That's a torch implementation of LSTM module with attention mechanism base on Karpathy's implementation in NeuralTalk2

gradcheck.lua

-- from https://github.com/karpathy/neuraltalk2/blob/master/misc/gradcheck.lua
-- by Andrej Karpathy
local gradcheck = {}


function gradcheck.relative_error(x, y, h)
  h = h or 1e-12
  if torch.isTensor(x) and torch.isTensor(y) then
    local top = torch.abs(x - y)
    local bottom = torch.cmax(torch.abs(x) + torch.abs(y), h)
    return torch.max(torch.cdiv(top, bottom))
  else
    return math.abs(x - y) / math.max(math.abs(x) + math.abs(y), h)
  end
end


function gradcheck.numeric_gradient(f, x, df, eps)
  df = df or 1.0
  eps = eps or 1e-8
  local n = x:nElement()
  local x_flat = x:view(n)
  local dx_num = x.new(#x):zero()
  local dx_num_flat = dx_num:view(n)
  for i = 1, n do
    local orig = x_flat[i]

    x_flat[i] = orig + eps
    local pos = f(x)
    if torch.isTensor(df) then
      pos = pos:clone()
    end

    x_flat[i] = orig - eps
    local neg = f(x)
    if torch.isTensor(df) then
      neg = neg:clone()
    end

    local d = nil
    if torch.isTensor(df) then
      d = torch.dot(pos - neg, df) / (2 * eps)
    else
      d = df * (pos - neg) / (2 * eps)
    end

    dx_num_flat[i] = d
    x_flat[i] = orig
  end
  return dx_num
end


--[[
Inputs:
- f is a function that takes a tensor and returns a scalar
- x is the point at which to evalute f
- dx is the analytic gradient of f at x
--]]
function gradcheck.check_random_dims(f, x, dx, eps, num_iterations, verbose)
  if verbose == nil then verbose = false end
  eps = eps or 1e-4

  local x_flat = x:view(-1)
  local dx_flat = dx:view(-1)

  local relative_errors = torch.Tensor(num_iterations)

  for t = 1, num_iterations do
    -- Make sure the index is really random.
    -- We have to call this on the inner loop because some functions
    -- f may be stochastic, and eliminating their internal randomness for
    -- gradient checking by setting a manual seed. If this is the case,
    -- then we will always sample the same index unless we reseed on each
    -- iteration.
    torch.seed()
    local i = torch.random(x:nElement())

    local orig = x_flat[i]
    x_flat[i] = orig + eps
    local pos = f(x)

    x_flat[i] = orig - eps
    local neg = f(x)
    local d_numeric = (pos - neg) / (2 * eps)
    local d_analytic = dx_flat[i]

    x_flat[i] = orig

    local rel_error = gradcheck.relative_error(d_numeric, d_analytic)
    relative_errors[t] = rel_error
    if verbose then
      print(string.format('  Iteration %d / %d, error = %f',
            t, num_iterations, rel_error))
      print(string.format('  %f %f', d_numeric, d_analytic))
    end
  end
  return relative_errors
end


return gradcheck

LSTMAttention.lua

require 'nn'
require 'nngraph'

local LSTM = {}
function LSTM.lstm(input_size, output_size, rnn_size, n, frame_per_video, seq_per_video, dropout)
  dropout = dropout or 0
  -- TODO: No idea how to choose attention size...
  att_size = att_size or 512

  -- there will be 2*n+1 inputs
  local inputs = {}
  table.insert(inputs, nn.Identity()()) -- indices giving the sequence of symbols
  for L = 1,n do
    table.insert(inputs, nn.Identity()()) -- prev_c[L]
    table.insert(inputs, nn.Identity()()) -- prev_h[L]
  end
  table.insert(inputs, nn.Identity()()) -- img

  local x, input_size_L, feats
  local outputs = {}
  for L = 1,n do
    -- c,h from previos timesteps
    local prev_h = inputs[L*2+1]
    local prev_c = inputs[L*2]
    -- the input to this layer
    if L == 1 then
      x = inputs[1]
      input_size_L = input_size

      -- Attention model --
      -- TODO: more elegent way to do this?
      -- TODO: Share parameter or not?
      feats = inputs[(n+1)*2]
      local e = {}
      local featTable = {nn.SplitTable(1)(feats):split(frame_per_video)}
      local hxW = nn.Linear(rnn_size,att_size)(prev_h)
      local Ua = nn.Linear(input_size,att_size)
      local va = nn.Linear(att_size,1)
      -- assert(#featTable == frame_per_video, 'Currently only support batch_size = 1')
      for i = 1, frame_per_video do
        local va_t = va:clone('weight', 'bias', 'gradWeight', 'gradBias')
        local Ua_t = Ua:clone('weight', 'bias', 'gradWeight', 'gradBias')
        e[i] = va_t(nn.Tanh()(nn.CAddTable()({hxW,nn.Replicate(seq_per_video)(Ua_t(featTable[i]))})))
      end
      z = nn.MM()({nn.SoftMax()(nn.JoinTable(2)(e)),feats})
      -- Attention model end --
    else
      x = outputs[(L-1)*2]
      if dropout > 0 then x = nn.Dropout(dropout)(x):annotate{name='drop_' .. L} end -- apply dropout, if any
      input_size_L = rnn_size
    end
    -- evaluate the input sums at once for efficiency
    local i2h = nn.Linear(input_size_L, 4 * rnn_size)(x):annotate{name='i2h_'..L}
    local h2h = nn.Linear(rnn_size, 4 * rnn_size)(prev_h):annotate{name='h2h_'..L}
    local all_input_sums, z2h
    if L == 1 then
      z2h = nn.Linear(input_size, 4 * rnn_size)(z):annotate{name='z2h_'..L}
      all_input_sums = nn.CAddTable()({i2h, h2h, z2h})
    else
      all_input_sums = nn.CAddTable()({i2h, h2h})
    end

    local reshaped = nn.Reshape(4, rnn_size)(all_input_sums)
    local n1, n2, n3, n4 = nn.SplitTable(2)(reshaped):split(4)
    -- decode the gates
    local in_gate = nn.Sigmoid()(n1)
    local forget_gate = nn.Sigmoid()(n2)
    local out_gate = nn.Sigmoid()(n3)
    -- decode the write inputs
    local in_transform = nn.Tanh()(n4)
    -- perform the LSTM update
    local next_c           = nn.CAddTable()({
        nn.CMulTable()({forget_gate, prev_c}),
        nn.CMulTable()({in_gate,     in_transform})
      })
    -- gated cells form the output
    local next_h = nn.CMulTable()({out_gate, nn.Tanh()(next_c)})

    table.insert(outputs, next_c)
    table.insert(outputs, next_h)
  end

  -- set up the decoder
  local top_h = outputs[#outputs]
  if dropout > 0 then top_h = nn.Dropout(dropout)(top_h):annotate{name='drop_final'} end
  local proj = nn.Linear(rnn_size, output_size)(top_h):annotate{name='decoder'}
  local logsoft = nn.LogSoftMax()(proj)
  table.insert(outputs, logsoft)

  return nn.gModule(inputs, outputs)
end

return LSTM

test_attention.lua

--[
-- Test the attention calculation module
-- [Author] Haonan Chen
-- [Date] 08/16/2016
-- [Contact] chenhaonan1995@gmail.com
--]
require 'nn'
require 'nngraph'
local gradcheck = require 'misc.gradcheck'
local tests = {}
local tester = torch.Tester()

seq_per_video = 6
att_size = 15
rnn_size = 15
input_size = 15
frame_per_video = 5

local function build_attention()
    feats = nn.Identity()()
    prev_h = nn.Identity()()

    local e = {}
    local featTable = {nn.SplitTable(1)(feats):split(frame_per_video)}
    local nh = nn.Linear(rnn_size,att_size)(prev_h) -- Calculate this outside the loop to save time
    local ua = nn.Linear(input_size,att_size) -- Share parameters
    local va = nn.Linear(att_size,1)

    for i = 1, #featTable do
        -- This will share parameters between different clones
        local ua_t = ua:clone('weight', 'bias', 'gradWeight', 'gradBias')
        local va_t = va:clone('weight', 'bias', 'gradWeight', 'gradBias')
        e[i] = va_t(nn.Tanh()(nn.CAddTable()({nh,nn.Replicate(seq_per_video)(ua_t(featTable[i]))})))
    end
    jo = nn.SoftMax()(nn.JoinTable(2)(e))
    ca = nn.MM()({jo,feats})
    m = nn.gModule({feats,prev_h},{ca})
    return m
end

local function gradCheck()
    local in_feat = torch.rand(frame_per_video, input_size)
    local in_prev_h = torch.rand(seq_per_video, rnn_size)
    m = build_attention()
    res = m:forward({in_feat, in_prev_h})
    local w = torch.randn(res:size(1), res:size(2))
    local loss = torch.sum(torch.cmul(w,res))
    local gradOutput = w
    local gradInput, dummy = unpack(m:backward({in_feat,in_prev_h},gradOutput))
    local function f(x)
        local output = m:forward({x, in_prev_h})
        local loss = torch.sum(torch.cmul(w,output))
        return loss
    end

    local gradInput_num = gradcheck.numeric_gradient(f, in_feat, 1, 1e-6)

    print(gradInput)
    print(gradInput_num)
    local g = gradInput:view(-1)
    local gn = gradInput_num:view(-1)
    for i=1,g:nElement() do
      local r = gradcheck.relative_error(g[i],gn[i])
      print(i, r)
    end

    tester:assertTensorEq(gradInput, gradInput_num, 1e-6)
    tester:assertlt(gradcheck.relative_error(gradInput, gradInput_num, 1e-8), 5e-4)
end

tests.gradCheck = gradCheck
tester:add(tests)
tester:run()

test_lstm.lua

--[
-- This file shows how to use the LSTMAttention module (run a forward pass)
-- [Author] Haonan Chen
-- [Date] 08/02/2016
-- [Contact] chenhaonan1995@gmail.com
--]
require 'nn'
-- require 'nngraph'
local LSTM = require 'misc.LSTMAttention'

seq_per_video = 20
att_size = 512
rnn_size = 512
input_size = 512
frame_per_video = 15
vocab_size = 80
num_layers = 1
dropout = 0
seq_length = 7
num_state = 2*num_layers

model = LSTM.lstm(input_size, vocab_size + 1, rnn_size, num_layers, frame_per_video, seq_per_video, dropout)

-- Clone LSTM cell
clones = {model}
for t = 2, seq_length + 2 do
  clones[t] = model:clone('weight', 'bias', 'gradWeight', 'gradBias')
end

-- initialize
function createInitState(batch_size)
  assert(batch_size ~= nil, 'batch size must be provided')
  -- construct the initial state for the LSTM
  if not init_state then init_state = {} end -- lazy init
  for h=1,num_layers*2 do
    -- note, the init state Must be zeros because we are using init_state to init grads in backward call too
    if init_state[h] then
      if init_state[h]:size(1) ~= batch_size then
        init_state[h]:resize(batch_size, rnn_size):zero() -- expand the memory
      end
    else
      init_state[h] = torch.zeros(batch_size, rnn_size)
    end
  end
  return init_state
end
state = {[0] = createInitState(seq_per_video)} -- For the convenience to apply state[t-1]
imgs = torch.rand(frame_per_video, input_size) -- Doesn't change
inputs = {}
output = {} -- size: seq_length+2, seq_per_image, vocab_size+1

-- Forward the network
for t = 1, seq_length + 2 do
  if t == 1 then
    inputs[t] = {torch.rand(seq_per_video, input_size), unpack(state[t-1])}
    table.insert(inputs[t],imgs)
    print(inputs[t])
  else
    lookup_table_out = torch.rand(seq_per_video, input_size)
    inputs[t] = {lookup_table_out, unpack(state[t-1])}
    table.insert(inputs[t],imgs)
    print(inputs[t])
  end
  local out = clones[t]:forward(inputs[t])
  output[t] = out[num_state+1]
  state[t] = {}
  for i=1,num_state do table.insert(state[t],out[i]) end
end

print(output)