A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Neural networks are mathematically represented via quiver representations.
We study how finite Bayesian neural networks adapt their hidden representations.
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…
Equivariant neural networks use symmetry to interpret complex data.
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…
Neural networks benefit from intermediate representations, reducing sample complexity.
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.
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.
The paper proposes a model to learn street network representations directly from graphs.
Combines global and local features for better social circle prediction in ego-networks.
Enhanced BCPNN learns hidden representations without labels.
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…
Knowledge representation of graph-based systems is fundamental across many disciplines. To date, most existing methods for representation learning primarily focus on networks with simplex labels, yet real-world objects (nodes) are inherently complex in nature and often contain rich semantics or labels, e.g., a user may…
Batch normalization makes deep neural networks' representations increasingly orthogonal.
Defines metrics to compare neural network representations.
GNNs learn graph representations, with new theory on their power and limitations.
Deconfounds neural network representation similarity metrics to improve consistency and accuracy.
New method finds Lie group representations without explicit groups, enabling new neural network architectures.
Neural networks learn spectral representations for group composition.
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.
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.
Study compares atom representations in graph neural networks for molecular properties.
ACERL embeds networks into a low-dimensional space preserving structural and semantic properties.
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…
Document network embedding aims at learning representations for a structured text corpus i.e. when documents are linked to each other. Recent algorithms extend network embedding approaches by incorporating the text content associated with the nodes in their formulations. In most cases, it is hard to interpret the learn…
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.
i-cNRL learns network differences 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.
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
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.
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.
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.
GSAN learns adaptive node representations using geometric scattering and attention.
Unified taxonomy for graph representation learning.
Topo-MLP learns network representations without message passing.