Expert AI Analysis
Information Routing in Atomistic Foundation Models: How Task Alignment and Equivariance Shape Linear Disentanglement
What determines whether a molecular property prediction model organizes its representations so that geometric and compositional information can be cleanly separated? We introduce Compositional Probe Decomposition (CPD), which linearly projects out composition signal and measures how much geometric information remains accessible to a Ridge probe. We validate CPD with four independent checks, including a structural isomer benchmark where compositional projections score at chance while geometric residuals reach 94.6% pairwise classification accuracy.
Applying CPD to ten models from five architectural families on QM9, we find a linear accessibility gradient: models differ by 6.6× in geometric information accessible after composition removal (Reom from 0.081 to 0.533 for HOMO-LUMO gap). Three factors explain this gradient. Task alignment dominates: models trained on HOMO-LUMO gap (Reom 0.44–0.53) outscore energy-trained models by ~0.25 R2 regardless of architecture. Within-architecture ablations on two independent architectures confirm this: PaiNN drops from 0.53 to 0.31 when retrained on energy, and MACE drops from 0.44 to 0.08. Data diversity partially compensates for misaligned objectives, with MACE pretrained on MPTraj (0.36) outperforming QM9-only energy models. Inside MACE's representations, information routes by symmetry type: L=1 (vector) channels preferentially encode dipole moment (R2 = 0.59 vs. 0.38 in L=0), while L=0 (scalar) channels encode HOMO-LUMO gap (R2 = 0.76 vs. 0.34 in L=1). This pattern is absent in ViSNet. We also show that nonlinear probes produce misleading results on residualized representations, recovering R2 = 0.68–0.95 on a purely compositional target, and recommend linear probes for this setting.
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Spread in Geometric Information
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Isomer Classification Accuracy
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Task Alignment Advantage
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Lowest R² geom
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Enterprise Process Flow
Extract Raw Representations (X)
→
OLS Project Composition (Zβ)
→
Geometric Residual (Xgeom)
→
Ridge Probe (Rgeom)
We introduce Compositional Probe Decomposition (CPD), which fits an OLS projection to remove composition signal within each cross-validation fold, then probes the residual with Ridge regression to quantify linearly accessible geometric information. We validate CPD with four independent checks, including a structural isomer benchmark where compositional projections score at chance while geometric residuals reach 94.6% pairwise classification accuracy.
6.6x
Spread in geometric information accessible after composition removal
Across ten models from five architectural families on QM9, we find a linear accessibility gradient: models differ by 6.6× in geometric information accessible after composition removal (Reom from 0.081 to 0.533 for HOMO-LUMO gap).
Factors Shaping the Gradient
The gradient is shaped by three interacting factors: task alignment, equivariance, and data diversity. Task alignment dominates, with models trained on HOMO-LUMO gap outscoring energy-trained models by ~0.25 R² geom. Equivariance amplifies this only with task alignment. Data diversity partially compensates for misaligned objectives.
| Factor | Impact on R² geom | Key Evidence |
|---|---|---|
| Task Alignment | Dominant (~0.25 R² gap) |
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| Equivariance | Amplifies (conditionally) |
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| Data Diversity | Partial Compensation |
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Symmetry-Matched Information Routing
MACE vs. ViSNet on Property Encoding
MACE's equivariant architecture routes scalar properties (HOMO-LUMO gap) through L=0 channels and vector properties (dipole moment) through L=1 channels, matching their physical symmetry. This pattern is absent in ViSNet, which concentrates information in its scalar stream.
MACE constructs messages using tensor products of spherical harmonics, producing features explicitly tagged by angular momentum order L. This leads to distinct L=0 channels for scalar properties (e.g., HOMO-LUMO gap R²=0.756) and L=1 channels for vector properties (e.g., dipole moment R²=0.586). ViSNet, while maintaining scalar and vector streams, computes geometric interactions at runtime without maintaining persistent irreducible decomposition, resulting in virtually all information being concentrated in its scalar stream (HOMO-LUMO gap R²=0.877, dipole moment R²=0.018 in vector stream). This indicates a qualitative difference in how equivariant architectures use equivariance.
R² ≈ 0
Correct linear probe score on composition-erased target
Nonlinear probes (e.g., GBTs) produce misleading results on residualized representations, recovering R² = 0.68–0.95 on a purely compositional target after composition signal was linearly removed. Linear probes correctly return R² ≈ 0, providing a faithful measure.
ρ = 1.0
Model ranking stability (N=500)
The linear accessibility gradient is a stable, measurable property of representations, emerging even at small sample sizes (N=50) with Spearman ρ=0.964, and stabilizing perfectly by N=500. PaiNN at N=50 already exceeds SchNet at N=2000, demonstrating sample-efficient disentanglement.
Practical Implications for Molecular R&D
When selecting a pre-trained molecular encoder, the training objective matters more than architecture. Geometry-sensitive objectives yield representations with linearly accessible geometric signal. Data diversity can partially compensate for objective misalignment but doesn't eliminate it. Equivariance only helps with aligned objectives.
| Factor | Recommendation | Why it Matters |
|---|---|---|
| Task Alignment | Prioritize geometry-sensitive training for geometry-sensitive downstream tasks. |
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| Data Diversity | Leverage large-scale pretraining on diverse structures, even with objective misalignment. |
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| Equivariance | Use equivariant models with an aligned training objective. |
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Your Path to Smarter Molecular Discovery
Our structured implementation roadmap ensures a seamless integration of advanced AI models into your R&D pipeline, maximizing impact and minimizing disruption.
Phase 1: Discovery & Strategy
(2-4 Weeks)
Initial consultation to understand current workflows and pain points.
Define key molecular properties and AI integration targets.
Develop a tailored AI strategy and success metrics.
Phase 2: Model Integration & Customization
(6-10 Weeks)
Select and deploy optimal foundation models based on task alignment and data.
Fine-tune models with proprietary data and specific molecular domains.
Integrate AI outputs into existing R&D platforms.
Phase 3: Validation & Optimization
(4-8 Weeks)
Rigorous validation against experimental benchmarks and internal data.
Iterative refinement of model parameters and deployment strategies.
Training for your R&D team on new AI tools and workflows.
Phase 4: Scaling & Continuous Improvement
(Ongoing)
Expand AI deployment across additional molecular targets and projects.
Monitor model performance and retrain with new data for sustained accuracy.
Identify new opportunities for AI-driven innovation in your pipeline.
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