When a policy with memory is trained through a differentiable simulator, credit can reach what it stores along two routes: \emph{representation credit} teaches the network that writes the memory what to summarize, while \emph{closed-loop credit} travels back through the physical states that earlier actions produced and that the memory later stored. Stopping gradients at stored history, as truncated backpropagation and Transformer-XL do, removes both routes at once. Keeping every forward computation identical and removing one route at a time, we trained Transformer policies for quadrotor tracking to determine when each route matters. Credit through memory improved learning only when velocity observations were noisy or hidden. When velocity was hidden, mildly decaying the gradient between consecutive physical states ($γ= 0.8$) eliminated the truncation cost of removing closed-loop credit while leaving representation credit essential, a separation that held in 14 of 16 new seeds. Two further systems bound this result: in a fixed-wing aircraft, representation credit could replace closed-loop credit on its own, leaving no cost to separate, and in a cart-pole, training with full state-edge credit was too unstable to compare the routes. In both the quadrotor and a fully observed vessel model, static gradient norms failed to predict which cut cost more, so memory truncation choices are best guided by short training runs.

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