feat(models): implement GNN model layer for assembly constraint analysis

Add complete model layer with GIN and GAT encoders, 5 task-specific
prediction heads, uncertainty-weighted multi-task loss (Kendall et al.
2018), and config-driven factory functions.

New modules:
- graph_conv.py: datagen dict -> PyG Data conversion (22D node/edge features)
- encoder.py: GINEncoder (3-layer, 128D) and GATEncoder (4-layer, 256D, 8-head)
- heads.py: edge classification, graph classification, joint type,
  DOF regression, per-body DOF tracking heads
- assembly_gnn.py: AssemblyGNN wiring encoder + configurable heads
- losses.py: MultiTaskLoss with learnable log-variance per task
- factory.py: build_model() and build_loss() from YAML configs

Supporting changes:
- generator.py: serialize anchor_a, anchor_b, pitch in joint dicts
- configs: fix joint_type num_classes 12 -> 11 (matches JointType enum)

92 tests covering shapes, gradients, edge cases, and end-to-end
datagen-to-model pipeline.

configs/model/baseline.yaml

@@ -19,6 +19,6 @@ heads:
     num_classes: 4 # rigid, under, over, mixed
   joint_type:
     enabled: true
-    num_classes: 12
+    num_classes: 11
   dof_regression:
     enabled: true

configs/model/gat.yaml

@@ -21,7 +21,7 @@ heads:
     num_classes: 4
   joint_type:
     enabled: true
-    num_classes: 12
+    num_classes: 11
   dof_regression:
     enabled: true
   dof_tracking:

solver/datagen/generator.py

@@ -877,6 +877,9 @@ class SyntheticAssemblyGenerator:
                             "body_b": j.body_b,
                             "type": j.joint_type.name,
                             "axis": j.axis.tolist(),
+                            "anchor_a": j.anchor_a.tolist(),
+                            "anchor_b": j.anchor_b.tolist(),
+                            "pitch": j.pitch,
                         }
                         for j in joints
                     ],

solver/models/__init__.py

@@ -0,0 +1,31 @@
+"""GNN models for assembly constraint analysis."""
+
+from solver.models.assembly_gnn import AssemblyGNN
+from solver.models.encoder import GATEncoder, GINEncoder
+from solver.models.factory import build_loss, build_model
+from solver.models.graph_conv import ASSEMBLY_CLASSES, JOINT_TYPE_NAMES, assembly_to_pyg
+from solver.models.heads import (
+    DOFRegressionHead,
+    DOFTrackingHead,
+    EdgeClassificationHead,
+    GraphClassificationHead,
+    JointTypeHead,
+)
+from solver.models.losses import MultiTaskLoss
+
+__all__ = [
+    "ASSEMBLY_CLASSES",
+    "AssemblyGNN",
+    "DOFRegressionHead",
+    "DOFTrackingHead",
+    "EdgeClassificationHead",
+    "GATEncoder",
+    "GINEncoder",
+    "GraphClassificationHead",
+    "JOINT_TYPE_NAMES",
+    "JointTypeHead",
+    "MultiTaskLoss",
+    "assembly_to_pyg",
+    "build_loss",
+    "build_model",
+]

solver/models/assembly_gnn.py

@@ -0,0 +1,131 @@
+"""AssemblyGNN -- main model wiring encoder and task heads."""
+
+from __future__ import annotations
+
+from typing import TYPE_CHECKING
+
+import torch.nn as nn
+
+from solver.models.encoder import GATEncoder, GINEncoder
+from solver.models.heads import (
+    DOFRegressionHead,
+    DOFTrackingHead,
+    EdgeClassificationHead,
+    GraphClassificationHead,
+    JointTypeHead,
+)
+
+if TYPE_CHECKING:
+    from typing import Any
+
+    import torch
+
+__all__ = ["AssemblyGNN"]
+
+_ENCODERS = {
+    "gin": GINEncoder,
+    "gat": GATEncoder,
+}
+
+
+class AssemblyGNN(nn.Module):
+    """Multi-task GNN for assembly constraint analysis.
+
+    Wires an encoder (GIN or GAT) with optional task-specific prediction
+    heads for edge classification, graph classification, joint type
+    prediction, DOF regression, and per-body DOF tracking.
+
+    Args:
+        encoder_type: ``"gin"`` or ``"gat"``.
+        encoder_config: Kwargs passed to the encoder constructor.
+        heads_config: Dict of head name → config dict. Each entry must have
+            an ``enabled`` bool. Additional keys are passed as kwargs.
+    """
+
+    def __init__(
+        self,
+        encoder_type: str = "gin",
+        encoder_config: dict[str, Any] | None = None,
+        heads_config: dict[str, dict[str, Any]] | None = None,
+    ) -> None:
+        super().__init__()
+        encoder_config = encoder_config or {}
+        heads_config = heads_config or {}
+
+        if encoder_type not in _ENCODERS:
+            msg = f"Unknown encoder type: {encoder_type!r}. Choose from {list(_ENCODERS)}"
+            raise ValueError(msg)
+
+        self.encoder = _ENCODERS[encoder_type](**encoder_config)
+        hidden_dim = self.encoder.hidden_dim
+
+        self.heads = nn.ModuleDict()
+        self._build_heads(heads_config, hidden_dim)
+
+    def _build_heads(
+        self,
+        heads_config: dict[str, dict[str, Any]],
+        hidden_dim: int,
+    ) -> None:
+        """Instantiate enabled heads."""
+        cfg = heads_config.get("edge_classification", {})
+        if cfg.get("enabled", False):
+            self.heads["edge_pred"] = EdgeClassificationHead(
+                hidden_dim=hidden_dim,
+                inner_dim=cfg.get("hidden_dim", 64),
+            )
+
+        cfg = heads_config.get("graph_classification", {})
+        if cfg.get("enabled", False):
+            self.heads["graph_pred"] = GraphClassificationHead(
+                hidden_dim=hidden_dim,
+                num_classes=cfg.get("num_classes", 4),
+            )
+
+        cfg = heads_config.get("joint_type", {})
+        if cfg.get("enabled", False):
+            self.heads["joint_type_pred"] = JointTypeHead(
+                hidden_dim=hidden_dim,
+                num_classes=cfg.get("num_classes", 11),
+            )
+
+        cfg = heads_config.get("dof_regression", {})
+        if cfg.get("enabled", False):
+            self.heads["dof_pred"] = DOFRegressionHead(hidden_dim=hidden_dim)
+
+        cfg = heads_config.get("dof_tracking", {})
+        if cfg.get("enabled", False):
+            self.heads["body_dof_pred"] = DOFTrackingHead(hidden_dim=hidden_dim)
+
+    def forward(
+        self,
+        x: torch.Tensor,
+        edge_index: torch.Tensor,
+        edge_attr: torch.Tensor,
+        batch: torch.Tensor | None = None,
+    ) -> dict[str, torch.Tensor]:
+        """Run encoder and all enabled heads.
+
+        Returns:
+            Dict with keys matching enabled head names:
+            ``edge_pred``, ``graph_pred``, ``joint_type_pred``,
+            ``dof_pred``, ``body_dof_pred``.
+        """
+        node_emb, edge_emb, graph_emb = self.encoder(x, edge_index, edge_attr, batch)
+
+        preds: dict[str, torch.Tensor] = {}
+
+        # Route embeddings to the appropriate heads.
+        _edge_heads = {"edge_pred", "joint_type_pred"}
+        _graph_heads = {"graph_pred", "dof_pred"}
+        _node_heads = {"body_dof_pred"}
+
+        for name, head in self.heads.items():
+            if name in _edge_heads:
+                preds[name] = head(edge_emb)
+            elif name in _graph_heads:
+                preds[name] = head(graph_emb)
+            elif name in _node_heads:
+                preds[name] = head(node_emb)
+
+        return preds

solver/models/encoder.py

@@ -0,0 +1,194 @@
+"""GIN and GAT graph neural network encoders."""
+
+from __future__ import annotations
+
+import torch
+import torch.nn as nn
+from torch_geometric.nn import GATv2Conv, GINEConv, global_mean_pool
+
+__all__ = ["GATEncoder", "GINEncoder"]
+
+
+def _make_gin_mlp(in_dim: int, hidden_dim: int) -> nn.Sequential:
+    """Two-layer MLP used inside GINEConv."""
+    return nn.Sequential(
+        nn.Linear(in_dim, hidden_dim),
+        nn.BatchNorm1d(hidden_dim),
+        nn.ReLU(),
+        nn.Linear(hidden_dim, hidden_dim),
+    )
+
+
+class GINEncoder(nn.Module):
+    """Graph Isomorphism Network encoder with edge features (GINE).
+
+    Args:
+        node_features_dim: Input node feature dimension.
+        edge_features_dim: Input edge feature dimension.
+        hidden_dim: Hidden dimension for all layers.
+        num_layers: Number of GINEConv layers.
+        dropout: Dropout probability.
+    """
+
+    def __init__(
+        self,
+        node_features_dim: int = 22,
+        edge_features_dim: int = 22,
+        hidden_dim: int = 128,
+        num_layers: int = 3,
+        dropout: float = 0.1,
+    ) -> None:
+        super().__init__()
+        self._hidden_dim = hidden_dim
+
+        self.node_proj = nn.Sequential(
+            nn.Linear(node_features_dim, hidden_dim),
+            nn.BatchNorm1d(hidden_dim),
+            nn.ReLU(),
+        )
+        self.edge_proj = nn.Sequential(
+            nn.Linear(edge_features_dim, hidden_dim),
+            nn.BatchNorm1d(hidden_dim),
+            nn.ReLU(),
+        )
+
+        self.convs = nn.ModuleList()
+        self.norms = nn.ModuleList()
+        for _ in range(num_layers):
+            conv = GINEConv(nn=_make_gin_mlp(hidden_dim, hidden_dim), edge_dim=hidden_dim)
+            self.convs.append(conv)
+            self.norms.append(nn.BatchNorm1d(hidden_dim))
+
+        self.dropout = nn.Dropout(dropout)
+
+        # Edge embedding from endpoint + edge features.
+        self.edge_mlp = nn.Linear(hidden_dim * 3, hidden_dim)
+
+    @property
+    def hidden_dim(self) -> int:
+        return self._hidden_dim
+
+    def forward(
+        self,
+        x: torch.Tensor,
+        edge_index: torch.Tensor,
+        edge_attr: torch.Tensor,
+        batch: torch.Tensor | None = None,
+    ) -> tuple[torch.Tensor, torch.Tensor, torch.Tensor]:
+        """Encode graph and return node, edge, and graph embeddings.
+
+        Returns:
+            node_emb: [N, hidden_dim]
+            edge_emb: [E, hidden_dim]
+            graph_emb: [B, hidden_dim]
+        """
+        h = self.node_proj(x)
+        e = self.edge_proj(edge_attr)
+
+        for conv, norm in zip(self.convs, self.norms):
+            h = conv(h, edge_index, e)
+            h = norm(h)
+            h = torch.relu(h)
+            h = self.dropout(h)
+
+        # Edge embeddings from endpoint concatenation.
+        src, dst = edge_index
+        edge_emb = self.edge_mlp(torch.cat([h[src], h[dst], e], dim=1))
+
+        # Graph embedding via mean pooling.
+        graph_emb = global_mean_pool(h, batch)
+
+        return h, edge_emb, graph_emb
+
+
+class GATEncoder(nn.Module):
+    """Graph Attention Network v2 encoder with edge features and residuals.
+
+    Args:
+        node_features_dim: Input node feature dimension.
+        edge_features_dim: Input edge feature dimension.
+        hidden_dim: Hidden dimension (must be divisible by num_heads).
+        num_layers: Number of GATv2Conv layers.
+        num_heads: Number of attention heads.
+        dropout: Dropout probability.
+        residual: Use residual connections.
+    """
+
+    def __init__(
+        self,
+        node_features_dim: int = 22,
+        edge_features_dim: int = 22,
+        hidden_dim: int = 256,
+        num_layers: int = 4,
+        num_heads: int = 8,
+        dropout: float = 0.1,
+        residual: bool = True,
+    ) -> None:
+        super().__init__()
+        if hidden_dim % num_heads != 0:
+            msg = f"hidden_dim ({hidden_dim}) must be divisible by num_heads ({num_heads})"
+            raise ValueError(msg)
+
+        self._hidden_dim = hidden_dim
+        self.residual = residual
+        head_dim = hidden_dim // num_heads
+
+        self.node_proj = nn.Sequential(
+            nn.Linear(node_features_dim, hidden_dim),
+            nn.LayerNorm(hidden_dim),
+            nn.ReLU(),
+        )
+        self.edge_proj = nn.Sequential(
+            nn.Linear(edge_features_dim, hidden_dim),
+            nn.LayerNorm(hidden_dim),
+            nn.ReLU(),
+        )
+
+        self.convs = nn.ModuleList()
+        self.norms = nn.ModuleList()
+        for _ in range(num_layers):
+            conv = GATv2Conv(
+                in_channels=hidden_dim,
+                out_channels=head_dim,
+                heads=num_heads,
+                edge_dim=hidden_dim,
+                concat=True,
+            )
+            self.convs.append(conv)
+            self.norms.append(nn.LayerNorm(hidden_dim))
+
+        self.dropout = nn.Dropout(dropout)
+
+        # Edge embedding from endpoint + edge features.
+        self.edge_mlp = nn.Linear(hidden_dim * 3, hidden_dim)
+
+    @property
+    def hidden_dim(self) -> int:
+        return self._hidden_dim
+
+    def forward(
+        self,
+        x: torch.Tensor,
+        edge_index: torch.Tensor,
+        edge_attr: torch.Tensor,
+        batch: torch.Tensor | None = None,
+    ) -> tuple[torch.Tensor, torch.Tensor, torch.Tensor]:
+        """Encode graph and return node, edge, and graph embeddings."""
+        h = self.node_proj(x)
+        e = self.edge_proj(edge_attr)
+
+        for conv, norm in zip(self.convs, self.norms):
+            h_new = conv(h, edge_index, e)
+            h_new = norm(h_new)
+            h_new = torch.relu(h_new)
+            h_new = self.dropout(h_new)
+            if self.residual:
+                h = h + h_new
+            else:
+                h = h_new
+
+        src, dst = edge_index
+        edge_emb = self.edge_mlp(torch.cat([h[src], h[dst], e], dim=1))
+        graph_emb = global_mean_pool(h, batch)
+
+        return h, edge_emb, graph_emb

solver/models/factory.py

@@ -0,0 +1,82 @@
+"""Factory functions to build model and loss from config dicts."""
+
+from __future__ import annotations
+
+from typing import TYPE_CHECKING
+
+from solver.models.assembly_gnn import AssemblyGNN
+from solver.models.losses import MultiTaskLoss
+
+if TYPE_CHECKING:
+    from typing import Any
+
+__all__ = ["build_loss", "build_model"]
+
+
+def build_model(config: dict[str, Any]) -> AssemblyGNN:
+    """Construct an AssemblyGNN from a parsed YAML model config.
+
+    Expected config structure (matches ``configs/model/*.yaml``)::
+
+        architecture: gin  # or gat
+        encoder:
+          hidden_dim: 128
+          num_layers: 3
+          ...
+        node_features_dim: 22
+        edge_features_dim: 22
+        heads:
+          edge_classification:
+            enabled: true
+            ...
+
+    Args:
+        config: Parsed YAML model config dict.
+
+    Returns:
+        Configured ``AssemblyGNN`` instance.
+    """
+    encoder_type = config.get("architecture", "gin")
+
+    encoder_config: dict[str, Any] = dict(config.get("encoder", {}))
+    encoder_config.setdefault("node_features_dim", config.get("node_features_dim", 22))
+    encoder_config.setdefault("edge_features_dim", config.get("edge_features_dim", 22))
+
+    heads_config = config.get("heads", {})
+
+    return AssemblyGNN(
+        encoder_type=encoder_type,
+        encoder_config=encoder_config,
+        heads_config=heads_config,
+    )
+
+
+def build_loss(config: dict[str, Any]) -> MultiTaskLoss:
+    """Construct a MultiTaskLoss from a parsed YAML training config.
+
+    Expected config structure (from ``configs/training/*.yaml`` ``loss`` section)::
+
+        loss:
+          edge_weight: 1.0
+          graph_weight: 0.5
+          joint_type_weight: 0.3
+          dof_weight: 0.2
+          body_dof_weight: 0.2
+          redundant_penalty: 2.0
+
+    Args:
+        config: Parsed YAML training config dict (full config, not just loss section).
+
+    Returns:
+        Configured ``MultiTaskLoss`` instance.
+    """
+    loss_config = config.get("loss", {})
+
+    return MultiTaskLoss(
+        edge_weight=loss_config.get("edge_weight", 1.0),
+        graph_weight=loss_config.get("graph_weight", 0.5),
+        joint_type_weight=loss_config.get("joint_type_weight", 0.3),
+        dof_weight=loss_config.get("dof_weight", 0.2),
+        body_dof_weight=loss_config.get("body_dof_weight", 0.2),
+        redundant_penalty=loss_config.get("redundant_penalty", 2.0),
+    )

solver/models/graph_conv.py

@@ -0,0 +1,260 @@
+"""Convert datagen assembly dicts to PyTorch Geometric Data objects."""
+
+from __future__ import annotations
+
+from typing import TYPE_CHECKING
+
+import torch
+from torch_geometric.data import Data
+
+from solver.datagen.types import JointType
+
+if TYPE_CHECKING:
+    from typing import Any
+
+__all__ = [
+    "ASSEMBLY_CLASSES",
+    "JOINT_TYPE_NAMES",
+    "assembly_to_pyg",
+]
+
+# Ordered list matching JointType ordinal values (0-10).
+JOINT_TYPE_NAMES: list[str] = [jt.name for jt in JointType]
+
+# Assembly classification label mapping.
+ASSEMBLY_CLASSES: dict[str, int] = {
+    "well-constrained": 0,
+    "underconstrained": 1,
+    "overconstrained": 2,
+    "mixed": 3,
+}
+
+# Joint type name -> ordinal for fast lookup.
+_JOINT_TYPE_TO_ORD: dict[str, int] = {jt.name: jt.value[0] for jt in JointType}
+
+# Joint type name -> DOF removed.
+_JOINT_TYPE_TO_DOF: dict[str, int] = {jt.name: jt.dof for jt in JointType}
+
+_NUM_JOINT_TYPES = len(JointType)
+
+
+def _encode_node_features(
+    body_positions: list[list[float]],
+    body_orientations: list[list[list[float]]],
+    joints: list[dict[str, Any]],
+    grounded: bool,
+) -> torch.Tensor:
+    """Encode node features as a [N, 22] tensor.
+
+    Dims 0-2:   position (centered per graph)
+    Dims 3-11:  flattened 3x3 rotation matrix
+    Dim  12:    is grounded flag
+    Dim  13:    node degree / 10
+    Dims 14-19: degree bucket one-hot (0, 1, 2, 3, 4, 5+)
+    Dim  20:    total incident DOF removed / 30
+    Dim  21:    fraction of incident joints that are FIXED
+    """
+    n_bodies = len(body_positions)
+
+    # Positions centered per graph.
+    pos = torch.tensor(body_positions, dtype=torch.float32)
+    centroid = pos.mean(dim=0, keepdim=True)
+    pos = pos - centroid
+
+    # Flattened orientation matrices [N, 9].
+    orient = torch.tensor(body_orientations, dtype=torch.float32).reshape(n_bodies, 9)
+
+    # Compute per-node degree and incident joint stats.
+    degree = torch.zeros(n_bodies, dtype=torch.float32)
+    dof_removed = torch.zeros(n_bodies, dtype=torch.float32)
+    fixed_count = torch.zeros(n_bodies, dtype=torch.float32)
+
+    for j in joints:
+        a, b = j["body_a"], j["body_b"]
+        jtype = j["type"]
+        dof = _JOINT_TYPE_TO_DOF.get(jtype, 0)
+        degree[a] += 1
+        degree[b] += 1
+        dof_removed[a] += dof
+        dof_removed[b] += dof
+        if jtype == "FIXED":
+            fixed_count[a] += 1
+            fixed_count[b] += 1
+
+    # Grounded flag: body 0 if assembly is grounded.
+    grounded_flag = torch.zeros(n_bodies, 1, dtype=torch.float32)
+    if grounded and n_bodies > 0:
+        grounded_flag[0, 0] = 1.0
+
+    # Degree normalized.
+    degree_norm = (degree / 10.0).unsqueeze(1)
+
+    # Degree bucket one-hot [N, 6]: buckets 0, 1, 2, 3, 4, 5+.
+    bucket = degree.clamp(max=5).long()
+    degree_onehot = torch.zeros(n_bodies, 6, dtype=torch.float32)
+    degree_onehot.scatter_(1, bucket.unsqueeze(1), 1.0)
+
+    # Total incident DOF removed, normalized.
+    dof_norm = (dof_removed / 30.0).unsqueeze(1)
+
+    # Fraction of incident joints that are FIXED.
+    safe_degree = degree.clamp(min=1)
+    fixed_frac = (fixed_count / safe_degree).unsqueeze(1)
+
+    # Concatenate: [N, 3+9+1+1+6+1+1] = [N, 22].
+    x = torch.cat(
+        [pos, orient, grounded_flag, degree_norm, degree_onehot, dof_norm, fixed_frac], dim=1
+    )
+    return x
+
+
+def _encode_edge_features(
+    joints: list[dict[str, Any]],
+    body_positions: list[list[float]],
+) -> tuple[torch.Tensor, torch.Tensor]:
+    """Encode edge features and build bidirectional edge_index.
+
+    Returns:
+        edge_index: [2, 2*n_joints] (each joint as two directed edges).
+        edge_attr: [2*n_joints, 22] edge features.
+    """
+    n_joints = len(joints)
+    if n_joints == 0:
+        return (
+            torch.zeros(2, 0, dtype=torch.long),
+            torch.zeros(0, 22, dtype=torch.float32),
+        )
+
+    pos = body_positions
+    src_list: list[int] = []
+    dst_list: list[int] = []
+    features: list[list[float]] = []
+
+    for j in joints:
+        a, b = j["body_a"], j["body_b"]
+        jtype_name = j["type"]
+        ordinal = _JOINT_TYPE_TO_ORD.get(jtype_name, 0)
+        dof = _JOINT_TYPE_TO_DOF.get(jtype_name, 0)
+
+        # One-hot joint type [11].
+        onehot = [0.0] * _NUM_JOINT_TYPES
+        onehot[ordinal] = 1.0
+
+        # Axis [3].
+        axis = j.get("axis", [0.0, 0.0, 1.0])
+
+        # Anchor offsets relative to body positions (fallback to zeros).
+        anchor_a_raw = j.get("anchor_a")
+        anchor_b_raw = j.get("anchor_b")
+        if anchor_a_raw is not None:
+            anchor_a_off = [anchor_a_raw[k] - pos[a][k] for k in range(3)]
+        else:
+            anchor_a_off = [0.0, 0.0, 0.0]
+        if anchor_b_raw is not None:
+            anchor_b_off = [anchor_b_raw[k] - pos[b][k] for k in range(3)]
+        else:
+            anchor_b_off = [0.0, 0.0, 0.0]
+
+        pitch = j.get("pitch", 0.0)
+        dof_norm = dof / 6.0
+
+        feat = onehot + axis + anchor_a_off + anchor_b_off + [pitch, dof_norm]
+
+        # Bidirectional: a->b and b->a with identical features.
+        src_list.extend([a, b])
+        dst_list.extend([b, a])
+        features.append(feat)
+        features.append(feat)
+
+    edge_index = torch.tensor([src_list, dst_list], dtype=torch.long)
+    edge_attr = torch.tensor(features, dtype=torch.float32)
+    return edge_index, edge_attr
+
+
+def assembly_to_pyg(
+    example: dict[str, Any],
+    *,
+    include_labels: bool = True,
+) -> Data:
+    """Convert a datagen training example dict to a PyG Data object.
+
+    Args:
+        example: Dict from ``SyntheticAssemblyGenerator.generate_training_batch()``.
+        include_labels: Attach ground truth labels to the Data object.
+
+    Returns:
+        ``torch_geometric.data.Data`` with node features ``x``, ``edge_index``,
+        ``edge_attr``, and optionally label tensors ``y_edge``, ``y_graph``,
+        ``y_joint_type``, ``y_dof``, ``y_body_dof``.
+    """
+    body_positions = example["body_positions"]
+    body_orientations = example["body_orientations"]
+    joints = example["joints"]
+    grounded = example.get("grounded", False)
+
+    x = _encode_node_features(body_positions, body_orientations, joints, grounded)
+    edge_index, edge_attr = _encode_edge_features(joints, body_positions)
+
+    data = Data(x=x, edge_index=edge_index, edge_attr=edge_attr)
+    data.num_nodes = x.size(0)
+
+    if include_labels:
+        _attach_labels(data, example, joints)
+
+    return data
+
+
+def _attach_labels(
+    data: Data,
+    example: dict[str, Any],
+    joints: list[dict[str, Any]],
+) -> None:
+    """Attach ground truth label tensors to a Data object."""
+    joint_labels = example.get("joint_labels", {})
+    labels = example.get("labels", {})
+
+    # Per-edge: binary independent (1) / redundant (0).
+    # Duplicated for bidirectional edges.
+    n_joints = len(joints)
+    edge_labels: list[float] = []
+    joint_type_labels: list[int] = []
+    for j in joints:
+        jid = j["joint_id"]
+        jl = joint_labels.get(jid) or joint_labels.get(str(jid), {})
+        is_independent = 1.0 if jl.get("redundant_constraints", 0) == 0 else 0.0
+        ordinal = _JOINT_TYPE_TO_ORD.get(j["type"], 0)
+        # Bidirectional: duplicate.
+        edge_labels.extend([is_independent, is_independent])
+        joint_type_labels.extend([ordinal, ordinal])
+
+    if n_joints > 0:
+        data.y_edge = torch.tensor(edge_labels, dtype=torch.float32)
+        data.y_joint_type = torch.tensor(joint_type_labels, dtype=torch.long)
+    else:
+        data.y_edge = torch.zeros(0, dtype=torch.float32)
+        data.y_joint_type = torch.zeros(0, dtype=torch.long)
+
+    # Assembly classification.
+    classification = example.get("assembly_classification", "")
+    data.y_graph = torch.tensor(
+        [ASSEMBLY_CLASSES.get(classification, 0)],
+        dtype=torch.long,
+    )
+
+    # Total DOF.
+    assembly_labels = labels.get("assembly", {})
+    data.y_dof = torch.tensor(
+        [float(assembly_labels.get("total_dof", 0))],
+        dtype=torch.float32,
+    )
+
+    # Per-body DOF: [N, 2] (translational, rotational).
+    per_body = labels.get("per_body", [])
+    n_bodies = data.num_nodes
+    body_dof = torch.zeros(n_bodies, 2, dtype=torch.float32)
+    for entry in per_body:
+        bid = entry["body_id"]
+        if 0 <= bid < n_bodies:
+            body_dof[bid, 0] = float(entry["translational_dof"])
+            body_dof[bid, 1] = float(entry["rotational_dof"])
+    data.y_body_dof = body_dof

solver/models/heads.py

@@ -0,0 +1,119 @@
+"""Task-specific prediction heads for assembly GNN."""
+
+from __future__ import annotations
+
+import torch
+import torch.nn as nn
+
+__all__ = [
+    "DOFRegressionHead",
+    "DOFTrackingHead",
+    "EdgeClassificationHead",
+    "GraphClassificationHead",
+    "JointTypeHead",
+]
+
+
+class EdgeClassificationHead(nn.Module):
+    """Binary edge classification (independent vs redundant).
+
+    Args:
+        hidden_dim: Input embedding dimension.
+        inner_dim: Internal MLP hidden dimension.
+    """
+
+    def __init__(self, hidden_dim: int = 128, inner_dim: int = 64) -> None:
+        super().__init__()
+        self.mlp = nn.Sequential(
+            nn.Linear(hidden_dim, inner_dim),
+            nn.ReLU(),
+            nn.Linear(inner_dim, 1),
+        )
+
+    def forward(self, edge_emb: torch.Tensor) -> torch.Tensor:
+        """Return logits [E, 1]."""
+        return self.mlp(edge_emb)
+
+
+class GraphClassificationHead(nn.Module):
+    """Assembly classification (well/under/over-constrained/mixed).
+
+    Args:
+        hidden_dim: Input embedding dimension.
+        num_classes: Number of classification categories.
+    """
+
+    def __init__(self, hidden_dim: int = 128, num_classes: int = 4) -> None:
+        super().__init__()
+        self.mlp = nn.Sequential(
+            nn.Linear(hidden_dim, hidden_dim),
+            nn.ReLU(),
+            nn.Linear(hidden_dim, num_classes),
+        )
+
+    def forward(self, graph_emb: torch.Tensor) -> torch.Tensor:
+        """Return logits [B, num_classes]."""
+        return self.mlp(graph_emb)
+
+
+class JointTypeHead(nn.Module):
+    """Joint type classification from edge embeddings.
+
+    Args:
+        hidden_dim: Input embedding dimension.
+        num_classes: Number of joint types.
+    """
+
+    def __init__(self, hidden_dim: int = 128, num_classes: int = 11) -> None:
+        super().__init__()
+        self.mlp = nn.Sequential(
+            nn.Linear(hidden_dim, hidden_dim // 2),
+            nn.ReLU(),
+            nn.Linear(hidden_dim // 2, num_classes),
+        )
+
+    def forward(self, edge_emb: torch.Tensor) -> torch.Tensor:
+        """Return logits [E, num_classes]."""
+        return self.mlp(edge_emb)
+
+
+class DOFRegressionHead(nn.Module):
+    """Total DOF regression from graph embedding.
+
+    Args:
+        hidden_dim: Input embedding dimension.
+    """
+
+    def __init__(self, hidden_dim: int = 128) -> None:
+        super().__init__()
+        self.mlp = nn.Sequential(
+            nn.Linear(hidden_dim, hidden_dim // 2),
+            nn.ReLU(),
+            nn.Linear(hidden_dim // 2, 1),
+            nn.Softplus(),
+        )
+
+    def forward(self, graph_emb: torch.Tensor) -> torch.Tensor:
+        """Return non-negative DOF prediction [B, 1]."""
+        return self.mlp(graph_emb)
+
+
+class DOFTrackingHead(nn.Module):
+    """Per-body DOF prediction (translational, rotational) from node embeddings.
+
+    Args:
+        hidden_dim: Input embedding dimension.
+    """
+
+    def __init__(self, hidden_dim: int = 128) -> None:
+        super().__init__()
+        self.mlp = nn.Sequential(
+            nn.Linear(hidden_dim, hidden_dim // 2),
+            nn.ReLU(),
+            nn.Linear(hidden_dim // 2, 2),
+            nn.Softplus(),
+        )
+
+    def forward(self, node_emb: torch.Tensor) -> torch.Tensor:
+        """Return non-negative per-body DOF [N, 2]."""
+        return self.mlp(node_emb)

solver/models/losses.py

@@ -0,0 +1,161 @@
+"""Uncertainty-weighted multi-task loss (Kendall et al., 2018)."""
+
+from __future__ import annotations
+
+from typing import TYPE_CHECKING
+
+import torch
+import torch.nn as nn
+
+if TYPE_CHECKING:
+    pass
+
+__all__ = ["MultiTaskLoss"]
+
+
+class MultiTaskLoss(nn.Module):
+    """Multi-task loss with learnable uncertainty weighting.
+
+    Each task has a learnable ``log_var`` parameter (log variance) that
+    automatically balances task contributions during training. The loss
+    for task *i* is::
+
+        (1 / (2 * sigma_i^2)) * weight_i * L_i + 0.5 * log(sigma_i^2)
+
+    which simplifies to::
+
+        exp(-log_var_i) * weight_i * L_i + 0.5 * log_var_i
+
+    Args:
+        edge_weight: Initial scale for edge classification loss.
+        graph_weight: Initial scale for graph classification loss.
+        joint_type_weight: Initial scale for joint type loss.
+        dof_weight: Initial scale for DOF regression loss.
+        body_dof_weight: Initial scale for per-body DOF loss.
+        redundant_penalty: Extra weight on redundant edges (label=0) in
+            the edge BCE loss.
+    """
+
+    def __init__(
+        self,
+        edge_weight: float = 1.0,
+        graph_weight: float = 0.5,
+        joint_type_weight: float = 0.3,
+        dof_weight: float = 0.2,
+        body_dof_weight: float = 0.2,
+        redundant_penalty: float = 2.0,
+    ) -> None:
+        super().__init__()
+        self.weights = {
+            "edge": edge_weight,
+            "graph": graph_weight,
+            "joint_type": joint_type_weight,
+            "dof": dof_weight,
+            "body_dof": body_dof_weight,
+        }
+        self.redundant_penalty = redundant_penalty
+
+        # Learnable log-variance parameters, one per task.
+        # Initialized to 0 → sigma^2 = 1.
+        self.log_vars = nn.ParameterDict(
+            {name: nn.Parameter(torch.zeros(1)) for name in self.weights}
+        )
+
+    def forward(
+        self,
+        predictions: dict[str, torch.Tensor],
+        targets: dict[str, torch.Tensor],
+    ) -> tuple[torch.Tensor, dict[str, torch.Tensor]]:
+        """Compute total loss and per-task breakdown.
+
+        Args:
+            predictions: Dict with keys from AssemblyGNN output:
+                ``edge_pred``, ``graph_pred``, ``joint_type_pred``,
+                ``dof_pred``, ``body_dof_pred``.
+            targets: Dict with label tensors:
+                ``y_edge``, ``y_graph``, ``y_joint_type``,
+                ``y_dof``, ``y_body_dof``.
+
+        Returns:
+            total_loss: Scalar total loss.
+            breakdown: Dict of per-task raw loss values (before weighting).
+        """
+        total = torch.tensor(0.0, device=self._device(predictions))
+        breakdown: dict[str, torch.Tensor] = {}
+
+        # Edge classification (BCE with asymmetric redundancy penalty).
+        if "edge_pred" in predictions and "y_edge" in targets:
+            loss = self._edge_loss(predictions["edge_pred"], targets["y_edge"])
+            total = total + self._weighted(loss, "edge")
+            breakdown["edge"] = loss.detach()
+
+        # Graph classification.
+        if "graph_pred" in predictions and "y_graph" in targets:
+            loss = nn.functional.cross_entropy(
+                predictions["graph_pred"],
+                targets["y_graph"],
+            )
+            total = total + self._weighted(loss, "graph")
+            breakdown["graph"] = loss.detach()
+
+        # Joint type classification.
+        if "joint_type_pred" in predictions and "y_joint_type" in targets:
+            loss = nn.functional.cross_entropy(
+                predictions["joint_type_pred"],
+                targets["y_joint_type"],
+            )
+            total = total + self._weighted(loss, "joint_type")
+            breakdown["joint_type"] = loss.detach()
+
+        # DOF regression.
+        if "dof_pred" in predictions and "y_dof" in targets:
+            loss = nn.functional.smooth_l1_loss(
+                predictions["dof_pred"],
+                targets["y_dof"],
+            )
+            total = total + self._weighted(loss, "dof")
+            breakdown["dof"] = loss.detach()
+
+        # Per-body DOF tracking.
+        if "body_dof_pred" in predictions and "y_body_dof" in targets:
+            loss = nn.functional.smooth_l1_loss(
+                predictions["body_dof_pred"],
+                targets["y_body_dof"],
+            )
+            total = total + self._weighted(loss, "body_dof")
+            breakdown["body_dof"] = loss.detach()
+
+        return total, breakdown
+
+    def _edge_loss(
+        self,
+        pred: torch.Tensor,
+        target: torch.Tensor,
+    ) -> torch.Tensor:
+        """BCE loss with asymmetric weighting for redundant edges."""
+        # pred: [E, 1] logits, target: [E] binary.
+        pred_flat = pred.squeeze(-1)
+        # Weight: redundant (0) gets higher penalty, independent (1) gets 1.0.
+        weight = torch.where(
+            target == 0,
+            torch.tensor(self.redundant_penalty, device=pred.device),
+            torch.tensor(1.0, device=pred.device),
+        )
+        return nn.functional.binary_cross_entropy_with_logits(
+            pred_flat,
+            target,
+            weight=weight,
+        )
+
+    def _weighted(self, loss: torch.Tensor, task_name: str) -> torch.Tensor:
+        """Apply uncertainty weighting: exp(-log_var) * w * L + 0.5 * log_var."""
+        log_var = self.log_vars[task_name].squeeze()
+        weight = self.weights[task_name]
+        return torch.exp(-log_var) * weight * loss + 0.5 * log_var
+
+    @staticmethod
+    def _device(predictions: dict[str, torch.Tensor]) -> torch.device:
+        """Infer device from prediction tensors."""
+        for v in predictions.values():
+            return v.device
+        return torch.device("cpu")

tests/models/test_assembly_gnn.py

@@ -0,0 +1,188 @@
+"""Tests for solver.models.assembly_gnn -- main model wiring."""
+
+from __future__ import annotations
+
+import pytest
+import torch
+
+from solver.models.assembly_gnn import AssemblyGNN
+
+
+def _default_heads_config(dof_tracking: bool = False) -> dict:
+    return {
+        "edge_classification": {"enabled": True, "hidden_dim": 64},
+        "graph_classification": {"enabled": True, "num_classes": 4},
+        "joint_type": {"enabled": True, "num_classes": 11},
+        "dof_regression": {"enabled": True},
+        "dof_tracking": {"enabled": dof_tracking},
+    }
+
+
+def _random_graph(
+    n_nodes: int = 8,
+    n_edges: int = 16,
+    batch_size: int = 2,
+) -> tuple[torch.Tensor, torch.Tensor, torch.Tensor, torch.Tensor]:
+    x = torch.randn(n_nodes, 22)
+    edge_index = torch.randint(0, n_nodes, (2, n_edges))
+    edge_attr = torch.randn(n_edges, 22)
+    batch = torch.arange(batch_size).repeat_interleave(n_nodes // batch_size)
+    if len(batch) < n_nodes:
+        batch = torch.cat([batch, torch.full((n_nodes - len(batch),), batch_size - 1)])
+    return x, edge_index, edge_attr, batch
+
+
+class TestAssemblyGNNGIN:
+    """AssemblyGNN with GIN encoder."""
+
+    def test_forward_all_heads(self) -> None:
+        model = AssemblyGNN(
+            encoder_type="gin",
+            encoder_config={"hidden_dim": 64, "num_layers": 2},
+            heads_config=_default_heads_config(),
+        )
+        x, ei, ea, batch = _random_graph()
+        preds = model(x, ei, ea, batch)
+        assert "edge_pred" in preds
+        assert "graph_pred" in preds
+        assert "joint_type_pred" in preds
+        assert "dof_pred" in preds
+
+    def test_output_shapes(self) -> None:
+        model = AssemblyGNN(
+            encoder_type="gin",
+            encoder_config={"hidden_dim": 64, "num_layers": 2},
+            heads_config=_default_heads_config(),
+        )
+        x, ei, ea, batch = _random_graph(n_nodes=10, n_edges=20, batch_size=3)
+        preds = model(x, ei, ea, batch)
+        assert preds["edge_pred"].shape == (20, 1)
+        assert preds["graph_pred"].shape == (3, 4)
+        assert preds["joint_type_pred"].shape == (20, 11)
+        assert preds["dof_pred"].shape == (3, 1)
+
+    def test_gradients_flow(self) -> None:
+        model = AssemblyGNN(
+            encoder_type="gin",
+            encoder_config={"hidden_dim": 32, "num_layers": 2},
+            heads_config=_default_heads_config(),
+        )
+        x, ei, ea, batch = _random_graph()
+        x.requires_grad_(True)
+        preds = model(x, ei, ea, batch)
+        total = sum(p.sum() for p in preds.values())
+        total.backward()
+        assert x.grad is not None
+
+    def test_no_heads_returns_empty(self) -> None:
+        model = AssemblyGNN(
+            encoder_type="gin",
+            encoder_config={"hidden_dim": 32, "num_layers": 2},
+            heads_config={},
+        )
+        x, ei, ea, batch = _random_graph()
+        preds = model(x, ei, ea, batch)
+        assert len(preds) == 0
+
+
+class TestAssemblyGNNGAT:
+    """AssemblyGNN with GAT encoder."""
+
+    def test_forward_all_heads(self) -> None:
+        model = AssemblyGNN(
+            encoder_type="gat",
+            encoder_config={"hidden_dim": 64, "num_layers": 2, "num_heads": 4},
+            heads_config=_default_heads_config(dof_tracking=True),
+        )
+        x, ei, ea, batch = _random_graph()
+        preds = model(x, ei, ea, batch)
+        assert "edge_pred" in preds
+        assert "graph_pred" in preds
+        assert "joint_type_pred" in preds
+        assert "dof_pred" in preds
+        assert "body_dof_pred" in preds
+
+    def test_body_dof_shape(self) -> None:
+        model = AssemblyGNN(
+            encoder_type="gat",
+            encoder_config={"hidden_dim": 64, "num_layers": 2, "num_heads": 4},
+            heads_config=_default_heads_config(dof_tracking=True),
+        )
+        x, ei, ea, batch = _random_graph(n_nodes=10, n_edges=20)
+        preds = model(x, ei, ea, batch)
+        assert preds["body_dof_pred"].shape == (10, 2)
+
+
+class TestAssemblyGNNEdgeCases:
+    """Edge cases and error handling."""
+
+    def test_unknown_encoder_raises(self) -> None:
+        with pytest.raises(ValueError, match="Unknown encoder"):
+            AssemblyGNN(encoder_type="transformer")
+
+    def test_selective_heads(self) -> None:
+        """Only enabled heads produce output."""
+        config = {
+            "edge_classification": {"enabled": True},
+            "graph_classification": {"enabled": False},
+            "joint_type": {"enabled": True, "num_classes": 11},
+        }
+        model = AssemblyGNN(
+            encoder_type="gin",
+            encoder_config={"hidden_dim": 32, "num_layers": 2},
+            heads_config=config,
+        )
+        x, ei, ea, batch = _random_graph()
+        preds = model(x, ei, ea, batch)
+        assert "edge_pred" in preds
+        assert "joint_type_pred" in preds
+        assert "graph_pred" not in preds
+        assert "dof_pred" not in preds
+
+    def test_no_batch_single_graph(self) -> None:
+        model = AssemblyGNN(
+            encoder_type="gin",
+            encoder_config={"hidden_dim": 32, "num_layers": 2},
+            heads_config=_default_heads_config(),
+        )
+        x = torch.randn(6, 22)
+        ei = torch.randint(0, 6, (2, 10))
+        ea = torch.randn(10, 22)
+        preds = model(x, ei, ea)
+        assert preds["graph_pred"].shape == (1, 4)
+        assert preds["dof_pred"].shape == (1, 1)
+
+    def test_parameter_count_reasonable(self) -> None:
+        """Sanity check that model has learnable parameters."""
+        model = AssemblyGNN(
+            encoder_type="gin",
+            encoder_config={"hidden_dim": 64, "num_layers": 2},
+            heads_config=_default_heads_config(),
+        )
+        n_params = sum(p.numel() for p in model.parameters())
+        assert n_params > 1000  # non-trivial model
+
+
+class TestAssemblyGNNEndToEnd:
+    """End-to-end test with datagen pipeline."""
+
+    def test_datagen_to_model(self) -> None:
+        from solver.datagen.generator import SyntheticAssemblyGenerator
+        from solver.models.graph_conv import assembly_to_pyg
+
+        gen = SyntheticAssemblyGenerator(seed=42)
+        batch = gen.generate_training_batch(batch_size=2, complexity_tier="simple")
+
+        model = AssemblyGNN(
+            encoder_type="gin",
+            encoder_config={"hidden_dim": 32, "num_layers": 2},
+            heads_config=_default_heads_config(),
+        )
+        model.eval()
+
+        for ex in batch:
+            data = assembly_to_pyg(ex)
+            with torch.no_grad():
+                preds = model(data.x, data.edge_index, data.edge_attr)
+            assert "edge_pred" in preds
+            assert preds["edge_pred"].shape[0] == data.edge_index.shape[1]

tests/models/test_encoder.py

@@ -0,0 +1,183 @@
+"""Tests for solver.models.encoder -- GIN and GAT graph encoders."""
+
+from __future__ import annotations
+
+import pytest
+import torch
+
+from solver.models.encoder import GATEncoder, GINEncoder
+
+
+def _random_graph(
+    n_nodes: int = 8,
+    n_edges: int = 20,
+    node_dim: int = 22,
+    edge_dim: int = 22,
+    batch_size: int = 2,
+) -> tuple[torch.Tensor, torch.Tensor, torch.Tensor, torch.Tensor]:
+    """Create a random graph for testing."""
+    x = torch.randn(n_nodes, node_dim)
+    edge_index = torch.randint(0, n_nodes, (2, n_edges))
+    edge_attr = torch.randn(n_edges, edge_dim)
+    # Assign nodes to batches roughly evenly.
+    batch = torch.arange(batch_size).repeat_interleave(n_nodes // batch_size)
+    # Handle remainder nodes.
+    if len(batch) < n_nodes:
+        batch = torch.cat([batch, torch.full((n_nodes - len(batch),), batch_size - 1)])
+    return x, edge_index, edge_attr, batch
+
+
+class TestGINEncoder:
+    """GINEncoder shape and gradient tests."""
+
+    def test_output_shapes(self) -> None:
+        enc = GINEncoder(node_features_dim=22, edge_features_dim=22, hidden_dim=64, num_layers=2)
+        x, ei, ea, batch = _random_graph(n_nodes=10, n_edges=16, batch_size=3)
+        node_emb, edge_emb, graph_emb = enc(x, ei, ea, batch)
+        assert node_emb.shape == (10, 64)
+        assert edge_emb.shape == (16, 64)
+        assert graph_emb.shape == (3, 64)
+
+    def test_hidden_dim_property(self) -> None:
+        enc = GINEncoder(hidden_dim=128)
+        assert enc.hidden_dim == 128
+
+    def test_default_dimensions(self) -> None:
+        enc = GINEncoder()
+        x, ei, ea, batch = _random_graph()
+        node_emb, edge_emb, graph_emb = enc(x, ei, ea, batch)
+        assert node_emb.shape[1] == 128
+        assert edge_emb.shape[1] == 128
+        assert graph_emb.shape[1] == 128
+
+    def test_no_batch_defaults_to_single_graph(self) -> None:
+        enc = GINEncoder(hidden_dim=64, num_layers=2)
+        x, ei, ea, _ = _random_graph(n_nodes=6, n_edges=10)
+        node_emb, edge_emb, graph_emb = enc(x, ei, ea, batch=None)
+        assert graph_emb.shape == (1, 64)
+
+    def test_gradients_flow(self) -> None:
+        enc = GINEncoder(hidden_dim=32, num_layers=2)
+        x, ei, ea, batch = _random_graph(n_nodes=8, n_edges=12)
+        x.requires_grad_(True)
+        node_emb, edge_emb, graph_emb = enc(x, ei, ea, batch)
+        loss = graph_emb.sum()
+        loss.backward()
+        assert x.grad is not None
+        assert x.grad.abs().sum() > 0
+
+    def test_zero_edges(self) -> None:
+        enc = GINEncoder(hidden_dim=32, num_layers=2)
+        x = torch.randn(4, 22)
+        ei = torch.zeros(2, 0, dtype=torch.long)
+        ea = torch.zeros(0, 22)
+        batch = torch.tensor([0, 0, 1, 1])
+        node_emb, edge_emb, graph_emb = enc(x, ei, ea, batch)
+        assert node_emb.shape == (4, 32)
+        assert edge_emb.shape == (0, 32)
+        assert graph_emb.shape == (2, 32)
+
+    def test_single_node(self) -> None:
+        enc = GINEncoder(hidden_dim=32, num_layers=2)
+        # Train with a small batch first to populate BN running stats.
+        x_train = torch.randn(4, 22)
+        ei_train = torch.zeros(2, 0, dtype=torch.long)
+        ea_train = torch.zeros(0, 22)
+        batch_train = torch.tensor([0, 0, 1, 1])
+        enc.train()
+        enc(x_train, ei_train, ea_train, batch_train)
+        # Now test single node in eval mode (BN uses running stats).
+        enc.eval()
+        x = torch.randn(1, 22)
+        ei = torch.zeros(2, 0, dtype=torch.long)
+        ea = torch.zeros(0, 22)
+        with torch.no_grad():
+            node_emb, edge_emb, graph_emb = enc(x, ei, ea)
+        assert node_emb.shape == (1, 32)
+        assert graph_emb.shape == (1, 32)
+
+    def test_eval_mode(self) -> None:
+        """Encoder works in eval mode (BatchNorm uses running stats)."""
+        enc = GINEncoder(hidden_dim=32, num_layers=2)
+        # Forward pass in train mode to populate BN stats.
+        x, ei, ea, batch = _random_graph(n_nodes=8, n_edges=12)
+        enc.train()
+        enc(x, ei, ea, batch)
+        # Switch to eval.
+        enc.eval()
+        with torch.no_grad():
+            node_emb, edge_emb, graph_emb = enc(x, ei, ea, batch)
+        assert node_emb.shape[1] == 32
+
+
+class TestGATEncoder:
+    """GATEncoder shape and gradient tests."""
+
+    def test_output_shapes(self) -> None:
+        enc = GATEncoder(
+            node_features_dim=22,
+            edge_features_dim=22,
+            hidden_dim=64,
+            num_layers=2,
+            num_heads=4,
+        )
+        x, ei, ea, batch = _random_graph(n_nodes=10, n_edges=16, batch_size=3)
+        node_emb, edge_emb, graph_emb = enc(x, ei, ea, batch)
+        assert node_emb.shape == (10, 64)
+        assert edge_emb.shape == (16, 64)
+        assert graph_emb.shape == (3, 64)
+
+    def test_hidden_dim_property(self) -> None:
+        enc = GATEncoder(hidden_dim=256, num_heads=8)
+        assert enc.hidden_dim == 256
+
+    def test_default_dimensions(self) -> None:
+        enc = GATEncoder()
+        x, ei, ea, batch = _random_graph()
+        node_emb, edge_emb, graph_emb = enc(x, ei, ea, batch)
+        assert node_emb.shape[1] == 256
+        assert edge_emb.shape[1] == 256
+        assert graph_emb.shape[1] == 256
+
+    def test_no_batch_defaults_to_single_graph(self) -> None:
+        enc = GATEncoder(hidden_dim=64, num_layers=2, num_heads=4)
+        x, ei, ea, _ = _random_graph(n_nodes=6, n_edges=10)
+        node_emb, edge_emb, graph_emb = enc(x, ei, ea, batch=None)
+        assert graph_emb.shape == (1, 64)
+
+    def test_gradients_flow(self) -> None:
+        enc = GATEncoder(hidden_dim=64, num_layers=2, num_heads=4)
+        x, ei, ea, batch = _random_graph(n_nodes=8, n_edges=12)
+        x.requires_grad_(True)
+        node_emb, edge_emb, graph_emb = enc(x, ei, ea, batch)
+        loss = graph_emb.sum()
+        loss.backward()
+        assert x.grad is not None
+        assert x.grad.abs().sum() > 0
+
+    def test_residual_connection(self) -> None:
+        """With residual=True, output should differ from residual=False."""
+        x, ei, ea, batch = _random_graph(n_nodes=8, n_edges=12)
+        torch.manual_seed(0)
+        enc_res = GATEncoder(hidden_dim=64, num_layers=2, num_heads=4, residual=True)
+        torch.manual_seed(0)
+        enc_no = GATEncoder(hidden_dim=64, num_layers=2, num_heads=4, residual=False)
+        with torch.no_grad():
+            n1, _, _ = enc_res(x, ei, ea, batch)
+            n2, _, _ = enc_no(x, ei, ea, batch)
+        # Outputs should generally differ (unless by very unlikely coincidence).
+        assert not torch.allclose(n1, n2, atol=1e-4)
+
+    def test_hidden_dim_must_divide_heads(self) -> None:
+        with pytest.raises(ValueError, match="divisible"):
+            GATEncoder(hidden_dim=100, num_heads=8)
+
+    def test_eval_mode(self) -> None:
+        enc = GATEncoder(hidden_dim=64, num_layers=2, num_heads=4)
+        x, ei, ea, batch = _random_graph(n_nodes=8, n_edges=12)
+        enc.train()
+        enc(x, ei, ea, batch)
+        enc.eval()
+        with torch.no_grad():
+            node_emb, edge_emb, graph_emb = enc(x, ei, ea, batch)
+        assert node_emb.shape[1] == 64

tests/models/test_factory.py

@@ -0,0 +1,110 @@
+"""Tests for solver.models.factory -- model and loss construction from config."""
+
+from __future__ import annotations
+
+import yaml
+
+from solver.models.assembly_gnn import AssemblyGNN
+from solver.models.factory import build_loss, build_model
+from solver.models.losses import MultiTaskLoss
+
+
+def _load_yaml(path: str) -> dict:
+    with open(path) as f:
+        return yaml.safe_load(f)
+
+
+class TestBuildModel:
+    """build_model constructs AssemblyGNN from config."""
+
+    def test_baseline_config(self) -> None:
+        config = _load_yaml("configs/model/baseline.yaml")
+        model = build_model(config)
+        assert isinstance(model, AssemblyGNN)
+        assert model.encoder.hidden_dim == 128
+
+    def test_gat_config(self) -> None:
+        config = _load_yaml("configs/model/gat.yaml")
+        model = build_model(config)
+        assert isinstance(model, AssemblyGNN)
+        assert model.encoder.hidden_dim == 256
+
+    def test_baseline_heads_present(self) -> None:
+        config = _load_yaml("configs/model/baseline.yaml")
+        model = build_model(config)
+        assert "edge_pred" in model.heads
+        assert "graph_pred" in model.heads
+        assert "joint_type_pred" in model.heads
+        assert "dof_pred" in model.heads
+
+    def test_gat_has_dof_tracking(self) -> None:
+        config = _load_yaml("configs/model/gat.yaml")
+        model = build_model(config)
+        assert "body_dof_pred" in model.heads
+
+    def test_baseline_no_dof_tracking(self) -> None:
+        config = _load_yaml("configs/model/baseline.yaml")
+        model = build_model(config)
+        assert "body_dof_pred" not in model.heads
+
+    def test_minimal_config(self) -> None:
+        config = {"architecture": "gin"}
+        model = build_model(config)
+        assert isinstance(model, AssemblyGNN)
+        # No heads enabled.
+        assert len(model.heads) == 0
+
+    def test_custom_config(self) -> None:
+        config = {
+            "architecture": "gin",
+            "encoder": {"hidden_dim": 64, "num_layers": 2},
+            "heads": {
+                "edge_classification": {"enabled": True},
+                "graph_classification": {"enabled": True, "num_classes": 4},
+            },
+        }
+        model = build_model(config)
+        assert model.encoder.hidden_dim == 64
+        assert "edge_pred" in model.heads
+        assert "graph_pred" in model.heads
+        assert "joint_type_pred" not in model.heads
+
+
+class TestBuildLoss:
+    """build_loss constructs MultiTaskLoss from training config."""
+
+    def test_pretrain_config(self) -> None:
+        config = _load_yaml("configs/training/pretrain.yaml")
+        loss_fn = build_loss(config)
+        assert isinstance(loss_fn, MultiTaskLoss)
+
+    def test_weights_from_config(self) -> None:
+        config = _load_yaml("configs/training/pretrain.yaml")
+        loss_fn = build_loss(config)
+        assert loss_fn.weights["edge"] == 1.0
+        assert loss_fn.weights["graph"] == 0.5
+        assert loss_fn.weights["joint_type"] == 0.3
+        assert loss_fn.weights["dof"] == 0.2
+
+    def test_redundant_penalty_from_config(self) -> None:
+        config = _load_yaml("configs/training/pretrain.yaml")
+        loss_fn = build_loss(config)
+        assert loss_fn.redundant_penalty == 2.0
+
+    def test_empty_config_uses_defaults(self) -> None:
+        loss_fn = build_loss({})
+        assert isinstance(loss_fn, MultiTaskLoss)
+        assert loss_fn.weights["edge"] == 1.0
+
+    def test_custom_weights(self) -> None:
+        config = {
+            "loss": {
+                "edge_weight": 2.0,
+                "graph_weight": 1.0,
+                "redundant_penalty": 5.0,
+            },
+        }
+        loss_fn = build_loss(config)
+        assert loss_fn.weights["edge"] == 2.0
+        assert loss_fn.weights["graph"] == 1.0
+        assert loss_fn.redundant_penalty == 5.0

tests/models/test_graph_conv.py

@@ -0,0 +1,144 @@
+"""Tests for solver.models.graph_conv -- assembly to PyG conversion."""
+
+from __future__ import annotations
+
+import torch
+
+from solver.datagen.generator import SyntheticAssemblyGenerator
+from solver.datagen.types import JointType
+from solver.models.graph_conv import ASSEMBLY_CLASSES, JOINT_TYPE_NAMES, assembly_to_pyg
+
+
+def _make_example(n_bodies: int = 4, grounded: bool = True, seed: int = 0) -> dict:
+    """Generate a single training example via the datagen pipeline."""
+    gen = SyntheticAssemblyGenerator(seed=seed)
+    batch = gen.generate_training_batch(batch_size=1, n_bodies_range=(n_bodies, n_bodies + 1))
+    return batch[0]
+
+
+class TestAssemblyToPyg:
+    """assembly_to_pyg converts datagen dicts to PyG Data correctly."""
+
+    def test_node_feature_shape(self) -> None:
+        ex = _make_example(n_bodies=5)
+        data = assembly_to_pyg(ex)
+        assert data.x.shape == (5, 22)
+
+    def test_edge_feature_shape(self) -> None:
+        ex = _make_example(n_bodies=4)
+        data = assembly_to_pyg(ex)
+        n_joints = ex["n_joints"]
+        assert data.edge_attr.shape == (n_joints * 2, 22)
+
+    def test_edge_index_bidirectional(self) -> None:
+        ex = _make_example(n_bodies=4)
+        data = assembly_to_pyg(ex)
+        ei = data.edge_index
+        # Each joint produces 2 directed edges: a->b and b->a.
+        for i in range(0, ei.size(1), 2):
+            assert ei[0, i].item() == ei[1, i + 1].item()
+            assert ei[1, i].item() == ei[0, i + 1].item()
+
+    def test_edge_index_shape(self) -> None:
+        ex = _make_example(n_bodies=4)
+        data = assembly_to_pyg(ex)
+        n_joints = ex["n_joints"]
+        assert data.edge_index.shape == (2, n_joints * 2)
+
+    def test_node_features_centered(self) -> None:
+        ex = _make_example(n_bodies=5)
+        data = assembly_to_pyg(ex)
+        # Positions (dims 0-2) should be centered (mean ~0).
+        pos = data.x[:, :3]
+        assert pos.mean(dim=0).abs().max().item() < 1e-5
+
+    def test_grounded_flag_set(self) -> None:
+        ex = _make_example(n_bodies=4, grounded=True)
+        ex["grounded"] = True
+        data = assembly_to_pyg(ex)
+        assert data.x[0, 12].item() == 1.0
+
+    def test_ungrounded_flag_clear(self) -> None:
+        ex = _make_example(n_bodies=4)
+        ex["grounded"] = False
+        data = assembly_to_pyg(ex)
+        assert (data.x[:, 12] == 0.0).all()
+
+    def test_edge_type_one_hot_valid(self) -> None:
+        ex = _make_example(n_bodies=5)
+        data = assembly_to_pyg(ex)
+        if data.edge_attr.size(0) > 0:
+            onehot = data.edge_attr[:, :11]
+            # Each row should have exactly one 1.0.
+            assert (onehot.sum(dim=1) == 1.0).all()
+
+    def test_labels_present_when_requested(self) -> None:
+        ex = _make_example(n_bodies=4)
+        data = assembly_to_pyg(ex, include_labels=True)
+        assert hasattr(data, "y_edge")
+        assert hasattr(data, "y_graph")
+        assert hasattr(data, "y_joint_type")
+        assert hasattr(data, "y_dof")
+        assert hasattr(data, "y_body_dof")
+
+    def test_labels_absent_when_not_requested(self) -> None:
+        ex = _make_example(n_bodies=4)
+        data = assembly_to_pyg(ex, include_labels=False)
+        assert not hasattr(data, "y_edge")
+        assert not hasattr(data, "y_graph")
+
+    def test_graph_classification_label_mapping(self) -> None:
+        ex = _make_example(n_bodies=4)
+        data = assembly_to_pyg(ex)
+        cls = ex["assembly_classification"]
+        expected = ASSEMBLY_CLASSES[cls]
+        assert data.y_graph.item() == expected
+
+    def test_body_dof_shape(self) -> None:
+        ex = _make_example(n_bodies=5)
+        data = assembly_to_pyg(ex)
+        assert data.y_body_dof.shape == (5, 2)
+
+    def test_edge_labels_binary(self) -> None:
+        ex = _make_example(n_bodies=5)
+        data = assembly_to_pyg(ex)
+        if data.y_edge.numel() > 0:
+            assert ((data.y_edge == 0.0) | (data.y_edge == 1.0)).all()
+
+    def test_dof_removed_normalized(self) -> None:
+        ex = _make_example(n_bodies=4)
+        data = assembly_to_pyg(ex)
+        if data.edge_attr.size(0) > 0:
+            dof_norm = data.edge_attr[:, 21]
+            assert (dof_norm >= 0.0).all()
+            assert (dof_norm <= 1.0).all()
+
+    def test_roundtrip_with_generator(self) -> None:
+        """Generate a real example and convert -- no crash."""
+        gen = SyntheticAssemblyGenerator(seed=42)
+        batch = gen.generate_training_batch(batch_size=5, complexity_tier="simple")
+        for ex in batch:
+            data = assembly_to_pyg(ex)
+            assert data.x.shape[1] == 22
+            assert data.edge_attr.shape[1] == 22
+
+
+class TestAssemblyClasses:
+    """ASSEMBLY_CLASSES covers all classifications."""
+
+    def test_four_classes(self) -> None:
+        assert len(ASSEMBLY_CLASSES) == 4
+
+    def test_values_are_0_to_3(self) -> None:
+        assert set(ASSEMBLY_CLASSES.values()) == {0, 1, 2, 3}
+
+
+class TestJointTypeNames:
+    """JOINT_TYPE_NAMES matches the JointType enum."""
+
+    def test_length_matches_enum(self) -> None:
+        assert len(JOINT_TYPE_NAMES) == len(JointType)
+
+    def test_order_matches_ordinal(self) -> None:
+        for i, name in enumerate(JOINT_TYPE_NAMES):
+            assert JointType[name].value[0] == i

tests/models/test_heads.py

@@ -0,0 +1,182 @@
+"""Tests for solver.models.heads -- task-specific prediction heads."""
+
+from __future__ import annotations
+
+import torch
+
+from solver.models.heads import (
+    DOFRegressionHead,
+    DOFTrackingHead,
+    EdgeClassificationHead,
+    GraphClassificationHead,
+    JointTypeHead,
+)
+
+
+class TestEdgeClassificationHead:
+    """EdgeClassificationHead produces correct shape and gradients."""
+
+    def test_output_shape(self) -> None:
+        head = EdgeClassificationHead(hidden_dim=128)
+        edge_emb = torch.randn(20, 128)
+        out = head(edge_emb)
+        assert out.shape == (20, 1)
+
+    def test_output_shape_small(self) -> None:
+        head = EdgeClassificationHead(hidden_dim=32)
+        edge_emb = torch.randn(5, 32)
+        out = head(edge_emb)
+        assert out.shape == (5, 1)
+
+    def test_gradients_flow(self) -> None:
+        head = EdgeClassificationHead(hidden_dim=64)
+        edge_emb = torch.randn(10, 64, requires_grad=True)
+        out = head(edge_emb)
+        out.sum().backward()
+        assert edge_emb.grad is not None
+        assert edge_emb.grad.abs().sum() > 0
+
+    def test_zero_edges(self) -> None:
+        head = EdgeClassificationHead(hidden_dim=64)
+        edge_emb = torch.zeros(0, 64)
+        out = head(edge_emb)
+        assert out.shape == (0, 1)
+
+    def test_output_is_logits(self) -> None:
+        """Output should be unbounded logits (not probabilities)."""
+        head = EdgeClassificationHead(hidden_dim=64)
+        torch.manual_seed(42)
+        edge_emb = torch.randn(100, 64)
+        out = head(edge_emb)
+        # Logits can be negative.
+        assert out.min().item() < 0 or out.max().item() > 1
+
+
+class TestGraphClassificationHead:
+    """GraphClassificationHead produces correct shape and gradients."""
+
+    def test_output_shape(self) -> None:
+        head = GraphClassificationHead(hidden_dim=128, num_classes=4)
+        graph_emb = torch.randn(3, 128)
+        out = head(graph_emb)
+        assert out.shape == (3, 4)
+
+    def test_custom_num_classes(self) -> None:
+        head = GraphClassificationHead(hidden_dim=64, num_classes=8)
+        graph_emb = torch.randn(2, 64)
+        out = head(graph_emb)
+        assert out.shape == (2, 8)
+
+    def test_gradients_flow(self) -> None:
+        head = GraphClassificationHead(hidden_dim=64)
+        graph_emb = torch.randn(2, 64, requires_grad=True)
+        out = head(graph_emb)
+        out.sum().backward()
+        assert graph_emb.grad is not None
+
+    def test_single_graph(self) -> None:
+        head = GraphClassificationHead(hidden_dim=128)
+        graph_emb = torch.randn(1, 128)
+        out = head(graph_emb)
+        assert out.shape == (1, 4)
+
+
+class TestJointTypeHead:
+    """JointTypeHead produces correct shape and gradients."""
+
+    def test_output_shape(self) -> None:
+        head = JointTypeHead(hidden_dim=128, num_classes=11)
+        edge_emb = torch.randn(20, 128)
+        out = head(edge_emb)
+        assert out.shape == (20, 11)
+
+    def test_custom_classes(self) -> None:
+        head = JointTypeHead(hidden_dim=64, num_classes=7)
+        edge_emb = torch.randn(10, 64)
+        out = head(edge_emb)
+        assert out.shape == (10, 7)
+
+    def test_gradients_flow(self) -> None:
+        head = JointTypeHead(hidden_dim=64)
+        edge_emb = torch.randn(10, 64, requires_grad=True)
+        out = head(edge_emb)
+        out.sum().backward()
+        assert edge_emb.grad is not None
+
+    def test_zero_edges(self) -> None:
+        head = JointTypeHead(hidden_dim=64)
+        edge_emb = torch.zeros(0, 64)
+        out = head(edge_emb)
+        assert out.shape == (0, 11)
+
+
+class TestDOFRegressionHead:
+    """DOFRegressionHead produces correct shape and non-negative output."""
+
+    def test_output_shape(self) -> None:
+        head = DOFRegressionHead(hidden_dim=128)
+        graph_emb = torch.randn(3, 128)
+        out = head(graph_emb)
+        assert out.shape == (3, 1)
+
+    def test_output_non_negative(self) -> None:
+        """Softplus ensures non-negative output."""
+        head = DOFRegressionHead(hidden_dim=64)
+        torch.manual_seed(0)
+        graph_emb = torch.randn(50, 64)
+        out = head(graph_emb)
+        assert (out >= 0).all()
+
+    def test_gradients_flow(self) -> None:
+        head = DOFRegressionHead(hidden_dim=64)
+        graph_emb = torch.randn(2, 64, requires_grad=True)
+        out = head(graph_emb)
+        out.sum().backward()
+        assert graph_emb.grad is not None
+
+    def test_single_graph(self) -> None:
+        head = DOFRegressionHead(hidden_dim=32)
+        graph_emb = torch.randn(1, 32)
+        out = head(graph_emb)
+        assert out.shape == (1, 1)
+        assert out.item() >= 0
+
+
+class TestDOFTrackingHead:
+    """DOFTrackingHead produces correct shape and non-negative output."""
+
+    def test_output_shape(self) -> None:
+        head = DOFTrackingHead(hidden_dim=128)
+        node_emb = torch.randn(10, 128)
+        out = head(node_emb)
+        assert out.shape == (10, 2)
+
+    def test_output_non_negative(self) -> None:
+        """Softplus ensures non-negative output."""
+        head = DOFTrackingHead(hidden_dim=64)
+        torch.manual_seed(0)
+        node_emb = torch.randn(50, 64)
+        out = head(node_emb)
+        assert (out >= 0).all()
+
+    def test_gradients_flow(self) -> None:
+        head = DOFTrackingHead(hidden_dim=64)
+        node_emb = torch.randn(10, 64, requires_grad=True)
+        out = head(node_emb)
+        out.sum().backward()
+        assert node_emb.grad is not None
+
+    def test_single_node(self) -> None:
+        head = DOFTrackingHead(hidden_dim=32)
+        node_emb = torch.randn(1, 32)
+        out = head(node_emb)
+        assert out.shape == (1, 2)
+        assert (out >= 0).all()
+
+    def test_two_columns_independent(self) -> None:
+        """Translational and rotational DOF are independently predicted."""
+        head = DOFTrackingHead(hidden_dim=64)
+        node_emb = torch.randn(20, 64)
+        out = head(node_emb)
+        # The two columns should generally differ.
+        assert not torch.allclose(out[:, 0], out[:, 1], atol=1e-6)

tests/models/test_losses.py

@@ -0,0 +1,156 @@
+"""Tests for solver.models.losses -- uncertainty-weighted multi-task loss."""
+
+from __future__ import annotations
+
+import torch
+
+from solver.models.losses import MultiTaskLoss
+
+
+def _make_predictions_and_targets(
+    n_edges: int = 20,
+    batch_size: int = 3,
+    n_nodes: int = 10,
+) -> tuple[dict[str, torch.Tensor], dict[str, torch.Tensor]]:
+    preds = {
+        "edge_pred": torch.randn(n_edges, 1),
+        "graph_pred": torch.randn(batch_size, 4),
+        "joint_type_pred": torch.randn(n_edges, 11),
+        "dof_pred": torch.rand(batch_size, 1) * 10,
+        "body_dof_pred": torch.rand(n_nodes, 2) * 6,
+    }
+    targets = {
+        "y_edge": torch.randint(0, 2, (n_edges,)).float(),
+        "y_graph": torch.randint(0, 4, (batch_size,)),
+        "y_joint_type": torch.randint(0, 11, (n_edges,)),
+        "y_dof": torch.rand(batch_size, 1) * 10,
+        "y_body_dof": torch.rand(n_nodes, 2) * 6,
+    }
+    return preds, targets
+
+
+class TestMultiTaskLoss:
+    """MultiTaskLoss computation tests."""
+
+    def test_returns_scalar_and_breakdown(self) -> None:
+        loss_fn = MultiTaskLoss()
+        preds, targets = _make_predictions_and_targets()
+        total, breakdown = loss_fn(preds, targets)
+        assert total.dim() == 0  # scalar
+        assert isinstance(breakdown, dict)
+
+    def test_all_tasks_in_breakdown(self) -> None:
+        loss_fn = MultiTaskLoss()
+        preds, targets = _make_predictions_and_targets()
+        _, breakdown = loss_fn(preds, targets)
+        assert "edge" in breakdown
+        assert "graph" in breakdown
+        assert "joint_type" in breakdown
+        assert "dof" in breakdown
+        assert "body_dof" in breakdown
+
+    def test_total_is_positive(self) -> None:
+        loss_fn = MultiTaskLoss()
+        preds, targets = _make_predictions_and_targets()
+        total, _ = loss_fn(preds, targets)
+        # With random predictions, loss should be positive.
+        assert total.item() > 0
+
+    def test_skips_missing_predictions(self) -> None:
+        loss_fn = MultiTaskLoss()
+        preds = {"edge_pred": torch.randn(10, 1)}
+        targets = {"y_edge": torch.randint(0, 2, (10,)).float()}
+        total, breakdown = loss_fn(preds, targets)
+        assert "edge" in breakdown
+        assert "graph" not in breakdown
+        assert "joint_type" not in breakdown
+
+    def test_skips_missing_targets(self) -> None:
+        loss_fn = MultiTaskLoss()
+        preds = {
+            "edge_pred": torch.randn(10, 1),
+            "graph_pred": torch.randn(2, 4),
+        }
+        targets = {"y_edge": torch.randint(0, 2, (10,)).float()}
+        _, breakdown = loss_fn(preds, targets)
+        assert "edge" in breakdown
+        assert "graph" not in breakdown
+
+    def test_gradients_flow_to_log_vars(self) -> None:
+        loss_fn = MultiTaskLoss()
+        preds, targets = _make_predictions_and_targets()
+        # Make preds require grad.
+        for k in preds:
+            preds[k] = preds[k].requires_grad_(True)
+        total, _ = loss_fn(preds, targets)
+        total.backward()
+        for name, param in loss_fn.log_vars.items():
+            assert param.grad is not None, f"No gradient for log_var[{name}]"
+
+    def test_gradients_flow_to_predictions(self) -> None:
+        loss_fn = MultiTaskLoss()
+        preds, targets = _make_predictions_and_targets()
+        for k in preds:
+            preds[k] = preds[k].requires_grad_(True)
+        total, _ = loss_fn(preds, targets)
+        total.backward()
+        for k, v in preds.items():
+            assert v.grad is not None, f"No gradient for prediction[{k}]"
+
+    def test_redundant_penalty_applies(self) -> None:
+        """Redundant edges (label=0) should have higher loss contribution."""
+        loss_fn = MultiTaskLoss(redundant_penalty=5.0)
+        # All-zero predictions, label=0 (redundant).
+        preds_red = {"edge_pred": torch.zeros(10, 1)}
+        targets_red = {"y_edge": torch.zeros(10)}
+        total_red, _ = loss_fn(preds_red, targets_red)
+
+        loss_fn2 = MultiTaskLoss(redundant_penalty=1.0)
+        total_eq, _ = loss_fn2(preds_red, targets_red)
+
+        # Higher penalty should produce higher loss.
+        assert total_red.item() > total_eq.item()
+
+    def test_empty_predictions_returns_zero(self) -> None:
+        loss_fn = MultiTaskLoss()
+        total, breakdown = loss_fn({}, {})
+        assert total.item() == 0.0
+        assert len(breakdown) == 0
+
+
+class TestUncertaintyWeighting:
+    """Test uncertainty weighting mechanism specifically."""
+
+    def test_log_vars_initialized_to_zero(self) -> None:
+        loss_fn = MultiTaskLoss()
+        for param in loss_fn.log_vars.values():
+            assert param.item() == 0.0
+
+    def test_log_vars_are_learnable(self) -> None:
+        loss_fn = MultiTaskLoss()
+        params = list(loss_fn.parameters())
+        log_var_params = [p for p in params if p.shape == (1,)]
+        assert len(log_var_params) == 5  # one per task
+
+    def test_weighting_reduces_high_loss_influence(self) -> None:
+        """After a few gradient steps, log_var for a noisy task should increase."""
+        loss_fn = MultiTaskLoss(edge_weight=1.0, graph_weight=1.0)
+        optimizer = torch.optim.SGD(loss_fn.parameters(), lr=0.1)
+
+        # Simulate: edge task has high loss, graph has low.
+        for _ in range(20):
+            preds = {
+                "edge_pred": torch.randn(10, 1) * 10,  # high variance -> high loss
+                "graph_pred": torch.zeros(2, 4),  # near-zero loss
+            }
+            targets = {
+                "y_edge": torch.randint(0, 2, (10,)).float(),
+                "y_graph": torch.zeros(2, dtype=torch.long),
+            }
+            optimizer.zero_grad()
+            total, _ = loss_fn(preds, targets)
+            total.backward()
+            optimizer.step()
+
+        # The edge task log_var should have increased (higher uncertainty).
+        assert loss_fn.log_vars["edge"].item() > loss_fn.log_vars["graph"].item()