trivalent graphs.
method Using branched covers to define and relate new signatures to classical knot signatures.
result Computable invariants for Kinoshita's knotted theta graph.
Paper interprets UMAP and t-SNE as probabilistic MAP inference.
problem Understanding and interpreting UMAP and t-SNE.
method Interprets UMAP and t-SNE as MAP inference methods corresponding to a probabilistic model of the graph Laplacian.
result Shows UMAP and t-SNE can be understood as probabilistic inference methods.
This paper extends the C*-signature to non-Witt spaces using noncommutative geometric methods.
problem Extending the signature to non-Witt spaces with noncommutative geometric methods.
method Noncommutative geometric methods, combinatorial framework, and comparison with analytical signature.
result Constructing the C*-signature on non-Witt spaces.
Paper generalizes path signature using fractional calculus for improved machine learning.
problem Improving path signature for machine learning applications.
method Introduces two new signatures inspired by fractional calculus and machine learning considerations.
result Significant accuracy improvements in handwritten digit recognition.
New method classifies signatures of group actions on Riemann surfaces.
problem Classifying signatures of group actions on Riemann surfaces.
method Analyzes arithmetic conditions first, then uses group theory.
result Complete list of signatures for every genus, subset that appears as group action.
Handwritten signature verification remains challenging, especially offline.
problem Discriminate genuine from forged signatures in static scenarios.
method Review of past research and analysis of recent advancements in Deep Learning.
result Deep Learning has shown promise in feature representation learning from signature images.
pySigLib speeds up signature-based computations on CPUs and GPUs.
problem Efficient signature-based computations on large datasets and long sequences.
method Optimised Python library for CPU and GPU, novel differentiation scheme.
result Accurate gradients at a fraction of the runtime of existing libraries.
Efficiently computes sparse signature coefficients using kernels.
problem Lack of efficient methods for sparse signature coefficients.
method Signature kernels and PDE-based methods.
result Sparse groups of signature coefficients can be isolated effectively.
Paper introduces branched signature model for efficient computation and data-driven applications.
problem Efficient computation and data-driven modeling of branched rough paths.
method Develops a universal approximation theorem and constructs an extension map to realize branched signatures.
result Explicit construction of branched signatures via an extension map for efficient computation.
New method calculates signatures of biquotients.
problem Signature calculation for homogeneous spaces.
method Generalization of Hirzebruch's computation to biquotients.
result Signature of biquotients computed for equal rank cases.
Link signature limit depends on linking matrix under specific polynomial condition.
problem Limits of Tristam-Levine signature function under precise polynomial conditions.
method Analysis of Alexander polynomial and linking matrix.
result Limit of Tristam-Levine signature at 1 determined by linking matrix under specific polynomial condition.
Path signatures improve hedging of exotic derivatives in non-Markovian models.
problem Hedging exotic derivatives under non-Markovian stochastic volatility models.
method Investigates path signatures in deep and shallow learning contexts, comparing neural networks and regression approaches.
result Path signatures outperform LSTM in most cases and yield more accurate results in hedging.
Knot signature function defined and conditions for its existence are given.
problem Defining and characterizing the signature function of knots.
method Presentation of necessary and sufficient conditions for a function to be a knot signature function.
result Conditions for a function to be the signature function of a knot are established.
Develops a new family of signature-changing models on metric manifolds.
problem Signature changes in metric manifolds.
method One-parameter family of Lorentz-Riemann models, local expressions around change.
result Generalizes existing signature-changing models.
Motivation: Cell-biological processes are regulated through a complex network of interactions between genes and their products. The processes, their activating conditions, and the associated transcriptional responses are often unknown. Organism-wide modeling of network activation can reveal unique and shared mechanisms…
We prove that the signature of an even, symmetric form on a finite rank integral lattice, has signature divisible by 8, provided its associated linking form vanishes in the Witt group of linking forms. Our result generalizes the well know fact that an even, unimodular form has signature divisible by 8. We give applicat…
Introduces signature method for machine learning data.
problem Transforming complex data into usable features.
method Signature method applied to data paths, capturing analytic and geometric properties.
result Signature method effectively transforms data for machine learning tasks.
Paper confirms Kashaev's signature conjecture for links.
problem Proving Kashaev's conjecture about link invariants.
method Using Seifert surface definition and diagrammatic approach.
result Established Kashaev's conjecture, providing a new formula for Alexander polynomial.
The paper defines signatures for Witt spaces with boundary and proves their equality.
problem Defining and proving signatures for Witt spaces with boundary.
method Introducing de Rham and Hodge signatures, extending index theory, and using von Neumann algebras.
result Equality of de Rham and Hodge signatures on Witt spaces with boundary.
A new method uses signatures to classify shapes efficiently.
problem Classifying shapes succinctly and invariantly.
method Proposes a method using signatures for shape classification.
result Outperforms current methods like SRV transform and dynamic programming.
Link signature jumps linked to polynomial roots.
problem Understanding signature jumps of link diagrams.
method Relating signature jumps to roots of Alexander polynomials.
result Signature jumps connected to polynomial roots.
A new deep learning approach enhances signature transforms for data analysis.
problem Improving data analysis through more flexible signature transforms.
method Combining deep learning with signature transforms to select terms data-dependently.
result Signature transform can be used as a pooling operation within neural networks.
A new graph signature invariant to graph automorphisms.
problem Graph symmetry and feature generation.
method Power spectrum signature derived from squared graph Fourier transform.
result Power spectrum signature is stable under graph perturbations.
Study finds infinitely many surface bundle types with zero signature.
problem Characterizing homeomorphism types of surface bundles with specific signatures.
method Analyzing atoroidal surface bundles over surfaces.
result Infinitely many homeomorphism types of atoroidal surface bundles over surfaces with signature zero.
The study explains why signature methods work in commodity futures term structure classification.
problem Lack of interpretability in signature methods for term structure classification.
method Introducing signature perturbations to explain the success of signature-based classification.
result The volatility of the convenience yield is the major discriminant for commodity markets classification.
Study links' concordance using signatures and nullity.
problem Link concordance invariance of Levine-Tristram signatures.
method Determine invariance for complex numbers on the unit circle.
result Signature and nullity give link concordance invariants.
Study on signatures of positive braids with bounds derived.
problem Understanding signatures of positive braids and their invariants.
method Derived lower bounds for Levine-Tristram signatures, and upper and lower bounds on signature ratios.
result Established bounds on signatures of positive braids, uniformly valid across monoids.
For a normal covering over a closed oriented topological manifold we give a proof of the L2-signature theorem with twisted coefficients, using Lipschitz structures and the Lipschitz signature operator introduced by Teleman. We also prove that the L-theory isomorphism conjecture as well as the C^*_max-version of the Bau…