Graph ML for Dynamic Financial Networks — Full Deck
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EPFL Workshop on Graph Learning in Financial Networks

Graph Machine Learning for Dynamic Financial Networks

From Foundations to the Lightning Network

A Bit About Myself

🎓
Bachelor and Master in Computer Science at Imperial College and Cambridge (2015-2019)
🤖
PhD on Machine Learning on Graphs between Twitter and Imperial College (2019-2023)
🧬
ML Researcher on generative models for structural biology and drug discovery at Vant AI (2024-2025)
🐬
PostDoc on ML for decoding non-human communication @ Sapienza (2026 - Current)
₿
ML Advisor at Amboss Technologies, working on ML for the Lightning Network (2024-Current)
🤖 🎓 🧠 🧬 💊 🔬 🦜 🐘 🐬 🐠 🐙 🤿

Why Should We Care About ML on Graphs?

Networks are everywhere
And graphs are a great way to model them
Functional Networks
Interaction Networks
Social Networks
Molecules
Image Credit: wolfram.com · gatton.uky.edu · Papo et al., Frontiers in Human Neuroscience 2014 · Madhavicmu / Wikimedia Commons CC-BY-SA-4.0
Networks are everywhere
Also in finance
Interbank exposure network
Bank A Bank B Bank C Bank D Bank E exposure systemic bank
Bitcoin Lightning network
₿ Alice Node Routing hub Node ₿ Bob payment channel routed payment
What model should we use for graphs?
Modality
Data
Architecture
🖼️ Images
Example image
CNN
📝 Text
The cat sat on the mat
Transformer
🕸️ Graphs
Social network graph
?

(Static) Graphs and Graph Tasks

Graphs: nodes, edges, and features
G = (V, E)
V = nodes
E = edges
w x u v
A ∈ ℝn×n
A = Adjacency Matrix
u
v
w
x
u
0
1
1
1
v
1
0
0
1
w
1
0
0
1
x
1
1
1
0
X ∈ ℝn×d
X = node features
f1
f2
f3
u
0.8
0.4
1.7
v
0.2
0.9
1.4
w
0.6
0.1
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Tasks on Graphs
Graph-wise
Predict a label (or scalar) for the whole graph.
Model Drug-like? Yes No
Example: molecular property prediction, fraud detection, document classification.
Node-wise
Predict labels (or scalars) for individual nodes.
Model Omnivore Vegetarian
Example: user attributes, protein function, paper topic prediction.
Edge-wise
Predict labels (or scalars) for edges. Link prediction is the special case of scoring missing or future edges.
?
Example: recommendations, knowledge graph completion, social tie prediction.

(Static) Graph Neural Networks

Graph Neural Networks (GNNs)
Convolutional GNN
$\mathbf{H}^{(k)}$ = $\sigma(\tilde{\mathbf{A}} \mathbf{H}^{(k-1)} \mathbf{W}^{(k)})$ $\mathbf{H}^{(0)}$ = $\mathbf{X}$
H (k) = σ( Ã H (k-1) W (k) )
Message-Passing GNN
$\mathbf{m}_i^{(k)}$ = $\text{AGG}^{(k)}\!\left(\{\{\mathbf{h}_j^{(k-1)}: (i,j) \in E\}\}\right)$ $\mathbf{h}_i^{(k)}$ = $\text{COM}^{(k)}\!\left(\mathbf{h}_i^{(k-1)}, \mathbf{m}_i^{(k)}\right)$ $\mathbf{h}_i^{(0)}$ = $\mathbf{x}_i$
Transformers are GNNs
On the fully connected graph
This sentence is a also
Graph Transformers
Transformer-style attention, but with graph structure injected
Core idea
  • Self-attention lets every node aggregate from all other nodes
  • Graph information enters through special positional encodings
$\mathrm{Attn}(i,j) \leftarrow q_i^\top k_j + b_{\mathrm{graph}}(i,j)$
A B C D E

Dynamic Graphs

Some Examples of (Continuous) Dynamic Graphs
Graphs changing over time
Social Networks
Interaction Networks
From Static to Dynamic Graphs
$G=(V,E,X)$
Static Graph
• No notion of time
• Examples: molecules, syntax trees
$G_t=(V,E,X_t)$
Spatio-Temporal Graph
• Fixed topology; changing features
• Regular time intervals
• Examples: traffic, weather sensors
$G(t)=\{x_{t_1},x_{t_2},...\}\quad t_1\leq t_2\leq ...$
Continuous-Time DG (CTDG)
• Most general formulation
• Sequence of timestamped events
• Examples: social, financial
$G_t=(V_t,E_t,X_t)$
Discrete-Time DG (DTDG)
• Changing topology and features
• Regular time intervals -> sequence of snapshots
• Examples: weekly trade networks
Less General
More General
Why static GNNs are not enough
Collapsing event history into one snapshot loses order, timing and evolution
→
latest snapshot only
  • Information loss: the last snapshot hides the evolution path, ie. what happened and when
  • Inefficiency: every new event forces repeated computation
  • No timing prediction: static GNNs do not support predicting when something will happen

Models

Temporal Graph Model
Graph up to time t (ordered event history) Encoder z₁(t) z₂(t) z₃(t) z₄(t) z₅(t) Temporal node embeddings Decoder ŷ prediction Node / Edge prediction
Memory-based Models [11, 12]
Update time
u t v message state, Δt features memory update u memory update v

Edge (u,v) builds a message from partner state, features & Δt; only the two touched nodes update their memory.

Predict time
memory node u memory node v decoder MLP ŷ prediction

Memories serve directly as node embeddings, fed into decoder with no extra computation at query time.

Memory-based Models: Pros and Cons
A strong online model, but not yet a full temporal graph encoder
Pros
  • Strong sequentiality inductive bias
  • Cheap online updates after each new event
Cons
  • Inactive nodes can become stale
  • Graph context is mostly local or indirect
  • Forced to process previous edges in sequential order
Graph-based Models [13]
GNN on the graph of previous interactions, with timestamps as edge features
Update time
u t v G(t) new edge appended (orange)

Edge (u,v,t) is simply appended to G(t) — no computation performed at event time.

Predict time
G(t) graph GNN GAT layers Z(t) embeddings decoder MLP ŷ prediction

GNN runs on full G(t) to produce node embeddings; must re-run for every new query — expensive at inference.

Graph-based Models: Pros and Cons
Explicit graph structure mitigates staleness, but the GNN must re-run on every query
Pros
  • No need for sequential processing in training
  • Using the graph explicitly → mitigates staleness problem
Cons
  • Can only handle edge addition events
  • Need to re-run GNN after each new event → inefficient at inference
TGN: Temporal Graph Networks [14]
Our work: a modular framework that combines memory-based and graph-based temporal learning
Update time
u t v messages m_u(t), m_v(t) memory update u, v interaction graph G(t) new edge appended in orange

The event is its own object: it creates messages, updates memories for u and v, and is also appended to G(t).

Predict time
memory G(t) structure GNN GAT layers Z(t) embeddings decoder MLP ŷ prediction

Memory and graph structure are inputs to the GNN, which produces Z(t) for the decoder.

TGN: Best of Both Worlds
Memory-based online updates plus graph-based structural context
Pros
  • Prediction-time GNN can be cheaper (shallower) thanks to leveraging the memory
  • Graph context at prediction time mitigates stale local state
  • Combines sequentiality inductive bias with topological information
  • One modular notation covers memory-based and graph-based models
TGN: State-of-the-Art in 2020
High accuracy with much lower per-epoch cost than the previous methods
TGN: Still a Strong Baseline Today
Years of follow-up work, yet TGN remains hard to beat on standard benchmarks

Benchmarks

Temporal Graph Benchmark
Diverse, large datasets and unified evaluation
Key Findings
  • Previous datasets were too easy and saturated
  • Exposed that simple historical baselines can be surprisingly strong
  • Large new datasets make scalability part of the benchmark
9 datasets · 5 domains · up to 72M edges
Temporal Graph Benchmark 2.0
TGB but for knowledge graphs
Key findings
  • Edge and relation type information is crucial for strong performance
  • Simple heuristic baselines remain competitive with more complex methods
  • Many methods fail to run on the largest datasets, making scalability a central result
8 datasets · 5 domains · up to 53M edges

Unifying Models for Discrete and Continuous Time Graphs

UTG: Unifying Snapshot & Event-Based Models
Huang, Poursafaei, Rabbany, Rabusseau, Rossi, LoG 2024
The problem

Snapshot (DTDG) and event-based (CTDG) models developed in isolation: limited cross-comparison and no unified evaluation.

Contribution
  • Input mapper: convert CTDG to snapshots and DTDG to events, so any model can run on any data
  • UTG training: use streaming training to make snapshot-based models operate on event streams
  • Output mapper: align predictions to either continuous-time or discrete-time tasks
UTG Framework
UTG: Key Findings
Speed

Snapshot-based models are ≥ 10× faster at inference than most event-based models.

Performance

With UTG training, snapshot-based models match TGN & GraphMixer even on event-based (CTDG) datasets.

Insight

NAT & DyGFormer's edge comes from joint neighbourhood features, not from the event-based format: these can be added to snapshot models too.

Next Frontiers

Foundation Models for TG
Existing TG models are trained and tested on the same graph.
Can we train a single TG model that works on unseen graphs, ideally from different domains?
MiNT: Multi-Network Transfer Benchmark for Temporal Graph Learning
  • New dataset: 84 distinct ERC-20 token transaction networks
  • New framework to train existing TG models on multiple graphs simultaneously
  • Scaling law for TGs: model performance improves as it is trained on more networks
Can we use LMs directly on temporal graphs?
TGTalker
Translate temporal graph structure into natural language and feed it to a pre-trained LLM — no fine-tuning required.
Four prompt components
  • Background set — recent edges as context
  • Example set — 5-shot Q&A pairs
  • Query set — target edge to predict
  • Temporal neighbors — 1-hop recent neighbours
TGTalker: Results & Explainability
Results
  • Competitive without fine-tuning
  • Consistently outperforms TGN and HTGN
10 explanation categories discovered
  • Most Recent Interaction ≈ EdgeBank heuristic
  • Most Frequent Destination ≈ PopTrack heuristic
  • Novel patterns: sequence logic, analogy-based inference
TGTalker results and explanations
Resources for TGL
Blog posts, talks, surveys, libraries & datasets
💻 Libraries
TGM
Temporal Graph Models library
📊 Datasets
TGB
Temporal Graph Benchmark
TGB-Seq
Sequential Temporal Graph Benchmark
(a small taste of ongoing work)

My Current Directions

🔊 Communicating Sound Through Natural Language
A sender agent describes a sound; a receiver agent decodes the description back to audio
Original audio
→
Transmitted sentence
"At entry the envelope carries mid-power, punchy, and extreme-oscillation; through sustain and release, the trace returns swift-onset and aggressive..."
→
Reconstructed audio
Comparison
🔊 Communicating Sound Through Natural Language
A sender agent describes a sound; a receiver agent decodes the description back to audio
Original audio
→
Transmitted sentence
"At entry the envelope carries mid-power, punchy, and extreme-oscillation; through sustain and release, the trace returns swift-onset and aggressive..."
→
Reconstructed audio
Waveforms
Original and reconstructed sample 1 waveforms
🐬 OpenWhistle Dataset
  • Very rich and unique dolphin dataset collected over 5 years
  • New benchmark for whistle detection and classification
Dataset
# Whistles
Voc. hours
Time span (yrs)
Stable pod (# indiv.)
Setting
Seq. context
Open
OpenWhistle Pretraining ~180,000* 114.3 5.0 (5) Semi-nat.
OpenWhistle Expert subset 8,354 1.9 0.42 (5) Semi-nat.
DOLPHINFREE 4,600 7.3 2.0 Wild
Di Nardo et al., 2025 3,111 0.6 0.003 (7) Captive
Watkins MMSD 566 N/R 70+ Wild
Korkmaz et al., 2023 ~29,000* 6.8 0.07 Semi-nat.
Sicily Strait PAM 14,048 N/R 1.2 Wild
DCLDE 2011 6,011 0.7 4.0 Wild
SDWD N/R N/R 43+ (293) Wild (C&R)
* Estimated from total vocalization duration and mean whistle duration.

Graph Machine Learning on the Bitcoin Lightning Network

Lightning Network: Motivation
Making Bitcoin scalable for everyday payments
Lightning Network payment volume year-over-year report
  • Problem: BTC has a bottleneck of ~5 transactions/sec, 1000x less than Mastercard.
  • Solution: The Lightning Network enables 5M+ transactions/sec through fast, low-cost off-chain payments.
  • Why it matters: Makes BTC more practical for everyday payments, micropayments, and future agent-to-agent transactions.
  • Adoption: ~$15B in 2025, with 300% YoY growth.
Lightning Network Basics
Payments move through channels, one hop at a time
Lightning Network: Balances and Payments
Payments move only where liquidity exists in the right direction
Problem 1: Channel Balances are Actually Hidden
A node can only see the directional balances of its channels
Channel Balance Interpolation
RQ: Can we predict the hidden directional balances for the network channels?
Balance Interpolation: Methods
Random forests over public node, channel and graph features
Channel fees and limits Node local context Graph network position Random forest Predicted balance share
Balance Interpolation: Results
The model combining node, edge and graph features improves by 27% over simple heuristics
Balance-share MAE, lower is better
0.40 0.20 0.00 Naive baselines Learned methods 0.358 0.316 0.313 0.285 0.259 Equal Split Edge Node Graph Node+Edge +Graph
Problem 2: The Lightning Network Changes over Time
New edges can be opened, mutually closed, or forced closed
Channel Closure Prediction
RQ: Which channels will stay open, close mutually, or force close?
Closure Prediction: Methods
Temporal link classification given past history
Channel fees, capacity Node open/close history Time age, recency Graph network topology or position Classifier MLP, GNN or TGN Open, mutual close, or forced close
Closure Prediction: Results
A simple MLP beats graph-aware models, but the overall performance is modest
Macro F1 by model, higher is better
0.40 0.20 0.00 Naive baselines Learned methods 0.25 0.32 0.35 0.36 0.38 Uniform Random Stratified Random GNN TGN MLP
The Model Struggles to Predict Closures
Public information lacks balances, payment failures and uptime, the private signals that would be most useful here
Normalized confusion matrix for the MLP
Predicted True Open Forced Mutual Open Forced Mutual 0.75 0.08 0.16 0.66 0.14 0.20 0.60 0.10 0.30
Problem 3: How to optimally allocate a given budget?
When joining the network, a node has to choose who to connect to and how to allocate its budget
MP-Flow: Methods
Channel placement as reinforcement learning: a graph policy picks peers one at a time
ENVIRONMENT Lightning graph BUDGET S new node opened candidates AGENT MPNN policy scores every feasible node pick best 1) state st current graph 2) action at open one channel, 0.2 ₿ 3) reward rt max flow gain
MP-Flow: Results
MP-Flow outperforms all other methods, with a 88.5% relative gain over a random baseline
Mean max flow uplift in ₿, higher is better
0.18 0.09 0.00 Naive baselines Heuristic baselines Learned methods 0.089 0.150 0.154 0.163 0.168 Random GCN Degree Betweenness MP-Flow
MP-Flow is learning more than just connecting to big hubs
Relative improvement over Betweenness grows as top-degree hubs are pruned
Relative improvement over Betweenness, higher is better
0 5 10 Relative improvement (%) 0 5 10 25 50 k highest-degree hubs removed +2.16 +3.19 +3.07 +8.89 +7.69
MP-Flow is in production at Amboss
The learned policy now powers peer recommendations for real Lightning channel openings
Decisions executed
4,640
channel-open actions selected by the agent
Capital allocated
267.3 ₿
over $16M deployed into Lightning channels
Managed nodes
30
managed production nodes receiving recommendations
Conclusion: main points
Graphs are everywhere, and most real financial graphs are dynamic
Dynamic graphs

Graphs are everywhere, and most graphs, particularly in finance, are dynamic.

Temporal graph models

Temporal Graph Models leverage the sequence and timing of events, on top of the topology.

Lightning Network
An exciting application where we have worked on:
  • Predicting the directional balance of channels
  • Predicting whether channels will stay open or close
  • Optimally selecting the channels to which to allocate liquidity
Thank You

Questions?

Graph Machine Learning for Dynamic Financial Networks  ·  EPFL Workshop on Graph Learning in Financial Networks  ·