# Piecewise-Velocity Model for Learning Continuous-time Dynamic Node Representations

arXiv: https://arxiv.org/abs/2212.12345 · HTML: https://mlsanity.com/paper/2212.12345/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 45 references that are in the map.
- First posted on arXiv 23 Dec 2022.

## Builds on (most cited first, 16 of 16)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Temporal Graph Networks for Deep Learning on Dynamic Graphs](https://mlsanity.com/paper/2006.10637/) (2020)
- [Representation Learning for Dynamic Graphs: A Survey](https://mlsanity.com/paper/1905.11485/) (2019)
- [Motifs in Temporal Networks](https://mlsanity.com/paper/1612.09259/) (2016)
- [Temporal Network Embedding with Micro- and Macro-dynamics](https://mlsanity.com/paper/1909.04246/) (2019)
- [Dynamic Network Embedding Survey](https://mlsanity.com/paper/2103.15447/) (2021)
- [Latent Space Models for Dynamic Networks](https://mlsanity.com/paper/2005.08808/) (2020)
- [A Review of Dynamic Network Models with Latent Variables](https://mlsanity.com/paper/1711.10421/) (2017)
- [Can co-location be used as a proxy for face-to-face contacts?](https://mlsanity.com/paper/1712.06346/) (2017)
- [A Hierarchical Block Distance Model for Ultra Low-Dimensional Graph Representations](https://mlsanity.com/paper/2204.05885/) (2022)
- [Locally Adaptive Dynamic Networks](https://mlsanity.com/paper/1505.05668/) (2015)
- [HM-LDM: A Hybrid-Membership Latent Distance Model](https://mlsanity.com/paper/2206.03463/) (2022)

## Built on by (most cited first, 10 of 10)

- [DyG-Mamba: Continuous State Space Modeling on Dynamic Graphs](https://mlsanity.com/paper/2408.06966/) (2024)
- [Characterizing Polarization in Social Networks using the Signed Relational Latent Distance Model](https://mlsanity.com/paper/2301.09507/) (2023)
- [MedLA: A Logic-Driven Multi-Agent Framework for Complex Medical Reasoning with Large Language Models](https://mlsanity.com/paper/2509.23725/) (2025)
- [Intensity Profile Projection: A Framework for Continuous-Time Representation Learning for Dynamic Networks](https://mlsanity.com/paper/2306.06155/) (2023)
- [Continuous-time Graph Representation with Sequential Survival Process](https://mlsanity.com/paper/2312.13068/) (2023)
- [Neural Minimum Weight Perfect Matching for Quantum Error Codes](https://mlsanity.com/paper/2601.00242/) (2026)
- [A Hybrid Membership Latent Distance Model for Unsigned and Signed Integer Weighted Networks](https://mlsanity.com/paper/2308.15293/) (2023)
- [Time to Cite: Modeling Citation Networks using the Dynamic Impact Single-Event Embedding Model](https://mlsanity.com/paper/2403.00032/) (2024)
- [SAQ: Stabilizer-Aware Quantum Error Correction Decoder](https://mlsanity.com/paper/2512.08914/) (2025)
- [ART: Adaptive Reasoning Trees for Explainable Claim Verification](https://mlsanity.com/paper/2601.05455/) (2026)

## Abstract (arXiv)

Networks have become indispensable and ubiquitous structures in many fields to model the interactions among different entities, such as friendship in social networks or protein interactions in biological graphs. A major challenge is to understand the structure and dynamics of these systems. Although networks evolve through time, most existing graph representation learning methods target only static networks. Whereas approaches have been developed for the modeling of dynamic networks, there is a lack of efficient continuous time dynamic graph representation learning methods that can provide accurate network characterization and visualization in low dimensions while explicitly accounting for prominent network characteristics such as homophily and transitivity. In this paper, we propose the Piecewise-Velocity Model (PiVeM) for the representation of continuous-time dynamic networks. It learns dynamic embeddings in which the temporal evolution of nodes is approximated by piecewise linear interpolations based on a latent distance model with piecewise constant node-specific velocities. The model allows for analytically tractable expressions of the associated Poisson process likelihood with scalable inference invariant to the number of events. We further impose a scalable Kronecker structured Gaussian Process prior to the dynamics accounting for community structure, temporal smoothness, and disentangled (uncorrelated) latent embedding dimensions optimally learned to characterize the network dynamics. We show that PiVeM can successfully represent network structure and dynamics in ultra-low two-dimensional spaces. It outperforms relevant state-of-art methods in downstream tasks such as link prediction. In summary, PiVeM enables easily interpretable dynamic network visualizations and characterizations that can further improve our understanding of the intrinsic dynamics of time-evolving networks.