Add a new loss for jointly training on continuous and categorical targets.

disentangled_rnns/library/rnn_utils.py

@@ -509,6 +509,69 @@ def normalized_likelihood(
   return normlik
 
 
+def avg_nll_and_log_mse(
+    ys: np.ndarray,
+    y_hats: np.ndarray,
+    likelihood_weight: float = 0.5,
+    n_categorical_targets: int = 2,
+    n_continuous_targets: int = 1,
+) -> float:
+  """Computes a scale-normalized weighted sum of avg NLL and log(MSE).
+
+  This loss is suitable for joint training on heterogeneous objectives
+  (categorical + continuous) by putting both losses on the same log scale.
+  The log(MSE) formulation helps keep the gradients from the MSE term from
+  dominating the overall gradient.
+
+  By convention, for mixed targets:
+  - `ys` contains categorical targets at index 0 and continuous targets at
+    indices [1, 1 + n_continuous_targets).
+  - `y_hats` contains logits for categorical targets at indices
+    [0, n_categorical_targets) and predictions for continuous targets at indices
+    [n_categorical_targets, n_categorical_targets + n_continuous_targets).
+
+  Args:
+    ys: Ground truth targets.
+    y_hats: Network predictions (logits for categorical, values for continuous).
+    likelihood_weight: The weight for the average NLL. The log(MSE) is weighted
+      by (1 - likelihood_weight). Default is 0.5 for equal weighting.
+    n_categorical_targets: The number of output logits for the categorical
+      target.
+    n_continuous_targets: The number of continuous targets.
+
+  Returns:
+    The weighted sum of average NLL and log(MSE + eps).
+  """
+  categorical_y_hats = y_hats[:, :, 0:n_categorical_targets]
+  categorical_ys = ys[:, :, 0:1]
+
+  mask = jnp.logical_not(categorical_ys < 0)
+  continuous_y_hats = y_hats[
+      :, :, n_categorical_targets : n_categorical_targets + n_continuous_targets
+  ]
+  continuous_ys = ys[:, :, 1 : 1 + n_continuous_targets]
+  continuous_ys = jnp.where(mask, continuous_ys, jnp.nan)
+
+  nll, n_unmasked_samples = categorical_neg_log_likelihood(
+      categorical_ys, categorical_y_hats
+  )
+  avg_nll = nll / n_unmasked_samples
+
+  mse_val = mse(continuous_ys, continuous_y_hats)
+
+  # This is a trick to scale the gradients from the mse as:
+  # derivative(log(1+mse)) = 1 / (1 + mse) * derivative(1+mse)
+  # So early in the training when mse is large, the gradient is damped, later
+  # when mse is small, the gradient is almost the same as the original gradient.
+  # Note that log(mse) is follows the same monotonic trend as mse, so this
+  # transform will lead to a similar optimization as the original mse.
+  log_mse_val = jnp.log(1.0 + mse_val)
+
+  # Likelihood weight should ideally be set to 0.5, but can be used as a toggle
+  # to train on just one objective at a time (e.g. likelihood or mse).
+  return avg_nll * likelihood_weight + log_mse_val * (1 - likelihood_weight)
+
+
 @jax.jit
 def compute_penalty(
     targets: np.ndarray, outputs: np.ndarray
@@ -594,7 +657,8 @@ def train_network(
       {'penalty_scale': 0.1, 'likelihood_weight': 0.8}) or a single float for
       simpler losses.
     loss: The loss function to use. Options are 'mse', 'penalized_mse',
-      'categorical', 'penalized_categorical', 'hybrid', 'penalized_hybrid'.
+      'categorical', 'penalized_categorical', 'hybrid', 'penalized_hybrid',
+      'penalized_log_hybrid'.
     log_losses_every: How many training steps between each time we check for
       errors and log the loss.
     do_plot: Boolean that controls whether a learning curve is plotted.
@@ -719,24 +783,35 @@ def hybrid_loss(
   def penalized_hybrid_loss(
       params, xs, ys, random_key, loss_param=loss_param_dict
   ) -> float:
-    """A hybrid loss with a penalty."""
+    """A hybrid loss with a penalty.
+
+    Useful for jointly training on categorical and continuous targets. Uses a
+    log of MSE loss for the continuous targets, so that the loss is similar
+    units as the categorical loss.
+
+    Args:
+      params: The network parameters.
+      xs: The input data.
+      ys: The target data.
+      random_key: A JAX random key.
+      loss_param: Parameters for the loss function, potentially including
+        'penalty_scale' and 'likelihood_weight'.
+
+    Returns:
+      The computed penalized hybrid loss.
+    """
 
     penalty_scale = get_loss_param(loss_param, 'penalty_scale', 1.0)
     model_output = model.apply(params, random_key, xs)
 
-    # model_output has the continuous and categorical targets first followed by
-    # the penalty. The likelihood_and_sse functions handles
-    # ignoring the penalty, hence we don't need to do anything special here.
     y_hats = model_output
-    likelihood_weight = get_loss_param(loss_param, 'likelihood_weight', 1.0)
-    supervised_loss = likelihood_and_sse(
+    likelihood_weight = get_loss_param(loss_param, 'likelihood_weight', 0.5)
+    supervised_loss = avg_nll_and_log_mse(
         ys, y_hats, likelihood_weight=likelihood_weight
     )
-    # Supervised loss here is a sum not an average, so use the raw penalty
-    # without dividing by n_unmasked_samples
-    # TODO(siddhantjain): Evaluate whether we should use averaging here too.
-    penalty, _ = compute_penalty(ys, y_hats)
-    loss = supervised_loss + penalty_scale * penalty
+    penalty, n_unmasked_samples = compute_penalty(ys, y_hats)
+    avg_penalty = penalty / n_unmasked_samples
+    loss = supervised_loss + penalty_scale * avg_penalty
     return loss
 
   losses = {