Gil Harari

Maya Bechler-Speicher, Gilad Yehudai, Gil Harari et al.

Transformers have become a central architecture for graph learning, but their application to graphs requires first choosing a tokenization: a graph-to-token map that determines which structural information is exposed at the input. In this work, we show that this choice is a fundamental component of transformer expressivity. We examine three tokenizations that serve as building blocks for many existing graph tokenizations: spectral, random-walk, and adjacency tokenizations. We prove that different tokenizations induce distinct depth regimes: the same graph computation may be realizable by a shallow transformer under one tokenization, while requiring substantially larger depth under another. For example, we prove that random-walk tokenization is lossy for any walk length, making it impossible in general to recover the graph from it, and that while spectral tokenization is lossless, it is ill-conditioned for local tasks. We further show that although both random-walk and spectral tokenizations are derived from adjacency information, it is impossible for a limited-depth transformer to convert between tokenization families in general. In particular, we establish lower bounds and impossibility results showing that unfavorable tokenizations may preclude the efficient recovery of more suitable structural representations. Finally, we complement our theory with controlled experiments on synthetic and real-world tasks, validating the predicted separations and showing that different tasks favor different structural views, and combining complementary tokenizations allows the transformer to leverage distinct signals from each representation.

Gil Harari, Yoel Zimmermann, Ola Tangen Kulseng et al.

Machine learning interatomic potentials (MLIPs) have become a hallmark of AI for scientific simulation. While efforts on new architectures and datasets have led to increasingly accurate and general models, the choice of optimizer for training has largely remained unexplored, defaulting to Adam and its variants in the community. Here, we implement and systematically compare a class of recently proposed matrix-structured optimizers, including Muon, SOAP, and the hybrid SOAP-Muon, for training NequIP and Allegro MLIP models. We find that these optimizers can substantially outperform Adam in both convergence speed and final accuracy. SOAP and SOAP-Muon emerge as robust and consistently strong methods, while Muon only provides partial gains relative to Adam. The improvements are particularly pronounced under partial force supervision. Our results indicate that optimizer choice is an overlooked yet impactful design axis for MLIPs.