A new method clusters complex networks using topological and geometric structure.
problem Clustering complex networks with intricate topology.
method Centroid-based clustering strategy using Wasserstein distance and barycenter for persistence barcodes.
result Demonstrated effectiveness on simulated and real-world networks.
New method for inferring network topology from partial data.
problem Inferring network topology from limited node data.
method Vector autoregressive model and Gaussian mixture algorithm.
result The proposed method converges to the network combination matrix in probability.
This work introduces a method to compare sparse neural network topologies using graph theory.
problem Comparing and understanding sparse neural network topologies, especially during training.
method Introducing Neural Network Sparse Topology Distance (NNSTD) to measure distances between different sparse neural networks.
result Sparse neural networks can outperform over-parameterized models without further structure optimization.
This paper introduces a new method for neural networks that doesn't need a global coordinate system.
problem The lack of a global coordinate system in neural networks limits their performance and explainability.
method Proposes a learnable topological layer that works in a general metric space (Hilbert space) without requiring a Euclidean space.
result The proposed method eliminates the need for a costly parametrization stage and achieves optimal network performance.
The paper sets limits on neural network sizes based on dataset shapes.
problem Understanding the size of neural networks needed for accurate predictions.
method Examined how the shape of data influences neural network complexity.
result Established upper limits on neural network width based on dataset topology.
Topology aids in solving machine learning classification problems.
problem Machine learning classification problems.
method Classical topology applied to neural networks.
result Topology guides neural network architecture and training.
Introduces topological deep learning for neural network classification problems.
problem Classifying neural networks using minimal topological structures.
method Formalizes classification problems in a topological setting.
result Demonstrates conditions for the feasibility of classification problems in neural networks.
Neural networks simplify complex data topologies into simpler ones.
problem Understanding why deep neural networks perform better than shallow ones and why ReLU activations are superior.
method Persistent homology analysis of neural network layers on various data sets.
result Neural networks reduce the topological complexity of input data sets, often to their simplest form.
A new method learns node embeddings for signed directed networks by capturing both first-order and high-order topologies.
problem Learning representative node embeddings for signed directed networks considering both first-order and high-order topologies.
method Proposes a decoupled variational embedding (DVE) method that leverages a specially designed auto-encoder structure to capture both first-order and high-order topologies.
result Extensive experiments on real-world datasets show the effectiveness of DVE in link sign prediction and node recommendation tasks.
Long training times of deep neural networks are a bottleneck in machine learning research. The major impediment to fast training is the quadratic growth of both memory and compute requirements of dense and convolutional layers with respect to their information bandwidth. Recently, training `a priori' sparse networks ha…
The interplay between inter-neuronal network topology and cognition has been studied deeply by connectomics researchers and network scientists, which is crucial towards understanding the remarkable efficacy of biological neural networks. Curiously, the deep learning revolution that revived neural networks has not paid …
New method identifies network dynamics and noise structure.
problem Estimating network and disturbance topologies in dynamic systems.
method Extended multi-step Sequential Linear Regression and Weighted Null Space Fitting methods.
result Consistent estimation of dynamic networks with reduced computational burden.
In this empirical paper, we investigate how learning agents can be arranged in more efficient communication topologies for improved learning. This is an important problem because a common technique to improve speed and robustness of learning in deep reinforcement learning and many other machine learning algorithms is t…
The topological information is essential for studying the relationship between nodes in a network. Recently, Network Representation Learning (NRL), which projects a network into a low-dimensional vector space, has been shown their advantages in analyzing large-scale networks. However, most existing NRL methods are desi…
Novel framework explains generalization in deep neural networks.
problem Understanding and improving generalization in deep neural networks.
method Topological Quantum Neural Networks as the semi-classical limit of Deep Neural Networks.
result Demonstrates that the perceptron, viewed as the semi-classical limit, achieves similar results to standard neural networks without training.
Improvements in the performance of deep neural networks have often come through the design of larger and more complex networks. As a result, fast memory is a significant limiting factor in our ability to improve network performance. One approach to overcoming this limit is the design of sparse neural networks, which ca…
Recently, in the paper "Weight Agnostic Neural Networks" Gaier & Ha utilized architecture search to find networks where the topology completely encodes the knowledge. However, architecture search in topology space is expensive. We use the existing framework of binarized networks to find performant topologies by constra…
Proposes a model for identifying edges in low-rank dynamical networks.
problem Inability of conventional methods to handle low-rank dynamical networks.
method Low rank dynamical network model with causal Wiener filtering.
result Consistent method for estimating all network edges.
Graph neural network using Beltrami flow for feature and topology evolution.
problem Efficient feature learning and topology evolution on graphs.
method Discretized Beltrami flow applied to graph neural networks with positional encodings.
result Achieves state-of-the-art results on various benchmarks.
The paper examines topological features of ReLU networks and their relation to decision boundaries and training loss.
problem Understanding the topological structure of ReLU neural network activation patterns.
method Polytope decomposition of feature space, Fiedler partition of dual graph, homology computation of cellular decomposition.
result The Fiedler partition of the dual graph correlates with decision boundaries in binary classification tasks, and similar patterns in training loss and polyhedral cell-count emerge in regression tasks.
This paper finds efficient algorithms for approximating Markov networks with k-tree topologies.
problem Efficiently approximating Markov networks with complex topologies.
method Developed O(n^{k+1})-time algorithms for finding maximum spanning k-trees (MSkT) that retain certain subgraphs.
result Optimal approximation of Markov networks with k-tree topology is achieved in polynomial time.
Method monitors neural networks using topological properties.
problem Detecting data shifts and out-of-distribution samples.
method Topological Uncertainty based on activation graphs.
result Validates network predictions without retraining.
Contagions such as the spread of popular news stories, or infectious diseases, propagate in cascades over dynamic networks with unobservable topologies. However, "social signals" such as product purchase time, or blog entry timestamps are measurable, and implicitly depend on the underlying topology, making it possible …
Study shows effective resistance distance yields more accurate network barycenter than Hamming distance.
problem Identifying the best metric for computing the Fréchet mean network.
method Compared the effectiveness of Hamming distance and effective resistance distance in capturing network topology.
result Effective resistance distance produces a more accurate Fréchet mean network.
Graph neural networks improve topology control of power grids.
problem Grid congestion due to renewable energy and electrification.
method Investigated the effect of graph representation on GNN effectiveness for topology control.
result Heterogeneous graph representation outperforms homogeneous in topology control tasks.
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 TSBP for matching topological signal distributions.
problem Matching signal distributions on topological domains.
method Topological Schrödinger Bridge (TSBP) with linear topology-aware stochastic dynamics.
result Derives closed-form topological SB (TSB) for Gaussian boundary distributions.
We analyze oversquashing in topological message-passing using relational structures.
problem Oversquashing in topological message-passing remains understudied.
method A unifying axiomatic framework that bridges graph and topological message-passing.
result Potential to advance topological deep learning.
The learnability of different neural architectures can be characterized directly by computable measures of data complexity. In this paper, we reframe the problem of architecture selection as understanding how data determines the most expressive and generalizable architectures suited to that data, beyond inductive bias.…
Study enhances neural network predictions for wave height using topological features.
problem Challenges in predicting wave heights due to short-term and long-term factors.
method Hybridization of persistent homology with neural networks for feature engineering.
result Significant improvements in R2 score and reductions in errors for various neural network models. The paper explores the geometry and topology of DNN decision boundaries.
problem Understanding the geometric and topological properties of DNN decision boundaries.
method Differential geometry and the Gauss-Bonnet-Chern theorem.
result Computed the Euler characteristics of compact decision boundaries.
Proposes a method to infer complex network topologies from multiple graphs.
problem Learning multiple graph Laplacian matrices from heterogeneous graph signals with intricate topological patterns.
method Structured fusion regularization and ADMM algorithm for efficient computation.
result Establishes a non-asymptotic bound of the estimation error and reflects the effect of key factors on convergence rate.
CT improves neural network performance on cell complex data.
problem Improving predictive performance of neural networks on complex data.
method Introducing the Cellular Transformer (CT) that generalizes graph-based transformers to cell complexes.
result CT achieves state-of-the-art performance on cell complex datasets without complex enhancements.
We propose Sparse Neural Network architectures that are based on random or structured bipartite graph topologies. Sparse architectures provide compression of the models learned and speed-ups of computations, they can also surpass their unstructured or fully connected counterparts. As we show, even more compact topologi…
TVS-FNNs can approximate any continuous function on expanded input spaces.
problem Processing a broader range of inputs like sequences and matrices.
method Proving a universal approximation theorem for TVS-FNNs.
result TVS-FNNs can approximate any continuous function on expanded input spaces.
SM-netFusion estimates brain network atlas by considering multiple topological measures.
problem Limited BNA estimation methods that overlook topological measures and lack discriminative power.
method Supervised multi-topology network cross-diffusion framework using degree, closeness, and eigenvector centrality measures.
result SM-netFusion produces more centered and representative templates, and improves classification accuracy.
Enhanced neural network framework improves constraint satisfaction with topological conditioning.
problem Maintaining semantic coherence while satisfying physical and logical constraints in neuro-symbolic reasoning.
method Integrates topological conditioning with gradient stabilization mechanisms using Forman-Ricci curvature, Deep Delta Learning, and Covariance Matrix Adaptation Evolution Strategy.
result Achieves mean energy reduction to 1.15 compared to baseline values of 11.68, with 95 percent success rate.
Paper estimates neural network size needed for topology learning.
problem Estimating the smallest neural network size for topology learning.
method Using algebraic topology and Lie theory, the paper introduces a procedure based on persistent homology to determine the required dimension.
result The derived dimension is the smallest capable of capturing the topology of the data manifold.
Neural network learns its size and structure during training.
problem Adapting neural network architecture to specific datasets.
method Flexible setup allowing neural network to learn size and topology during training.
result Trained networks achieve virtually identical performance and have learned optimal structure.
The sizes of deep neural networks (DNNs) are rapidly outgrowing the capacity of hardware to store and train them. Research over the past few decades has explored the prospect of sparsifying DNNs before, during, and after training by pruning edges from the underlying topology. The resulting neural network is known as a …
A new method for predicting uncertainties in stream networks.
problem Uncertainty quantification in spatiotemporal graphs with directional flow constraints.
method Spatio-Temporal Adaptive Conformal Inference (STACI) integrating network topology and temporal dynamics.
result STACI effectively balances prediction efficiency and coverage, outperforming existing methods.
Topology design optimization offers tremendous opportunity in design and manufacturing freedoms by designing and producing a part from the ground-up without a meaningful initial design as required by conventional shape design optimization approaches. Ideally, with adequate problem statements, to formulate and solve the…
Detect anomalies in complex networks using topological subspace detectors.
problem Detect anomalies in complex networks defined by simplicial complexes.
method Formulate a hypothesis testing framework using Neyman-Pearson matched topological subspace detectors.
result Effective detection of anomalies in foreign currency exchange networks and other real-world data.
The paper deals with the problem of reconstructing the topological structure of a network of dynamical systems. A distance function is defined in order to evaluate the "closeness" of two processes and a few useful mathematical properties are derived. Theoretical results to guarantee the correctness of the identificatio…
Network science provides valuable insights across numerous disciplines including sociology, biology, neuroscience and engineering. A task of major practical importance in these application domains is inferring the network structure from noisy observations at a subset of nodes. Available methods for topology inference t…
New method detects uncertainty in neural networks for out-of-distribution detection.
problem Detecting out-of-distribution inputs to ensure model reliability.
method Predictive topological uncertainty (pTU) based on persistent homology.
result pTU provides a statistical framework for OOD detection.
This work develops agents to learn generalizable policies for dynamic network environments.
problem Real-world network topologies change due to attackers, defenders, or system failures, leading to failures in adaptive ACD systems.
method Developing agents to learn generalizable policies across dynamic network environments.
result Agents can learn robust policies for dynamic network topologies and diverse attackers.
TOGL adds topological info to GNNs, improving graph and node classification.
problem Graph neural networks lack substructure awareness, especially cycles.
method Integrates global topological information using persistent homology.
result Improves predictive performance for graph and node classification.