Graph-Structured Hyperdimensional Computing for Data-Efficient and Explainable Process-Structure-Property Prediction

Hyperdimensional computing (HDC) is an approach from the cognitive science literature for solving information processing tasks using data represented as high-dimensional random vectors. The technique has a rigorous mathematical backing, and is easy to implement in energy-efficient and highly parallel hardware like FPGAs and "processing-in-memory" architectures. The effectiveness of HDC in machine learning largely depends on how raw data is mapped to high-dimensional space. In this work, we propose NysHD, a new method for constructing this mapping that is based on the Nyström method from the literature on kernel approximation. Our approach provides a simple recipe to turn any user-defined positive-semidefinite similarity function into an equivalent mapping in HDC. There is a vast literature on the design of such functions for learning problems. Our approach provides a mechanism to import them into the HDC setting, expanding the types of problems that can be tackled using HDC. Empirical evaluation against existing HDC encoding methods shows that NysHD can achieve, on average, 11% and 17% better classification accuracy on graph and string datasets respectively.

Background: Timely, uncertainty-aware forecasting from irregular electronic health records (EHR) can support critical-care decisions, yet most approaches either impute to a grid or sacrifice interpretability. We introduce StructGP, a continuous-time multi-task Gaussian process that couples process convolutions with differentiable structure learning to uncover a sparse, ordered directed acyclic graph (DAG) of inter-variable dependencies while preserving principled uncertainty. We further propose LP-StructGP, which augments StructGP with latent pathways-shared, temporally shifted trajectories inferred via subject-specific coupling filters and a softmax gating mechanism-to capture cross-patient progression patterns. Both models are trained under sparsity and acyclicity constraints (augmented Lagrangian, Adam) using scalable low-rank updates. Results: In simulations, the approach reliably recovers ground-truth graphs (Structural Hamming Distance approaching 0 as cohorts grow) and pathway assignments (high Adjusted Rand Index). On a MIMIC-IV septic shock cohort (n=1,008; norepinephrine, creatinine, mean arterial pressure), StructGP improves short-horizon (6 h) forecasting over independent-task baselines (average RMSE 0.68 [95%CI: 0.63--0.74] vs. 0.88 [0.83-0.94]) and, with 15 additional inputs, markedly outperforms unstructured kernels (0.63 [0.58-0.69] vs. 3.02 [2.85-3.18]) with superior calibration (coverage 0.96 vs. 0.84). On the PhysioNet Challenge (12k patients, 41 variables), StructGP attains competitive accuracy (MAE 3.72e-2) relative to a state-of-the-art graph neural model while maintaining calibrated uncertainty. Conclusion: These results show that structured process convolutions with latent pathways deliver interpretable, scalable, and well-calibrated forecasting for irregular clinical time series.

Computational molecular representations underpin virtual screening, property prediction, and materials discovery. Conventional fingerprints are efficient and deterministic but lose structural information through hash-based compression, particularly at low dimensionalities. Learned representations from graph neural networks recover this expressiveness but require task-specific training and substantial computational resources. Here we introduce hyperdimensional fingerprints (HDF), which replace the learned transformations of message-passing neural networks with algebraic operations on high-dimensional vectors, producing deterministic molecular representations without any training. Across diverse property prediction benchmarks, HDF outperforms conventional fingerprints in the majority of tasks while exhibiting greater consistency across datasets and models. Crucially, HDF embeddings preserve molecular similarity faithfully: at 32 dimensions, distances in HDF space achieve a 0.9 Pearson correlation with graph edit distance, compared to 0.55 for Morgan fingerprints at equivalent size. This structural fidelity persists at low dimensions where hash-based methods degrade, allowing simple nearest-neighbor regression to remain predictive with as few as 64 components. We further demonstrate the practical impact in Bayesian molecular optimization, where HDF-based surrogate models achieve substantially improved sample efficiency in regimes where Morgan fingerprints perform comparably to random search. HDF thus provides a general-purpose, training-free alternative to conventional molecular fingerprints, suggesting that the information loss long accepted as inherent to fixed-length fingerprints is a limitation of the hash-based encoding scheme rather than the fingerprint paradigm itself.