Backend method inventory (T1.2)

Cross-reference between device.Backend embedded interface methods and ir.RequiredOperationIDs(). Machine-checkable source of truth: pkg/backend/device/inventory.go, inventory_links.go, validated by pkg/backend/device/inventory_test.go.

CPU per-domain dispatch registration (T1.3): docs/cpu-dispatch-matrix.md (pkg/backend/device/cpu/dispatchaudit/).

Metal / CUDA / XLA tensor backend matrix (T1.4): docs/device-backend-matrix.md (pkg/backend/device/backendaudit/).

Combined ISA/backend coverage (T1.5): backend-coverage.md (pkg/backend/device/coverageaudit/).

Summary (2026-05-19)

Item	Count
device.Backend methods (25 embedded interfaces)	151
ir.RequiredOperationIDs() entries	119
Required ops → direct Backend method	74
Required ops → composite Backend methods	3
Required ops → kernel registry (not on Backend)	32
Required ops → graph-only (no compute kernel)	10
Backend methods with no required-op ID	88

Embedded surfaces

Surface	Methods
Activation	55
Physics	9
Causal	10
Elementwise	11
PosPop	5
VSA	5
Losses	6
Hawkes	5
Pool	4
Convolution	4
ActiveInference	4
PredictiveCoding	4
Masking	3
Attention	3
Sampling	3
Normalization	3
Reduction	5
LayerNorm	2
RoPE	2
Embedding	2
Dequant	2
Dot	1
Matmul	1
Dropout	1
Quant	1

Cross-link kinds

Direct (74)

Each required operation ID maps to a single Surface.Method on device.Backend. Examples: math.add → Elementwise.Add, convolution.conv2d → Convolution.Conv2D, train.loss.mse → Losses.MSE.

Composite (3)

Operation ID	Backend methods
attention.mqa	Attention.MultiHeadAttention, Attention.FlashAttention
attention.gqa	Attention.MultiHeadAttention, Attention.FlashAttention
projection.fused_qkv	Matmul.Matmul, Attention.MultiHeadAttention

Kernel registry (32)

Implemented under CPU/Metal/CUDA kernel registries, not as device.Backend methods:

• Shape (9): shape.reshape, shape.transpose, shape.concat, shape.split, shape.upsample_nearest2d, shape.view_as_heads, shape.merge_heads, shape.last_token, shape.slice → pkg/backend/device/cpu/shape
• Optimizers (12): train.optimizer.* → pkg/backend/device/cpu/optimizer, pkg/backend/device/metal optimizer kernels (not on Backend)
• Training grads (4): train.loss.*_grad, train.grad.* → losses kernel registry
• Math helpers (4): math.sin, math.cos, math.outer, math.sign → elementwise/matmul registries
• Other (3): math.logsumexp, hawkes.simulate, math.inv_sqrt_dim_scale

Graph-only (10)

Operation ID	Note
OpInput	Graph input binding
OpFused	Fusion pass composite
bench.accuracy, bench.perplexity, bench.f1	Metric nodes
bench.metric.accuracy, bench.metric.perplexity, bench.metric.f1	Metric nodes
model.graft, model.freeze	Model-editing graph ops

Backend-only methods (88)

Methods on device.Backend not referenced by any ir.RequiredOperationIDs() entry. Includes extended activations (Activation.Exp, Activation.GeluTanh, gated tensor variants), PosPop, Physics, Sampling, Dequant/Quant, duplicate Elementwise.ReLU, and most of the Activation parametric variants.

Use device.BackendMethodsWithoutRequiredOperation() for the authoritative list.

Gaps for R1

• Optimizer steps are required IR ops but are not on device.Backend; they live in per-backend kernel registries.
• Shape ops are required IR ops but are not on device.Backend.
• 88 Backend methods have no required-op ID (extended/specialized surfaces).