code: def lossFun(self, inputs, errors, init_state=None):
      """
      Does a forward and backward pass on the network using (inputs, errors)
      inputs is a bit-vector of seq-length
      errors is a bit-vector of seq-length
      """
  
      xs, rbars, rs, zbars, zs, cbars, cs, hs = (
          {},
          {},
          {},
          {},
          {},
          {},
          {},
          {},
      )
  
      # xs are inputs
      # hs are hiddens
  
      # This resets the hidden state after every new sequence
      # TODO: maybe we don't need to
      if init_state is None:
          hs[-1] = np.zeros((self.hidden_size, 1))
      else:
          hs[-1] = init_state
  
      seq_len = len(inputs)
  
      hs_list = np.zeros((self.hidden_size, seq_len))
  
      # forward pass, compute outputs, t indexes time
      for t in range(seq_len):
          # For every variable V, Vbar represents the pre-activation version
          # For every variable Q, Qnext represents that variable at time t+1
          # where t is understood from context
  
          # xs is the input vector at this time
          xs[t] = np.matrix(inputs[t])
  
          # The r gate, which modulates how much signal from h[t-1] goes to
          # the candidate
          rbars[t] = (
              np.dot(self.Wxr, xs[t])
              + np.dot(self.Rhr, hs[t - 1])
              + self.br
          )
          rs[t] = 1.0 / (1 + np.exp(-rbars[t]))
          # TODO: use an already existing sigmoid function
  
          # The z gate, which interpolates between candidate and h[t-1] to
          # compute h[t]
          zbars[t] = (
              np.dot(self.Wxz, xs[t])
              + np.dot(self.Rhz, hs[t - 1])
              + self.bz
          )
          zs[t] = 1.0 / (1 + np.exp(-zbars[t]))
  
          # The candidate, which is computed and used as described above.
          cbars[t] = (
              np.dot(self.Wxc, xs[t])
              + np.dot(self.Rhc, np.multiply(rs[t], hs[t - 1]))
              + self.bc
          )
          cs[t] = np.tanh(cbars[t])
  
          # TODO: get rid of this
          ones = np.ones_like(zs[t])
  
          # Compute new h by interpolating between candidate and old h
          hs[t] = np.multiply(cs[t], zs[t]) + np.multiply(
              hs[t - 1], ones - zs[t]
          )
  
          hs_list[:, t] = hs[t].flatten()
  
      # allocate space for the grads of loss with respect to the weights
      dWxc = np.zeros_like(self.Wxc)
      dWxr = np.zeros_like(self.Wxr)
      dWxz = np.zeros_like(self.Wxz)
      dRhc = np.zeros_like(self.Rhc)
      dRhr = np.zeros_like(self.Rhr)
      dRhz = np.zeros_like(self.Rhz)
  
      # allocate space for the grads of loss with respect to biases
      dbc = np.zeros_like(self.bc)
      dbr = np.zeros_like(self.br)
      dbz = np.zeros_like(self.bz)
  
      # no error is received from beyond the end of the sequence
      dhnext = np.zeros_like(hs[0])
      drbarnext = np.zeros_like(rbars[0])
      dzbarnext = np.zeros_like(zbars[0])
      dcbarnext = np.zeros_like(cbars[0])
      zs[len(inputs)] = np.zeros_like(zs[0])
      rs[len(inputs)] = np.zeros_like(rs[0])
  
      dh_list = errors
      dh_list_out = np.zeros_like(dh_list)
      dr_list = np.zeros((self.hidden_size, seq_len))
      dz_list = np.zeros((self.hidden_size, seq_len))
      dc_list = np.zeros((self.hidden_size, seq_len))
  
      # go backwards through time
      for t in reversed(range(seq_len)):
          # For every variable X, dX represents dC/dX
          # For variables that influence C at multiple time steps,
          # such as the weights, the dw is a sum of dw at multiple
          # time steps
  
          # h[t] influences the cost in 5 ways:
          # through the interpolation using z at t+1
          dha = np.multiply(dhnext, ones - zs[t + 1])
  
          # through transformation by weights into rbar
          dhb = np.dot(self.Rhr.T, drbarnext)
  
          # through transformation by weights into zbar
          dhc = np.dot(self.Rhz.T, dzbarnext)
  
          # through transformation by weights into cbar
          dhd = np.multiply(rs[t + 1], np.dot(self.Rhc.T, dcbarnext))
  
          # through bp errors
          dhe = dh_list[t]
  
          dh = dha + dhb + dhc + dhd + dhe
  
          dh_list_out[t] = dh
  
          dc = np.multiply(dh, zs[t])
  
          # backprop through tanh
          dcbar = np.multiply(dc, ones - np.square(cs[t]))
  
          dr = np.multiply(hs[t - 1], np.dot(self.Rhc.T, dcbar))
          dz = np.multiply(dh, (cs[t] - hs[t - 1]))
  
          # backprop through sigmoids
          drbar = np.multiply(dr, np.multiply(rs[t], (ones - rs[t])))
          dzbar = np.multiply(dz, np.multiply(zs[t], (ones - zs[t])))
  
          dWxr += np.dot(drbar, xs[t].T)
          dWxz += np.dot(dzbar, xs[t].T)
          dWxc += np.dot(dcbar, xs[t].T)
  
          dRhr += np.dot(drbar, hs[t - 1].T)
          dRhz += np.dot(dzbar, hs[t - 1].T)
          dRhc += np.dot(dcbar, np.multiply(rs[t], hs[t - 1]).T)
  
          dbr += drbar
          dbc += dcbar
          dbz += dzbar
  
          dhnext = dh
  
          drbarnext = drbar
          dzbarnext = dzbar
          dcbarnext = dcbar
  
          dr_list[:, t] = drbar.flatten()
          dz_list[:, t] = dzbar.flatten()
          dc_list[:, t] = dcbar.flatten()
  
      dw = [dWxc, dWxr, dWxz, dRhc, dRhr, dRhz, dbc, dbr, dbz]
  
      self.dW_ind_Wxc = 0
      self.dW_ind_Wxr = 1
      self.dW_ind_Wxz = 2
      self.dW_ind_Rhc = 3
      self.dW_ind_Rhr = 4
      self.dW_ind_Rhz = 5
  
      self.dW_ind_bc = 6
      self.dW_ind_br = 7
      self.dW_ind_bz = 8
  
      return dw, hs_list, dh_list_out, dr_list, dz_list, dc_list
  
imports: import numpy
label_desc: Use image node_id 2 for calling the GRU obj's underlying member method code with example usage: obj.lossFun(inputs, errors, init_state) and returns: dw,  hs_list,  dh_list_out,  dr_list,  dz_list,  dc_list