New condition for big data recovery from sparse samples.
problem Accurate recovery of graph signals from limited data.
method Network Nullspace Property that combines network structure and sampling geometry.
result Efficient sampling strategies designed based on network topology.
NullSpaceNet maps inputs to a joint-nullspace for clearer class separability.
problem Class separability and interpretability in image classification.
method NullSpaceNet maps inputs to a joint-nullspace, collapsing same-class inputs and separating different classes.
result NullSpaceNet achieves superior performance with reduced parameters and time.
The nullspace and regularization impact high-dimensional linear regression interpretability.
problem Interpreting high-dimensional linear regression coefficients in complex data.
method Optimization formulation to compare coefficients and physical knowledge.
result Regularization and z-scoring choices affect interpretability and true coefficient closeness.
Random walk sampling recovers smooth graph signals from few samples.
problem Efficiently sampling graph signals from large networks.
method Random walk sampling strategy based on network nullspace property.
result Graph signals can be accurately recovered from few samples.
We study conformal invariants that arise from functions in the nullspace of conformally covariant differential operators. The invariants include nodal sets and the topology of nodal domains of eigenfunctions in the kernel of GJMS operators. We establish that on any manifold of dimension n≥3, there exist many metr…
We discuss a general notion of "sparsity structure" and associated recoveries of a sparse signal from its linear image of reduced dimension possibly corrupted with noise. Our approach allows for unified treatment of (a) the "usual sparsity" and "usual ℓ1 recovery," (b) block-sparsity with possibly overlapping blo…
L2-Boosting fails to recover sparse parameters in high-dimensional models.
problem Theoretical differences between L2-Boosting and L1-penalized methods like Lasso.
method Proof of theoretical property differences between L2-Boosting and L1-penalized methods.
result L2-Boosting does not guarantee parameter recovery in high-dimensional models.
Semi-supervised learning improves with partial label information.
problem Improving model performance with limited labeled data.
method Contrastive learning with partial label information to encourage same labels.
result Partial label information reduces test error by up to 5.5 times.
New algorithm speeds up fair clustering by 12x.
problem Achieving fair clustering in scalable algorithms.
method s-FairSC algorithm incorporating nullspace projection and Hotelling's deflation.
result s-FairSC is 12x faster and maintains fairness.
A new principle minimizes residual and introduces momentum to improve PDE solution dynamics.
problem Ill-conditioning in Dirac-Frenkel residual minimization leads to non-unique parameter dynamics.
method Introduces a history variable (momentum) to select better-conditioned parameter velocities, preserving residual minimization while promoting smooth parameter evolutions.
result The approach leads to increased robustness in singular and near-singular PDE solution regimes.
A generalization of Callias' index theorem for self adjoint Dirac operators with skew adjoint potentials on asymptotically conic manifolds is presented in which the potential term may have constant rank nullspace at infinity. The index obtained depends on the choice of a family of Fredholm extensions, though as in the …
Paper solves the chicken-and-egg problem in unsupervised learning of signal models.
problem Learning signal models from incomplete data when the model is unknown.
method Necessary and sufficient sensing conditions for learning signal models from multiple measurement operators or group invariance.
result Agrees with the fundamental limitations of learning from incomplete data.
Unified approach to data processing using gauge theory.
problem Data representation and analysis with consistent symmetry.
method Geometric gauge theory for discrete vector bundles.
result Unified understanding of heat kernel properties and data transformation.
The nullity of a minimal submanifold M⊂Sn is the dimension of the nullspace of the second variation of the area functional. That space contains as a subspace the effect of the group of rigid motions SO(n+1) of the ambient space, modulo those motions which preserve M, whose dimension is the Killing nulli…
The paper sets bounds on how much regret is unavoidable in adaptive LQR with unknown B-matrix.
problem Understanding the limits of adaptive LQR with unknown B-matrix.
method Local asymptotic minimax regret lower bounds using van Trees' inequality and Bellman error representation.
result Logarithmic regret is impossible if the parametrization induces an uninformative optimal policy.
We examine the space of surfaces in $\RR^{3}$ which are complete, properly embedded and have nonzero constant mean curvature. These surfaces are noncompact provided we exclude the case of the round sphere. We prove that the space $\Mk$ of all such surfaces with k ends (where surfaces are identified if they differ by …
Paper addresses unsupervised learning from incomplete measurements in inverse problems.
problem Learning from incomplete measurements is challenging in inverse problems.
method Use multiple measurement operators to overcome nullspace issues; propose a novel unsupervised learning loss.
result Presented necessary and sufficient conditions for successful unsupervised learning.
For a Hamiltonian K∈C2(RN×n) and a map u:Ω⊆Rn⟶RN, we consider the supremal functional \[ \label{1} \tag{1} E_\infty (u,Ω) \ :=\ \big\|K(Du)\big\|_{L^\infty(Ω)} . \] The "Euler-Lagrange" PDE associated to \eqref{1} is the quasilinear system \[ \lab…
Paper tackles treatment leakage in text-based causal inference, proposing methods to mitigate bias.
problem Treatment leakage in text-as-confounder applications introduces bias in causal estimates.
method Formal definitions, four text distillation methods (passage removal, classification, salient feature removal, nullspace projection).
result Moderate distillation optimally balances bias reduction against confounder retention.
Study classifies traveling solitary waves in energy-critical half-wave maps.
problem Energy-critical half-wave maps into S2. method Geometric characterization, conformal Möbius group, Jacobi operators.
result Explicit classification and detailed analysis of traveling solitary waves.
Survey on deep learning for social network analysis.
problem Encoding social network data into useful low-dimensional representations.
method Review of neural network models for node and subgraph embeddings in various network types.
result Advancements in deep learning for complex network analysis.
RFN improves GCNs for road networks, outperforming state-of-the-art by 21%-40%.
problem Leveraging the structure of road networks effectively in machine learning tasks.
method Introducing RFN, a novel GCN specifically designed for road networks.
result RFN outperforms state-of-the-art GCNs by 21%-40% on road network tasks.
New model reconstructs networks by identifying regular components.
problem Uncovering the complexity of network structures.
method Low-rank pursuit based self-representation network model.
result Reconstructs networks and measures their regulability.
Algorithm reconstructs conserved networks from flow data.
problem Network reconstruction from flow data.
method Polynomial time algorithm exploiting graph theoretic properties and learning techniques.
result Exact network reconstruction possible for arborescence networks.
This survey clarifies dynamic network terminology and reviews GNN models for dynamic networks.
problem Ambiguity in dynamic network terminology and lack of GNN models for dynamic networks.
method Established consistent terminology and notation for dynamic networks, reviewed GNN models.
result Comprehensive survey of dynamic graph neural network models.
DCNs mimic neuronal networks for improved neural classification.
problem Lack of topological similarity between DNNs and biological neural networks.
method Developed DCNs with topologies inspired by real-world neuronal networks.
result High classification accuracy achieved by DCNs.
Study 986 diverse networks to reveal structural diversity across domains.
problem Understanding structural diversity in networks across various domains.
method Machine learning techniques (random forest, confusion matrix) on 986 real-world networks and 575 generated networks.
result Networks in the same partition have similar underlying functions, constraints, and generative mechanisms, regardless of their origins.
Network recasting transforms network architecture for faster inference.
problem Accelerate inference process through network transformation.
method Block-wise recasting of source blocks in a teacher network to target blocks in a student network.
result Transforms network architecture while preserving accuracy and reducing inference time.
Highly accurate classification of network categories achieved.
problem Distinguishing between different types of networks (e.g., social vs. web graphs).
method Used a random forest classifier on both real-world and synthetic networks.
result Achieved a 94.2% classification accuracy.
Network Lens identifies node behaviors in heterogeneous networks with high accuracy.
problem Identifying different behaviors in various parts of large heterogeneous networks.
method Zoom into network using different-sized lenses to capture local structure, weight signatures to predict node labels.
result Achieved a peak accuracy of ~42% on two networks with ~100,000 and ~1,000,000 nodes, significantly better than random.
DANE adapts network embeddings across multiple domains.
problem Learning embeddings for multiple networks without transferability.
method Graph Convolutional Network with adversarial learning.
result DANE achieves superior performance in cross-network domain adaptation.
Capsule networks are vulnerable to adversarial attacks, similar to convolutional neural networks.
problem Vulnerability of capsule networks to adversarial attacks.
method Compared capsule networks to convolutional neural networks using various adversarial attacks.
result Capsule networks are vulnerable to adversarial attacks, similar to convolutional neural networks.
Chemical networks outperform spiking neural networks in classification tasks.
problem Learning tasks with spiking neural networks require hidden layers, which are computationally expensive.
method Used deterministic mass-action kinetics to prove chemical reaction networks without hidden layers can solve tasks previously solved by spiking neural networks.
result A chemical reaction network without hidden layers outperforms a spiking neural network with hidden layers in a handwritten digit classification task.
Deep ReLU networks can be simplified to a three-layer model.
problem Understanding the behavior of deep neural networks.
method Constructive proof and algorithm to transform deep networks into shallow ones.
result Deep ReLU networks can be represented by a simpler three-layer structure.
Tackles network structure inference from time series data using GNN.
problem Inferring network structure from incomplete or no information.
method Gumbel Graph Network (GGN) model for network reconstruction and completion.
result GGN can reconstruct up to 100% network structure and infer missing parts with up to 90% accuracy.
Paper proposes algorithms for embedding directed networks with text associated nodes.
problem Learning embeddings for directed networks with text associated nodes.
method PCTADW-1 and PCTADW-2 neural network algorithms.
result Embeddings improve node classification quality on software package dependency networks.
Network embedding helps predict speed limits on incomplete Danish road network.
problem Incomplete speed limit data on Danish roads limits machine learning applications.
method Applied node2vec network embedding to Danish road network.
result Network embedding can derive useful features for predicting speed limits.
New method identifies common organizational principles in networks.
problem Challenging to cluster networks of different size and density.
method Introduces a new network comparison methodology.
result Identifies common organizational principles in networks.
This paper explores loss landscapes of sparse neural networks, finding unique characteristics compared to dense networks.
problem Understanding the loss landscape of sparse neural networks, especially one-hidden-layer networks.
method Analyzes sparse networks with dense and sparse final layers, focusing on linear and non-linear models.
result Sparse networks can have no spurious valleys under certain conditions, but spurious valleys and minima can exist for wide sparse networks.
New approach learns latent motifs in networks for mesoscale structure analysis.
problem Understanding large-scale behavior in complex systems through mesoscale structures.
method Network dictionary learning (NDL) combining network sampling and nonnegative matrix factorization.
result Networks can be approximated using a small set of latent motifs.
The paper surveys network methods for understanding economic and financial systems.
problem Understanding interconnectedness among economic and financial entities.
method Survey of network theory, measures, and structures for economic and financial networks.
result Network methods provide tools to quantify structural properties of economic systems.
Researchers develop a method to count and analyze motifs in temporal networks.
problem Understanding the role of network motifs in temporal networks.
method Developed a notion of temporal network motifs and designed fast algorithms for counting them.
result Different motifs occur at different time scales, providing insights into temporal network structure and function.
Paper links network Lasso to network flow optimization.
problem Joint clustering and optimization of networked data.
method Exploration of duality between network Lasso and network flow optimization.
result nLasso is equivalent to a minimum-cost flow problem on the data network structure.
SyNGLER generates synthetic networks efficiently while preserving key structural properties.
problem Efficiently generating realistic synthetic networks with preserved structural properties.
method SyNGLER uses latent space network models to learn and reconstruct node embeddings, then generates synthetic networks.
result SyNGLER produces synthetic networks that better preserve key network characteristics than existing approaches.
Taking inspiration from biological evolution, we explore the idea of "Can deep neural networks evolve naturally over successive generations into highly efficient deep neural networks?" by introducing the notion of synthesizing new highly efficient, yet powerful deep neural networks over successive generations via an ev…
Paper introduces method to make neural networks symmetrical.
problem Creating symmetrical neural networks for data with inherent symmetries.
method Introduces a method for modifying neural networks to enforce equivariance.
result Group convolutional neural networks are a special case of the introduced framework.
Deep networks better approximate functions with compositional structure.
problem Approximating functions with complex structures.
method Design deep networks with compositional structure, leveraging the blessing of compositionality.
result Deep networks can approximate functions better than shallow networks when the function has a compositional structure.
Secret neural networks hidden within trained models.
problem Excess capacity in neural networks allows embedding secret models.
method Novel framework for hiding secret neural networks within carrier networks.
result Detection of hidden networks is computationally infeasible.