4 papers
Loss Landscape Geometry and the Learning of Symmetries: Or, What Influence Functions Reveal About Robust Generalization
James Amarel, Robyn Miller, Nicolas Hengartner +5
We study how neural emulators of partial differential equation solution operators internalize physical symmetries by introducing an influence-based diagnostic that measures the pro…
Towards Reasoning for PDE Foundation Models: A Reward-Model-Driven Inference-Time-Scaling Algorithm
Siddharth Mansingh, James Amarel, Ragib Arnab +10
Partial Differential Equations (PDEs) are the bedrock for modern computational sciences and engineering, and inherently computationally expensive. While PDE foundation models have…
Generalization vs. Memorization in Autoregressive Deep Learning: Or, Examining Temporal Decay of Gradient Coherence
James Amarel, Nicolas Hengartner, Robyn Miller +8
Foundation models trained as autoregressive PDE surrogates hold significant promise for accelerating scientific discovery through their capacity to both extrapolate beyond training…
Posterior Mean Matching: Generative Modeling through Online Bayesian Inference
Sebastian Salazar, Michal Kucer, Yixin Wang +2
This paper introduces posterior mean matching (PMM), a new method for generative modeling that is grounded in Bayesian inference. PMM uses conjugate pairs of distributions to model…