diff --git a/src/baskerville/metrics.py b/src/baskerville/metrics.py
index 8aa549f..8948880 100644
--- a/src/baskerville/metrics.py
+++ b/src/baskerville/metrics.py
@@ -115,6 +115,8 @@ def poisson_multinomial(
     y_true,
     y_pred,
     total_weight: float = 1,
+    weight_range: float = 1,
+    weight_exp: int = 4,
     epsilon: float = 1e-7,
     rescale: bool = False,
 ):
@@ -126,6 +128,18 @@ def poisson_multinomial(
         rescale (bool): Rescale loss after re-weighting.
     """
     seq_len = y_true.shape[1]
+    pos_start = -(seq_len / 2 - 0.5)
+    pos_end = seq_len / 2 + 0.5
+    sigma = -pos_start / (np.log(weight_range)) ** (1 / weight_exp)
+
+    positions = tf.range(pos_start, pos_end, dtype=tf.float32)
+    position_weights = tf.exp(-((positions / sigma) ** weight_exp))
+    position_weights /= tf.reduce_max(position_weights)
+    position_weights = tf.expand_dims(position_weights, axis=0)
+    position_weights = tf.expand_dims(position_weights, axis=-1)
+
+    y_true = tf.math.multiply(y_true, position_weights)
+    y_pred = tf.math.multiply(y_pred, position_weights)
 
     # sum across lengths
     s_true = tf.math.reduce_sum(y_true, axis=-2, keepdims=True)
@@ -133,7 +147,7 @@ def poisson_multinomial(
 
     # total count poisson loss, mean across targets
     poisson_term = poisson(s_true, s_pred)  # B x T
-    poisson_term /= seq_len
+    poisson_term /= tf.reduce_sum(position_weights)
 
     # add epsilon to protect against tiny values
     y_true += epsilon
@@ -146,7 +160,7 @@ def poisson_multinomial(
     pl_pred = tf.math.log(p_pred)  # B x L x T
     multinomial_dot = -tf.math.multiply(y_true, pl_pred)  # B x L x T
     multinomial_term = tf.math.reduce_sum(multinomial_dot, axis=-2)  # B x T
-    multinomial_term /= seq_len
+    multinomial_term /= tf.reduce_sum(position_weights)
 
     # normalize to scale of 1:1 term ratio
     loss_raw = multinomial_term + total_weight * poisson_term
@@ -167,12 +181,15 @@ class PoissonMultinomial(LossFunctionWrapper):
 
     def __init__(
         self,
-        total_weight=1,
+        total_weight: float = 1,
+        weight_range: float = 1,
+        weight_exp: int = 4,
         reduction=losses_utils.ReductionV2.AUTO,
         name: str = "poisson_multinomial",
     ):
-        self.total_weight = total_weight
-        pois_mn = lambda yt, yp: poisson_multinomial(yt, yp, self.total_weight)
+        pois_mn = lambda yt, yp: poisson_multinomial(
+            yt, yp, total_weight, weight_range, weight_exp
+        )
         super(PoissonMultinomial, self).__init__(
             pois_mn, name=name, reduction=reduction
         )
diff --git a/src/baskerville/trainer.py b/src/baskerville/trainer.py
index 5c55f52..d779066 100644
--- a/src/baskerville/trainer.py
+++ b/src/baskerville/trainer.py
@@ -27,6 +27,8 @@ def parse_loss(
     keras_fit: bool = True,
     spec_weight: float = 1,
     total_weight: float = 1,
+    weight_range: float = 1,
+    weight_exp: int = 1,
 ):
     """Parse loss function from label, strategy, and fitting method.
 
@@ -51,7 +53,10 @@ def parse_loss(
             )
         elif loss_label == "poisson_mn":
             loss_fn = metrics.PoissonMultinomial(
-                total_weight, reduction=tf.keras.losses.Reduction.NONE
+                total_weight=total_weight,
+                weight_range=weight_range,
+                weight_exp=weight_exp,
+                reduction=tf.keras.losses.Reduction.NONE,
             )
         else:
             loss_fn = tf.keras.losses.Poisson(reduction=tf.keras.losses.Reduction.NONE)
@@ -65,7 +70,11 @@ def parse_loss(
         elif loss_label == "poisson_kl":
             loss_fn = metrics.PoissonKL(spec_weight)
         elif loss_label == "poisson_mn":
-            loss_fn = metrics.PoissonMultinomial(total_weight)
+            loss_fn = metrics.PoissonMultinomial(
+                total_weight=total_weight,
+                weight_range=weight_range,
+                weight_exp=weight_exp,
+            )
         else:
             loss_fn = tf.keras.losses.Poisson()
 
@@ -127,9 +136,17 @@ def __init__(
         # loss
         self.spec_weight = self.params.get("spec_weight", 1)
         self.total_weight = self.params.get("total_weight", 1)
+        self.weight_range = self.params.get("weight_range", 1)
+        self.weight_exp = self.params.get("weight_exp", 1)
         self.loss = self.params.get("loss", "poisson").lower()
         self.loss_fn = parse_loss(
-            self.loss, self.strategy, keras_fit, self.spec_weight, self.total_weight
+            self.loss,
+            self.strategy,
+            keras_fit,
+            self.spec_weight,
+            self.total_weight,
+            self.weight_range,
+            self.weight_exp,
         )
 
         # optimizer