Long contexts break transformers: attention scores dilute across thousands of tokens, critical information gets lost in the middle, and the model cannot adapt to novel patterns at inference time. Recent work on test-time adaptation addresses this by maintaining a form of working memory—transient parameters updated on the current context—but existing approaches employ uniform write policies that waste computation on low-value regions and suffer from high gradient variance across semantically heterogeneous contexts. In this work, we reframe test-time adaptation as a budget-constrained memory consolidation problem, asking: given limited computational budget, which parts of the context should be consolidated into working memory? We propose GDWM (Gated Differentiable Working Memory), a framework that introduces a Write Controller to gate the memory consolidation process. Our controller estimates Contextual Utility—an information-theoretic measure quantifying how much each region depends on long-range context—and allocates gradient steps accordingly, subject to a coverage constraint that ensures global representation. Theoretically, we prove that our chunk-restricted sampling strategy reduces gradient variance by eliminating inter-chunk variance via the Law of Total Variance. Experiments on ZeroSCROLLS and LongBench v2 benchmarks demonstrate that GDWM achieves comparable or superior performance with 4 ×fewer gradient steps compared to uniform baselines—excelling on sparse-information tasks (+6–13% on Qasper, +5–13% on GovReport for smaller models) while revealing principled trade-offs on dense-coverage tasks, establishing a new efficiency-performance Pareto frontier for test-time adaptation.