Paper analyzes sample complexity of polynomial neural networks.
problem Understanding the sample complexity of polynomial neural networks.
method Extends previous literature to polynomial neural networks and analyzes sample complexity.
result Obtains novel results on sample complexity of polynomial neural networks.
Paper tackles complex risk in deep neural networks.
problem Complex risk in deep neural networks.
method Developed new approach for complex risk statistics.
result Derived dual representation for complex risk.
Study analyzes Echo State Network parameters for Rossler attractor dynamics.
problem Understanding the influence of network type on Echo State Network performance.
method Experimental analysis of Echo State Network parameters using Rossler attractor.
result Exploration of how network type affects Echo State Network performance.
Complex network analysis reveals dominant stocks in financial stock returns correlations.
problem Inferring financial stock returns correlations from complex network analysis.
method Simulated geometric Brownian motion for stocks, complex network analysis, eigenvector centrality, clustering.
result Returns correlation matrix is dominated by stocks with high eigenvector centrality and clustering.
This study analyzes cryptocurrency market crashes using complex network analysis.
problem Identifying and understanding dynamics of cryptocurrency market crashes.
method Complex network analysis of cryptocurrency market during pre-crash, crash, and post-crash periods.
result Network density and clustering coefficient spike during crashes, indicating uninformed panic sell-off.
New bounds on ReLU networks for low-regular functions.
problem Bounding approximation error for ReLU networks on low-regular functions.
method Complexity analysis of Fourier features residual networks to ReLU networks.
result Approximation error bound proportional to target function norm and inversely proportional to network width and depth.
Paper analyzes NAC with neural networks for efficient policy optimization.
problem Improving sample and iteration complexity in policy optimization.
method Entropy regularization, averaging, neural network approximation, and optimization techniques.
result Entropy regularization and averaging ensure stability and sharp sample complexity bounds.
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…
The paper analyzes adversarial robustness for linear models and neural networks using Rademacher complexity.
problem Understanding adversarial robustness of linear models and neural networks.
method The paper uses Rademacher complexity to provide upper and lower bounds for adversarial robustness of linear hypotheses and neural networks.
result The paper provides bounds on adversarial Rademacher complexity for linear hypotheses and neural networks, offering a finer analysis of input dimensionality.
Defines complexity measure for neural networks and feature representations, revealing scaling patterns.
problem Understanding the nonlinearity and dimensionality of neural network computations and feature representations.
method Introduces complexity and effective dimension measures, investigates their dynamics during training, and analyzes their scaling properties.
result Power law scaling of complexity and effective dimension during training, revealing hidden structure of datasets.
This study uses persistent homology to analyze complex transitional networks from time series data.
problem Lack of effective tools to summarize complex topology in transitional networks.
method Persistent homology from topological data analysis applied to coarse-grained state-space networks (CGSSN).
result CGSSN improves dynamic state detection and noise robustness compared to other methods.
New method combines FMEA and Bayesian Network for root cause analysis in lithium-ion battery production.
problem Complex cause-effect relationships in lithium-ion battery production.
method Combining FMEA with Bayesian Network to detect and resolve inconsistencies.
result Holistic method builds large-scale cross-process Bayesian Failure Network for root cause analysis.
New protocol reduces communication costs for heterogeneous bandits over complex networks.
problem Minimizing group regret in a multi-agent, heterogeneous bandit setting over complex networks.
method Flooding with Absorption (FwA) protocol for heterogeneous bandits over complex networks.
result FwA protocol significantly reduces communication costs compared to flooding while maintaining similar regret performance.
New method amplifies hidden structure in complex networks.
problem Difficulty in uncovering hidden structure in complex networks.
method Iterative weakening of dominant structure through randomization.
result Theoretical support for the effectiveness of structure amplification.
We derive a novel sensitivity analysis of input variables for predictive epistemic and aleatoric uncertainty. We use Bayesian neural networks with latent variables as a model class and illustrate the usefulness of our sensitivity analysis on real-world datasets. Our method increases the interpretability of complex blac…
Based on the assumption that economic complexity is characterised by the interactions of economic agents (who) constantly change their actions and strategies in response to the outcome they mutually create, this paper presents how network models can be used a proxies for the mapping, quantification and analysis of Roma…
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.
New framework combines simple machines into complex ones for better neural network performance.
problem Improving neural network performance with limited training data.
method Developed a framework using topology and functional analysis to combine simple machines into complex ones, and used kernel methods to find optimal architectures.
result Kernel-inspired networks can outperform classical neural networks when training data is small.
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.
New KNN test improves association analysis of high-dimensional sequencing data.
problem Challenges in using neural networks for high-dimensional sequencing data analysis.
method Kernel-based neural network (KNN) test for complex association analysis.
result KNN test outperforms SKAT in detecting non-linear and interaction effects.
Paper analyzes neural network complexity for planning problems.
problem Understanding neural network complexity for planning policies.
method Circuit complexity analysis for relational neural networks.
result Three classes of planning problems identified based on network complexity.
Combining neural networks and multiscale decomposition for financial market analysis.
problem Financial markets' complexity and mainstream models' limitations in capturing non-linear structures.
method Neural networks for non-linear associations combined with multiscale decomposition.
result Improved understanding of financial market data substructures.
The study examines network analysis for predicting stock market performance.
problem Understanding lead-lag relationships in the NYSE.
method Network analysis of the NYSE to identify lead-lag effects.
result Network analysis reveals valuable insights for investors and analysts.
Tutorials on signal processing on higher-order networks like simplicial complexes and hypergraphs.
problem Processing complex data structures with polyadic relationships.
method Introduction to simplicial complexes and hypergraphs, Fourier analysis, signal denoising, interpolation, embeddings, neural networks.
result Multi-relational operators like the Hodge Laplacian for simplicial complexes and tensor representations for hypergraphs.
Simplifies deep learning scaling analysis without sacrificing accuracy.
problem Interpreting feature learning mechanisms and determining network implicit bias in high-dimensional settings.
method Developed a heuristic approach for predicting data and width scales of feature learning patterns.
result Predictions align with known results and extend to complex architectures.
Network analysis improves stock return forecasting.
problem Improving stock return forecasting using network properties.
method Network analysis of stock return correlations, using individual and global properties of stocks.
result 50% improvement in R2 score for long-term stock returns forecasting, 3% for short-term.
Networks are a fundamental model of complex systems throughout the sciences, and network datasets are typically analyzed through lower-order connectivity patterns described at the level of individual nodes and edges. However, higher-order connectivity patterns captured by small subgraphs, also called network motifs, de…
H-GAT improves stock selection by capturing complex higher-order stock relations and integrating both technical and fundamental analysis.
problem Stock selection difficulty and lack of comprehensive analysis.
method Higher-order Graph Attention Network (H-GAT) that incorporates both technical and fundamental analysis.
result H-GAT outperforms existing methods in stock selection metrics.
Unified analysis of neural networks for sparse signal recovery.
problem Sparse signal recovery from few linear measurements.
method Introduces a general class of neural networks with weight-sharing, analyzes their Rademacher complexity, and derives generalization bounds.
result Derives generalization bounds that depend linearly on the number of parameters and depth, applicable to various neural network types.
Deep neural networks (DNNs) transform stimuli across multiple processing stages to produce representations that can be used to solve complex tasks, such as object recognition in images. However, a full understanding of how they achieve this remains elusive. The complexity of biological neural networks substantially exc…
Develops 2-categorical methods for multi-parameter persistence.
problem Fundamental limitations of traditional persistence modules.
method 2-categorical structures to capture hierarchical interactions.
result New invariants effectively characterize multidimensional topological features.
We propose the labeled Čech complex, the plain labeled Vietoris-Rips complex, and the locally scaled labeled Vietoris-Rips complex to perform persistent homology inference of decision boundaries in classification tasks. We provide theoretical conditions and analysis for recovering the homology of a decision boundary fr…
ENN method uses expectile regression for genetic data analysis of complex diseases.
problem Discover additional genetic variants contributing to complex diseases.
method Developed an expectile neural network (ENN) method integrating expectile regression and neural networks.
result ENN method outperforms existing expectile regression in discovering genetic variants predisposing to sub-populations.
CBNNs model survival with time-varying interactions, outperforming other methods.
problem Complex covariate effects and time-varying interactions in survival analysis.
method Combines case-base sampling with neural networks to model time-varying effects and complex baseline hazards.
result CBNNs outperform regression and neural network-based survival methods in simulations and real data applications.
We have performed an empirical comparison of two distinct notions of discrete Ricci curvature for graphs or networks, namely, the Forman-Ricci curvature and Ollivier-Ricci curvature. Importantly, these two discretizations of the Ricci curvature were developed based on different properties of the classical smooth notion…
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.
Transformers show strengths and weaknesses in complexity analysis.
problem Understanding the strengths and limitations of attention layers in transformers.
method Analysis of representation power through complexity parameters and task-specific constructions.
result Transformers can solve sparse averaging tasks with logarithmic complexity, but triple detection tasks require linear complexity.
New findings show learning deeper neural networks is hard even with Gaussian inputs and non-degenerate weights.
problem The computational complexity of learning neural networks, especially deeper ones.
method Smoothed analysis framework and local pseudorandom generators.
result Learning depth-3 ReLU networks under Gaussian input distribution is hard even if weight matrices are non-degenerate.
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 method combines neural networks with Monte Carlo for complex system reliability.
problem Estimating small failure probabilities in complex systems.
method Subset Simulation with Hamiltonian Neural Networks.
result High acceptance rates and computational efficiency in low-probability regions.
Complex networks are ubiquitous to several Computer Science domains. Centrality measures are an important analysis mechanism to uncover vital elements of complex networks. However, these metrics have high computational costs and requirements that hinder their applications in large real-world networks. In this tutorial,…
This work improves interpretability and calibration of complex-valued neural networks using Newton-Puiseux analysis.
problem Insufficient interpretability and probability calibration of complex-valued neural networks.
method Newton-Puiseux framework to examine local decision geometry, fitting a polynomial surrogate and factorizing it using Newton-Puiseux expansions.
result Enhanced Expected Calibration Error in ECG and wireless modulation datasets compared to uncalibrated softmax and standard post-hoc baselines.
Automates perturbation analysis for neural networks, enabling certified robustness on complex architectures.
problem Limited applicability of existing perturbation analysis methods to complex neural network architectures.
method Developed an automatic framework to generalize LiRPA algorithms to any neural network structure, enabling loss fusion and state-of-the-art certified defense results.
result Demonstrated LiRPA based certified defense on Tiny ImageNet and Downscaled ImageNet.
Self-attention prefers sparse functions of input sequences, reducing sample complexity.
problem Understanding the inductive biases of self-attention in modeling long-range dependencies.
method Theoretical analysis and synthetic experiments to probe sample complexity of learning sparse functions with Transformers.
result Bounded-norm Transformer networks can represent sparse functions of the input sequence with logarithmic sample complexity.
New analysis shows halting time is predictable for large models, improving optimization efficiency.
problem Understanding the average-case complexity of optimization algorithms for large-scale models.
method Average-case analysis of first-order methods on random least squares and neural networks.
result Halting time is independent of input distribution, leading to tighter convergence rates.
In this review we establish various connections between complex networks and symmetry. While special types of symmetries (e.g., automorphisms) are studied in detail within discrete mathematics for particular classes of deterministic graphs, the analysis of more general symmetries in real complex networks is far less de…
Randomly guessing weights helps analyze RL benchmarks objectively.
problem Understanding the complexity of reinforcement learning benchmarks.
method Generate policy networks by randomly guessing their parameters, evaluate on benchmarks, and analyze results.
result Small untrained networks can provide a robust baseline for various RL tasks.
New method measures generalizability of deep neural networks based on decision boundary complexity.
problem Lack of generalization methods for deep neural networks.
method Created Decision Boundary Complexity (DBC) score to measure DNN complexity.
result Simpler decision boundaries lead to better generalizability, supporting Occam's Razor.