Neural networks are mathematically represented via quiver representations.
problem Understanding how neural networks process data and create representations.
method Representing neural networks as quiver representations with activation functions.
result Neural networks' computations can be studied algebraically and geometrically.
We study how finite Bayesian neural networks adapt their hidden representations.
problem Understanding how finite Bayesian neural networks differ from infinite ones.
method We analyze the asymptotics of learned feature kernels for various network architectures.
result The leading finite-width corrections to feature kernels have a universal form.
Analysis and manipulation of trained neural networks is a challenging and important problem. We propose a symbolic representation for piecewise-linear neural networks and discuss its efficient computation. With this representation, one can translate the problem of analyzing a complex neural network into that of analyzi…
Proposes ML-GCN for multi-label network node representation learning.
problem Complex multi-label networks with correlated labels.
method Two Siamese GCNs model node-label and label-label interactions, integrated under a unified objective function.
result Effective node representation learning with preserved label interactions.
Equivariant neural networks use symmetry to interpret complex data.
problem Interpreting and understanding the behavior of equivariant neural networks.
method Decompose layers into simple representations and analyze nonlinear activation functions.
result Equivariant neural networks can be interpreted using a filtration generalizing Fourier series.
Social network analysis is an important problem in data mining. A fundamental step for analyzing social networks is to encode network data into low-dimensional representations, i.e., network embeddings, so that the network topology structure and other attribute information can be effectively preserved. Network represen…
Proposes a new method for medical diagnosis using network-based representation learning.
problem Improving medical diagnosis accuracy through better data representation.
method Heterogeneous network-based model and modified metapath2vec algorithm for learning latent node representations.
result Significant performance boost in symptom/disease classification and disease prediction tasks.
Neural networks benefit from intermediate representations, reducing sample complexity.
problem Understanding how neural networks leverage intermediate representations for hierarchical learning.
method Fixed, randomly initialized neural network as a representation function, compared with raw inputs and other trainable networks.
result Neural representations can achieve improved sample complexities compared to raw inputs, especially for low-rank polynomials.
Comparing different neural network representations and determining how representations evolve over time remain challenging open questions in our understanding of the function of neural networks. Comparing representations in neural networks is fundamentally difficult as the structure of representations varies greatly, e…
Math theory explains how neural networks learn abstract representations.
problem Understanding how neural networks learn abstract representations.
method Mathematical theory reformulating network optimization into mean field optimization over neural preactivations.
result Abstract representations of latent variables are guaranteed to appear in neural networks trained on tasks that depend on these variables.
Learning distributed node representations in networks has been attracting increasing attention recently due to its effectiveness in a variety of applications. Existing approaches usually study networks with a single type of proximity between nodes, which defines a single view of a network. However, in reality there usu…
Optimal transport metric transfers deep network representations efficiently.
problem Efficiently transfer deep network representations for new tasks.
method Use optimal transport to quantify representation similarity and regularize student network.
result Optimal transport distance promotes similarity between teacher and student representations.
The paper proposes a model to learn street network representations directly from graphs.
problem Loss of detailed topological data in raster representations of street networks.
method Variational autoencoder with graph convolutional layers and a probabilistic fully-connected graph decoder.
result The model infers good representations directly from street networks, capturing both local structure and spatial distribution.
Combines global and local features for better social circle prediction in ego-networks.
problem Efficiently analyzing ego-networks with hidden local structures.
method Evolved deep learning techniques to capture both global and local network features.
result Social circle prediction benefits from a combination of global and local features.
Graph representation converts complex networks into vectors for easier analysis.
problem Efficient analysis of large network data.
method Introduces graph representation and network embedding models.
result Efficiently converts graph data into low-dimensional vectors.
Enhanced BCPNN learns hidden representations without labels.
problem Unsupervised learning of hierarchical representations in neural networks.
method Extended BCPNN architecture with local Hebbian learning mechanisms.
result Demonstrated capability for unsupervised learning of salient hidden representations.
Recent work has argued that neural networks can be understood theoretically by taking the number of channels to infinity, at which point the outputs become Gaussian process (GP) distributed. However, we note that infinite Bayesian neural networks lack a key facet of the behaviour of real neural networks: the fixed kern…
Batch normalization makes deep neural networks' representations increasingly orthogonal.
problem Orthogonality of deep neural network representations.
method Random linear transformations in successive batch-normalizations.
result Orthogonality of representations improves SGD performance.
Defines metrics to compare neural network representations.
problem Comparing neural network representations across different architectures and tasks.
method Developed a family of metric spaces and modified existing measures to quantify representational dissimilarity.
result Identified relationships between neural representations and anatomical features.
GNNs learn graph representations, with new theory on their power and limitations.
problem Understanding the capabilities and limitations of GNNs.
method Theoretical analysis of GNNs, focusing on approximation and learning properties.
result New insights into the representation, generalization, and extrapolation of GNNs.
Deconfounds neural network representation similarity metrics to improve consistency and accuracy.
problem Confounding by population structure in similarity metrics like RSA and CKA.
method Covariate adjustment regression to adjust for confounders.
result Improves detection of semantically similar neural networks and consistency in transfer learning.
New method finds Lie group representations without explicit groups, enabling new neural network architectures.
problem Building neural networks equivariant to arbitrary Lie groups.
method Algorithm to find Lie group representations from Lie algebra structure constants. Self-contained method for constructing Lie group-equivariant neural networks.
result First object-tracking model equivariant to the Poincaré group.
Neural networks learn spectral representations for group composition.
problem Understanding structured emergence in neural network training.
method Lifting gradient flow to Fourier domain, proving convergence to irreducible representations.
result Neurons converge to single irreducible representations, cross-layer coefficients align.
We consider deep feedforward neural networks with rectified linear units from a signal processing perspective. In this view, such representations mark the transition from using a single (data-driven) linear representation to utilizing a large collection of affine linear representations tailored to particular regions of…
Study reveals differences in medical image models' hidden representation refinement.
problem Understanding how intrinsic dimensionality changes in neural network hidden representations across different domains.
method Analysis of 11 natural and medical image datasets using 6 network architectures.
result Medical image models refine hidden representations earlier, suggesting differences in feature abstraction.
Understanding and learning the characteristics of network paths has been of particular interest for decades and has led to several successful applications. Such analysis becomes challenging for urban networks as their size and complexity are significantly higher compared to other networks. The state-of-the-art machine …
We present a novel neural network algorithm, the Tensor Switching (TS) network, which generalizes the Rectified Linear Unit (ReLU) nonlinearity to tensor-valued hidden units. The TS network copies its entire input vector to different locations in an expanded representation, with the location determined by its hidden un…
Algorithm removes spurious concepts from neural network representations without harming task performance.
problem Spurious correlations hinder neural network out-of-distribution generalization.
method Iterative algorithm that identifies two orthogonal subspaces in neural network representation.
result Algorithm outperforms existing methods on computer vision and natural language processing benchmarks.
Study compares atom representations in graph neural networks for molecular properties.
problem Incorrect attribution of results in molecular property prediction due to varying atom features.
method Evaluated multiple atom representations on free energy, solubility, and metabolic stability predictions.
result Different atom representations can lead to varying predictive performance in graph neural networks.
ACERL embeds networks into a low-dimensional space preserving structural and semantic properties.
problem Challenges in brain connectivity data analysis with subject-specific, high-dimensional, and sparse networks.
method Contrastive learning of augmented network pairs with adaptive random masking.
result Achieves minimax optimal convergence rate for edge representation learning.
Graph Neural Networks (GNNs) have been widely studied for graph data representation and learning. However, existing GNNs generally conduct context-aware learning on node feature representation only which usually ignores the learning of edge (weight) representation. In this paper, we propose a novel unified GNN model, n…
Recent work has sought to understand the behavior of neural networks by comparing representations between layers and between different trained models. We examine methods for comparing neural network representations based on canonical correlation analysis (CCA). We show that CCA belongs to a family of statistics for mea…
In a dynamic network, the neighborhood of the vertices evolve across different temporal snapshots of the network. Accurate modeling of this temporal evolution can help solve complex tasks involving real-life social and interaction networks. However, existing models for learning latent representation are inadequate for …
Researchers create integral representations for two-layer ReLU networks with quantitative bounds.
problem Approximating functions with two-layer ReLU networks using explicit integral representations.
method Developed integral representations involving harmonic extension and projection, providing L2 bounds. result Functions can be approximated with L2 errors independent of dimension or degree, depending on coefficients and distribution. A new method for document network embedding interprets and generalizes well.
problem Lack of interpretability and generalization to new documents in existing methods.
method Introduces Topic-Word Attention (TWA) and Inductive Document Network Embedding (IDNE) to generate document representations.
result Achieves state-of-the-art performance on various networks and produces meaningful representations.
i-cNRL learns network differences with interpretability.
problem Comparing unique network characteristics.
method Contrastive network representation learning (cNRL) integrating machine learning schemes.
result i-cNRL reveals unique network patterns with interpretability.
Recent successes in word embedding and document embedding have motivated researchers to explore similar representations for networks and to use such representations for tasks such as edge prediction, node label prediction, and community detection. Such network embedding methods are largely focused on finding distribute…
There is some theoretical evidence that deep neural networks with multiple hidden layers have a potential for more efficient representation of multidimensional mappings than shallow networks with a single hidden layer. The question is whether it is possible to exploit this theoretical advantage for finding such represe…
Proposes an unsupervised graph neural network for entire graph representation.
problem Lack of unsupervised methods for entire graph representation.
method Combines hierarchical graph neural networks and mutual information maximization.
result Improves state-of-the-art performance on multiple graph level tasks.
Centered Kernel Alignment (CKA) was recently proposed as a similarity metric for comparing activation patterns in deep networks. Here we experiment with the modified RV-coefficient (RV2), which has very similar properties as CKA while being less sensitive to dataset size. We compare the representations of networks that…
Representation costs in data science: Unifying function-space views of parametric methods
problem Analyzing representation costs of parametric data-fitting methods
method Developing a general framework for analyzing representation costs through parameter-space regularizers
result Proving that many natural results hold in this abstract setting, including representer theorems for parametric methods on their native spaces
Deep neural networks progressively transform their inputs across multiple processing layers. What are the geometrical properties of the representations learned by these networks? Here we study the intrinsic dimensionality (ID) of data-representations, i.e. the minimal number of parameters needed to describe a represent…
New approach uses prior knowledge to improve neural network representations.
problem Difficulty in learning robust internal representations without a large training set.
method Incorporates prior information into a pre-trained reasoning module.
result Improves representation learning in diverse self-supervised learning settings.
It is widely believed that learning good representations is one of the main reasons for the success of deep neural networks. Although highly intuitive, there is a lack of theory and systematic approach quantitatively characterizing what representations do deep neural networks learn. In this work, we move a tiny step to…
RedEx improves neural network optimization with convex optimization guarantees.
problem Difficult optimization of neural networks.
method RedEx architecture using convex optimization with semi-definite constraints.
result RedEx can efficiently learn functions fixed methods cannot.
Most artificial networks today rely on dense representations, whereas biological networks rely on sparse representations. In this paper we show how sparse representations can be more robust to noise and interference, as long as the underlying dimensionality is sufficiently high. A key intuition that we develop is that …
DORA analyzes deep neural networks' internal representations to detect spurious correlations.
problem Detecting spurious correlations in deep neural networks' internal representations.
method DORA uses Extreme-Activation (EA) distance measure to assess representation similarities.
result Identifies internal representations capable of detecting spurious correlations.
GSAN learns adaptive node representations using geometric scattering and attention.
problem Oversmoothing in node representation learning.
method Attention-based architecture integrating geometric scattering and GCN channels.
result GSAN outperforms previous networks in semi-supervised node classification.