VK Tech researchers report comparable accuracy and lower inference times from PINN-based diffusion in graph models using sheaves and bundles.
VK Tech reported on October 16 that physics-informed neural networks, or PINNs, reduced inference time in experiments approximating diffusion in graph neural networks built with cellular sheaves and vector bundles. The research was conducted by students from a joint HSE University and VK workshop with AI VK engineer Alexander Tarakanov. According to the authors, accuracy remained broadly comparable with the other evaluated methods.
The study focuses on feature propagation between graph vertices as a continuous diffusion process. Instead of an ordinary graph Laplacian, the researchers use a sheaf Laplacian, which also captures linear restriction maps between the local feature spaces associated with connected vertices.
The proposed approach combines a learnable sheaf representation with a PINN. During training, the differential equation acts as a constraint: the network approximates the system’s time-dependent state while minimizing the equation residual. A Krylov representation supplies successive applications of the operator to the initial state, avoiding a dense representation while retaining the graph operator’s sparsity.
The researchers examined two implementations. One trains the PINN jointly with the model’s other layers for a specific task. The other inserts a pretrained FiLM-PINN into Bundle Neural Networks to approximate the action of a matrix exponential; its weights are frozen after pretraining. A truncated Taylor series of order 16 served as the baseline numerical method in that experiment.
FiLM-PINN processes time and matrix inputs separately: Fourier features encode time, one-dimensional convolutions handle the matrix stream, and FiLM modulation controls feature scaling and shifting. The parameterization enforces the initial condition and preserves the solution norm. The authors say exact solutions were unnecessary for training and were used only for validation.
In the published PINN+AFM comparison, inference was faster than SVR+AFM on all seven datasets, although classification accuracy did not consistently improve and the reported results include run-to-run variability. On Pubmed, PINN+AFM reached 75.46 ± 2.38% versus 77.36 ± 0.50% for SVR+AFM; on Actor, the corresponding results were 37.42 ± 0.98% and 36.39 ± 0.49%. The table below presents results for four of those datasets.
The practical proposition is to shift part of the differential-equation computation into pretraining and later obtain an approximation through a neural-network forward pass. These are research results published by VK Tech rather than evidence of a universal model improvement: lower latency did not reliably produce better classification, and the authors explicitly identify classification quality as an area requiring separate study.
| Dataset | Method | Test accuracy, % | Inference, ms |
|---|---|---|---|
| Cora | PINN+AFM | 81.42 ± 1.25 | 3.76 ± 0.02 |
| Cora | SVR+AFM | 81.26 ± 1.27 | 6.17 ± 0.05 |
| Citeseer | PINN+AFM | 71.30 ± 0.88 | 4.14 ± 0.02 |
| Citeseer | SVR+AFM | 71.36 ± 0.83 | 6.51 ± 0.12 |
| Pubmed | PINN+AFM | 75.46 ± 2.38 | 8.16 ± 0.16 |
| Pubmed | SVR+AFM | 77.36 ± 0.50 | 11.61 ± 0.02 |
| Chameleon | PINN+AFM | 49.34 ± 1.28 | 3.43 ± 0.31 |
| Chameleon | SVR+AFM | 50.31 ± 1.43 | 10.26 ± 0.18 |
Sources
Originally published by AI Feed: VK Tech Tests PINNs to Accelerate Graph Diffusion Inference.
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