Normalize edge weights with sum normalization

- Each soft factor is sum-normalized across all edge candidates
- Ensures factors compete equally regardless of native value ranges
- Skip factors with no variance (all candidates same value)
- Base weight of 1.0 ensures minimum probability

src/graph.py

@@ -169,48 +169,90 @@ class PathFinder:
 
         Uses hybrid approach:
         - Hard factors (direct tuning, voice crossing): multiplication (eliminate if factor fails)
-        - Soft factors (melodic, contrary, hamiltonian, dca, target range): weighted sum
+        - Soft factors: sum normalized per factor, then weighted sum
         """
-        weights = []
+        if not out_edges:
+            return []
 
-        for edge_idx, edge in enumerate(out_edges):
+        # First pass: collect raw factor values for all edges
+        melodic_values = []
+        contrary_values = []
+        hamiltonian_values = []
+        dca_values = []
+        target_values = []
+
+        for edge in out_edges:
+            edge_data = edge[2]
+
+            # Hard factors first (to filter invalid edges)
+            direct_tuning = self._factor_direct_tuning(edge_data, config)
+            voice_crossing = self._factor_voice_crossing(edge_data, config)
+
+            # Skip if hard factors eliminate this edge
+            if direct_tuning == 0 or voice_crossing == 0:
+                melodic_values.append(0)
+                contrary_values.append(0)
+                hamiltonian_values.append(0)
+                dca_values.append(0)
+                target_values.append(0)
+                continue
+
+            # Soft factors
+            melodic_values.append(self._factor_melodic_threshold(edge_data, config))
+            contrary_values.append(self._factor_contrary_motion(edge_data, config))
+            hamiltonian_values.append(
+                self._factor_hamiltonian(edge, graph_path, config)
+            )
+            dca_values.append(
+                self._factor_dca(edge, path, voice_stay_count, config, cumulative_trans)
+            )
+            target_values.append(
+                self._factor_target_range(edge, path, config, cumulative_trans)
+            )
+
+        # Helper function for sum normalization
+        def sum_normalize(values: list) -> list | None:
+            """Normalize values to sum to 1. Returns None if no discrimination."""
+            total = sum(values)
+            if total == 0 or len(set(values)) <= 1:
+                return None  # no discrimination
+            return [v / total for v in values]
+
+        # Sum normalize each factor
+        melodic_norm = sum_normalize(melodic_values)
+        contrary_norm = sum_normalize(contrary_values)
+        hamiltonian_norm = sum_normalize(hamiltonian_values)
+        dca_norm = sum_normalize(dca_values)
+        target_norm = sum_normalize(target_values)
+
+        # Second pass: calculate final weights
+        weights = []
+        for i, edge in enumerate(out_edges):
             w = 1.0  # base weight
             edge_data = edge[2]
 
-            # Hard factors (multiplication - eliminate edge if factor = 0)
-            # Direct tuning
-            direct_tuning_factor = self._factor_direct_tuning(edge_data, config)
-            w *= direct_tuning_factor
-
+            # Hard factors
+            w *= self._factor_direct_tuning(edge_data, config)
             if w == 0:
                 weights.append(0)
                 continue
 
-            # Voice crossing
-            voice_crossing_factor = self._factor_voice_crossing(edge_data, config)
-            w *= voice_crossing_factor
-
+            w *= self._factor_voice_crossing(edge_data, config)
             if w == 0:
                 weights.append(0)
                 continue
 
-            # Soft factors (weighted sum)
-            w += self._factor_melodic_threshold(edge_data, config) * config.get(
-                "weight_melodic", 1
-            )
-            w += self._factor_contrary_motion(edge_data, config) * config.get(
-                "weight_contrary_motion", 0
-            )
-            w += self._factor_hamiltonian(edge, graph_path, config) * config.get(
-                "weight_hamiltonian", 1
-            )
-
-            w += self._factor_dca(
-                edge, path, voice_stay_count, config, cumulative_trans
-            ) * config.get("weight_dca", 1)
-            w += self._factor_target_range(
-                edge, path, config, cumulative_trans
-            ) * config.get("weight_target_range", 1)
+            # Soft factors (sum normalized, then weighted)
+            if melodic_norm:
+                w += melodic_norm[i] * config.get("weight_melodic", 1)
+            if contrary_norm:
+                w += contrary_norm[i] * config.get("weight_contrary_motion", 0)
+            if hamiltonian_norm:
+                w += hamiltonian_norm[i] * config.get("weight_hamiltonian", 1)
+            if dca_norm:
+                w += dca_norm[i] * config.get("weight_dca", 1)
+            if target_norm:
+                w += target_norm[i] * config.get("weight_target_range", 1)
 
             weights.append(w)