We hypothesize that incorporating the proven Hodge Laplacian eigenvalue bounds as a spectral regularization constraint in a simplicial GNN will significantly improve its predictive accuracy for QUBO docking outcomes compared to standard GNNs.

Adversarial Debate Score

55% survival rate under critique

Supporting Research Papers

• Eigenvalue growth of the discrete Hodge Laplacian across dimensions

  We prove several bounds on the largest and smallest eigenvalues of the combinatorial Hodge Laplacian Δ^H_k of a finite simplicial complex Σ. As a consequence, we obtain new vanishing criteria for coho...

• A Physically-Informed Subgraph Isomorphism Approach to Molecular Docking Using Quantum Annealers

  Molecular docking is a crucial step in the development of new drugs as it guides the positioning of a small molecule (ligand) within the pocket of a target protein. In the literature, a feasibility st...

• Quantum Geometric Tensor Preconditioning for Stable Training of Recurrent Neural Quantum States

  Neural Quantum States (NQS) provide a powerful neural network-based variational framework for representing many-body wave functions and solving for ground states. Recurrent Neural Networks (RNNs) are ...

• Adjacency Spectral Radius Under Laplacian Sparsification: Deterministic and Probabilistic Bounds

  Spielman-Srivastava spectral sparsification preserves Laplacian quadratic forms to within (1 +/- epsilon), but does not directly control the adjacency spectral radius lambda_1, which governs the NIMFA...

• Topology-Preserving Neural Operator Learning via Hodge Decomposition

  In this paper, we study solution operators of physical field equations on geometric meshes from a function-space perspective. We reveal that Hodge orthogonality fundamentally resolves spectral interfe...

Formal Verification

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