network definition for an Auto-encoder with tied weights. The weight are tied by sharing parameter names in 'permissive mode' and setting the decoder's ip params to use tranposed weigts.

mnist_ae_tied_weights_trainval.prototxt

name: "MNISTAutoencoderTiedWeights"
layer {
  name: "mnist"
  type: "Data"
  top: "data"
  top: "label"
  include {
    phase: TRAIN
  }
  transform_param {
    scale: 0.00390625
  }
  data_param {
    source: "examples/mnist/mnist_train_lmdb"
    batch_size: 100
    backend: LMDB
  }
}
layer {
  name: "mnist"
  type: "Data"
  top: "data"
  top: "label"
  include {
    phase: TEST
  }
  transform_param {
    scale: 0.00390625
  }
  data_param {
    source: "examples/mnist/mnist_test_lmdb"
    batch_size: 100
    backend: LMDB
  }
}
layer {
  name: "silence_label"
  type: "Silence"
  bottom: "label"
}
layer {
  name: "flatdata"
  type: "Flatten"
  bottom: "data"
  top: "flatdata"
}
layer {
  name: "encode1"
  type: "InnerProduct"
  bottom: "data"
  top: "encode1"
  param {
    name: "w"
    lr_mult: 1
    decay_mult: 1
    share_mode: PERMISSIVE
  }
  param {
    lr_mult: 2
    decay_mult: 0
  }
  inner_product_param {
    num_output: 10
    weight_filler {
      type: "gaussian"
      std: 1
    }
    bias_filler {
      type: "constant"
      value: 0
    }
  }
}
layer {
  name: "encode1neuron"
  type: "Sigmoid"
  bottom: "encode1"
  top: "encode1neuron"
}
layer {
  name: "decode1"
  type: "InnerProduct"
  bottom: "encode1neuron"
  top: "decode1"
  param {
    name: "w"
    lr_mult: 1
    decay_mult: 1
    share_mode: PERMISSIVE
  }
  param {
    lr_mult: 2
    decay_mult: 0
  }
  inner_product_param {
    num_output: 784
    weight_filler {
      type: "gaussian"
      std: 1
    }
    bias_filler {
      type: "constant"
      value: 0
    }
  }
}
layer {
  name: "loss"
  type: "SigmoidCrossEntropyLoss"
  bottom: "decode1"
  bottom: "flatdata"
  top: "cross_entropy_loss"
  loss_weight: 1
}
layer {
  name: "decode1neuron"
  type: "Sigmoid"
  bottom: "decode1"
  top: "decode1neuron"
}
layer {
  name: "loss"
  type: "EuclideanLoss"
  bottom: "decode1neuron"
  bottom: "flatdata"
  top: "l2_error"
  loss_weight: 0
}