The paper predicts edge weights in weighted directed networks using metric geometry.
problem Predicting edge weights in weighted directed networks.
method Introducing new types of weighted directed networks (AWDNs), constructing metrics, and proposing modified kNN and SVM methods.
result The proposed methods outperform traditional approaches in predicting edge weights.
New graph kernel for weighted directed networks using functor homology.
problem Studying weighted directed networks with functor homology.
method Proposes a new homological method to define graph kernels for weighted directed graphs.
result Defined a new graph kernel for weighted directed graphs.
New method clusters weighted directed networks using motifs.
problem Clustering directed networks fails to consider higher-order structure and edge weights.
method Motif-based weighted spectral clustering with new matrix formulae.
result Scalable and effective clustering on large graphs and real-world data.
Novel Haar-Laplacian for directed graphs enhances spectral graph applications.
problem Lack of suitable Laplacian for directed graphs in spectral graph theory.
method Inspired by Haar-like transformation, introduces a Hermitian matrix preserving direction and weight.
result HaarNet outperforms in weight prediction and denoising on directed graphs.
A goal in network science is the geometrical characterization of complex networks. In this direction, we have recently introduced Forman's discretization of Ricci curvature to the realm of undirected networks. Investigation of this edge-centric network measure, Forman-Ricci curvature, in diverse model and real-world un…
CDFD analyzes circularity and directionality in weighted directed networks.
problem Analyzing circularity and directionality in weighted directed networks.
method CDFD framework separates flow into circular and acyclic components.
result CDFD yields a normalized circularity index capturing flow in cycles and directionality.
The paper studies neural networks' convergence near origin and saddle points.
problem Directional convergence of neural networks near small initializations and saddle points.
method Gradient flow dynamics analysis of two-homogeneous neural networks.
result Neural networks' weights approximately converge in direction to KKT points for small initializations.
Optimizes CNNs by directing gradients along output channels.
problem Improving generalization error in CNNs.
method Output-channel directed re-weighted L2 or Sobolev metrics.
result Improves generalization error by optimizing gradients.
Early training of deep neural networks leads to small, directionally converging weights.
problem Training dynamics of deep homogeneous neural networks with small initializations.
method Gradient flow analysis and study of KKT points for neural correlation function.
result Weights converge in direction to KKT points during early training stages.
AB-SAGA optimizes distributed optimization over directed graphs using variance reduction and stochastic weights.
problem Optimizing distributed stochastic optimization over directed graphs with stochastic weights.
method AB-SAGA combines variance reduction and network-level gradient tracking, using both row and column stochastic weights.
result AB-SAGA converges linearly to the global optimal with a constant step-size and achieves a linear speed-up over centralized methods.
New duality found linking neural network weights and activities for better generalization.
problem Understanding and improving neural network generalization.
method Activity-weight duality mapping between neural network layers.
result Generalization loss can be decomposed into geometric factors of sharpness and weight standard deviation.
Online CPD for weighted and directed graphs using RDPG model.
problem Monitoring and detecting changes in weighted and directed graph data.
method Spectral embeddings of RDPG models for online updates and error-rate control.
result A lightweight online CPD algorithm with improved detection resolution and delay.
Deep ReLU networks escape from the origin via saddle points with a low-rank bias.
problem Understanding the dynamics of gradient descent in deep ReLU networks.
method Analysis of escape directions and singular values of weight matrices.
result The first singular value of the ℓ-th layer weight matrix is at least ℓ41 larger than any other singular value. Neural network pruning is an important step in design process of efficient neural networks for edge devices with limited computational power. Pruning is a form of knowledge transfer from the weights of the original network to a smaller target subnetwork. We propose a new method for compute-constrained structured channe…
Transfer learning have been frequently used to improve deep neural network training through incorporating weights of pre-trained networks as the starting-point of optimization for regularization. While deep transfer learning can usually boost the performance with better accuracy and faster convergence, transferring wei…
New Ricci flow method for directed graphs with balancing factor.
problem Analyzing asymmetry in directed networks.
method Rigorous formulation of Ricci flow on directed weighted graphs with balancing factor.
result Existence and uniqueness of discrete Ricci flow solutions.
We propose a new variational family for Bayesian neural networks. We decompose the variational posterior into two components, where the radial component captures the strength of each neuron in terms of its magnitude; while the directional component captures the statistical dependencies among the weight parameters. The …
Under what conditions is an edge present in a social network at time t likely to decay or persist by some future time t + Delta(t)? Previous research addressing this issue suggests that the network range of the people involved in the edge, the extent to which the edge is embedded in a surrounding structure, and the age…
The paper analyzes neural network dynamics after weights escape the origin.
problem Understanding gradient flow dynamics of neural networks after the origin.
method Analyzes gradient flow of homogeneous neural networks with locally Lipschitz gradients.
result Characterizes the first saddle point encountered after escaping the origin.
Gradient descent converges to perfect classification in neural nets for non-separable data.
problem Classifying linearly non-separable data using neural networks.
method Analysis of gradient descent dynamics in neural networks with sufficient but not large number of neurons.
result Gradient descent converges to global minima with perfect classification in the landscape of minimization problems.
Hybrid Bayesian neural networks use function uncertainty for probabilistic inference.
problem Uncertainty in neural network weights is hard to specify and interpret.
method Integrates probabilistic layers with standard deterministic layers for function uncertainty.
result Improves probabilistic inference by encoding function uncertainty.
Forward gradients improve neural network training without backpropagation issues.
problem Training neural networks without backpropagation's locking and memorization problems.
method Using directional derivatives in forward differentiation mode, with biased guesses based on feedback from small auxiliary networks.
result Using gradients from a local loss as a candidate direction improves Forward Gradient methods.
Investigate the evolving structure of cryptocurrency interactions using high-frequency returns.
problem Evolution of cryptocurrency interactions
method Construct directed and weighted networks from Granger causal relationships between cryptocurrency log-returns.
result Normalized returns exhibit heavy-tailed distributions.
NetOTC compares and aligns directed or undirected networks via random walk transitions.
problem Comparing and aligning networks of different types and sizes.
method NetOTC uses a transport-based approach to find optimal transition couplings of random walks.
result NetOTC quantifies network differences and provides vertex and edge alignments.
Partial fusion combines neural networks to balance accuracy and efficiency.
problem Balancing accuracy and computational cost in neural networks.
method Extending weight aggregation methods based on neuron-level similarity, using partial optimal transport to match similar neurons.
result Achieves a flexible tradeoff between computational cost and performance.
We present trellis networks, a new architecture for sequence modeling. On the one hand, a trellis network is a temporal convolutional network with special structure, characterized by weight tying across depth and direct injection of the input into deep layers. On the other hand, we show that truncated recurrent network…
New method identifies parameters of wider shallow neural networks with biases.
problem Identifying parameters of wide shallow neural networks with biases from finite samples.
method Two-step pipeline: direction of weights via second order information, signs via algebraic evaluations, biases via gradient descent.
result Constructive methods and theoretical guarantees of finite sample identification for wider shallow networks with biases.
Deep generative networks can simulate from a complex target distribution, by minimizing a loss with respect to samples from that distribution. However, often we do not have direct access to our target distribution - our data may be subject to sample selection bias, or may be from a different but related distribution. W…
Based on the misleading expectation that weighted network properties always offer a more complete description than purely topological ones, current economic models of the International Trade Network (ITN) generally aim at explaining local weighted properties, not local binary ones. Here we complement our analysis of th…
The study analyzes optimization trajectories in neural networks to reveal redundancy and redundancy-reducing strategies.
problem Understanding the directional structure and redundancy in neural network optimization.
method Introducing natural notions of complexity for optimization trajectories and analyzing their directional nature.
result Training only scalar batchnorm parameters can match the performance of training the entire network, indicating potential for hybrid optimization schemes.
Proposes FMS for more efficient neural network hyperparameter optimization.
problem Efficient hyperparameter optimization for deep learning models.
method Uses logged checkpoints of trained weights to guide hyperparameter selections.
result Proposes Forecasting Model Search (FMS) method.
Improved neural network convergence with causal Bayesian modeling in retail performance.
problem Improving neural network convergence in retail performance models.
method Causal Bayesian neural network implementation, removal of weakest SEM path, Flipout layers, Vadam optimizer.
result Neural network convergence improved with removal of the weakest SEM path.
New insights into neural network feature learning through multi-step gradient descent.
problem Understanding feature learning in two-layer neural networks with limited width.
method Characterization of feature learning through two steps of gradient descent with specific step sizes.
result The second step of gradient descent reveals multiple learned directions, not limited to a single direction as in the first step.
Proposes methods to add constraints to neural networks to improve stability and generalization.
problem Improving stability and generalization of neural networks.
method Constraint-based regularization using stochastic gradient Langevin dynamics.
result Constraints help stabilize and improve the robustness of deep neural networks.
New method trains neural networks in spectral domain for improved performance.
problem Training deep neural networks in the space of nodes.
method Trains neural networks in the spectral domain, modifying eigenvalues and eigenvectors of transfer operators.
result Superior performance compared to standard methods, especially when adjusting eigenvalues.
Single-hidden layer feed forward neural networks (SLFNs) are widely used in pattern classification problems, but a huge bottleneck encountered is the slow speed and poor performance of the traditional iterative gradient-based learning algorithms. Although the famous extreme learning machine (ELM) has successfully addre…
MLDS dataset reveals hidden model behavior via weight-space analysis.
problem Neural networks' opacity makes them hard to evaluate.
method Presented MLDS dataset of trained neural networks.
result Weight-space analysis reveals meaningful divergence with small changes in training data.
Novel Bayesian neural network method for robustness.
problem Adversarial robustness without online training.
method Distributes uncertainty across all inputs.
result Demonstrates robustness on benchmark datasets.
Recent work on mode connectivity in the loss landscape of deep neural networks has demonstrated that the locus of (sub-)optimal weight vectors lies on continuous paths. In this work, we train a neural network that serves as a hypernetwork, mapping a latent vector into high-performance (low-loss) weight vectors, general…
Develops exact and invariant study-based decompositions for network meta-analysis.
problem Lack of exact contribution decompositions in network meta-analysis.
method Contrast-space projection formulation of NMA, study-based definition of direct and indirect evidence.
result Exact covariance-aware decompositions of NMA estimator into direct and indirect contributions.
Estimates causal effects using neural networks for balancing covariates.
problem Estimating causal effects from observational data.
method Neural Balancing Weights (NBW) using α-divergence for density ratio estimation. result Generalized approach for balancing multidimensional data.
Improved loss functions adapt to weight-space anisotropy, outperforming isotropic counterparts.
problem Adapting to the anisotropic nature of deep weight spaces for better performance.
method Refined local entropic loss functions restricted to a subset of weights, exploiting anisotropy.
result Partial local entropies outperform isotropic counterparts on image classification tasks.
Heavy-tailed regularization improves deep neural network performance.
problem Improving generalization of deep neural networks.
method Introducing Heavy-Tailed Regularization, using differentiable penalty terms and Bayesian statistics.
result Heavy-tailed regularization outperforms conventional regularization techniques.
Study reveals decurve flows in graph propagation models.
problem Limitations of traditional graph analysis and propagation mechanisms.
method Introduces Generalized Propagation Neural Networks (GPNNs) and Continuous Unified Ricci Curvature (CURC).
result Observation of decurve flow during training of graph neural networks, revealing propagation dynamics.
A new method constrains deep networks during fine-tuning to improve generalization.
problem Improving generalization of fine-tuned deep networks.
method A neural network generalisation bound based on distance from initial weights constrains the hypothesis class to a small sphere.
result Empirical evaluation shows superior generalization performance compared to existing methods.
This work connects neural network training to convex optimization via the NTK.
problem Understanding and optimizing neural network training via convex programs.
method Interpreting gated ReLU network as MKL, showing NTK equivalence, and improving weights.
result The NTK cannot perform better than the optimal MKL kernel on the training set.
Generalizes neural network approximation to infinite-dimensional manifolds and derivatives.
problem Approximating differentiable maps on infinite-dimensional manifolds.
method Proves a weighted Nachbin theorem to establish universal approximation for differentiable maps, including derivatives.
result Linear functions of the signature can approximate path space functionals including their derivatives.
This paper establishes rates of universal approximation for the shallow neural tangent kernel (NTK): network weights are only allowed microscopic changes from random initialization, which entails that activations are mostly unchanged, and the network is nearly equivalent to its linearization. Concretely, the paper has …