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Cuequivariance Torch

NVIDIAOfficialCreated by Mario GeigerDistributed by NVIDIA

  • Skill
  • Tool integration
  • Software development
  • Apache-2.0
  • Medium risk
  • Has scripts
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Use when building or debugging cuEquivariance PyTorch tensor products or equivariant GNNs, especially CPU references, layouts, indexing, and gradients.
— the description by Mario Geiger

AutoGineer summary

Written by AutoGineer from the skill’s own files, not by the author

This skill provides instructions for integrating and debugging cuEquivariance PyTorch (cuet) within equivariant graph neural network projects. It covers environment setup, CPU reference implementations using the naive method, layout management, weight ownership, and gradient verification. It emphasizes maintaining environment consistency and provides specific patterns for tensor products, spherical harmonics, and message-passing architectures.

What it does

  • Configures CPU-based reference implementations for equivariant operations.
  • Manages tensor layout conversions between different irrep representations.
  • Handles weight ownership and batch dimensions for equivariant layers.
  • Provides patterns for autograd-compatible message passing and GNN layers.
  • Offers troubleshooting steps for API mismatches and numerical discrepancies.
  • Facilitates integration with external NumPy references for validation.

When to use it

  • When developing or debugging equivariant GNNs using cuEquivariance.
  • When creating CPU-based reference tests for GPU-accelerated equivariant modules.
  • When resolving layout or indexing issues in tensor product operations.
  • When verifying gradient correctness in complex equivariant architectures.

Advantages

  • Ensures numerical consistency between CPU references and CUDA backends.
  • Provides clear patterns for handling complex irrep layouts.
  • Supports robust gradient checking for custom equivariant layers.
  • Promotes environment stability by prioritizing existing project interpreters.

Usage examples

“How do I set up a CPU reference for a FullyConnectedTensorProduct?”
The agent provides a code snippet using method='naive', specifying the irreps, layout, and dtype, followed by a backward pass to verify gradient flow.
“My equivariant layer output values are correct but the gradients are missing or non-finite.”
The agent advises checking that all operations remain within the PyTorch autograd graph, ensuring inputs are non-zero, and verifying that all differentiable operands are correctly tracked.
“How do I convert between different irrep layouts in my GNN?”
The agent demonstrates the use of cuet.TransposeIrrepsLayout to perform blockwise conversion between mul_ir and ir_mul layouts.
“How can I implement a GNN message passing layer with external edge weights?”
The agent provides a class structure using ChannelWiseTensorProduct with shared_weights=False and internal_weights=False, showing how to pass external weights from a radial MLP.

Install

  1. Download the skill as a ZIP:

    https://autogineer.com/agent-skills/nvidia/cuequivariance-torch/download

  2. Unzip it into the cross-client skills folder of your project:

    mkdir -p .agents/skills && unzip cuequivariance-torch.zip -d .agents/skills

Documentation by Mario Geiger

cuEquivariance in PyTorch

Purpose

Execute cuequivariance (cue) descriptors with cuequivariance_torch (cuet): CPU references, CUDA backends, equivariant layers, and autograd. Preserve the project's environment.

Inputs

Required inputs: operation, SO3/O3 irreps, layout, device, dtype, and weight ownership; infer from the request or code. Graphs also need source/destination counts and indices. Optional inputs: backend, performance, export targets.

Instructions

  1. Probe once and reuse working PyTorch. Never recursively delete directories during setup or recovery, including partial temporary environments; use a fresh unique path when isolation is needed.

  2. Set method="naive" at construction for CPU. Match parameters, features, weights, and references in device and dtype. Use float64 for small numerical and gradient checks.

  3. Specify layout and weight ownership explicitly. Derive sizes and output order from the module/descriptor; do not guess multiplicities from a filter.

  4. Finish installation before running the saved script with the completion recipe below. A session/task ID, empty output, or a file write is not completion. Poll that session until it exits and inspect its results.

  5. For an API mismatch, inspect the installed signature/source once. Adapt or explain the requirement; preserve the requested library.

Prerequisites and environment reuse

Probe imports independently with the project's Python; a missing frontend must not hide working PyTorch:

import importlib
import sys

print("python:", sys.executable, sys.version.split()[0])
available, import_errors = {}, {}
for name in ("torch", "cuequivariance", "cuequivariance_torch"):
    try:
        module = importlib.import_module(name)
        available[name] = module
        print(name, getattr(module, "__version__", "unknown"), module.__file__)
    except (ImportError, OSError) as error:
        import_errors[name] = f"{type(error).__name__}: {error}"
        print(name, import_errors[name])
if "torch" in available:
    torch = available["torch"]
    print("CUDA build:", torch.version.cuda, "available:", torch.cuda.is_available())

Choose the next step from the probe:

  • Imports work: retain the interpreter; install nothing.

  • Only cuEquivariance is missing: install cuequivariance-torch in that interpreter; it does not require replacing PyTorch.

  • PyTorch is missing: check the project interpreter (e.g. .venv/bin/python). If the requested installation is inaccessible, say so; a new environment cannot verify it.

  • Binary/shared-library mismatch: diagnose the reported package/path and compatibility.

Use one interpreter for pip and execution. Honor project requirements and compatible core/frontend revisions. Retaining installed PyTorch takes priority over setup examples. Optional CUDA/optimization warnings are not failures.

For isolation, create a new unique environment. From this skill's directory, use host pip 22.3+ and the bundled hashed CPU wheels, then requirements:

set -e
cueq_python=python3  # Set to the selected project interpreter's path.
cueq_env=$(mktemp -d "${TMPDIR:-/tmp}/cueq-cpu.XXXXXX")
"$cueq_python" -m venv --without-pip "$cueq_env"
python3 -m pip --python "$cueq_env" install --cert "${PIP_CERT:-/etc/ssl/certs/ca-certificates.crt}" -q --no-deps -r scripts/torch-cpu-wheels.txt
python3 -m pip --python "$cueq_env" install --cert "${PIP_CERT:-/etc/ssl/certs/ca-certificates.crt}" -q -r scripts/requirements.txt
cueq_python="$cueq_env/bin/python"
"$cueq_python" -c 'import sys, torch, cuequivariance_torch; assert torch.version.cuda is None; print("CPU setup complete:", sys.executable, torch.__version__, cuequivariance_torch.__version__)'

Retain cueq_python for execution. For other platforms, use project setup. Without host pip, use installed uv with these requirements.

Use approved PIP_CERT for a private CA; retain TLS verification. If downloading fails, try a configured CPU mirror/cache or report the blocker. Do not replace CPU wheels with CUDA builds. Finish installs before retrying. See pip's certificates.

Complete and inspect a run

Save the preamble and checks in check.py. Set cueq_python to the probe's sys.executable, or retain it from setup. Run after setup exits successfully:

set -e
cueq_run=$(mktemp -d "${TMPDIR:-/tmp}/cueq-check.XXXXXX")
printf 'run directory: %s\n' "$cueq_run"
if "$cueq_python" -u check.py >"$cueq_run/output.txt" 2>&1; then
    cueq_status=0
else
    cueq_status=$?
fi
printf '%s\n' "$cueq_status" >"$cueq_run/exit-code.txt"
tail -n 30 "$cueq_run/output.txt"
printf 'exit code: %s\n' "$cueq_status"
test "$cueq_status" -eq 0

The exit-code file appears only when Python finishes. If the tool yields, poll its session, then inspect the file and numerical output. Deliver the script, command, observed results, and backend explanation; label unrun checks. Keep install output separate.

Limitations and backends

MethodUse and constraints
naivePure PyTorch reference implementation; supported CPU path and autograd.
uniform_1dCUDA; uniform segment shapes within each operand and a single mode after descriptor transformations.
fused_tpCUDA contractions with 3 or 4 operands; math dtype float32/float64. Some versions fall back on CPU, but select naive explicitly for a CPU reference.
indexed_linearCUDA indexed linear operations; indices must be sorted.

High-level defaults vary: SphericalHarmonics selects uniform_1d, FullyConnectedTensorProduct selects fused_tp, Linear selects naive, and ChannelWiseTensorProduct/SymmetricContraction select according to descriptor compatibility. Moving tensors to CPU does not change every constructor's backend choice. CUDA acceleration requires compatible PyTorch, GPU, and cuequivariance_ops_torch builds; CPU checks do not establish GPU performance or export compatibility.

Layouts and weights

  • cue.mul_ir is the high-level default, compatible with e3nn: each block is (multiplicity, irrep_dimension). Core descriptors commonly use cue.ir_mul: (irrep_dimension, multiplicity). Check each descriptor operand's .layout.

  • Convert each irrep block, not the whole flattened tensor with a reshape. cuet.TransposeIrrepsLayout(irreps, source=..., target=..., use_fallback=True) performs the blockwise conversion using PyTorch.

  • For externally supplied weights set internal_weights=False. Shared weights have shape (1, module.weight_numel); distinct weights per item have shape (batch, module.weight_numel) and require shared_weights=False. A gathered graph operation uses the edge count for this batch dimension.

  • filter_irreps_out selects allowed irrep types, not a requested output representation with prescribed multiplicities. Read module.irreps_out; preserve its actual order when constructing the next layer or reference.

  • For training, create learned parameters or an edge-weight network in __init__. Do not draw new random weights inside forward().

Examples

Each CPU example runs independently with this preamble; preserve layout, indexing, and gradient contracts when adapting inputs.

import numpy as np
import torch
import cuequivariance as cue
import cuequivariance_torch as cuet

torch.manual_seed(0)
dtype = torch.float64
print("torch:", torch.__version__, "CUDA build:", torch.version.cuda,
      "CUDA available:", torch.cuda.is_available(), "device: cpu", "dtype:", dtype,
      "method: naive")
CPU tensor product and backward

Use naive for both CPU modules. Here weights are internal trainable parameters.

irreps = cue.Irreps("SO3", "0 + 1")
sh = cuet.SphericalHarmonics([0, 1], normalize=False, method="naive")
tp = cuet.FullyConnectedTensorProduct(
    irreps, irreps, irreps, layout=cue.mul_ir, method="naive", dtype=dtype,
)
features = torch.randn(2, irreps.dim, dtype=dtype, requires_grad=True)
vectors = torch.tensor([[0.3, -0.7, 1.1], [1.2, 0.4, -0.2]],
                       dtype=dtype, requires_grad=True)
result = tp(features, sh(vectors))
assert result.device.type == "cpu" and result.shape == (2, irreps.dim)
result.square().sum().backward()
gradient_norms = {}
for name, tensor in [("features", features), ("vectors", vectors), *tp.named_parameters()]:
    assert tensor.grad is not None and torch.isfinite(tensor.grad).all()
    assert tensor.grad.abs().sum() > 0
    gradient_norms[name] = tensor.grad.norm().item()
print("CPU tensor product:", tuple(result.shape), "gradient norms:", gradient_norms)
Spherical harmonics and a NumPy reference

normalize=False evaluates the raw polynomial; normalize=True first normalizes the input vectors. Match that choice in the reference and use nonzero vectors for gradient checks.

ls = [0, 1, 2]
sh = cuet.SphericalHarmonics(ls, normalize=False, method="naive")
vectors = torch.tensor([[0.3, -0.7, 1.1], [1.2, 0.4, -0.2]],
                       dtype=dtype, requires_grad=True)
values = sh(vectors)
descriptor = cue.descriptors.spherical_harmonics(cue.SO3(1), ls)
reference = descriptor(vectors.detach().numpy())[0]
np.testing.assert_allclose(values.detach().numpy(), reference, atol=1e-12)
assert values.shape == (2, sum(2 * l + 1 for l in ls))
gradcheck_ok = torch.autograd.gradcheck(sh, (vectors,))
assert gradcheck_ok
print("Spherical harmonics:", tuple(values.shape), "normalize: False",
      "max error:", np.max(np.abs(values.detach().numpy() - reference)),
      "gradcheck:", gradcheck_ok)
Linear: layout conversion and rotations

Use identical explicit weights for a layout comparison. For row-vector features, apply the representation matrix as x @ D.T.

irreps_in = cue.Irreps("SO3", "3x0 + 2x1")
irreps_out = cue.Irreps("SO3", "2x0 + 4x1")
options = dict(internal_weights=False, shared_weights=True, method="naive", dtype=dtype)
linear = cuet.Linear(irreps_in, irreps_out, layout=cue.mul_ir, **options)
linear_ir = cuet.Linear(irreps_in, irreps_out, layout=cue.ir_mul, **options)
to_ir = cuet.TransposeIrrepsLayout(
    irreps_in, source=cue.mul_ir, target=cue.ir_mul, use_fallback=True
)
to_mul = cuet.TransposeIrrepsLayout(
    irreps_out, source=cue.ir_mul, target=cue.mul_ir, use_fallback=True
)
x = torch.randn(2, irreps_in.dim, dtype=dtype, requires_grad=True)
w = torch.randn(1, linear.weight_numel, dtype=dtype, requires_grad=True)
y = linear(x, w)
y_ir = to_mul(linear_ir(to_ir(x), w))
torch.testing.assert_close(y, y_ir)
rotation = np.array([0.2, -0.3, 0.1])
din, dout = [torch.from_numpy(cue.IrrepsAndLayout(r, cue.mul_ir).exp_map(rotation, []))
             for r in (irreps_in, irreps_out)]
rotated, expected_rotated = linear(x @ din.T, w), y @ dout.T
torch.testing.assert_close(rotated, expected_rotated)
grads = torch.autograd.grad(y.square().sum(), (x, w))
for g in grads:
    assert torch.isfinite(g).all() and g.abs().sum() > 0
print("Linear:", tuple(y.shape), "shared external weights:", tuple(w.shape),
      "layout error:", (y - y_ir).detach().abs().max().item(),
      "rotation error:", (rotated - expected_rotated).detach().abs().max().item(),
      "gradient norms:", [g.norm().item() for g in grads])
Channelwise product with external per-example weights

The core descriptor takes (weights, input1, input2) and returns a list; the high-level module takes (input1, input2, weight=...) and returns a tensor. Matching ir_mul layouts avoids transposition. Report tp.irreps_out and preserve its actual order: the filter selects types, not multiplicities.

a, b = cue.Irreps("SO3", "3x0 + 3x1"), cue.Irreps("SO3", "0 + 1")
keep = [cue.SO3(0), cue.SO3(1)]
tp = cuet.ChannelWiseTensorProduct(
    a, b, keep, layout=cue.ir_mul, shared_weights=False,
    internal_weights=False, method="naive", dtype=dtype,
)
x1, x2, w = [torch.randn(2, n, dtype=dtype, requires_grad=True)
             for n in (a.dim, b.dim, tp.weight_numel)]
y = tp(x1, x2, weight=w)
descriptor = cue.descriptors.channelwise_tensor_product(a, b, keep)
reference = descriptor(*(t.detach().numpy() for t in (w, x1, x2)))[0]
np.testing.assert_allclose(y.detach().numpy(), reference, atol=1e-12)
assert y.shape == (2, tp.irreps_out.dim)
grads = torch.autograd.grad(y.square().sum(), (x1, x2, w))
for g in grads:
    assert torch.isfinite(g).all() and g.abs().sum() > 0
print("Channelwise:", tuple(y.shape), "per-item weights:", tuple(w.shape),
      "filter selects types; actual ir_mul output order:", tp.irreps_out,
      "max error:", np.max(np.abs(y.detach().numpy() - reference)),
      "gradient norms:", [g.norm().item() for g in grads])

cuet.FullyConnectedTensorProduct(a, b, irreps_out, method="naive", dtype=dtype) accepts desired output irreps. Its weights are internal by default; use the same external-weight flags for caller-owned weights.

SegmentedPolynomial: gather and scatter

Input/output index keys refer to operand positions, not feature channels. Supply torch.int32 or torch.int64 indices on the computation's device. output_shapes takes a two-dimensional tensor, whose first dimension determines the destination count; it does not take a shape tuple. Repeated receivers sum, and destinations without incoming edges remain zero.

descriptor = cue.descriptors.linear(cue.Irreps("SO3", "3x0"), cue.Irreps("SO3", "2x0"))
sp = cuet.SegmentedPolynomial(descriptor.polynomial, method="naive")
nodes = torch.randn(5, 3, dtype=dtype, requires_grad=True)
w = torch.randn(1, descriptor.inputs[0].dim, dtype=dtype, requires_grad=True)
senders = torch.tensor([0, 2, 1, 0], dtype=torch.int64)
receivers = torch.tensor([1, 0, 1, 2], dtype=torch.int64)
[actual] = sp([w, nodes], input_indices={1: senders},
              output_indices={0: receivers}, output_shapes={0: nodes.new_empty(4, 1)})
[edges] = sp([w, nodes[senders]])
reference = nodes.new_zeros(4, descriptor.outputs[0].dim).index_add_(0, receivers, edges)
torch.testing.assert_close(actual, reference)
assert torch.count_nonzero(actual[3]) == 0
grads = torch.autograd.grad(actual.square().sum(), (nodes, w))
ref_grads = torch.autograd.grad(reference.square().sum(), (nodes, w))
for g, ref in zip(grads, ref_grads):
    torch.testing.assert_close(g, ref)
print("Gather/scatter:", tuple(actual.shape),
      "input/output index dtypes:", senders.dtype, receivers.dtype,
      "forward error:", (actual - reference).detach().abs().max().item(),
      "gradient errors:", [(g - r).abs().max().item() for g, r in zip(grads, ref_grads)],
      "isolated destination:", actual[3].detach().tolist())

Descriptor coefficients include normalization factors; retain them in references. High-level channelwise gathering/scattering uses indices_1, indices_2, indices_out, and size_out instead of dictionaries.

Trainable message passing

This CPU reference uses a radial MLP to produce one weight vector per edge. Its parameters persist across calls, and irreps_sh matches the single copy of each spherical harmonic degree.

class SimpleGNN(torch.nn.Module):
    def __init__(self, irreps_in, irreps_out):
        super().__init__()
        self.tp = cuet.ChannelWiseTensorProduct(
            irreps_in, cue.Irreps("SO3", "0 + 1 + 2"), layout=cue.mul_ir,
            shared_weights=False, internal_weights=False, method="naive",
        )
        self.radial = torch.nn.Sequential(
            torch.nn.Linear(1, 16), torch.nn.SiLU(),
            torch.nn.Linear(16, self.tp.weight_numel),
        )
        self.sh = cuet.SphericalHarmonics([0, 1, 2], normalize=True, method="naive")
        self.linear = cuet.Linear(
            self.tp.irreps_out, irreps_out, layout=cue.mul_ir, method="naive"
        )

    def forward(self, node_features, edge_vectors, senders, receivers, num_dst):
        weights = self.radial(edge_vectors.norm(dim=-1, keepdim=True))
        messages = self.tp(
            node_features, self.sh(edge_vectors), weight=weights,
            indices_1=senders, indices_out=receivers, size_out=num_dst,
        )
        return self.linear(messages)

Move the whole module and inputs to the same dtype/device (for example model.double() for float64 checks). Use nonzero edge vectors when normalizing spherical harmonics. After a scalar loss/backward pass, check gradients on the radial network as well as node features; repeated forwards should agree when no stochastic layers are present.

Other operations and layers

Inspect the requested operation via inspect.signature and inspect.getfile. Key contracts:

OperationContract
Species-indexed LinearSet weight_classes; pass weight_indices of shape (batch,) and weights of shape (weight_classes, weight_numel).
SymmetricContractionMACE-style; uniform multiplicities, contraction_degree, num_elements, and integer element indices in sc(x, indices).
Rotation / Inversionrot(gamma, beta, alpha, x) uses YXY Euler angles; inv(x) uses O3 parity. Specify layout. Angle helpers: encode_rotation_angle, vector_to_euler_angles.
layers.BatchNormEquivariant normalization; configure irreps and layout.
layers.FullyConnectedTensorProductConvConfigure input/SH/output irreps and edge MLP; call with (src_features, edge_sh, edge_emb, ((src, dst), (num_src, num_dst))). Supports reduce="mean" and optional src_scalars/dst_scalars.
Triangle operations and export

These paths require compatible optional GPU packages and their own shape checks. Do not install them for a CPU tensor-product request. Locate the installed primitives/triangle.py via cuet.__file__:

  • triangle_attention: Q/K/V (B,N,H,Q_or_K,D), bias (B,1,H,Q,K). mask_to_kv_lengths(prefix_mask) supplies kv_lengths; arbitrary dense masks use mask=... and the fallback.

  • triangle_multiplicative_update: input (B,I,J,C), mask (B,I,J), precision enum cuet.TriMulPrecision.

  • attention_pair_bias: OpenFold3/Boltz contract, returns (out, auxiliary); projection biases and query/key normalization keywords vary by version. Inspect its signature before assembling the weights.

  • ONNX: pass custom_translation_table=cuet.onnx_custom_translation_table() to torch.onnx.export. TensorRT: cuet.register_tensorrt_plugins(). Validate the actual exported runtime.

Troubleshooting

SymptomCheck and recovery
Missing CUDA kernels on CPUPass method="naive" at module construction; retain the installed CPU PyTorch.
opt_einsum_fx not available warningOptional optimization; continue the naive reference calculation without installing it.
Missing import after installationCompare sys.executable, module paths, and the interpreter used with pip. Reuse the working interpreter.
Unexpected keyword or missing descriptor methodInspect the installed signature/version. Use its documented equivalent or explain the mismatch; avoid repeated blind API guesses.
Correct shapes but wrong numerical valuesCheck per-block layout, output irrep order, normalization, and the shared/per-item weight convention.
Scatter shape/error or wrong destination sumsUse operand index keys, integral indices, a tensor in output_shapes, and accumulation for repeated receivers.
Missing/nonfinite gradientsKeep tensor operations in autograd; detach only the NumPy reference. Use nonzero vectors and a nonconstant loss; check every requested differentiable operand.

Files

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Requirements and compatibility

Works with: Claude Code, Claude apps, OpenAI Codex, GitHub Copilot, Cursor, Gemini CLI, Kiro, OpenCode, Goose, Amp, Roo Code, JetBrains Junie, Factory Droid, Devin (ex-Windsurf), Mistral Vibe, OpenHands, Letta

“Works with” means the tool reads the open Agent Skills format; a skill written for one tool may use features others lack.

Needs: Needs Python, Needs Node.js

Security

What our scanner noticed· Medium risk

  • Large base64-encoded blobs
  • Scripts that your agent may run

This skill includes scripts that your agent may run. Read them before you use it.

A static scan is not a guarantee. Skills are third-party content: review a skill before you let an agent use it.

Attribution and licence

Created by
Mario Geiger
Publisher
NVIDIA (Official)
Distributed by
NVIDIA
Source
NVIDIA/skills · skills/bionemo-cuequivariance-torch · commit fce3cca
Licence
Apache License 2.0 (redistribution allowed)
  • LICENSE (added by AutoGineer from LICENSE-APACHE)
  • ATTRIBUTION.md (written by AutoGineer)
Synced

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Download ZIP

The ZIP holds the skill’s files, its licence files and an ATTRIBUTION.md. Download cuequivariance-torch.zip