GANs predict injection molding parts geometry from hot parts images.
problem Predicting final part geometry from early-stage measurements in injection molding.
method Used pix2pix GAN architecture to translate thermographic images to geometry.
result DMD analysis of GAN predictions reveals geometrical parameters.
Proposes MVGPR for spatiotemporal data modal analysis.
problem Sparse and irregularly sampled data in complex flows.
method Multivariate Gaussian process regression (MVGPR) with kernel design.
result MVGPR outperforms DMD and SPOD in modal analysis of sparse and irregular data.
Efficient video captioning model captures cross-modal interactions.
problem Capturing frame-level cross-modal interactions in video captioning.
method Proposes High-Order Cross-Modal Attention (HOCA) and Low-Rank HOCA.
result Low-Rank HOCA achieves state-of-the-art performance.
Develops methods to analyze feature-outcome associations in subpopulations.
problem Challenges in understanding feature-outcome associations in high-dimensional data.
method Geometric decomposition framework using gradient flow and co-monotonicity decomposition.
result Identifies context-dependent patterns and improves statistical power and interpretability.
Efficient Discrete Supervised Hashing improves cross-modal retrieval by preserving semantic correlations and reducing quantization error.
problem Challenges in preserving semantic correlations and reducing quantization error in cross-modal hashing for large-scale retrieval.
method Collective matrix factorization on heterogenous features and semantic embedding with class labels to learn hash codes efficiently.
result EDSH produces superior performance in both accuracy and scalability over existing methods.
The paper improves SMC algorithm for multi-modal distributions by proving variance bounds.
problem Problems with SMC on multi-modal distributions, especially in terms of mixing time.
method Proves variance bounds for SMC on multi-modal distributions using soft decomposition.
result Bounds on SMC variance depend on local rather than global mixing times.
MMVAE learns multi-modal data with shared and private latent spaces.
problem Learning useful representations across multiple data modalities.
method Mixture-of-experts variational autoencoder (MMVAE).
result MMVAE satisfies four criteria for multi-modal learning.
HCL learns shared and modality-specific latent representations for multimodal data.
problem Binary shared-private decomposition inadequately represents shared information across subsets of modalities.
method Hierarchical Contrastive Learning framework combining latent-variable formulation, structural sparsity, and contrastive objective.
result HCL accurately recovers hierarchical structure and improves predictive performance on multimodal data.
Framework estimates multiple plausible solutions with uncertainty measures.
problem Machine learning models need to propose multiple plausible solutions with meaningful uncertainty.
method Discrete latent variables model one-to-many mappings, allowing effective conditional probability estimation.
result Framework outperforms state-of-the-art in uncertainty estimation and is practical.
Tensor models improve joint EEG and fMRI analysis.
problem Jointly analyzing EEG and fMRI for brain function studies.
method Soft and flexible coupling of tensor decompositions for EEG and fMRI.
result Tensorial methods outperform ICA in multi-modal analysis.
New method tackles heterogeneous breast cancer imaging data.
problem Challenges in multimodality breast cancer imaging data.
method Developed a multilayer tensor learning method to incorporate heterogeneity.
result Outperforms other existing methods in predicting disease status.
A key task in Bayesian statistics is sampling from distributions that are only specified up to a partition function (i.e., constant of proportionality). However, without any assumptions, sampling (even approximately) can be #P-hard, and few works have provided "beyond worst-case" guarantees for such settings. For log-c…
Formula derived for discrete improper affine spheres.
problem Constructing discrete improper affine spheres.
method Loop group factorizations and Birkhoff decomposition.
result Representation formula for discrete indefinite affine spheres.
Method trains multi-modal policy from unlabeled mixed demonstrations.
problem Training policies from unlabeled mixed demonstrations.
method Variational autoencoder with categorical latent variable to discover latent factors of variation.
result Policy can reproduce specific behaviors by conditioning on categorical vectors.
Paper proposes multimodal contrastive learning for EHR data.
problem Separate treatment of structured and unstructured EHR data.
method Proposes a multimodal feature embedding generative model and a multimodal contrastive loss.
result Multimodal learning yields better feature representation than single-modality learning.
A new Möbius invariant discretization and decomposition of the Möbius energy is proposed.
problem Lack of Möbius invariant discretization and decomposition in existing discrete Möbius energy.
method Proposed a new discretization of Möbius energy that is Möbius invariant and can be decomposed into Möbius invariant components.
result The proposed discretization and decomposition maintain Möbius invariance and converge to the original components in the continuum limit.
Optimal discrete harmonic maps between hyperbolic surfaces are found via minimizing energy.
problem Finding optimal discrete harmonic maps between hyperbolic surfaces.
method Minimizing Dirichlet energy over all possible hyperbolic structures and realizations within a fixed homotopy class.
result At the optimal hyperbolic structure, the discrete harmonic map and edge weights are induced from a weighted Delaunay decomposition.
Our aim in this paper is to provide a theory of discrete Riemann surfaces based on quadrilateral cellular decompositions of Riemann surfaces together with their complex structure encoded by complex weights. Previous work, in particular of Mercat, mainly focused on real weights corresponding to quadrilateral cells havin…
On the basis of loop group decompositions (Birkhoff decompositions), we give a discrete version of the nonlinear d'Alembert formula, a method of separation of variables of difference equations, for discrete constant negative Gauss curvature (pseudospherical) surfaces in Euclidean three space. We also compute two exampl…
A new mutual information lower bound for multimodal regression active learning.
problem Lack of effective acquisition functions for multimodal regression active learning.
method Introduces a Two-Index framework for separating epistemic and aleatoric sources of uncertainty, deriving MI-LB as a closed-form approximation.
result MI-LB consistently outperforms baselines on multimodal regression tasks.
New method decomposes profits and losses continuously, avoiding discrete reporting issues.
problem Analyzing profits and losses at discrete dates ignores detailed paths.
method Constructs a large class of continuous-time decompositions using extended Itô's formula.
result Identifies a preferred decomposition from exactness, symmetry, and normalization axioms.
Paper presents a consistent discretization for Hodge decomposition on volumetric meshes.
problem Discretization of Hodge decomposition for vector fields on volumetric meshes.
method Edge-based Nedelec elements and face-based Crouzeix-Raviart elements interplay.
result Stable and efficient method for large-sized models with good performance.
This article is an application of the author's paper about a construction method for discrete constant negative Gaussian curvature surfaces, the nonlinear d'Alembert formula. The heart of this formula is the Birkhoff decomposition, and we give a simple algorithm for the Birkhoff decomposition. As an application, we dra…
MTRGL learns temporal correlations from multi-modal data for improved pair trading.
problem Discerning temporal correlations among financial entities.
method Combines time series data and discrete features into a temporal graph, using a memory-based temporal graph neural network.
result MTRGL outperforms traditional methods in temporal graph link prediction and pair trading.
Study continuous paths in discrete subgroups of hyperbolic space, proving combination and decomposition theorems.
problem Understanding continuous paths in discrete subgroups of hyperbolic space.
method Combination theorem and chromatography technique.
result Construction of an exotic path of discrete subgroups with no isomorphic subgroups.
Decomposes flat nonlinear discrete-time systems into simpler components.
problem Flatness of nonlinear discrete-time systems.
method Coordinate transformations and feedback, using flow-box and Frobenius theorems.
result Flatness of a discrete-time system can be checked algorithmically.
This paper develops a discrete theory of real Riemann surfaces using quad-graphs and linear discretization.
problem Constructing a discrete theory of real Riemann surfaces.
method Using quad-graphs and linear discretization of Cauchy-Riemann equations, constructing a symplectic homology basis.
result The discrete period matrix has the same canonical decomposition as in the smooth setting.
Often, large, high dimensional datasets collected across multiple modalities can be organized as a higher order tensor. Low-rank tensor decomposition then arises as a powerful and widely used tool to discover simple low dimensional structures underlying such data. However, we currently lack a theoretical understanding …
MultiPath predicts multi-modal future trajectories for better motion planning.
problem Predicting human behavior in uncertain real-world domains like autonomous driving.
method Leverages fixed future state-sequence anchors and regresses offsets with uncertainties.
result Achieves more accurate predictions with an order of magnitude fewer trajectories.
VecMol generates 3D molecules as continuous vector fields, overcoming modality and geometry constraints.
problem Challenges in generating 3D molecules, especially in drug discovery and materials science.
method VecMol reimagines molecular representation by modeling 3D molecules as continuous vector fields over Euclidean space, parameterized by a neural field and generated using a latent diffusion model.
result Vector-field-based representations show promise for 3D molecular generation, validated on benchmarks.
Framework corrects model form errors in structural dynamics predictions.
problem Model form errors in parametric models of structural dynamics.
method Gaussian Process Latent Force Model (GPLFM) for non-parametric discrepancy representation, linear Bayesian filtering for state and discrepancy estimation, modal reduction for computational tractability.
result Significant reduction of displacement and rotation prediction errors under unseen excitations.
Analyzes vector fields in polytope decompositions, proving curve finiteness.
problem Analyzing vector fields in polytope decompositions.
method Proves integral curves are chopped into finitely many pieces by polytope decompositions.
result Finiteness of edge flips in discrete Yamabe flow.
The paper develops algorithms and topological invariants for distinguishing dynamic systems.
problem Distinguishing the topological type of surfaces and functions in dynamic systems.
method Construction of algorithms and topological invariants using discrete topological structures.
result The development of discrete topological structures for topological equivalence of dynamic systems.
New hierarchical tensor decomposition model for complex data.
problem Lack of natural generalization of hierarchical NMF to tensors.
method Proposes a new hierarchical nonnegative tensor decomposition (HNTF) model.
result Model more naturally illuminates topic hierarchy.
TWIST algorithm detects communities in multi-layer networks with tensor decomposition.
problem Community detection in multi-layer networks with multiple node-modality relationships.
method Tensor-based TWIST algorithm for global/local node and layer memberships.
result Accurate community detection with small misclassification error as network size increases.
A bridge between continuous signals and discrete Ising spins for associative memory.
problem Associative memory in continuous-signal-driven Ising spin systems.
method Multilayer Ising framework with PCA whitening and SimHash projection, coupled to pseudo-inverse memory couplings.
result Finite-size scaling of operational storage capacity with αc(N)=αc(∞)−cN−1/2, approaching αc(∞)≈0.50. In the paper, we introduce the notion of a local regular supermartingale relative to a convex set of equivalent measures and prove for it an optional Doob decomposition in the discrete case. This Theorem is a generalization of the famous Doob decomposition onto the case of supermartingales relative to a convex set of e…
We detail the theory of Discrete Riemann Surfaces. It takes place on a cellular decomposition of a surface, together with its Poincaré dual, equipped with a discrete conformal structure. A lot of theorems of the continuous theory follow through to the discrete case, we define the discrete analogs of period matrices, Ri…
The paper analyzes stability and asymptotic behavior of hedging strategies in binomial and trinomial models.
problem Stability and asymptotic analysis of hedging strategies in incomplete financial models.
method Discrete-time Föllmer-Schweizer decomposition, perturbation analysis, and asymptotic approximation.
result Explicit formulas for leading order correction terms in asymptotic analysis.
We solve the ANOVA decomposition for categorical inputs.
problem Lack of a closed-form expression for ANOVA decomposition with categorical dependent variables.
method Bridge functional analysis with discrete Fourier analysis to derive a closed-form decomposition.
result Closed-form decomposition for categorical inputs without assumptions.
This paper studies the effect of discretizing the parametrization of a dictionary used for Matching Pursuit decompositions of signals. Our approach relies on viewing the continuously parametrized dictionary as an embedded manifold in the signal space on which the tools of differential (Riemannian) geometry can be appli…
Area and orientation preserving diffeomorphisms of the standard 2-disc, referred to as symplectomorphisms of D2, allow decompositions in terms of positive twist diffeomorphisms. Using the latter decomposition we utilize the Conley index theory of discrete braid classes as introduced in [Ghrist et al., C. …
Shifts dataset evaluates uncertainty in real-world tasks across modalities.
problem Lack of standard datasets for evaluating uncertainty estimation and robustness to distributional shift.
method Proposes Shifts Dataset for evaluation of uncertainty estimates and robustness to distributional shift across tabular, audio, text, and sensor data.
result Baseline results for tabular weather prediction, machine translation, and SDC vehicle motion prediction.
A new method learns quantization boundaries in continuous space using tessellation.
problem Mapping between discrete and continuous distributions is difficult.
method Constructs normalizing flows on convex polytopes with exact likelihood evaluations.
result Improves likelihood evaluation and quantization learning across various data modalities.
Discretizes Hodge-Dirac operators on a torus.
problem Capturing geometric aspects of continuum Hodge theory in discrete settings.
method Discrete exterior calculus framework, Hodge-Dirac and Laplace operators.
result Proves discrete Hodge decomposition theorem on combinatorial torus.
This note introduces and studies an open set of PSL(2,C) characters of a nonabelian free group, on which the action of the outer automorphism group is properly discontinuous, and which is strictly larger than the set of discrete, faithful convex-cocompact (i.e. Schottky) characters. This implies, in particular, that th…
The paper tackles interpreting DCM with image data by addressing data isomorphism.
problem Interpreting DCM with image data due to isomorphic information.
method Proposes and benchmarks two methodologies: architectural adjustments and data source mitigation.
result Direct data source mitigation is more effective for maintaining DCM's interpretability.
Proposes a new method for analyzing multimodal neuroimaging data.
problem Combining interpretability and flexibility in multimodal data analysis.
method Orthogonalized kernel debiased machine learning approach.
result Established consistency and asymptotic normality of the estimated primary parameter.