Stroke order and velocity are helpful features in the fields of signature\nverification, handwriting recognition, and handwriting synthesis. Recovering\nthese features from offline handwritten text is a challenging and well-studied\nproblem. We propose a new model called TRACE (Trajectory Recovery by an\nAdaptively-trained Convolutional Encoder). TRACE is a differentiable approach\nthat uses a convolutional recurrent neural network (CRNN) to infer temporal\nstroke information from long lines of offline handwritten text with many\ncharacters and dynamic time warping (DTW) to align predictions and ground truth\npoints. TRACE is perhaps the first system to be trained end-to-end on entire\nlines of text of arbitrary width and does not require the use of dynamic\nexemplars. Moreover, the system does not require images to undergo any\npre-processing, nor do the predictions require any post-processing.\nConsequently, the recovered trajectory is differentiable and can be used as a\nloss function for other tasks, including synthesizing offline handwritten text.\n We demonstrate that temporal stroke information recovered by TRACE from\noffline data can be used for handwriting synthesis and establish the first\nbenchmarks for a stroke trajectory recovery system trained on the IAM online\nhandwriting dataset.\n