There have been a number of recent works putting graphical models on top of ConvNets and training end to end.

True: by 2016-07-28 there were several (at least about three) published works, recent at the time (roughly 2014–2016), that combined graphical models (for example CRFs or MRFs) with ConvNets and trained the combined system end to end (for example CRF-as-RNN, deep structured models, jointly trained CNN-CRF segmentation). Mostly true: such works existed but were fewer, or some only partly trained the parts jointly. Mixed: about half of the cited combinations were trained end to end. Mostly false: CNN+graphical-model works existed but almost all trained the parts separately (pipeline post-processing), with one or two end-to-end exceptions. False: no such end-to-end works existed by that date.

Set before the research began.

1. E1 Joint Training of Generic CNN-CRF Models with Stochastic Optimization ar5iv (arXiv:1511.05067)

   “We propose a new CNN-CRF end-to-end learning framework, which is based on joint stochastic optimization with respect to both Convolutional Neural Network (CNN) and Conditional Random Field (CRF) parameters.”

2. E2 Joint Training of Generic CNN-CRF Models with Stochastic Optimization ar5iv (arXiv:1511.05067)

   “This separate training procedure was recently improved in [11] with an end-to-end learning algorithm. To achieve this, they represent the Mean Field iterations as a Recurrent Neural Network. The same idea was published in [12].”

3. E3 Joint Training of Generic CNN-CRF Models with Stochastic Optimization ar5iv (arXiv:1511.05067)

   “[11] Zheng, S., Jayasumana, S., Romera-Paredes, B., Vineet, V., Su, Z., Du, D., Huang, C., Torr, P.H.S.: Conditional random fields as recurrent neural networks. In: ICCV. (2015)”

4. E4 Joint Training of Generic CNN-CRF Models with Stochastic Optimization ar5iv (arXiv:1511.05067)

   “[19] Tompson, J.J., J., A., LeCun, Y., Bregler, C.: Joint training of a convolutional network and a graphical model for human pose estimation. In: NIPS. (2014)”

I judged this true. Several recent works trained a graphical model on top of a ConvNet end to end before 2016-07-28. arXiv:1511.05067 (November 2015) proposes a CNN-CRF framework that trains the CNN and CRF parameters together (E1). It also describes 'Conditional random fields as recurrent neural networks' (ICCV 2015) and its reference [12] as end-to-end versions of earlier CNN-CRF methods that had been trained separately (E2, E3). It cites a 2014 NIPS paper, 'Joint training of a convolutional network and a graphical model', as well (E4). The evidence describes at least three end-to-end CNN-CRF works (the framework proposed in arXiv:1511.05067 [E1], the ICCV 2015 CRF-as-RNN paper [E2][E3] and reference [12] [E2]), plus a 2014 NIPS paper titled as joint training of a convolutional network and a graphical model [E4]; this meets the "at least about three" bar in the criteria.