The general problem for consistency between arbitrary transports along paths in fibre bundles and bundle morphisms between them is formulated and investigated. The special case of one fibre bundle, its morphism and transport along paths acting in it is considered. The consistency between linear transports along paths i…
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48 results for “path consistency”
The problem for consistency between linear transports along paths and real bundle metrics in real vector bundles is stated. Necessary and/or sufficient conditions, as well as conditions for existence, for such consistency are derived. All metrics (resp. transports) consistent with a given transport (resp. metric) are e…
In this paper, we recover sparse signals from their noisy linear measurements by solving nonlinear differential inclusions, which is based on the notion of inverse scale space (ISS) developed in applied mathematics. Our goal here is to bring this idea to address a challenging problem in statistics, \emph{i.e.} finding …
Unified dynamic approach for sparse model selection improves efficiency and accuracy.
problem Sparse model selection challenges in various fields.
method Iterative regularization path using Mirror Descent or Linearized Bregman Iterations.
result Path consistency theory with no false positives and minimax optimal error rate.
New algebraic structures for topological pairs.
problem No specific problem stated; generalization of knot quandles.
method Introducing multi-quandles for topological pairs.
result New algebraic structures for topological pairs.
Deep network solves maze path planning without training.
problem Efficient path planning in large mazes with obstacles.
method Max pooling layers without training.
result Solves mazes with over half a billion nodes in short time.
The study compares different game-theoretic attribution methods and finds that interventional Shapley values yield less consistent results than Aumann-Shapley due to path symmetry.
problem Investigating the influence of path choice on game-theoretic attribution algorithms.
method Comparative analysis of interventional Shapley values and Generalized Integrated Gradients (GIG) methods.
result Interventional Shapley values yield less consistent attributions than Aumann-Shapley due to path symmetry and extended away from the training data manifold.
Path-connectivity of thick laminations on high-genus surfaces.
problem Path-connectivity of thick laminations on high-genus surfaces.
method Teichmüller ray analysis and subshift of finite type construction.
result Path-connectedness of the Morse boundary of the mapping class group.
For a 3-manifold with fibered over and the fiberwise gradient of a fiberwise Morse function on , we introduce the notion of amidakuji-like path (AL-path) on . An AL-path is a piecewise smooth path on consisting of edges each of which is either a part of a critical locus of or a fl…
Predicts path failures in evolving networks using deep learning.
problem Predicting path failures in time-evolving graphs.
method LRGCN, SAPE
result LRGCN outperforms other methods in path failure prediction.
Path Integral Method for Proportional Step and Proportional Double-Barrier Step Option Pricingq-fin.PR
Path integral method calculates barrier option prices.
problem Barrier option pricing in finance.
method Path integral method applied to trapezoid and square potential barriers.
result Analytical expressions for option pricing derived.
In this thesis, we study the problem of feature learning on heterogeneous knowledge graphs. These features can be used to perform tasks such as link prediction, classification and clustering on graphs. Knowledge graphs provide rich semantics encoded in the edge and node types. Meta-paths consist of these types and abst…
Anticipatory Reinforcement Learning: From Generative Path-Laws to Distributional Value Functionscs.LG
ARL bridges non-Markovian decision processes with reinforcement learning, improving foresight and stability.
problem Inaccurate foresight in non-Markovian environments due to state-based methods' limitations.
method Lifted state space into a signature-augmented manifold, using a self-consistent field approach to anticipate future path-law.
result ARL achieves deterministic evaluation of expected returns with reduced computational complexity and variance.
Flow Matching enables robust training of CNFs with various probability paths.
problem Training Continuous Normalizing Flows (CNFs) at large scales.
method Flow Matching (FM) is a simulation-free approach for training CNFs by regressing vector fields of conditional probability paths.
result Flow Matching with diffusion paths yields more robust and stable training compared to diffusion-based methods.
Linear time dynamic programming for the exact path of optimal models selected from a finite setcs.LG
New algorithm speeds up path computation for optimal models.
problem Finding the exact path of optimal models from a finite set.
method Dynamic programming approach for linear time computation.
result Dynamic programming achieves linear time for breakpoints computation.
Paper develops approximation and statistical theory for signature-based path regression.
problem Understanding how fast signatures approximate continuous path functionals.
method Develops \(L^2\) approximation rate for smooth functionals of Itô diffusions and establishes consistency of statistical learning procedures.
result Signature-based methods improve prediction over handcrafted features in various real-data applications.
We provide a general construction of time-consistent sublinear expectations on the space of continuous paths. It yields the existence of the conditional G-expectation of a Borel-measurable (rather than quasi-continuous) random variable, a generalization of the random G-expectation, and an optional sampling theorem that…
Develops a new solver for path-dependent PDEs using signature kernels.
problem Solving path-dependent PDEs (PPDEs) efficiently and accurately.
method Uses signature kernels to solve PPDEs by approximating the solution with minimal norm in a reproducing kernel Hilbert space.
result Proves the consistency of the numerical scheme, ensuring convergence to PPDE solutions as the number of collocation points increases.
New method infers population dynamics from snapshots using path space optimization.
problem Recover dynamics of a population from its temporal marginals.
method Grid-free algorithm using Schrödinger bridges coupled via noisy gradient descent in mean-field limit.
result Global convergence to min-entropy estimator with end-to-end theoretical guarantees.
PDGM uses neural nets to solve complex financial equations.
problem Solving path-dependent partial differential equations (PPDEs)
method Generalized Deep Galerkin Method (PDGM) combining feed-forward and LSTM architectures
result PDGM successfully models solutions to various PPDEs, including financial derivatives.
Neural A* uses machine learning to improve path planning efficiency.
problem Challenges in applying machine learning to search-based path planning.
method Reformulated A* search as a differentiable network coupled with a convolutional encoder.
result Neural A* outperforms state-of-the-art planners in optimality and efficiency.
The Viterbi process can be extended indefinitely in a pairwise Markov model.
problem Estimating hidden chains in pairwise Markov models.
method Construction of barriers to ensure Viterbi path goes through states.
result The Viterbi process is regenerative in the PMM.
New method generates realistic financial price paths with drawdowns.
problem Lack of realistic drawdown scenarios in financial simulations.
method Variational autoencoder with drawdown reconstruction loss and path signatures.
result Simulated paths closely match empirical drawdown data.
PSLR classifies functional data with scalar covariates using path signatures.
problem Classical functional logistic regression models have limitations in capturing nonlinear and cross-channel dependencies.
method PSLR uses truncated path signatures to create a basis-free representation of functional data.
result PSLR outperforms traditional functional classifiers in accuracy and robustness, especially under non-uniform sampling.
PAGTN improves molecular property prediction by leveraging longer-range graph dependencies.
problem Local aggregation in GCNs misses higher-order graph properties.
method PAGTN uses path features and global attention layers to capture longer-range dependencies.
result PAGTN outperforms GCNs on various molecular property prediction datasets.
EntroPath learns manifold geometry from diffusion paths.
problem Learning geodesic geometry from data graphs with spurious shortcuts.
method Maximum Entropy Path Ensemble Embedding (MERW) with k-step diffusion paths.
result EntroPath converges to squared geodesic distance in the short-time limit.
The recently developed bag-of-paths (BoP) framework consists in setting a Gibbs-Boltzmann distribution on all feasible paths of a graph. This probability distribution favors short paths over long ones, with a free parameter (the temperature ) controlling the entropic level of the distribution. This formalism enables…
This paper optimizes paths for generative models using kinetic energy.
problem Improving generative model performance and sample quality.
method Investigating and optimizing Gaussian probability paths with kinetic energy.
result Kinetic optimal Gaussian paths simplify particle trajectories and improve model performance.
Generating solution paths of Markovian stochastic differential equations using diffusion modelscs.LG
New AI method generates SDE paths without explicit coefficients.
problem Simulating unknown Markovian SDEs with limited data.
method Uses conditional diffusion models on sample paths.
result Consistently outperforms alternative methods in KL divergence.
Proposes HetSANN for learning heterogeneous graph structures without meta-paths.
problem Learning low-dimensional vector space of heterogeneous information networks.
method Implicitly represents heterogeneous information through entity space transformation and attention mechanism.
result Significant improvements over state-of-the-art solutions on public datasets.
Collective classification has been intensively studied due to its impact in many important applications, such as web mining, bioinformatics and citation analysis. Collective classification approaches exploit the dependencies of a group of linked objects whose class labels are correlated and need to be predicted simulta…
It is shown how to obtain accurate values for American options using Monte Carlo simulation. The main feature of the novel algorithm consists of tracking the boundary between exercise and hold regions via optimization of a certain payoff function. We compare estimates from simulation for some types of claims with resul…
Tutorial on recursive models for predicting path choices.
problem Modeling path choice behavior of network users.
method Recursive discrete choice models.
result Advantages of recursive models over path-based models.
New method for learning on heterogeneous graphs without meta-paths.
problem Learning on heterogeneous graphs is sensitive to meta-paths choice, leading to poor performance.
method Decompose heterogeneous graph into homogeneous relation-type graphs, combine higher-order representations, use attention mechanisms.
result Our model outperforms state-of-the-art baselines in vertex classification tasks on heterogeneous graph datasets.
The abstract discusses the linear and smooth structures of mapping spaces.
problem The structure of mapping spaces in differential geometry.
method Proving diffeomorphisms and fibre bundle properties.
result Path spaces and base point preserving mapping spaces are Fréchet spaces.
AdaPID optimizes diffusion-based samplers by dynamically adjusting schedules.
problem Optimizing the intermediate-time dynamics in diffusion-based samplers.
method Develops a time-varying stiffness schedule using Piece-Wise-Constant (PWC) parametrizations and a hierarchical refinement approach.
result QoS-driven PWC schedules consistently improve sampling fidelity and accuracy.
Efficient Path Prediction for Semi-Supervised and Weakly Supervised Hierarchical Text Classificationcs.LG
Efficiently predicts paths in hierarchical text classification using unlabeled data.
problem Costly labeling of documents in hierarchical text classification.
method Path cost-sensitive learning algorithm using generative model and path constraints.
result Significantly reduces computational cost and improves efficiency.
An almost complex structure J on a 4-manifold X may be described in terms of a rank 2 vector bundle E. A splitting of J consists of a pair of line bundles spanning E. A hypersurface M in X satisfying a nondegeneracy condition inherits a CR-structure from J and a path geometry from the splitting. Using the Cartan-Kähler…
Temporal Coarse-Graining of Latent Default-Probability Paths Generates Effective Default Correlationq-fin.ST
Temporal aggregation reveals latent default correlation from monthly data.
problem Understanding effective default correlation from monthly default data.
method Temporal coarse-graining of latent default-probability paths.
result Temporal coarse-graining improves identifiability and reduces over-allocation of long-horizon fluctuations.
A new path development layer reduces dimensionality for irregular time series.
problem High-dimensional irregular paths in machine learning.
method Finite-dimensional Lie group representations for dimension reduction.
result The development layer outperforms signature features in accuracy and dimensionality.
Non-parametric Determination of Real-Time Lag Structure between Two Time Series: the "Optimal Thermal Causal Path" Methodcond-mat.stat-mech
We introduce a novel non-parametric methodology to test for the dynamical time evolution of the lag-lead structure between two arbitrary time series. The method consists in constructing a distance matrix based on the matching of all sample data pairs between the two time series. Then, the lag-lead structure is searched…
New SigSwap model for path-dependent financial risk.
problem Managing complex, path-dependent financial risks.
method Geometry-based approach using path-signature and Signature Expected Shortfall.
result Path-dependent risks can be converted into transparent risk factors.
Temporal Coarse-Graining of Latent Default-Probability Paths Generates Effective Default Correlationq-fin.ST
Temporal coarse-graining of latent default paths explains effective correlation in corporate defaults.
problem Understanding effective default correlation in corporate defaults.
method Temporal coarse-graining of latent default-probability paths, applied to corporate default-count data.
result Temporal coarse-graining provides a scale-consistent baseline that improves identifiability and reduces over-allocation of long-horizon fluctuations.
A conformal procedure improves CoT reasoning by aggregating reasoning paths and calibrating abstention rules.
problem Aggregation uncertainty in chain-of-thought reasoning makes correct answers less reliable.
method Introduces a conformal procedure for CoT reasoning that uses weighted score aggregation and abstention rules.
result Achieves higher selective accuracy with abstention, reducing confident-error rate.
Certain natural geometric approximation schemes are developed for Wiener measure on a compact Riemannian manifold. These approximations closely mimic the informal path integral formulas used in the physics literature for representing the heat semi-group on Riemannian manifolds. The path space is approximated by finite …
New bounds on knotting probability of equilateral hexagons found.
problem Determining the knotting probability of equilateral hexagons.
method Symplectic geometry techniques to parametrize and analyze the space of equilateral hexagons.
result New bounds on the knotting probability of equilateral hexagons.
Sparse neural networks training is difficult due to optimization failures and energy landscape issues.
problem Training sparse neural networks leads to suboptimal solutions and optimization failures.
method Investigated optimization dynamics and energy landscape in sparse neural networks.
result Sparse neural networks have a linear path with a monotonically decreasing objective from initialization to a good solution, but not from a bad solution.
If a knot is represented by an m-strand braid, then HOMFLY polynomial in representation R is a sum over characters in all representations Q\in R^{\otimes m}. Coefficients in this sum are traces of products of quantum R-matrices along the braid, but these matrices act in the space of intertwiners, and their size is equa…