<p>In fact, training recurrent nets is often done by unrolling the net. That is, replicating the net over the temporal steps (sharing weights across the temporal steps) and simply doing forward-backward passes on the unrolled model.</p>

<p>To unroll LSTM (or any other unit) you don't have to use <a href="http://jeffdonahue.com/" rel="noreferrer">Jeff Donahue</a>'s recurrent branch, but rather use <code>NetSpec()</code> to explicitly unroll the model.</p>

<p>Here's a simple example:</p>

<pre><code>from caffe import layers as L, params as P, to_proto
import caffe

# some utility functions
def add_layer_to_net_spec(ns, caffe_layer, name, *args, **kwargs):
  kwargs.update({'name':name})
  l = caffe_layer(*args, **kwargs)
  ns.__setattr__(name, l)
  return ns.__getattr__(name)
def add_layer_with_multiple_tops(ns, caffe_layer, lname, ntop, *args, **kwargs):    
  kwargs.update({'name':lname,'ntop':ntop})
  num_in = len(args)-ntop # number of input blobs
  tops = caffe_layer(*args[:num_in], **kwargs)
  for i in xrange(ntop):
      ns.__setattr__(args[num_in+i],tops[i])
  return tops

# implement single time step LSTM unit
def single_time_step_lstm( ns, h0, c0, x, prefix, num_output, weight_names=None):
  """
  see arXiv:1511.04119v1
  """
  if weight_names is None:
      weight_names = ['w_'+prefix+nm for nm in ['Mxw','Mxb','Mhw']]
  # full InnerProduct (incl. bias) for x input
  Mx = add_layer_to_net_spec(ns, L.InnerProduct, prefix+'lstm/Mx', x,
                    inner_product_param={'num_output':4*num_output,'axis':2,
                                           'weight_filler':{'type':'uniform','min':-0.05,'max':0.05},
                                           'bias_filler':{'type':'constant','value':0}},
                    param=[{'lr_mult':1,'decay_mult':1,'name':weight_names[0]},
                           {'lr_mult':2,'decay_mult':0,'name':weight_names[1]}])
  Mh = add_layer_to_net_spec(ns, L.InnerProduct, prefix+'lstm/Mh', h0,
                    inner_product_param={'num_output':4*num_output, 'axis':2, 'bias_term': False,
                                       'weight_filler':{'type':'uniform','min':-0.05,'max':0.05},
                                       'bias_filler':{'type':'constant','value':0}},
                    param={'lr_mult':1,'decay_mult':1,'name':weight_names[2]})
  M = add_layer_to_net_spec(ns, L.Eltwise, prefix+'lstm/Mx+Mh', Mx, Mh,
                          eltwise_param={'operation':P.Eltwise.SUM})
  raw_i1, raw_f1, raw_o1, raw_g1 = \
  add_layer_with_multiple_tops(ns, L.Slice, prefix+'lstm/slice', 4, M,
                             prefix+'lstm/raw_i', prefix+'lstm/raw_f', prefix+'lstm/raw_o', prefix+'lstm/raw_g',
                             slice_param={'axis':2,'slice_point':[num_output,2*num_output,3*num_output]})
  i1 = add_layer_to_net_spec(ns, L.Sigmoid, prefix+'lstm/i', raw_i1, in_place=True)
  f1 = add_layer_to_net_spec(ns, L.Sigmoid, prefix+'lstm/f', raw_f1, in_place=True)
  o1 = add_layer_to_net_spec(ns, L.Sigmoid, prefix+'lstm/o', raw_o1, in_place=True)
  g1 = add_layer_to_net_spec(ns, L.TanH, prefix+'lstm/g', raw_g1, in_place=True)
  c1_f = add_layer_to_net_spec(ns, L.Eltwise, prefix+'lstm/c_f', f1, c0, eltwise_param={'operation':P.Eltwise.PROD})
  c1_i = add_layer_to_net_spec(ns, L.Eltwise, prefix+'lstm/c_i', i1, g1, eltwise_param={'operation':P.Eltwise.PROD})
  c1 = add_layer_to_net_spec(ns, L.Eltwise, prefix+'lstm/c', c1_f, c1_i, eltwise_param={'operation':P.Eltwise.SUM})
  act_c = add_layer_to_net_spec(ns, L.TanH, prefix+'lstm/act_c', c1, in_place=False) # cannot override c - it MUST be preserved for next time step!!!
  h1 = add_layer_to_net_spec(ns, L.Eltwise, prefix+'lstm/h', o1, act_c, eltwise_param={'operation':P.Eltwise.PROD})
  return c1, h1, weight_names
</code></pre>

<p>Once you have the single time step, you can unroll it as many times you want...</p>

<pre><code>def exmaple_use_of_lstm():
  T = 3 # number of time steps
  B = 10 # batch size
  lstm_output = 500 # dimension of LSTM unit

  # use net spec
  ns = caffe.NetSpec()

  # we need initial values for h and c
  ns.h0 = L.DummyData(name='h0', dummy_data_param={'shape':{'dim':[1,B,lstm_output]},
                               'data_filler':{'type':'constant','value':0}})

  ns.c0 = L.DummyData(name='c0', dummy_data_param={'shape':{'dim':[1,B,lstm_output]},
                                   'data_filler':{'type':'constant','value':0}})

  # simulate input X over T time steps and B sequences (batch size)
  ns.X = L.DummyData(name='X', dummy_data_param={'shape': {'dim':[T,B,128,10,10]}} )
  # slice X for T time steps
  xt = L.Slice(ns.X, name='slice_X',ntop=T,slice_param={'axis':0,'slice_point':range(1,T)})
  # unroling
  h = ns.h0
  c = ns.c0
  lstm_weights = None
  tops = []
  for t in xrange(T):
    c, h, lstm_weights = single_time_step_lstm( ns, h, c, xt[t], 't'+str(t)+'/', lstm_output, lstm_weights)
    tops.append(h)
    ns.__setattr__('c'+str(t),c)
    ns.__setattr__('h'+str(t),h)
  # concat all LSTM tops (h[t]) to a single layer
  ns.H = L.Concat( *tops, name='concat_h',concat_param={'axis':0} )
  return ns
</code></pre>

<p>Writing the prototxt:</p>

<pre><code>ns = exmaple_use_of_lstm()
with open('lstm_demo.prototxt','w') as W:
  W.write('name: "LSTM using NetSpec example"\n')
  W.write('%s\n' % ns.to_proto())
</code></pre>

<p>The resulting unrolled net (for three time steps) looks like</p>

<p><a href="https://i.stack.imgur.com/K11tK.png" rel="noreferrer"><img src="https://i.stack.imgur.com/K11tK.png" alt="LSTM"></a></p>
LSTM module for Caffe
<p>Does anyone know if there exists a nice LSTM module for Caffe? I found one from a github account by russel91 but apparantly the webpage containing examples and explanations disappeared (Formerly <a href="http://apollo.deepmatter.io/" rel="noreferrer">http://apollo.deepmatter.io/</a> --> it now redirects only to the <a href="https://github.com/russell91/apollocaffe" rel="noreferrer">github page</a> which has no examples or explanations anymore).</p>