Sanjit Shashi

Ehsan Mirafzali, Sanjit Shashi, Sanya Murdeshwar et al.

We present a framework for generative machine learning that leverages the holographic principle of quantum gravity, or to be more precise its manifestation as the anti-de Sitter/conformal field theory (AdS/CFT) correspondence, with techniques for deep learning and transport theory. Our proposal is to represent the flow of data from a base distribution to some learned distribution using the bulk-to-boundary mapping of scalar fields in AdS. In the language of machine learning, we are representing and augmenting the flow-matching algorithm with AdS physics. Using a checkerboard toy dataset and MNIST, we find that our model achieves faster and higher quality convergence than comparable physics-free flow-matching models. Our method provides a physically interpretable version of flow matching. More broadly, it establishes the utility of AdS physics and geometry in the development of novel paradigms in generative modeling.

Sanya Murdeshwar, Sanjit Shashi, Kevin Bachelor et al.

Coarse-grained (CG) molecular dynamics enables simulations of atomic systems such as biomolecules at timescales inaccessible to all-atom (AA) methods, but existing CG neural potentials trained via force matching capture only the gradient of the free-energy surface, leaving its curvature unconstrained. We introduce a framework that augments force matching with stochastic Hessian-vector product (HVP) matching, instilling second-order curvature information into CG potentials without constructing the full Hessian. We derive a decomposition of the target CG Hessian into a model-independent projected AA Hessian, precomputed once before training, and a model-dependent covariance correction computed online at negligible cost. We construct an unbiased stochastic estimator of the Hessian-matching objective by using random probe vectors. We evaluate our method by comparing against force matching on a benchmark of nine fast-folding proteins unseen during training. HVP matching outperforms plain force matching on 8 of 9 proteins on slow-mode metrics, with reductions of up to 85% in the Kullback--Leibler divergence between the CG and reference distributions along the slowest collective mode of the largest protein. Our results demonstrate that higher-order physical supervision is a practical path to more accurate and transferable CG potentials for biomolecular simulation.