Method predicts diffusion reach probabilities using node embeddings.
problem Estimating diffusion reach probabilities with limited cascades and network information.
method Representation learning on node embeddings for cascade prediction.
result Proposed method outperforms using available cascade data.
First order discretizations of Langevin diffusion can achieve better generalization error with additional smoothness assumptions.
problem Analyzing generalization error for first order discretizations of Langevin diffusion.
method Providing a sufficient smoothness condition to show that first order methods can achieve arbitrarily runtime complexity for a given expected generalization error.
result First order methods can achieve arbitrarily runtime complexity with additional smoothness assumptions.
The study characterizes diffusion model generalization using data-dependent ridge manifolds.
problem Understanding where diffusion model-generated samples lie when not memorizing the training set.
method Introduced a time-dependent family of log-density ridge manifolds to characterize reverse-time inference.
result Generated samples evolve by a reach-align-slide mechanism, controlled by normal and tangential components of training error.
New method learns diffusion bridges for rare events.
problem Simulating rare events in diffusion processes.
method Iterative online learning based on self-consistency.
result Strong performance in various empirical settings.
A new model captures diffusion dynamics in networks using hidden states.
problem Capturing temporal relationships and hidden content trajectories in network diffusion.
method A topological recurrent neural model that embeds diffusion history as hidden states.
result Good experimental performances for diffusion modeling and prediction.
Faster diffusion-based models generate data with fewer steps.
problem Slow and costly diffusion-based generative models.
method Truncate diffusion process to generate data more efficiently.
result Truncated models provide consistent improvements in performance.
ELM combines machine learning and feature engineering for anomalous diffusion detection.
problem Quantitative characterization of anomalous diffusion from single trajectories.
method Extreme Learning Machine (ELM) combined with feature engineering.
result ELM achieves satisfactory performance in AnDi challenge tasks.
A new method for efficient diffusion geometry computation from data regions.
problem Heavy computational load in diffusion maps for modern data analysis.
method Compressed diffusion process between data regions using an adapted MGC kernel.
result Efficient pointwise diffusion map embedding from data regions.
We propose a diffusion process to describe the global dynamic evolution of credit operations at a national level given observed operations at a subnational level in a sovereign country. Empirical analysis with a unique dataset from Brazilian federate constituents supports the conclusions. Despite the heterogeneity obse…
Diffusion-based classifiers such as those relying on the Personalized PageRank and the Heat kernel, enjoy remarkable classification accuracy at modest computational requirements. Their performance however is affected by the extent to which the chosen diffusion captures a typically unknown label propagation mechanism, t…
We introduce, test and discuss a method for classifying and clustering data modeled as directed graphs. The idea is to start diffusion processes from any subset of a data collection, generating corresponding distributions for reaching points in the network. These distributions take the form of high-dimensional numerica…
Combines SMC and diffusion-based samplers for improved sampling performance.
problem Sampling from unnormalized densities efficiently and robustly.
method Viewing SMC and diffusion-based samplers as continuous-time processes, SCLD combines their strengths.
result SCLD achieves improved performance on multiple benchmark problems with less training budget.
Method recovers causal diffusion mechanisms from steady-state data without parametric assumptions.
problem Recovering causal diffusion mechanisms from steady-state gene expression data.
method Non-parametric kernel estimator for drift function, cross-validation for hyperparameter tuning.
result Full causal mechanism can be non-parametrically identified under weak non-explosion criterion.
PolyNSD improves Neural Sheaf Diffusion with polynomial operators and spectral rescaling.
problem Limitations of common Neural Sheaf Diffusion implementations, including scalability and stability issues.
method Introduces Polynomial Neural Sheaf Diffusion (PolyNSD) with a degree-K polynomial propagation operator and spectral rescaling.
result PolyNSD achieves state-of-the-art results on both homophilic and heterophilic benchmarks with reduced runtime and memory requirements.
Develops a new model for controllable and realistic traffic simulation.
problem Lack of models that offer both controllability and realism in traffic simulation.
method Guided Conditional Diffusion (CTG) model using diffusion modeling and differentiable logic.
result Improves controllability-realism tradeoff over strong baselines.
Improved continuous-time consistency models for large-scale image generation.
problem Training instability and discretization errors in existing diffusion models.
method Unified theoretical framework, improved diffusion process, and network architecture.
result Trained continuous-time CMs at 1.5B parameters, achieving state-of-the-art FID scores.
FSD-CAP improves graph feature imputation under high missing rates.
problem Challenges in imputing missing node features in graphs, especially under high missing rates.
method Two-stage framework: subgraph expansion, fractional diffusion, class-aware propagation.
result Significantly improved imputation quality compared to existing methods, achieving high accuracy on benchmark datasets.
The study examines how shallow neural nets converge to training samples or manifold points during diffusion.
problem Understanding when and how shallow neural nets converge to training samples or manifold points during diffusion.
method Analysis of shallow ReLU neural network denoisers trained with minimal ℓ2 norm, comparing score flow and diffusion flow. result Probability flow converges to training points, sums of training points, or manifold points, depending on the diffusion time scheduler.
Optimizes search times by resetting agents when a threshold is reached.
problem Improving search efficiency in systems with thresholds.
method Develops a framework for correlated stochastic processes with threshold resetting.
result Optimal resetting can prevent larger losses and is applicable to various stochastic systems.
Study non-Gaussian measures' concentration properties in metric spaces.
problem Concentration properties for non-linear Gaussian functionals with non-Gaussian tails.
method Prove generalised Transportation-Cost Inequalities (TCIs) for specific functionals.
result Extended TCIs for rough volatility and Parabolic Anderson Model.
This research explores discrete diffusion models for natural language generation.
problem Challenges in applying diffusion models to discrete data, especially natural language.
method Investigates Discrete Denoising Diffusion Probabilistic Model (D3PM) and compares it with autoregressive models.
result Discrete diffusion models achieve better processing speed than autoregressive models.
Method generates anatomically-controllable medical images with segmentation guidance.
problem Challenging to enforce anatomical constraints in generated medical images.
method Segmentation-guided diffusion models with random mask ablation training.
result New state-of-the-art in faithfulness to input anatomical masks.
DM approximates submanifolds with error bounds.
problem Understanding the accuracy of Diffusion Maps in embedding submanifolds.
method Deriving geometric properties and deriving bounds on embedding errors.
result Error bounds for DM embeddings and tangent spaces.
A new framework maximizes influence spread in social networks by accounting for inter-community diffusion.
problem Real-world social networks have inter-community influence that is often overlooked in community-based IM approaches.
method Community-IM++ uses a heuristic based on community-based diffusion degree and progressive budgeting to model and prioritize cross-community diffusion.
result Community-IM++ achieves near-greedy influence spread at up to 100 times lower runtime than existing methods.
Discrete time hedging in a complete diffusion market is considered. The hedge portfolio is rebalanced when the absolute difference between delta of the hedge portfolio and the derivative contract reaches a threshold level. The rate of convergence of the expected squared hedging error as the threshold level approaches z…
Diffusion models generalize well until a threshold is reached, preventing memorization.
problem Understanding why diffusion models don't memorize training data.
method Investigation of training dynamics and two timescales: τgen and τmem. result The threshold τmem increases linearly with training set size n, preventing memorization. We consider here a Fokker--Planck equation with variable coefficient of diffusion which appears in the modeling of the wealth distribution in a multi-agent society. At difference with previous studies, to describe a society in which agents can have debts, we allow the wealth variable to be negative. It is shown that, e…
Optimal threshold resetting reduces search time for multiple diffusive searchers.
problem Optimizing search time for multiple diffusive searchers in a one-dimensional space.
method Threshold resetting (TR) is introduced as an event-driven optimization strategy, coupling resetting to the internal dynamics of searchers.
result Optimal threshold distance u significantly reduces mean first-passage time for N≥2 searchers, with a minimum at Nopt(u). In this paper we consider two semimartingales driven by diffusions and jumps. We allow both for finite activity and for infinite activity jump components. Given discrete observations we disentangle the {\it integrated covariation} (the covariation between the two diffusion parts, indicated by IC) from the co-jumps. Thi…
Proposes D2D-LSTM for predicting mobile social network content diffusion paths.
problem Lack of accurate content popularity prediction considering time and location in mobile social networks.
method D2D-LSTM, a deep neural network combining user social features and files features.
result Significantly improved prediction accuracy (up to 85.858%) and faster convergence (less than 100 steps).
A new method combines classical and machine learning PDE solvers efficiently.
problem Combining classical and machine learning PDE solvers to reduce computational cost and improve accuracy.
method Proposes an approximate greedy router to select solvers at each iteration, mimicking a greedy approach.
result Consistently reduces final error and AUC of the error trajectory compared to single-solver baselines and hybrid approaches.
We analyze the valuation partial differential equation for European contingent claims in a general framework of stochastic volatility models where the diffusion coefficients may grow faster than linearly and degenerate on the boundaries of the state space. We allow for various types of model behavior: the volatility pr…
Study on sets with positive reach in Euclidean and Riemannian spaces.
problem Understanding sets with positive reach in various spaces.
method Structural results on subsets of positive reach.
result New insights into sets with positive reach in Euclidean and Riemannian spaces.
Study calculates reach and curvature of a specific geometric variety.
problem Computing geometric properties of a specific variety.
method Computed reach, extremal curvature, and volume of a tubular neighborhood.
result Computed geometric properties of the Segre-Veronese variety.
Computes bounds on reach and r-convexity from point cloud data.
problem Computing geometric properties of sets from sparse data.
method Computes upper bounds on reach and r-convexity from point cloud data.
result Bounds converge to true values as point cloud density increases.
Study improves understanding of submanifold reach in Riemannian geometry.
problem Understanding the reach of submanifolds in Riemannian geometry.
method Using the second variation formula to derive geometric results.
result Generalizes previous theorems on reach of submanifolds in Euclidean space.
Deep learning dynamics exhibit anomalous superdiffusion initially, aiding escape from local minima.
problem Understanding the dynamics of learning in deep neural networks.
method Novel analysis of SGD dynamics and loss landscape structure.
result SGD exhibits anomalous superdiffusion initially, transitioning to subdiffusion as learning progresses.
Proposes a new method for GNNs that avoids iterative node state convergence.
problem Iterative computation of node states in GNNs is inefficient and requires many epochs.
method Constrained optimization in the Lagrangian framework to learn transition function and node states simultaneously.
result The proposed method compares favorably with existing models on various benchmarks.
Paper estimates manifold reach using convexity defect function.
problem Estimating the reach of submanifolds from point clouds.
method Relates reach to convexity defect function, uses stability properties, and combines with recent estimators.
result Uniform expected loss bound and minimax rate lower bounds for reach estimation are provided.
We give new characterisations of sets of positive reach and show that a closed hypersurface has positive reach if and only if it is of class C1,1. These results are then used to prove new alternating Steiner formulæ for hypersurfaces of positive reach. Furthermore, it will turn out that every hypersurface that sat…
Paper proposes a method to learn goal-reaching behaviors from scratch using imitation learning.
problem Current reinforcement learning algorithms are brittle and require expert demonstrations.
method Iterated supervised learning where agents relabel and imitate generated trajectories.
result Improved goal-reaching performance and robustness over current RL algorithms.
Continuous-time interpolation of volatility surfaces preserving mixtures and arbitrage-free.
problem Interpolation of volatility surfaces
method Constructing a mixture-preserving, arbitrage-free interpolation
result Lifts Brigo-Mercurio to time-varying weights with additive cost
SciRE-Solver accelerates DMs sampling by recursively calculating the score function derivative.
problem Slow iterative process of diffusion models due to estimating the score function derivative.
method Recursive Difference (RD) method combined with truncated Taylor expansion of score-integrand.
result SciRE-Solver achieves state-of-the-art FIDs with significantly fewer score function evaluations.
We determine the optimal strategy for investing in a Black-Scholes market in order to maximize the probability that wealth at death meets a bequest goal b, a type of goal-seeking problem, as pioneered by Dubins and Savage (1965, 1976). The individual consumes at a constant rate c, so the level of wealth required fo…
Paper proposes an algorithm for sampling from complex mixture distributions without requiring smoothness.
problem Sampling from a mixture of weakly smooth potentials.
method Unadjusted Langevin algorithm with Euler discretization for a mixture of weakly smooth distributions.
result Convergence in Kullback-Leibler divergence and Lβ-Wasserstein metric with polynomial dependence on dimension. Various problems in manifold estimation make use of a quantity called the reach, denoted by τ_M, which is a measure of the regularity of the manifold. This paper is the first investigation into the problem of how to estimate the reach. First, we study the geometry of the reach through an approximation perspective. W…
New algorithm solves complex mean-field Schrödinger bridge problem.
problem Designing a controller for diffusion processes with nonlocal interaction.
method Generalized Hopf-Cole transform and Sinkhorn-type algorithm.
result Convergence guarantees for the proposed algorithm under mild assumptions.
The paper extends submanifold reach to less regular C1,α classes.
problem Extending submanifold reach to less regular classes.
method Using μ-reach and C1,α regularity to quantify reach. result Intermediate regularities C1,α induce quantitative results on reach.