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LaM-SLidE: Latent Space Modeling of Spatial Dynamical Systems via Linked Entities
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Proposes LaM-SLidE, a latent-space generative model for spatial dynamical systems that uses learned identifier embeddings to trace individual entities through a fixed-size latent representation, with a flow-matching approximator.
Problem
Generative trajectory modeling of spatial dynamical systems with a varying number of entities is hard to move into latent space, because latent modeling typically loses the traceability of individual entities (e.g., atoms, pedestrians, particles) and GNN approaches don't follow latent-space trends.
Approach
Assign each entity a unique learned identifier from a finite pool; encode entities via cross-attention into a fixed set of L latent tokens, decode per-entity coordinates by cross-attending from identifier queries to the latent tokens, and model latent trajectories with a flow-matching (stochastic interpolant) transformer conditioned on observed frames.
Key results
- On MD17, LaM-SLidE reports the lowest ADE/FDE on all 8 molecules, e.g., Aspirin ADE 0.059 vs. GeoTDM 0.107.
- On N-body, LaM-SLidE achieves Charged Particles ADE/FDE 0.104/0.238 and Gravity 0.157/0.406, best on those scenarios; Spring Dynamics is second behind GeoTDM.
- On Tetrapeptides, LaM-SLidE beats MDGen on TICA and MSM metrics (MSM 0.224 vs 0.235) and runs in ~53s vs ~60s, though it is worse on side-chain torsions.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use LaM-SLidE instead of GeoTDM | N-body particle forecasting · N-body Particle | ADE/FDE: 0.110 / 0.258 -> 0.104 / 0.238 | Helped |
| Use LaM-SLidE instead of GeoTDM | N-body gravity forecasting · N-body Gravity | ADE/FDE: 0.256 / 0.613 -> 0.157 / 0.406 | Helped |
| Use LaM-SLidE instead of GeoTDM | N-body spring forecasting · N-body Spring | ADE/FDE: 0.0030 / 0.0079 -> 0.0070 / 0.0135 | Hurt |
| Train one model across all molecules | GeoTDM on MD17 · MD17 | ADE/FDE | Helped |
| Use LaM-SLidE instead of MDGen | Tetrapeptide forecasting · Tetrapeptides | torsion-angle JSD, BB/SC/All: .130 / .093 / .109 -> .128 / .122 / .125 | Mixed |
| Use LaM-SLidE instead of MDGen | Tetrapeptide forecasting · Tetrapeptides | TICA 0 / joint 0,1: .230 / .316 -> .227 / .315 | Helped |
| Use LaM-SLidE instead of MDGen | Tetrapeptide forecasting · Tetrapeptides | MSM metric: .235 -> .224 | Helped |
| Increase identifier pool size (ablation) | LaM-SLidE first-stage model · MD17 | reconstruction error | Hurt |
| Vary the random entity-to-identifier assignment (ablation) | LaM-SLidE · MD17 | performance | No clear effect |
| Increase model parameter count (ablation) | LaM-SLidE · model-size evaluation | performance | Helped |
Surprising findings
- Despite using no explicit bond information or equivariance inductive bias, LaM-SLidE surpasses all equivariant GNN baselines on MD17.
- On ETH-UCY, LaM-SLidE achieves average minADE/minFDE of 0.24/0.41, roughly tied with GeoTDM and SVAE rather than clearly best.
Limitations
- Tradeoff between the number of latent vectors used to encode system states and latent model performance.
- Does not reach best performance on Spring Dynamics and some ETH-UCY scenes; Tetrapeptide side-chain torsion JSD worse than MDGen.
- Not a graph foundation model; generalization across molecules/scenes is observed but not systematically studied.
Experimental setup
Datasets: ETH-UCY SportVU NBA N-body (Charged Particles, Spring, Gravity) MD17 Tetrapeptides (4AA)
Benchmarks: ETH-UCY SportVU NBA N-body MD17 Tetrapeptides (4AA)
Metrics: minADE minFDE ADE FDE JSD TICA MSM NFE
Baselines: GeoTDM SVAE MID Traj++ BiTraP PECNet SocialVAE EqMotion EGNN MDGen SGNet-ED SE(3)-Transformer
Builds on: latent diffusion models stochastic interpolants Perceiver IO GeoTDM Diffusion Transformer
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