Adam and its variants dominate neural network training, but a single run only reveals whether a configuration works well after most of its budget is spent, a poor fit for hyperparameter or architecture search, where configurations must be ranked cheaply and pruned early. We introduce EvE (Evolutionary Explorer), a steady-state, population-of-four differential evolution (DE) optimizer with a targeted Adam fallback: each iteration proposes one candidate via DE, running a short burst of gradient descent only if the DE step fails to improve on the incumbent. Selection is greedy, so on a deterministic objective the best-so-far value is provably monotone non-increasing, and since gradients are used only as a targeted rescue, per-iteration cost stays within a constant factor of a single Adam step regardless of dimension. Under a fixed, evaluation-cost-matched budget, EvE wins or ties Adam on 76% of 70 (problem, dimension) cells across seven scalable benchmarks up to one million variables. On three real neural-network tasks (an MLP on MNIST, and LoRA fine-tuning of a 1.5B-parameter language model on two datasets) EvE finishes the same charged budget 1.7-3.9x faster, at a modest cost in final quality (about one accuracy point on MNIST, 9-11% higher relative test loss on the two fine-tuning tasks; on GSM8K, Adam is about 5 accuracy points more accurate, and fine-tuning lowers accuracy below the base model for both). Inside successive halving on UCI Adult, EvE completes hyperparameter and architecture searches 3.1-3.5x faster, ranking configurations about as consistently with Adam as Adam does with itself across seeds (Kendall's tau 0.66-0.69). EvE is not a total replacement for Adam as a final-stage trainer, but a fast, gradient-aware proxy for the search-heavy, budget-constrained regime one level up.

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