Complex-valued neural networks perform similarly to real-valued models for real-valued classification tasks.
problem Comparing real-valued and complex-valued neural networks for real-valued classification tasks.
method Comparison of neural networks with similar capacity sizes, using various activation functions and weight initialisation strategies.
result Complex-valued neural networks perform equal to or slightly worse than real-valued models for real-valued classification tasks.
Paper proposes LANN to measure model complexity of neural networks with curve activation functions.
problem Measuring model complexity of neural networks with curve activation functions.
method Proposes LANN, a piecewise linear framework to approximate curve activation functions, and derives complexity measure based on the number of linear regions.
result Demonstrates positive correlation between overfitting and model complexity during training.
Paper introduces a new edge exchangeable block model for complex networks.
problem Limitations of the stochastic block model in analyzing complex networks.
method Develops a Bayesian nonparametric edge exchangeable block model.
result The new model outperforms state-of-the-art SBMs for link prediction.
Modeling structure in complex networks using Bayesian non-parametrics makes it possible to specify flexible model structures and infer the adequate model complexity from the observed data. This paper provides a gentle introduction to non-parametric Bayesian modeling of complex networks: Using an infinite mixture model …
Method reconstructs networks from contagion dynamics.
problem Fitting contagion models assumes simple dynamics, ignoring complex contagions.
method Nonparametric method to reconstruct network and dynamics from node states.
result Networks are easier to reconstruct through complex contagions in dense or saturated networks.
Machine learning speeds up centrality measure calculations for large networks.
problem High computational costs of traditional centrality measures in large networks.
method Neural network learning algorithms to approximate centrality measures.
result Regression model approximates centrality measures efficiently and accurately.
Measures neural network complexity via effective degrees of freedom.
problem Challenges in quantifying neural network complexity.
method Adapts generalized degrees of freedom (GDF) for binary outcomes and compares with cross-validation and null degrees of freedom.
result GDF provides a robust measure of model complexity for neural networks.
A hybrid model reduces graph complexity for improved classification accuracy.
problem High computational complexity and large number of parameters in higher-order graph convolutional networks.
method Weight sharing mechanism and novel fusion pooling layer to reduce parameters and complexity.
result The proposed model achieves highest classification accuracy with fewer trainable parameters.
Proposes Neural Complexity (NC) for predicting and explaining generalization in deep neural networks.
problem Challenges in specifying a suitable complexity measure for deep neural networks to predict and explain generalization.
method A meta-learning framework that learns a scalar complexity measure through interactions with many heterogeneous tasks.
result Trained NC model can be added to standard training loss to regularize any task learner.
Develops a tensor network framework to reduce RNN complexity for high-dimensional sequence modeling.
problem Exponential parameter growth in RNNs for large multidimensional data.
method Embeds a multi-linear graph filter in a tensor network architecture to approximate RNN hidden states.
result Demonstrates superior performance and reduced complexity compared to traditional RNNs.
New embeddings capture local structure in complex networks.
problem Embeddings cannot capture local structure in complex networks.
method Logistic Principal Component Analysis (LPCA) algorithm for exact low-rank representations.
result Exact low-rank representations of real-world networks are possible.
Active learning reduces spin network inference complexity by 10^6-fold.
problem Difficulty in inferring direct interactions in complex networks.
method Information geometry framework to quantify inference difficulty and information gain from perturbations.
result Designed perturbations reduce sampling complexity by 10^6-fold across various network architectures.
Unified recurrent networks reveal differences in complexity levels of grammars.
problem Understanding the complexity and behavior of recurrent networks.
method Connecting recurrent networks with deterministic finite automata and formal grammars.
result Unified recurrent networks improve performance and match grammars from different complexity levels.
Analyzing and understanding the structure of complex relational data is important in many applications including analysis of the connectivity in the human brain. Such networks can have prominent patterns on different scales, calling for a hierarchically structured model. We propose two non-parametric Bayesian hierarchi…
Deep learning predicts contagion dynamics on complex networks.
problem Forecasting contagion dynamics on complex networks is challenging.
method Graph neural network learns local mechanisms from time series data.
result Deep learning offers new and accurate models of contagion dynamics.
New bound on neural network generalization error using geometric complexity.
problem Understanding the generalization capabilities of deep neural networks.
method Derive a new upper bound on generalization error using margin-normalized geometric complexity.
result Empirical validation of the bound for ResNet-18 on CIFAR-10 and CIFAR-100 datasets.
Model-based neural networks generalize better than ReLU networks for sparse recovery.
problem Understanding and quantifying the superior generalization of model-based neural networks.
method Using complexity measures like global and local Rademacher complexities, the paper provides theoretical bounds on generalization and estimation errors.
result Model-based neural networks exhibit higher generalization capabilities for sparse recovery problems compared to ReLU networks.
New topological complexity measures for neural networks.
problem Measuring complexity of neural network functions.
method Generalized piecewise-linear Morse theory applied to ReLU networks.
result Local complexity can be arbitrarily high.
Proposes a method to control model complexity in neural network optimization.
problem Reduces the computational cost of neural architecture search.
method Probabilistic model-based dynamic optimization with a penalty term to control model complexity.
result The proposed method controls model complexity while maintaining performance.
New neural network models for complex functional data analysis.
problem Complex relations between functional predictors and responses.
method Function-on-Function regression models using neural networks with continuous hidden layers.
result Demonstrated power and flexibility in handling complex functional models.
Method uses network biology to construct gene expression models for cancer.
problem Building models for cancer phenotypes using gene expression data.
method Unsupervised construction of computational graphs based on protein-protein networks.
result The method outperforms other models in cancer phenotype analysis.
Paper defines untangling number to measure entanglement complexity in 3-periodic networks.
problem Measuring the complexity of entanglement in 3-periodic networks.
method Defining ground states through knot-theoretic crossing diagrams and measuring untangling number.
result Introduced untangling number as a measure of entanglement complexity.
The paper analyzes reducing model complexity for better generalization.
problem Improving model generalization with reduced complexity networks.
method Upper bound on Vapnik-Chervonenkis dimension, pruning, quantization, and a novel loss function.
result Quantization and the proposed loss function lead to sparser models with comparable accuracy.
Neural networks improve predictions of complex network dynamics.
problem Improving neural network predictions for complex network dynamics.
method Extended neural network models to complex systems, ensuring they conform to dynamical model assumptions and using a statistical significance test.
result Achieved advanced generalization of neural network predictions for complex systems.
Measures neural network complexity using tangent space diversity.
problem Estimating the true complexity of neural networks.
method Entropy-based measure of tangent spaces from different inputs.
result Captures effective complexity, not just theoretical capacity.
We discuss two views on extending existing methods for complex network modeling which we dub the communities first and the networks first view, respectively. Inspired by the networks first view that we attribute to White, Boorman, and Breiger (1976)[1], we formulate the multiple-networks stochastic blockmodel (MNSBM), …
Transformers can outperform feedforward and recurrent networks due to dynamic sparsity.
problem Understanding when and why Transformers outperform other neural network architectures.
method Analyzing a sequence-to-sequence data generating model with dynamic sparsity, proving sample complexity differences between feedforward, recurrent, and Transformers.
result Transformers can learn dynamic sparsity models with lower sample complexity than feedforward and recurrent networks.
Study uses complex networks and machine learning to predict soccer match outcomes.
problem Predicting soccer match outcomes with complex networks and machine learning.
method Complex network metrics and match statistics were used to build machine learning models.
result Models based on passing networks were as effective as traditional models using match statistics.
New neural network predicts accurate protein complex structures.
problem Predicting accurate protein complex structures from atomic coordinates.
method Rotation-equivariant neural network combining point-based representation, equivariance, local convolutions, and hierarchical subsampling.
result Significant improvement in identifying accurate structural models.
LocalDrop uses local Rademacher complexity for neural network regularization.
problem Overfitting in deep neural networks.
method Developed a new regularization function based on local Rademacher complexity.
result Demonstrated effectiveness of LocalDrop through extensive experiments.
Residual neural networks don't help overcome sampling complexity issues.
problem Learning invertible residual neural networks from samples is hard due to the curse of dimensionality.
method Investigated invertible residual neural networks and their sampling complexity.
result Invertible residual neural networks still suffer from the curse of dimensionality in sampling complexity.
Unified framework for complex financial networks using lattice theory.
problem Complex financial networks with multiple currencies and dependencies.
method Recast classical financial clearing model into lattice liability networks.
result Lattice-valued clearing sections form a complete lattice, enabling tractable analysis.
Percolation on complex networks has been used to study computer viruses, epidemics, and other casual processes. Here, we present conditions for the existence of a network specific, observation dependent, phase transition in the updated posterior of node states resulting from actively monitoring the network. Since tradi…
Paper reduces neural network complexity for image classification.
problem High computational complexity in deep neural networks.
method Proposes a two-step classification process: coarse-grain and fine-grain.
result Achieves similar accuracy with less computational complexity.
Survey of complex-valued neural networks for improved performance.
problem Lack of complex-valued neural networks in machine learning frameworks.
method Literature review of CVNNs.
result Advantages of CVNNs over real-valued neural networks.
Model for open, decentralized network with task load balancing.
problem Complex computational tasks in open, decentralized networks.
method Incentive-based load balancing using economic mechanisms.
result Optimized resource allocation and enhanced system resilience.
Proposes a new prior for complex models to improve prediction accuracy.
problem Difficulty in specifying priors for complex models like neural networks.
method Predictive complexity priors defined by comparing model predictions to a reference model, transferred to parameters via change of variables.
result Improves model predictions by reducing unintuitive effects of traditional priors.
Study builds complex network from multimodal physiological data.
problem Understanding dynamic interactions in biological systems.
method Network-based multimodal data fusion using recurrence plots and temporal metrics.
result Model accurately characterizes emotional states through physiological responses.
UDN adapts depth to data complexity, outperforming standard neural networks.
problem Adapting neural network depth to data complexity.
method Variational inference for infinitely deep neural networks with a novel algorithm.
result UDN outperforms standard neural networks and other infinite-depth approaches.
This research provides theoretical guarantees for hyperparameter estimation in complex network dynamical systems.
problem Theoretical guarantees for hyperparameter estimation in large, inhomogeneous complex network dynamical systems.
method Formulating the system's evolution in a measure transport perspective, proposing a theoretical framework for estimating hyperparameters with mean-type observations.
result A nonasymptotic bound for the deviation of hyperparameter estimates in inhomogeneous complex network dynamical systems with respect to network population size.
New research shows graph embeddings fail to capture key network properties.
problem Graph embeddings fail to capture salient properties of complex networks.
method Mathematical proof and empirical study of various embedding techniques.
result Any successful graph embedding must have a rank nearly linear in the number of vertices.
Modeling how network connectivity affects economic collapse and robustness.
problem Impact of network topology on systemic risk and collapse of complex economic systems.
method Proposed a model to study the effects of network structure on economic systems by varying connectivity.
result Emergent systemic risks arise with increased interconnections, leading to phase transitions and tipping points.
L-GCNs learn from complex multigraphs, improving node classification performance.
problem Learning from complex multigraphs with rich edge labels.
method Latent-Graph Convolutional Networks (L-GCNs) that propagate information to a latent adjacency tensor.
result L-GCNs improve node classification performance, especially with nonlinear interactions.
InferPy simplifies probabilistic modeling with deep neural networks in Python.
problem Complex probabilistic models with deep neural networks.
method User-friendly API for defining, learning, and evaluating models.
result Compact and simple way to define general hierarchical probabilistic models.
New neural networks model complex phenomena with fewer parameters.
problem Challenges in studying higher-order interactions in neural networks.
method Introducing curved neural networks using the maximum entropy principle.
result Curved neural networks accelerate memory retrieval and exhibit explosive phase transitions.
The study examines price formation in complex networks and finds efficiency varies by network structure.
problem Understanding price formation and efficiency in complex networks.
method Price formation experiments with human subjects in large networks, agent-based model construction.
result Prices are higher and trade less efficient in small-world networks compared to random networks.
Tag2Vec learns tag representations in hybrid networks with semantic and hierarchical information.
problem Lack of semantic and hierarchical information in tag networks.
method Tag2Vec model that combines nodes and tags into hybrid networks, using parameterized random walks and hyperbolic Skip-gram model.
result Tag2Vec outperforms other models in learning rich semantic tag representations.
The paper bounds the complexity of GCNs using Rademacher complexity.
problem Understanding the sample complexity of GCNs.
method Derived tight upper and lower bounds of Rademacher complexity for GCN models.
result The derived bounds depend on the largest eigenvalue of the graph filter and the degree distribution.