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"/root/projects/tdl_challenge_2026/TopoBench/logs/train/runs/notebook_gu_grid_2026-05-18_00-16-39__triangle_counting__11__h_hi__d_hi__pl_hi__s44" + } + ] +} diff --git a/2026_tdl_challenge/run_ablation_nsd_bundle.py b/2026_tdl_challenge/run_ablation_nsd_bundle.py new file mode 100644 index 00000000..08eb0237 --- /dev/null +++ b/2026_tdl_challenge/run_ablation_nsd_bundle.py @@ -0,0 +1,87 @@ +"""Run the full GraphUniverse challenge grid for upstream NSD-bundle. + +Apples-to-apples ablation against Conn-NSD: same harness, same grid, same +trainer budget, same hidden_dim — but with the *learned* bundle maps of +Bodnar et al. (NSDEncoder, sheaf_type="bundle") instead of the +deterministic Algorithm-1 maps of Conn-NSD. + +Hyperparameter overrides force NSD-bundle to use stalk dim ``d=4`` and +``dropout=0.0`` to match the Conn-NSD config; everything else is the +upstream default (``num_layers=2``, ``hidden_dim=64``, etc.). + +Output mirrors the conn_nsd_full layout:: + + 2026_tdl_challenge/outputs/nsd_bundle_full/ + results.json + heatmap_community_detection_accuracy.png + heatmap_triangle_mse_over_triangles.png + OOD/ + OOD_{low,mid,high}_homophily__{community_detection,triangle_counting}.png + +Run with:: + + cd 2026_tdl_challenge + WANDB_MODE=offline python run_ablation_nsd_bundle.py +""" + +from __future__ import annotations + +import sys +from pathlib import Path + +_HERE = Path(__file__).resolve().parent +_REPO = _HERE.parent +if str(_REPO) not in sys.path: + sys.path.insert(0, str(_REPO)) +if str(_HERE) not in sys.path: + sys.path.insert(0, str(_HERE)) + +from utils import ( # noqa: E402 — sys.path setup must precede this import + resolve_project_root, + run_challenge_grid, + save_challenge_artifacts, +) + +MODEL_CONFIG = "graph/nsd" +# Override NSD-bundle to match the Conn-NSD config (stalk_dim=4, dropout=0). +# Anything else left at upstream defaults — same num_layers, same hidden_dim. +EXTRA_OVERRIDES = [ + "model.backbone.d=4", + "model.backbone.dropout=0.0", + "model.backbone.sheaf_type=bundle", +] +OUTPUT_DIR_NAME = "nsd_bundle_full" + + +def main() -> None: + """Run the 72-cell grid for NSD-bundle and save artefacts.""" + project_root = resolve_project_root(_REPO) + print(f"Project root: {project_root}", flush=True) + print(f"Model: {MODEL_CONFIG}", flush=True) + print(f"Overrides: {EXTRA_OVERRIDES}", flush=True) + + results, study_id = run_challenge_grid( + project_root=project_root, + model_config=MODEL_CONFIG, + extra_overrides=EXTRA_OVERRIDES, + quiet=True, + ) + print( + f"\nGrid finished: {len(results)} runs; study_id={study_id}", + flush=True, + ) + + out_dir = _HERE / "outputs" / OUTPUT_DIR_NAME + out = save_challenge_artifacts( + results, + out_dir=out_dir, + model_config=MODEL_CONFIG, + study_id=study_id, + ) + print("Artefacts:") + for k, v in out.items(): + print(f" {k}: {v}", flush=True) + + +if __name__ == "__main__": + main() diff --git a/configs/model/graph/conn_nsd.yaml b/configs/model/graph/conn_nsd.yaml new file mode 100644 index 00000000..3c1b3863 --- /dev/null +++ b/configs/model/graph/conn_nsd.yaml @@ -0,0 +1,58 @@ +# Sheaf Neural Network with Connection Laplacians (Conn-NSD). +# +# Barbero et al., "Sheaf Neural Networks with Connection Laplacians," +# ICML 2022 TAG-ML Workshop, arXiv:2206.08702. +# +# The sheaf is constructed deterministically by Algorithm 1 of the paper: +# local PCA over each node's 1-hop neighbourhood gives an orthonormal +# tangent basis O_v; the restriction map F_{vu} = U V^T is the orthogonal +# Procrustes solution from the SVD of O_v^T O_u. There are no learnable +# sheaf parameters — only the diffusion weights W_1, W_2 (left/right) and +# the residual gates epsilon. + +_target_: topobench.model.TBModel + +model_name: conn_nsd +model_domain: graph + +feature_encoder: + _target_: topobench.nn.encoders.${model.feature_encoder.encoder_name} + encoder_name: AllCellFeatureEncoder + in_channels: ${infer_in_channels:${dataset},${oc.select:transforms,null}} + out_channels: 64 + proj_dropout: 0.0 + +backbone: + _target_: topobench.nn.backbones.ConnNSDEncoder + input_dim: ${model.feature_encoder.out_channels} + hidden_dim: ${model.feature_encoder.out_channels} # must be divisible by stalk_dim + num_layers: 2 # SWEEP candidate: [2, 4] + stalk_dim: 4 # SWEEP candidate: [2, 3, 4] + dropout: 0.0 # SWEEP candidate: [0.0, 0.25, 0.5] + input_dropout: 0.0 + connection_features: raw # features as seen by the backbone, after TopoBench feature encoding + +backbone_wrapper: + _target_: topobench.nn.wrappers.${model.backbone_wrapper.wrapper_name} + _partial_: true + wrapper_name: GNNWrapper + out_channels: ${model.feature_encoder.out_channels} + residual_connections: false + num_cell_dimensions: ${infer_num_cell_dimensions:${oc.select:model.feature_encoder.selected_dimensions,null},${model.feature_encoder.in_channels}} + +readout: + _target_: topobench.nn.readouts.${model.readout.readout_name} + readout_name: MLPReadout + num_cell_dimensions: ${infer_num_cell_dimensions:${oc.select:model.feature_encoder.selected_dimensions,null},${model.feature_encoder.in_channels}} + in_channels: ${model.feature_encoder.out_channels} + hidden_layers: [16] + out_channels: ${dataset.parameters.num_classes} + task_level: ${define_task_level:${dataset.parameters.task_level},${dataset.split_params.learning_setting}} + pooling_type: sum + dropout: 0.2 + act: "relu" + norm: null + final_act: null + +# compile model for faster training with pytorch 2.0 +compile: false diff --git a/test/nn/backbones/graph/test_conn_nsd.py b/test/nn/backbones/graph/test_conn_nsd.py new file mode 100644 index 00000000..571227a5 --- /dev/null +++ b/test/nn/backbones/graph/test_conn_nsd.py @@ -0,0 +1,594 @@ +"""Specification for the Conn-NSD connection construction. + +These tests are the spec. They encode the mathematical invariants of +Algorithm 1 in Barbero, Bodnar, Sáez de Ocáriz Borde, Bronstein, +Veličković, Liò ("Sheaf Neural Networks with Connection Laplacians", +ICML 2022 TAG-ML Workshop, arXiv:2206.08702): + + 1. orthogonality of every restriction map + 2. inverse transport on antiparallel edges + 3. permutation equivariance of the connection + 4. SE(p) invariance of the connection (rotation/translation of features) + 5. the |N(v)| < d fallback rule produces a valid orthonormal basis + 6. no gradients leak into the connection (it is pre-processing) + 7. hand-computed triangle: every entry is verified by direct calculation + +The triangle test is deliberately first and deliberately verbose — it is +the touchstone that anyone reading this file can re-derive on paper. +""" + +from __future__ import annotations + +import math + +import pytest +import torch +from torch import Tensor + +from topobench.nn.backbones.graph.conn_nsd import ConnNSDEncoder +from topobench.nn.backbones.graph.conn_nsd_utils.connection import ( + build_connection, + local_tangent_basis, +) + +# --------------------------------------------------------------------------- +# Helpers +# --------------------------------------------------------------------------- + + +def _is_orthogonal(matrix: Tensor, atol: float = 1e-5) -> bool: + """Return True iff `matrix` is square and matrix.T @ matrix ≈ I. + + Parameters + ---------- + matrix : torch.Tensor + Candidate matrix; need not be square. + atol : float, default 1e-5 + Absolute tolerance for the equality check. + + Returns + ------- + bool + Whether the matrix is orthogonal within ``atol``. + """ + if matrix.dim() < 2 or matrix.size(-1) != matrix.size(-2): + return False + d = matrix.size(-1) + identity = torch.eye(d, dtype=matrix.dtype, device=matrix.device) + return torch.allclose( + matrix.transpose(-1, -2) @ matrix, identity.expand_as(matrix), atol=atol + ) + + +def _is_column_orthonormal(matrix: Tensor, atol: float = 1e-5) -> bool: + """Return True iff matrix.T @ matrix ≈ I_d for matrix of shape [..., p, d]. + + Parameters + ---------- + matrix : torch.Tensor, shape ``[..., p, d]`` + Candidate basis matrix; only the trailing two dims matter. + atol : float, default 1e-5 + Absolute tolerance for the equality check. + + Returns + ------- + bool + Whether columns are orthonormal within ``atol``. + """ + d = matrix.size(-1) + identity = torch.eye(d, dtype=matrix.dtype, device=matrix.device) + gram = matrix.transpose(-1, -2) @ matrix + return torch.allclose(gram, identity.expand_as(gram), atol=atol) + + +# --------------------------------------------------------------------------- +# Tiny synthetic example: 3-node triangle in ℝ² with d = 2. +# +# Vertices are placed at the corners of an equilateral triangle: +# +# x_0 = (0, 0) +# x_1 = (1, 0) +# x_2 = (1/2, √3/2) +# +# Edges: (0,1), (1,2), (2,0), each in both directions. +# +# At every node v, the 1-hop neighbourhood has exactly 2 elements (the +# other two corners), so the centred matrix X̂_v is 2×2 and the SVD of +# the centred neighbours fully determines the tangent basis. With p = d +# the manifold assumption is *saturated*: the tangent space at every +# node is all of ℝ², and the basis is a rotation of the standard frame. +# +# Crucial sanity check: for any choice of bases the alignment +# F_{vu} ∈ O(2) is well-defined and we can verify orthogonality and +# invertibility by hand. +# --------------------------------------------------------------------------- + + +@pytest.fixture +def triangle(): + """Equilateral triangle in ℝ², stalk dim 2, bidirectional edges. + + Returns + ------- + tuple[torch.Tensor, torch.Tensor] + ``(node_features, edge_index)`` for the equilateral triangle. + """ + node_features = torch.tensor( + [ + [0.0, 0.0], + [1.0, 0.0], + [0.5, math.sqrt(3) / 2.0], + ], + dtype=torch.float64, + ) + edge_index = torch.tensor( + [ + [0, 1, 1, 2, 2, 0], + [1, 0, 2, 1, 0, 2], + ], + dtype=torch.long, + ) + return node_features, edge_index + + +class TestTriangle: + """Hand-computable Conn-NSD on a 3-node triangle.""" + + def test_tangent_basis_shape_and_orthonormality(self, triangle): + """Every O_v is a 2×2 orthonormal frame in the saturated p=d case. + + Parameters + ---------- + triangle : tuple[torch.Tensor, torch.Tensor] + Test fixture supplying ``(node_features, edge_index)``. + """ + node_features, edge_index = triangle + tangent_basis = local_tangent_basis( + node_features, edge_index, stalk_dim=2 + ) + + # Shape contract: [N, p, d] = [3, 2, 2]. + assert tangent_basis.shape == (3, 2, 2) + # Columns are orthonormal. + assert _is_column_orthonormal(tangent_basis) + # In the saturated p=d case the bases span all of ℝ² → they are + # full orthogonal matrices, so rows are orthonormal too. + for v in range(3): + assert _is_orthogonal(tangent_basis[v]) + + def test_restriction_maps_are_orthogonal(self, triangle): + """F[e] ∈ O(d) for every edge e — Algorithm 1 invariant (i). + + Parameters + ---------- + triangle : tuple[torch.Tensor, torch.Tensor] + Test fixture supplying ``(node_features, edge_index)``. + """ + node_features, edge_index = triangle + maps = build_connection(node_features, edge_index, stalk_dim=2) + assert maps.shape == (edge_index.size(1), 2, 2) + for e in range(edge_index.size(1)): + assert _is_orthogonal(maps[e]), ( + f"edge {e} = {edge_index[:, e].tolist()} produced a " + f"non-orthogonal map:\n{maps[e]}" + ) + + def test_antiparallel_edges_invert(self, triangle): + """F_{v→u} @ F_{u→v} ≈ I — parallel transport is invertible. + + Algorithm 1 produces F_{v→u} = U V^T from O_v^T O_u = U Σ V^T; + swapping (v,u) gives O_u^T O_v = (O_v^T O_u)^T = V Σ U^T, hence + F_{u→v} = V U^T = (F_{v→u})^T. Therefore F_{v→u} @ F_{u→v} = I. + + Parameters + ---------- + triangle : tuple[torch.Tensor, torch.Tensor] + Test fixture supplying ``(node_features, edge_index)``. + """ + node_features, edge_index = triangle + maps = build_connection(node_features, edge_index, stalk_dim=2) + + # Edge layout matches the fixture: + # 0: (0,1) 1: (1,0) + # 2: (1,2) 3: (2,1) + # 4: (2,0) 5: (0,2) + pairs = [(0, 1), (2, 3), (4, 5)] + identity = torch.eye(2, dtype=maps.dtype) + for forward, backward in pairs: + assert torch.allclose( + maps[forward] @ maps[backward], identity, atol=1e-10 + ), ( + f"edges {edge_index[:, forward].tolist()} and " + f"{edge_index[:, backward].tolist()} are not mutual inverses" + ) + + def test_no_gradient_into_features(self, triangle): + """Algorithm 1 is pre-processing: gradients must not flow in. + + Parameters + ---------- + triangle : tuple[torch.Tensor, torch.Tensor] + Test fixture supplying ``(node_features, edge_index)``. + """ + node_features, edge_index = triangle + node_features = node_features.clone().requires_grad_(True) + maps = build_connection(node_features, edge_index, stalk_dim=2) + # If a gradient *did* flow in, .grad_fn would not be None. + assert not maps.requires_grad, ( + "restriction maps must be detached — they encode a pre-computed " + "deterministic sheaf, not a learnable transformation." + ) + + +# --------------------------------------------------------------------------- +# Algebraic invariants on a randomly generated 5-node graph. +# --------------------------------------------------------------------------- + + +def _dense_sheaf_laplacian( + restriction_maps: Tensor, + edge_index: Tensor, + num_nodes: int, + stalk_dim: int, +) -> Tensor: + """Assemble the un-normalised sheaf Laplacian ``L_F = δ^⊤ δ`` densely. + + For an orthogonal sheaf this is the block matrix: + + L[v, v] = deg(v) · I_d + L[v, u] = − F_{vu}^⊤ F_{uv} (for v ≠ u, when edge (v,u) ∈ E) + + Used only in tests, where transparency beats efficiency. + + Parameters + ---------- + restriction_maps : torch.Tensor, shape ``[E, d, d]`` + Orthogonal restriction maps, one per directed edge. + edge_index : torch.Tensor, shape ``[2, E]`` + Edge index in PyG convention (directed, bidirectional pairs). + num_nodes : int + Number of nodes in the graph. + stalk_dim : int + Dimension ``d`` of each stalk. + + Returns + ------- + torch.Tensor, shape ``[N·d, N·d]`` + Dense sheaf Laplacian, symmetric and positive semi-definite. + """ + d = stalk_dim + dim = num_nodes * d + laplacian = torch.zeros(dim, dim, dtype=restriction_maps.dtype) + + directed = { + (int(edge_index[0, e]), int(edge_index[1, e])): e + for e in range(edge_index.size(1)) + } + + # Diagonal: deg(v) · I_d, where deg counts directed out-edges from v. + degrees = torch.zeros(num_nodes, dtype=torch.long) + for v in edge_index[0].tolist(): + degrees[v] += 1 + for v in range(num_nodes): + rng = slice(v * d, (v + 1) * d) + laplacian[rng, rng] = degrees[v].to(laplacian.dtype) * torch.eye( + d, dtype=laplacian.dtype + ) + + # Off-diagonal blocks for every unordered edge with both directions present. + seen: set[frozenset[int]] = set() + for (v, u), e_fwd in directed.items(): + if v == u or frozenset({v, u}) in seen: + continue + e_bwd = directed.get((u, v)) + if e_bwd is None: + continue + block = -(restriction_maps[e_fwd].T @ restriction_maps[e_bwd]) + rv = slice(v * d, (v + 1) * d) + ru = slice(u * d, (u + 1) * d) + laplacian[rv, ru] = block + laplacian[ru, rv] = block.T + seen.add(frozenset({v, u})) + + return laplacian + + +@pytest.fixture +def small_random_graph(): + """Connected 5-node graph in ℝ⁸ with bidirectional edges. + + Sized so that p > d and every node has at least d neighbours, hence + the fallback path is *not* triggered. Tested separately below. + + Returns + ------- + tuple[torch.Tensor, torch.Tensor] + ``(node_features, edge_index)`` for the pentagon-with-chords graph. + """ + torch.manual_seed(0) + node_features = torch.randn(5, 8, dtype=torch.float64) + # A pentagon-with-chords graph; every node has degree ≥ 3. + edges = [ + (0, 1), (1, 2), (2, 3), (3, 4), (4, 0), + (0, 2), (1, 3), + ] + src = [u for (u, _) in edges] + [v for (_, v) in edges] + dst = [v for (_, v) in edges] + [u for (u, _) in edges] + edge_index = torch.tensor([src, dst], dtype=torch.long) + return node_features, edge_index + + +class TestAlgebraicInvariants: + """Mathematical contracts the connection must obey on any graph.""" + + @pytest.mark.parametrize("stalk_dim", [2, 3]) + def test_orthogonality_invariant(self, small_random_graph, stalk_dim): + """F[e]^T F[e] = I_d for every edge — across stalk dimensions. + + Parameters + ---------- + small_random_graph : tuple[torch.Tensor, torch.Tensor] + Test fixture supplying ``(node_features, edge_index)``. + stalk_dim : int + Parametrised stalk dimension. + """ + node_features, edge_index = small_random_graph + maps = build_connection(node_features, edge_index, stalk_dim=stalk_dim) + assert maps.shape == (edge_index.size(1), stalk_dim, stalk_dim) + for e in range(maps.size(0)): + assert _is_orthogonal(maps[e], atol=1e-8) + + def test_inverse_transport_invariant(self, small_random_graph): + """F_{u→v} F_{v→u} = I — verified across all antiparallel pairs. + + Parameters + ---------- + small_random_graph : tuple[torch.Tensor, torch.Tensor] + Test fixture supplying ``(node_features, edge_index)``. + """ + node_features, edge_index = small_random_graph + maps = build_connection(node_features, edge_index, stalk_dim=3) + + # Build a lookup from (src, dst) tuple to row index. + directed_to_row = { + (int(edge_index[0, e]), int(edge_index[1, e])): e + for e in range(edge_index.size(1)) + } + identity = torch.eye(3, dtype=maps.dtype) + for (src, dst), e_fwd in directed_to_row.items(): + e_bwd = directed_to_row.get((dst, src)) + if e_bwd is None: + continue + assert torch.allclose( + maps[e_fwd] @ maps[e_bwd], identity, atol=1e-8 + ), f"edges ({src}->{dst}) and ({dst}->{src}) are not inverses" + + def test_permutation_invariance_of_laplacian_spectrum(self, small_random_graph): + """The sheaf-Laplacian spectrum is invariant under node relabelling. + + Subtlety + -------- + ``torch.linalg.svd`` does not fix the sign convention on the + left singular vectors. Two PCA basis matrices spanning the same + subspace can differ by a per-node signed diagonal ``S_v``, so the + alignment matrices ``F_{vu}`` acquire gauges ``S_v F_{vu} S_u``. + Generically this gauge does **not** compose into a single + block-diagonal conjugation of the sheaf Laplacian, so the + spectrum can shift slightly. We therefore test for *near-equality* + with a loose tolerance, not exact invariance. + + The Conn-NSD paper inherits this same gauge issue from the + underlying SVD-based vector-diffusion-maps construction + (Singer & Wu 2012). Removing it would require canonicalising the + SVD signs at every node — out of scope for a faithful + re-implementation of Algorithm 1. + + Parameters + ---------- + small_random_graph : tuple[torch.Tensor, torch.Tensor] + Test fixture supplying ``(node_features, edge_index)``. + """ + node_features, edge_index = small_random_graph + n = node_features.size(0) + d = 3 + + permutation = torch.tensor([2, 0, 4, 1, 3], dtype=torch.long) + inv = torch.empty_like(permutation) + inv[permutation] = torch.arange(n) + permuted_features = node_features[permutation] + permuted_edges = inv[edge_index] + + maps_orig = build_connection(node_features, edge_index, stalk_dim=d) + maps_perm = build_connection(permuted_features, permuted_edges, stalk_dim=d) + + l_orig = _dense_sheaf_laplacian(maps_orig, edge_index, n, d) + l_perm = _dense_sheaf_laplacian(maps_perm, permuted_edges, n, d) + + eig_orig = torch.linalg.eigvalsh(l_orig).sort().values + eig_perm = torch.linalg.eigvalsh(l_perm).sort().values + # Loose tolerance accommodates the SVD sign gauge (see docstring). + # In practice the spectrum shifts by ≤ a few percent of its scale. + assert torch.allclose(eig_orig, eig_perm, atol=0.5), ( + "Sheaf-Laplacian spectrum changed substantially under node " + "relabelling — beyond the expected SVD sign-gauge perturbation." + ) + + def test_determinism(self, small_random_graph): + """Algorithm 1 is deterministic: same input → same output. + + Two calls on identical tensors must produce bit-identical maps. + This is the strongest form of reproducibility available given the + SVD sign gauge, and is what the diffusion actually needs at + training time. + + Parameters + ---------- + small_random_graph : tuple[torch.Tensor, torch.Tensor] + Test fixture supplying ``(node_features, edge_index)``. + """ + node_features, edge_index = small_random_graph + maps_a = build_connection(node_features, edge_index, stalk_dim=3) + maps_b = build_connection(node_features, edge_index, stalk_dim=3) + assert torch.equal(maps_a, maps_b), ( + "build_connection is not deterministic on identical inputs — " + "the diffusion would see a different operator each forward pass." + ) + + +# --------------------------------------------------------------------------- +# The fallback rule: |N(v)| < d. +# --------------------------------------------------------------------------- + + +class TestFallback: + """When a node has fewer than d neighbours, top up with k-NN.""" + + def test_isolated_node_in_3d(self): + """Even an isolated node receives a valid 3-D tangent basis. + + Construction: 4 nodes in ℝ⁴, node 3 is isolated. With stalk_dim=3 + node 3's neighbour count is 0 < d = 3, so the fallback kicks in + and uses the three Euclidean-nearest non-self nodes — which is + all of them. The basis must still be orthonormal. + """ + torch.manual_seed(42) + node_features = torch.randn(4, 4, dtype=torch.float64) + # Make node 3 distant so the topology of the fallback is obvious. + node_features[3] = torch.tensor( + [10.0, 10.0, 10.0, 10.0], dtype=torch.float64 + ) + edge_index = torch.tensor( + [[0, 1, 2, 1, 2, 0], [1, 2, 0, 0, 1, 2]], dtype=torch.long + ) # nodes 0,1,2 form a triangle; node 3 isolated. + + tangent_basis = local_tangent_basis( + node_features, edge_index, stalk_dim=3 + ) + assert tangent_basis.shape == (4, 4, 3) + # Every basis is column-orthonormal, including the fallback one. + for v in range(4): + assert _is_column_orthonormal( + tangent_basis[v : v + 1], atol=1e-10 + ), f"basis at node {v} is not column-orthonormal" + + def test_partial_neighbourhood_topup(self): + """A node with one neighbour and stalk_dim=3 needs two top-up nodes.""" + torch.manual_seed(7) + node_features = torch.randn(5, 6, dtype=torch.float64) + # Node 0 has just one neighbour (node 1); needs 2 more for d=3. + edge_index = torch.tensor( + [[0, 1, 1, 2, 2, 3, 3, 4, 4, 1], [1, 0, 2, 1, 3, 2, 4, 3, 1, 4]], + dtype=torch.long, + ) + maps = build_connection(node_features, edge_index, stalk_dim=3) + for e in range(maps.size(0)): + assert _is_orthogonal(maps[e], atol=1e-8) + + def test_fallback_respects_batch_boundaries(self): + """Fallback nearest neighbours must not cross PyG graph boundaries.""" + torch.manual_seed(0) + node_features = torch.randn(5, 5) + node_features[2:] = node_features[2:] + 50.0 + edge_index = torch.tensor( + [[0, 1, 1, 0, 2, 3, 3, 2], [1, 0, 0, 1, 3, 2, 2, 3]], + dtype=torch.long, + ) + second_graph_features = node_features + 0.01 + batched_features = torch.cat([node_features, second_graph_features], dim=0) + batched_edges = torch.cat([edge_index, edge_index + 5], dim=1) + batch = torch.tensor([0, 0, 0, 0, 0, 1, 1, 1, 1, 1], dtype=torch.long) + + single = build_connection(node_features, edge_index, stalk_dim=4) + batched = build_connection( + batched_features, + batched_edges, + stalk_dim=4, + batch=batch, + ) + + assert torch.allclose(single, batched[: edge_index.size(1)], atol=1e-6) + + @pytest.mark.parametrize("num_nodes,stalk_dim", [(3, 3), (3, 4)]) + def test_too_small_graph_raises_clear_error(self, num_nodes, stalk_dim): + """A graph must have at least d + 1 nodes for the fallback rule. + + Parameters + ---------- + num_nodes : int + Number of nodes in the test graph. + stalk_dim : int + Tangent-space dimension requested from the fallback rule. + """ + node_features = torch.randn(num_nodes, 5) + edge_index = torch.tensor([[0, 1], [1, 0]], dtype=torch.long) + with pytest.raises(ValueError, match="graph too small"): + local_tangent_basis(node_features, edge_index, stalk_dim=stalk_dim) + + +class TestBatching: + """Conn-NSD must be invariant to PyG mini-batch grouping.""" + + def test_encoder_matches_unbatched_outputs_with_low_degree_fallback(self): + """The same graph alone or inside a batch receives the same output.""" + torch.manual_seed(0) + model = ConnNSDEncoder( + input_dim=5, + hidden_dim=8, + stalk_dim=4, + num_layers=1, + dropout=0.0, + input_dropout=0.0, + ).eval() + + node_features = torch.randn(5, 5) + node_features[2:] = node_features[2:] + 50.0 + edge_index = torch.tensor( + [[0, 1, 1, 0, 2, 3, 3, 2], [1, 0, 0, 1, 3, 2, 2, 3]], + dtype=torch.long, + ) + second_graph_features = node_features + 0.01 + batched_features = torch.cat([node_features, second_graph_features], dim=0) + batched_edges = torch.cat([edge_index, edge_index + 5], dim=1) + batch = torch.tensor([0, 0, 0, 0, 0, 1, 1, 1, 1, 1], dtype=torch.long) + + with torch.no_grad(): + single = model( + node_features, + edge_index, + batch=torch.zeros(5, dtype=torch.long), + ) + batched = model(batched_features, batched_edges, batch=batch)[:5] + + assert torch.allclose(single, batched, atol=1e-6) + + +# --------------------------------------------------------------------------- +# API-level shape / dtype contracts. +# --------------------------------------------------------------------------- + + +class TestApiContract: + """Type and dtype contracts at the module boundary.""" + + def test_float32_inputs_produce_float32_outputs(self): + """No silent dtype upcasting — surprises matter at scale.""" + node_features = torch.randn(6, 7, dtype=torch.float32) + edge_index = torch.tensor( + [[0, 1, 2, 3, 4, 5, 0], [1, 2, 3, 4, 5, 0, 2]], dtype=torch.long + ) + maps = build_connection(node_features, edge_index, stalk_dim=2) + assert maps.dtype == torch.float32 + + def test_rejects_3d_node_features(self): + """Reject ``node_features`` of shape ``[B, N, p]``.""" + bad = torch.randn(2, 5, 7) + edge_index = torch.tensor([[0, 1], [1, 0]], dtype=torch.long) + with pytest.raises(AssertionError, match="node_features must be"): + local_tangent_basis(bad, edge_index, stalk_dim=2) + + def test_rejects_negative_stalk_dim(self): + """Reject ``stalk_dim`` ≤ 0.""" + node_features = torch.randn(3, 5) + edge_index = torch.tensor([[0, 1], [1, 0]], dtype=torch.long) + with pytest.raises(AssertionError, match="stalk_dim must be positive"): + local_tangent_basis(node_features, edge_index, stalk_dim=0) diff --git a/test/pipeline/test_pipeline.py b/test/pipeline/test_pipeline.py index d41ebb9c..b12c0d31 100644 --- a/test/pipeline/test_pipeline.py +++ b/test/pipeline/test_pipeline.py @@ -1,11 +1,11 @@ """Test pipeline for a particular dataset and model.""" import hydra -from test._utils.simplified_pipeline import run +from test._utils.simplified_pipeline import run -DATASET = "graph/MUTAG" # ADD YOUR DATASET HERE -MODELS = ["graph/gcn", "cell/topotune", "simplicial/topotune"] # ADD ONE OR SEVERAL MODELS OF YOUR CHOICE HERE +DATASET = "graph/MUTAG" # ADD YOUR DATASET HERE +MODELS = ["graph/conn_nsd"] # ADD ONE OR SEVERAL MODELS OF YOUR CHOICE HERE class TestPipeline: diff --git a/topobench/nn/backbones/graph/conn_nsd.py b/topobench/nn/backbones/graph/conn_nsd.py new file mode 100644 index 00000000..47129c20 --- /dev/null +++ b/topobench/nn/backbones/graph/conn_nsd.py @@ -0,0 +1,288 @@ +"""Sheaf Neural Network with Connection Laplacians (Conn-NSD). + +Backbone implementing Barbero, Bodnar, Sáez de Ocáriz Borde, Bronstein, +Veličković, Liò. "Sheaf Neural Networks with Connection Laplacians." +ICML 2022 TAG-ML Workshop. arXiv:2206.08702. + +Notes +----- +**Scientific delta vs. Bodnar et al.'s NSD-O(d).** +NSD-O(d) learns the orthogonal restriction maps ``F_{vu}`` jointly with +the diffusion weights, recomputing them every layer from +``Φ(x_v, x_u)``. Conn-NSD instead *computes them once* at the start of +the forward pass — deterministically — from a local-PCA-plus-alignment +procedure on the raw node features (see :mod:`conn_nsd_utils.connection`, +Algorithm 1 of the paper). The diffusion equation (paper §2.3, Eq. 5) +is otherwise identical:: + + X_{t+1} = X_t − σ( Δ_F (I_n ⊗ W₁) X_t W₂ ) + +This removes one network of learnable parameters (the sheaf-learner MLPs +of NSD-O(d)) and one backward pass through an SVD/Cayley parametrisation +per layer. Empirically it acts as a regulariser on heterophilic +node-classification tasks (paper Table 1) and yields a noticeable +wall-clock speedup (paper Table 2). + +**Architectural notes.** +The class deliberately mirrors :class:`NSDEncoder` so a reader switching +between Bodnar's and Barbero's models is comparing exactly the parts +that differ: the construction of ``restriction_maps`` and the absence +of ``sheaf_learners``. We reuse the linear-channel left/right +transformations ``W₁``, ``W₂`` and the diffusion residual structure +``x_0 ← (1 + tanh(ε)) x_0 − x`` verbatim from the Bodnar code path; +both are part of the *diffusion* layer, not the *sheaf*. + +References +---------- +.. [1] F. Barbero, C. Bodnar, H. Sáez de Ocáriz Borde, M. Bronstein, + P. Veličković, P. Liò. "Sheaf Neural Networks with Connection + Laplacians." ICML 2022 TAG-ML Workshop. arXiv:2206.08702. +.. [2] C. Bodnar et al. "Neural Sheaf Diffusion." ICLR 2022 Workshop. + arXiv:2202.04579. +""" + +from __future__ import annotations + +import torch +import torch.nn.functional as F +import torch_sparse +from torch import Tensor, nn +from torch_geometric.utils import to_undirected + +from topobench.nn.backbones.graph.conn_nsd_utils import build_connection +from topobench.nn.backbones.graph.conn_nsd_utils.fixed_laplacian_builder import ( + FixedConnectionLaplacianBuilder, +) + + +class ConnNSDEncoder(nn.Module): + """Inductive Conn-NSD encoder for graph-level and node-level tasks. + + Parameters + ---------- + input_dim : int + Dimension of input node features. + hidden_dim : int + Dimension of the hidden state per node, *across* all stalk + components. Must be divisible by ``stalk_dim``. + num_layers : int, default 2 + Number of sheaf-diffusion layers ``T`` in paper Eq. 5. + stalk_dim : int, default 3 + Stalk dimension ``d`` (paper §3.2). Setting ``d = 1`` recovers a + classical normalised-Laplacian GCN; the model is only meaningful + for ``d ≥ 2``. + dropout : float, default 0.0 + Dropout on the diffusion state between layers. + input_dropout : float, default 0.0 + Dropout on the initial feature lift. + connection_features : str, default ``"raw"`` + Which features to feed Algorithm 1. + - ``"raw"``: features as received by this backbone, before ``lin1``. + In the standard TopoBench composition this is post-feature-encoder + data, because ``AllCellFeatureEncoder`` runs before every backbone. + - ``"lifted"``: the post-``lin1`` encoded features. Off-spec — kept + as an ablation knob but not the default behaviour. + **kwargs : dict + Ignored. Present so the encoder can be safely instantiated via + Hydra configs that pass extra wrapper-level keys. + + Attributes + ---------- + lin1, lin2 : nn.Linear + Input lift to ``hidden_dim`` and output projection. + lin_left_weights, lin_right_weights : nn.ModuleList + Per-layer ``W₁`` (acts on stalk dimension) and ``W₂`` (acts on + hidden channels) of paper Eq. 5. + epsilons : nn.ParameterList + Per-layer residual gates initialised to zero (so the first + training step recovers a pure diffusion step). + """ + + def __init__( + self, + input_dim: int, + hidden_dim: int, + num_layers: int = 2, + stalk_dim: int = 3, + dropout: float = 0.0, + input_dropout: float = 0.0, + connection_features: str = "raw", + **kwargs, + ): + super().__init__() + assert stalk_dim >= 2, ( + "Conn-NSD is only meaningful for stalk_dim ≥ 2 (d=1 collapses " + f"to a normalised GCN). Got stalk_dim={stalk_dim}." + ) + assert hidden_dim % stalk_dim == 0, ( + f"hidden_dim ({hidden_dim}) must be divisible by stalk_dim " + f"({stalk_dim}) so each stalk component has equal channel width." + ) + assert connection_features in {"raw", "lifted"}, ( + f"connection_features must be 'raw' or 'lifted', " + f"got {connection_features!r}" + ) + + self.input_dim = input_dim + self.hidden_dim = hidden_dim + self.num_layers = num_layers + self.stalk_dim = stalk_dim + self.channels_per_stalk = hidden_dim // stalk_dim + self.dropout = dropout + self.input_dropout = input_dropout + self.connection_features = connection_features + + # Input lift / output projection. + self.lin1 = nn.Linear(input_dim, hidden_dim) + self.lin2 = nn.Linear(hidden_dim, hidden_dim) + + # Per-layer diffusion weights. W₁ ∈ ℝ^{d × d}, W₂ ∈ ℝ^{c × c}. + self.lin_left_weights = nn.ModuleList() + self.lin_right_weights = nn.ModuleList() + for _ in range(num_layers): + left = nn.Linear(stalk_dim, stalk_dim, bias=False) + nn.init.eye_(left.weight.data) + self.lin_left_weights.append(left) + right = nn.Linear( + self.channels_per_stalk, self.channels_per_stalk, bias=False + ) + nn.init.orthogonal_(right.weight.data) + self.lin_right_weights.append(right) + + # Residual gate ε per layer; tanh(0) = 0 so the initial step is a + # pure diffusion step. + self.epsilons = nn.ParameterList( + nn.Parameter(torch.zeros((stalk_dim, 1))) + for _ in range(num_layers) + ) + + # ------------------------------------------------------------------ + # Forward — Algorithm 1 (pre-process) ∘ paper Eq. 5 (diffusion). + # ------------------------------------------------------------------ + + def forward( + self, + x: Tensor, + edge_index: Tensor, + edge_attr: Tensor | None = None, + edge_weight: Tensor | None = None, + batch: Tensor | None = None, + **kwargs, + ) -> Tensor: + """Run Conn-NSD on a single graph (or a PyG-batched union of graphs). + + Parameters + ---------- + x : torch.Tensor, shape ``[N, input_dim]`` + Node features. + edge_index : torch.Tensor, shape ``[2, E]`` + Edge indices. Made bidirectional internally; the diffusion + requires a symmetric sheaf Laplacian. + edge_attr, edge_weight : ignored + Conn-NSD operates on node features only, by construction. + batch : torch.Tensor, optional + PyG batch vector. Used to keep the local-PCA fallback inside each + graph of a mini-batch. + **kwargs : dict + Ignored. Present for forward-call compatibility with the + generic ``GNNWrapper`` signature. + + Returns + ------- + torch.Tensor, shape ``[N, hidden_dim]`` + Node embeddings after ``num_layers`` diffusion steps. + """ + num_nodes = x.size(0) + edge_index = to_undirected(edge_index, num_nodes=num_nodes) + + # ---- Step 1. Build the deterministic connection (Algorithm 1). ---- + # Detached by construction; see conn_nsd_utils.connection. + if self.connection_features == "raw": + features_for_connection = x + else: # "lifted" + features_for_connection = self.lin1(x).detach() + restriction_maps = build_connection( + features_for_connection, + edge_index, + stalk_dim=self.stalk_dim, + batch=batch, + ) # [E, d, d] + + # ---- Step 2. Assemble the normalised Δ_F once. ------------------- + laplacian_builder = FixedConnectionLaplacianBuilder( + num_nodes, edge_index, d=self.stalk_dim + ) + sparse_laplacian, _ = laplacian_builder(restriction_maps) + l_indices, l_values = sparse_laplacian + + # ---- Step 3. Sheaf diffusion (paper Eq. 5). ---------------------- + h = F.dropout(x, p=self.input_dropout, training=self.training) + h = F.elu(self.lin1(h)) + h = F.dropout(h, p=self.dropout, training=self.training) + # Reshape to [N · d, c]: per node, d stalk vectors of width c. + h = h.view(num_nodes * self.stalk_dim, self.channels_per_stalk) + + residual = h + for layer_idx in range(self.num_layers): + h = F.dropout(h, p=self.dropout, training=self.training) + h = self._left_right_linear( + h, + self.lin_left_weights[layer_idx], + self.lin_right_weights[layer_idx], + num_nodes, + ) + # Sparse mat-vec with the (fixed) normalised sheaf Laplacian. + h = torch_sparse.spmm(l_indices, l_values, h.size(0), h.size(0), h) + h = F.elu(h) + + # Residual gate, same form as Bodnar's bundle diffusion: + # x0 ← (1 + tanh(ε)) ⊙ x0 − x + gate = 1.0 + torch.tanh(self.epsilons[layer_idx]).tile( + num_nodes, 1 + ) + residual = gate * residual - h + h = residual + + h = h.reshape(num_nodes, self.hidden_dim) + return self.lin2(h) + + # ------------------------------------------------------------------ + # Internals + # ------------------------------------------------------------------ + + def _left_right_linear( + self, + h: Tensor, + left: nn.Linear, + right: nn.Linear, + num_nodes: int, + ) -> Tensor: + """Apply ``W₁`` along the stalk dim and ``W₂`` along the channel dim. + + Equivalent to ``(I_n ⊗ W₁) X W₂`` from paper Eq. 5, written as two + matmuls on the ``[N · d, c]`` reshape. We follow the data layout + used by the Bodnar bundle diffusion to keep the diffusion contract + identical. + + Parameters + ---------- + h : torch.Tensor, shape ``[N * d, c]`` + Stacked-stalk hidden state. + left : nn.Linear + ``W₁`` — acts on the stalk dimension ``d``. + right : nn.Linear + ``W₂`` — acts on the channel dimension ``c``. + num_nodes : int + Number of nodes ``N`` in the current graph. + + Returns + ------- + torch.Tensor, shape ``[N * d, c]`` + Transformed hidden state. + """ + # Stalk-mixing: reshape so each row is a stalk vector of width d. + h = h.t().reshape(-1, self.stalk_dim) + h = left(h) + h = h.reshape(-1, num_nodes * self.stalk_dim).t() + # Channel-mixing. + return right(h) diff --git a/topobench/nn/backbones/graph/conn_nsd_utils/__init__.py b/topobench/nn/backbones/graph/conn_nsd_utils/__init__.py new file mode 100644 index 00000000..3ae86653 --- /dev/null +++ b/topobench/nn/backbones/graph/conn_nsd_utils/__init__.py @@ -0,0 +1,25 @@ +"""Connection-Laplacian sheaf utilities. + +This sub-package implements the *deterministic* construction of orthogonal +restriction maps for a Sheaf Neural Network, following Algorithm 1 of: + + Barbero, Bodnar, Sáez de Ocáriz Borde, Bronstein, Veličković, Liò. + "Sheaf Neural Networks with Connection Laplacians." + ICML 2022 TAG-ML Workshop. arXiv:2206.08702. + +The construction is purely a function of the node features and the edge set: +no gradients flow through it. It mirrors Singer & Wu's vector diffusion maps +(2012) adapted to a graph rather than a point cloud. +""" + +from topobench.nn.backbones.graph.conn_nsd_utils.connection import ( + build_connection, + local_tangent_basis, + optimal_alignment, +) + +__all__ = [ + "build_connection", + "local_tangent_basis", + "optimal_alignment", +] diff --git a/topobench/nn/backbones/graph/conn_nsd_utils/connection.py b/topobench/nn/backbones/graph/conn_nsd_utils/connection.py new file mode 100644 index 00000000..7835b8e6 --- /dev/null +++ b/topobench/nn/backbones/graph/conn_nsd_utils/connection.py @@ -0,0 +1,328 @@ +"""Deterministic connection on a graph via local PCA + optimal alignment. + +This module implements Algorithm 1 of Barbero et al. (2022) — the scientific +heart of Conn-NSD. The Bodnar et al. (2022) NSD diffusion machinery in the +sibling ``nsd_utils`` package is reused unchanged; only the construction of +the orthogonal restriction maps changes. + +Notes +----- +**Mathematical setting.** +Assume node features ``X ∈ ℝ^{N×p}`` are sampled from a ``d``-dimensional +Riemannian manifold ``M`` embedded in ``ℝ^p``, with ``d ≪ p``. At every +node ``v`` we approximate the tangent space ``T_{x_v} M`` by local PCA +over its 1-hop neighbourhood (Singer & Wu, 2012, §3.1; Barbero et al., +2022, §3.2). The resulting orthonormal basis is a column-orthonormal +matrix ``O_v ∈ ℝ^{p×d}``. + +For each directed edge ``v → u`` we then build the orthogonal map +``F_{vu} = U V^⊤`` from the SVD ``O_v^⊤ O_u = U Σ V^⊤``. This is the +optimal alignment in Frobenius norm between the two tangent bases and is, +when ``v`` and ``u`` are nearby on ``M``, an approximation to the parallel +transport ``T_{x_v} M → T_{x_u} M``. + +In the language of cellular sheaves (Hansen & Ghrist, 2019), ``F_{vu}`` is +the restriction map from the node stalk ``ℝ^d`` at ``v`` to the edge stalk +at the unoriented edge ``{v,u}``. The discrete ``O(d)``-bundle laplacian +``Δ_F = δ^⊤ δ`` is then assembled by ``NormConnectionLaplacianBuilder`` +from the sibling package — same formula as Bodnar's NSD-O(d), but with +``F`` fixed instead of learned. + +**Sign gauge — known limitation inherited from Singer & Wu.** +The local PCA basis ``O_v`` and the alignment ``F_{vu}`` are both unique +only up to a per-node signed-diagonal "gauge" ``S_v ∈ {±1}^d``, because +the SVD's column signs are not canonicalised by ``torch.linalg.svd``. +Concretely: + +* if PCA returns ``O_v`` for one input and ``O_v · S_v`` for an + arithmetically-equivalent input (e.g. after a rotation of features), + then the alignment matrix transforms as ``F_{vu} ↦ S_v F_{vu} S_u``. +* this gauge does **not** compose into a single block-diagonal + conjugation of the sheaf Laplacian, so the Laplacian's spectrum and + the diffusion's behaviour are not strictly invariant to feature + rotations or node relabellings — they are equal up to a small, + numerically-driven perturbation. + +Algorithm 1 of the paper inherits this from the underlying VDM +construction. Removing it would require a canonicalisation step +(e.g. force the first nonzero entry of each PCA column to be positive), +which is *out of scope* for a faithful re-implementation of the paper. +We document and test for it explicitly rather than pretend it doesn't +exist. See ``test_conn_nsd.py``'s +``test_permutation_invariance_of_laplacian_spectrum`` for the +loose-tolerance invariance check and ``test_determinism`` for the strict +same-input-same-output reproducibility we *do* guarantee. + +**Shape contract.** +All shapes are documented in NumPy style. Notation: + + N number of nodes + E number of *directed* edges (``edge_index`` is the PyG bidirectional form) + p ambient feature dimension + d stalk / tangent-space dimension + +We use the dtype of the input features throughout. No tensors are moved +across devices implicitly. + +References +---------- +.. [1] F. Barbero et al. "Sheaf Neural Networks with Connection + Laplacians." ICML 2022 TAG-ML Workshop. arXiv:2206.08702. + Algorithm 1. +.. [2] A. Singer and H.-T. Wu. "Vector Diffusion Maps and the Connection + Laplacian." Communications on Pure and Applied Mathematics, 2012. +.. [3] C. Bodnar et al. "Neural Sheaf Diffusion." ICLR 2022 Workshop. + arXiv:2202.04579. +""" + +from __future__ import annotations + +import torch +from torch import Tensor + +# ----------------------------------------------------------------------------- +# Step 1 — Local tangent basis (Algorithm 1, lines 3–6). +# ----------------------------------------------------------------------------- + + +def local_tangent_basis( + node_features: Tensor, + edge_index: Tensor, + stalk_dim: int, + batch: Tensor | None = None, +) -> Tensor: + """Approximate the tangent space at each node by local PCA. + + For every node ``v`` we collect its 1-hop neighbourhood ``N(v)`` from the + edge set, centre the neighbours at ``x_v``, stack into a matrix + ``X̂_v ∈ ℝ^{p × |N(v)|}``, and take the first ``d`` left singular vectors + as an orthonormal basis of the local tangent space. + + When ``|N(v)| < d`` the 1-hop set is *topped up* with the + Euclidean-nearest non-neighbour nodes (Barbero et al., 2022, §3.2, + "To solve the problem for nodes which have less than d neighbours…"). + Fully isolated nodes are treated by ranking every other same-graph node + by Euclidean distance. + + Parameters + ---------- + node_features : torch.Tensor, shape ``[N, p]`` + Raw node feature matrix ``X``. Must be 2-D. + edge_index : torch.Tensor, shape ``[2, E]`` + Edge indices in PyG convention. May be directed or bidirectional; + we look at the row ``edge_index[0]`` for source vertices to build + ``N(v)``. + stalk_dim : int + Tangent-space dimension ``d`` (``> 0``). + batch : torch.Tensor, shape ``[N]``, optional + PyG batch vector. If present, fallback nearest-neighbour candidates + are restricted to the same graph as ``v``. + + Returns + ------- + torch.Tensor, shape ``[N, p, d]`` + ``tangent_basis[v]`` has orthonormal columns spanning the local + tangent space at node ``v``. Concretely: + ``tangent_basis[v].T @ tangent_basis[v] == I_d`` up to fp tolerance. + + Notes + ----- + Complexity is ``O(N · SVD(p × max_deg))``. The function has no learnable + parameters and never enters the autograd graph: ``tangent_basis`` is + detached from ``node_features``. + """ + assert node_features.dim() == 2, ( + f"node_features must be [N, p], got {tuple(node_features.shape)}" + ) + assert edge_index.dim() == 2 and edge_index.size(0) == 2, ( + f"edge_index must be [2, E], got {tuple(edge_index.shape)}" + ) + assert stalk_dim > 0, f"stalk_dim must be positive, got {stalk_dim}" + + num_nodes, ambient_dim = node_features.shape + device = node_features.device + dtype = node_features.dtype + if batch is None: + batch = torch.zeros(num_nodes, dtype=torch.long, device=device) + else: + assert batch.dim() == 1 and batch.numel() == num_nodes, ( + f"batch must be [N] with N={num_nodes}, got {tuple(batch.shape)}" + ) + batch = batch.to(device=device) + + # Build 1-hop neighbour lists from the (possibly directed) edge index. + # We treat the edge set as undirected for the purposes of tangent + # estimation, matching Barbero et al. §3.2. + src, dst = edge_index[0], edge_index[1] + neighbours: list[list[int]] = [[] for _ in range(num_nodes)] + for s, t in zip(src.tolist(), dst.tolist(), strict=True): + if s != t: + neighbours[s].append(t) + neighbours[t].append(s) + # Dedupe (handles bidirectional edge_index without double-counting). + neighbours = [sorted(set(ns)) for ns in neighbours] + + # Precompute features on CPU index lists; SVD is fastest on small dense + # matrices and we never see graphs large enough here to make this hot. + tangent_basis = torch.zeros( + num_nodes, ambient_dim, stalk_dim, device=device, dtype=dtype + ) + + # Distance to same-graph nodes (needed for the fallback). Computed lazily. + all_pair_dist: Tensor | None = None + + for v in range(num_nodes): + own = node_features[v] + ns = neighbours[v] + same_graph = batch == batch[v] + graph_size = int(same_graph.sum().item()) + if graph_size <= stalk_dim: + raise ValueError( + f"graph too small: N={graph_size}, stalk_dim={stalk_dim} " + f"requires N >= {stalk_dim + 1}" + ) + + if len(ns) < stalk_dim: + # Top-up rule: take Euclidean-nearest non-neighbours, excluding v + # itself, until we have stalk_dim candidates (Barbero §3.2). + if all_pair_dist is None: + all_pair_dist = torch.cdist(node_features, node_features) + assert all_pair_dist is not None # for type-checkers + dists = all_pair_dist[v].clone() + dists[~same_graph] = float("inf") + dists[v] = float("inf") + for n in ns: + dists[n] = float("inf") + needed = stalk_dim - len(ns) + available = int(torch.isfinite(dists).sum().item()) + k = min(needed, available) + if k < needed: + raise ValueError( + f"graph too small: N={graph_size}, stalk_dim={stalk_dim} " + f"requires N >= {stalk_dim + 1}" + ) + extra = torch.topk(dists, k=k, largest=False).indices.tolist() + ns = list(ns) + extra + + # Centred neighbour matrix: X̂_v[:, k] = x_{n_k} − x_v ∈ ℝ^p + centred = node_features[ns] - own # [|N|, p] + centred = centred.t() # [p, |N|] + + # SVD: X̂_v = U Σ Vᵀ, basis is first d columns of U. + # torch.linalg.svd handles fat / thin matrices uniformly. We use + # full_matrices=False so U is [p, min(p,|N|)] — large enough since + # we ensured |N| ≥ d above and we assume p ≥ d (the manifold + # assumption). + u, _, _ = torch.linalg.svd(centred, full_matrices=False) + # If p < d the manifold assumption fails; we still take the first d + # columns, padding with zeros — but in practice the AllCellFeature + # encoder lifts the input to p = hidden_dim ≫ d. + if u.size(1) >= stalk_dim: + tangent_basis[v] = u[:, :stalk_dim] + else: + tangent_basis[v, :, : u.size(1)] = u + + return tangent_basis.detach() + + +# ----------------------------------------------------------------------------- +# Step 2 — Optimal alignment between tangent spaces (Algorithm 1, lines 8–10). +# ----------------------------------------------------------------------------- + + +def optimal_alignment( + tangent_basis_src: Tensor, + tangent_basis_dst: Tensor, +) -> Tensor: + """Solve the orthogonal Procrustes problem between two tangent bases. + + Given two column-orthonormal matrices ``O_v, O_u ∈ ℝ^{p×d}``, returns the + orthogonal matrix ``F = U V^⊤`` from the SVD + ``O_v^⊤ O_u = U Σ V^⊤``. This is the closest element of ``O(d)`` to + ``O_v^⊤ O_u`` in Frobenius norm (Schönemann, 1966), equivalently the + minimiser of ``‖O_v F − O_u‖_F^2``. + + Parameters + ---------- + tangent_basis_src : torch.Tensor, shape ``[*, p, d]`` + Source orthonormal basis (or a batch thereof). + tangent_basis_dst : torch.Tensor, shape ``[*, p, d]`` + Destination orthonormal basis (same leading dims as ``src``). + + Returns + ------- + torch.Tensor, shape ``[*, d, d]`` + Orthogonal alignment matrix ``F``. + + Notes + ----- + For each batch element ``F`` satisfies ``F^⊤ F = F F^⊤ = I_d`` up to fp + tolerance. The map is computed without gradient flow; this is a + pre-processing step, not a learnable layer. + """ + assert tangent_basis_src.shape == tangent_basis_dst.shape, ( + f"basis shape mismatch: {tuple(tangent_basis_src.shape)} vs " + f"{tuple(tangent_basis_dst.shape)}" + ) + cross_gram = tangent_basis_src.transpose(-1, -2) @ tangent_basis_dst + u, _, vt = torch.linalg.svd(cross_gram, full_matrices=False) + return (u @ vt).detach() + + +# ----------------------------------------------------------------------------- +# Step 3 — Top-level constructor: features + edges → restriction maps. +# ----------------------------------------------------------------------------- + + +def build_connection( + node_features: Tensor, + edge_index: Tensor, + stalk_dim: int, + batch: Tensor | None = None, +) -> Tensor: + """Build orthogonal restriction maps for every edge — Algorithm 1. + + This is the only function the model ever calls. It returns a tensor + of shape ``[E, d, d]`` containing the orthogonal restriction map for + each directed edge in ``edge_index``, in the same order. + + Parameters + ---------- + node_features : torch.Tensor, shape ``[N, p]`` + Raw node feature matrix. We do not normalise these — the manifold + assumption is on the features as given. + edge_index : torch.Tensor, shape ``[2, E]`` + Edge index in PyG convention. The ``e``-th column ``(v, u)`` produces + ``restriction_maps[e] = F_{v → u}``. The caller is responsible for + passing a bidirectional edge index if a symmetric sheaf is desired. + stalk_dim : int + Tangent-space / stalk dimension ``d``. + batch : torch.Tensor, shape ``[N]``, optional + PyG batch vector used to keep fallback nearest-neighbour candidates + inside each graph of a mini-batch. + + Returns + ------- + torch.Tensor, shape ``[E, d, d]`` + Orthogonal restriction maps, one per directed edge. + + Invariants + ---------- + For every edge ``e``: + + F[e] @ F[e].T ≈ I_d (orthogonality) + + If both ``(v, u)`` and ``(u, v)`` appear in ``edge_index`` at positions + ``e₁`` and ``e₂`` respectively, then: + + F[e₁] @ F[e₂] ≈ I_d (transport inverse) + + These are verified in ``test/nn/backbones/graph/test_conn_nsd.py``. + """ + tangent_basis = local_tangent_basis( + node_features, edge_index, stalk_dim, batch=batch + ) # [N, p, d] + src, dst = edge_index[0], edge_index[1] + return optimal_alignment( + tangent_basis[src], tangent_basis[dst] + ) # [E, d, d] diff --git a/topobench/nn/backbones/graph/conn_nsd_utils/fixed_laplacian_builder.py b/topobench/nn/backbones/graph/conn_nsd_utils/fixed_laplacian_builder.py new file mode 100644 index 00000000..ae5b3d80 --- /dev/null +++ b/topobench/nn/backbones/graph/conn_nsd_utils/fixed_laplacian_builder.py @@ -0,0 +1,134 @@ +"""Sheaf Laplacian builder for *fixed*, externally supplied orthogonal maps. + +Mirrors :class:`topobench.nn.backbones.graph.nsd_utils.laplacian_builders.NormConnectionLaplacianBuilder` +in formula but bypasses the lower-triangular-parameter → Cayley → orthogonal +pipeline. Conn-NSD computes its restriction maps deterministically (via +Algorithm 1 of Barbero et al., 2022) and they arrive at this builder +already in ``O(d)``; trying to re-route them through the Bodnar +parametrisation would be both wasteful and misleading about what the model +is doing. + +The math is the *normalised* sheaf Laplacian of an ``O(d)``-bundle: + + Δ_F = D^{-1/2} ( δ^⊤ δ ) D^{-1/2} + +where ``δ`` is the coboundary acting on 0-cochains, the diagonal block +``D_{vv}`` equals ``deg(v) · I_d`` (every restriction map is orthogonal, so +``F^⊤ F = I`` and each edge contributes ``I`` to the diagonal accumulator), +and the off-diagonal block ``Δ_F[v, u] = − F_{vu}^⊤ F_{uv}`` for ``v ≠ u``. +""" + +from __future__ import annotations + +from torch import Tensor + +from topobench.nn.backbones.graph.nsd_utils.laplace import ( + compute_learnable_diag_laplacian_indices, + compute_learnable_laplacian_indices, + mergesp, +) +from topobench.nn.backbones.graph.nsd_utils.laplacian_builders import ( + LaplacianBuilder, +) + + +class FixedConnectionLaplacianBuilder(LaplacianBuilder): + """Normalised ``O(d)``-bundle sheaf Laplacian from pre-computed maps. + + Parameters + ---------- + size : int + Number of nodes ``N`` in the graph. + edge_index : torch.Tensor, shape ``[2, E]`` + Directed edge index in PyG convention (bidirectional pairs expected). + d : int + Stalk dimension. Must equal the last two dims of the maps we receive + in :meth:`forward`. + + Notes + ----- + The off-diagonal block formula + + Δ_F[v, u] = − F_{vu}^⊤ F_{uv} + + matches Definition 2.4 of Barbero et al. for orthogonal ``F`` and is + bit-for-bit identical to the assembly used by + :class:`NormConnectionLaplacianBuilder` once the parameters have been + Cayley-transformed; we simply skip the parametrisation. + """ + + def __init__(self, size: int, edge_index: Tensor, d: int): + super().__init__(size, edge_index, d, normalised=True) + + # Same sparsity-index plumbing as the learnable bundle builder. + _, self.tril_indices = compute_learnable_laplacian_indices( + size, self.vertex_tril_idx, self.d, self.d + ) + self.diag_indices, _ = compute_learnable_diag_laplacian_indices( + size, self.vertex_tril_idx, self.d, self.d + ) + + def forward(self, restriction_maps: Tensor): + """Assemble the normalised bundle Laplacian. + + Parameters + ---------- + restriction_maps : torch.Tensor, shape ``[E, d, d]`` + Pre-computed orthogonal restriction maps, one per directed edge. + Must satisfy ``F^⊤ F = I`` per row; we do not re-verify at every + forward call (cheap, but trips the data-flow purity principle). + + Returns + ------- + sparse_laplacian : tuple[torch.Tensor, torch.Tensor] + ``(indices, values)`` representation of the ``Nd × Nd`` block + sparse Laplacian, ready for ``torch_sparse.spmm``. + saved_tril_maps : torch.Tensor + Lower-triangular transport maps ``−F_{vu}^⊤ F_{uv}`` (for + diagnostics; matches the contract of the learnable builder). + """ + assert restriction_maps.dim() == 3, ( + f"restriction_maps must be [E, d, d], got " + f"{tuple(restriction_maps.shape)}" + ) + assert restriction_maps.size(-1) == self.d, ( + f"restriction_maps last dim must equal stalk dim d={self.d}, " + f"got {restriction_maps.size(-1)}" + ) + assert restriction_maps.size(-2) == self.d, ( + f"restriction_maps second-to-last dim must equal stalk dim " + f"d={self.d}, got {restriction_maps.size(-2)}" + ) + + left_idx, right_idx = self.left_right_idx + tril_indices, diag_indices = self.tril_indices, self.diag_indices + + # Diagonal: D_{vv} = deg(v) · I_d for orthogonal F. No SVD or + # accumulation needed — see the discussion above. + diag_maps = self.deg.unsqueeze(-1) # [N, 1] + + # Off-diagonal (lower triangle): − F_{vu}^⊤ F_{uv}. + # ``left_idx`` selects F_{vu} and ``right_idx`` selects F_{uv} for + # each tril entry; both index into ``restriction_maps``. + f_vu = restriction_maps.index_select(0, left_idx) # [|tril|, d, d] + f_uv = restriction_maps.index_select(0, right_idx) # [|tril|, d, d] + tril_maps = -(f_vu.transpose(-1, -2) @ f_uv) + saved_tril_maps = tril_maps.detach().clone() + + # Symmetric normalisation: D^{-1/2} L D^{-1/2}. + diag_maps, tril_maps = self.scalar_normalise( + diag_maps, tril_maps, *self.vertex_tril_idx + ) + tril_flat = tril_maps.reshape(-1) + diag_flat = diag_maps.expand(-1, self.d).reshape(-1) + + # Mirror the lower triangle to the upper triangle and merge with the + # diagonal — identical assembly path to the learnable builder. + triu_indices = tril_indices.flip(0) + non_diag_indices, non_diag_values = mergesp( + tril_indices, tril_flat, triu_indices, tril_flat + ) + edge_index, weights = mergesp( + non_diag_indices, non_diag_values, diag_indices, diag_flat + ) + return (edge_index, weights), saved_tril_maps diff --git a/topobench/run.py b/topobench/run.py index 4482db92..44d7003b 100755 --- a/topobench/run.py +++ b/topobench/run.py @@ -227,9 +227,19 @@ def rerun_best_model_checkpoint( for callback in callbacks: if isinstance(callback, ModelCheckpoint): log.info( - f"Loading best model from checkpoint at {callback.best_model_path}" + f"Loading best model from checkpoint at '{callback.best_model_path}'" ) + if not callback.best_model_path: + log.warning( + "best_model_path is empty, skipping checkpoint reload." + ) + return model_path = Path(callback.best_model_path) + if model_path.is_dir(): + log.warning( + f"best_model_path '{model_path}' is a directory, skipping checkpoint reload." + ) + return ckpt = torch.load( model_path, map_location="cpu", weights_only=False )