# Bayesian Optimization

In open-ended molecular design, candidates are generated on demand, and the scale of the search has usually been fixed in advance by a preset similarity criterion or candidate count. TRACE makes chemical extent and candidate breadth explicit as a Tanimoto-similarity threshold and a cardinality budget, expands or contracts both with a success/failure controller, and lets a fixed fragprint Gaussian process choose what to evaluate. Across six PMO objectives under a matched 1,000-evaluation budget, TRACE has a mean top-1 AUC rank of 1.73 and a mean top-10 AUC rank of 1.27; in a closed-loop DFT campaign on FePc derivatives, 80 designed-candidate evaluations raise the computed resistance to Fe dissolution from 0.42 to 2.59 eV.

In open-ended molecular design, candidates are generated on demand, and the scale of the search has usually been fixed in advance by a preset similarity criterion or candidate count. TRACE makes chemical extent and candidate breadth explicit as a Tanimoto-similarity threshold and a cardinality budget, expands or contracts both with a success/failure controller, and lets a fixed fragprint Gaussian process choose what to evaluate. Across six PMO objectives under a matched 1,000-evaluation budget, TRACE has a mean top-1 AUC rank of 1.73 and a mean top-10 AUC rank of 1.27; in a closed-loop DFT campaign on FePc derivatives, 80 designed-candidate evaluations raise the computed resistance to Fe dissolution from 0.42 to 2.59 eV.

Meta's ads ranking and retrieval fleet no longer allocates capacity by hand, one model at a time. Previously each scaling decision cost days to weeks of training, and the architecture dimensions are coupled, so they cannot be enlarged independently. Axia maps embedding dimension, interaction depth and interaction width through a scaling layer into complete architectures, then uses Bayesian surrogates to pick a small number of training trials. Across 34 model iterations in two development cycles, offline normalized entropy improved by a mean 0.66% relative and the online key metric by a cumulative 0.36%.

Meta's ads ranking and retrieval fleet no longer allocates capacity by hand, one model at a time. Previously each scaling decision cost days to weeks of training, and the architecture dimensions are coupled, so they cannot be enlarged independently. Axia maps embedding dimension, interaction depth and interaction width through a scaling layer into complete architectures, then uses Bayesian surrogates to pick a small number of training trials. Across 34 model iterations in two development cycles, offline normalized entropy improved by a mean 0.66% relative and the online key metric by a cumulative 0.36%.

Feeding an LLM's parameter-adjustment directions to Bayesian optimization as a soft prior raises hypervolume on a 3D CPU-GPU chiplet design space from 0.8210 to 0.8356, and to 0.8051 on a 2.5D space without retraining.

Feeding an LLM's parameter-adjustment directions to Bayesian optimization as a soft prior raises hypervolume on a 3D CPU-GPU chiplet design space from 0.8210 to 0.8356, and to 0.8051 on a 2.5D space without retraining.

TagBO treats candidate rankings produced by a large language model as coarse task-aware priors and fuses them with local structural smoothing into a similarity graph, reaching high-quality candidates in fewer evaluations under a fixed budget on six mixed-variable chemistry and materials optimization tasks.

TagBO treats candidate rankings produced by a large language model as coarse task-aware priors and fuses them with local structural smoothing into a similarity graph, reaching high-quality candidates in fewer evaluations under a fixed budget on six mixed-variable chemistry and materials optimization tasks.

The spin Hamiltonian parameters of α-RuCl₃ no longer come only from ab initio calculations: Bayesian optimization fits experimental magnetization curves along the b and c axes while optimizing five parameters, the Kitaev interaction K, the off-diagonal interactions Γ and Γ′, the Heisenberg interaction J, and the c-axis g-factor g_c. The cost-minimizing set is (K, Γ, Γ′, J, g_c) = (−6.0, 7.5, −0.3, −1.75, 2.3), with exchange couplings in meV. The cost function is insensitive to the absolute value of K, so magnetization data alone do not fix the energy scale of the Kitaev coupling; it depends only weakly on Γ′ and J, while the optimization favors a large positive Γ.

The spin Hamiltonian parameters of α-RuCl₃ no longer come only from ab initio calculations: Bayesian optimization fits experimental magnetization curves along the b and c axes while optimizing five parameters, the Kitaev interaction K, the off-diagonal interactions Γ and Γ′, the Heisenberg interaction J, and the c-axis g-factor g_c. The cost-minimizing set is (K, Γ, Γ′, J, g_c) = (−6.0, 7.5, −0.3, −1.75, 2.3), with exchange couplings in meV. The cost function is insensitive to the absolute value of K, so magnetization data alone do not fix the energy scale of the Kitaev coupling; it depends only weakly on Γ′ and J, while the optimization favors a large positive Γ.

ATLAS is a Bayesian optimization framework that, at each iteration, builds a Mapper graph over the surrogate-predicted feasible region to estimate the number of connected regions and uses a topological sensitivity score to label candidates as bridge, frontier, or interior points, injecting a targeted exploration bonus into the acquisition function; on four analog circuit benchmarks in the GF180 and SKY130 processes it attains the highest or tied-highest success rate on all four circuits, reaching 100% on the hardest circuit CMA where most baselines score 0%.

ATLAS is a Bayesian optimization framework that, at each iteration, builds a Mapper graph over the surrogate-predicted feasible region to estimate the number of connected regions and uses a topological sensitivity score to label candidates as bridge, frontier, or interior points, injecting a targeted exploration bonus into the acquisition function; on four analog circuit benchmarks in the GF180 and SKY130 processes it attains the highest or tied-highest success rate on all four circuits, reaching 100% on the hardest circuit CMA where most baselines score 0%.

Under a nested cross-validation framework, this study compared seven hyperparameter tuning strategies for classical KNN over a mixed search space comprising an integer neighborhood size k, a categorical distance metric, and a continuous Minkowski exponent p—grid search, random search, Bayesian optimization, genetic algorithm, surrogate optimization, particle swarm optimization (PSO), and grey wolf optimizer—evaluating them on 15 public classification datasets using accuracy, macro AUC, cross-validation loss, cross-entropy loss, and runtime, and found that PSO achieved the best overall mean rank but held a statistically significant advantage only over random search under Holm-corrected Wilcoxon signed-rank tests.

Under a nested cross-validation framework, this study compared seven hyperparameter tuning strategies for classical KNN over a mixed search space comprising an integer neighborhood size k, a categorical distance metric, and a continuous Minkowski exponent p—grid search, random search, Bayesian optimization, genetic algorithm, surrogate optimization, particle swarm optimization (PSO), and grey wolf optimizer—evaluating them on 15 public classification datasets using accuracy, macro AUC, cross-validation loss, cross-entropy loss, and runtime, and found that PSO achieved the best overall mean rank but held a statistically significant advantage only over random search under Holm-corrected Wilcoxon signed-rank tests.