[WS1] Backward-pass consistency across all ops

[Flink-ddd]

Part of WS1 — Full Batch-Invariant Forward Chain (epic: #)

Why

A forward-aligned chain still breaks training if gradient reductions drift with batch shape — the optimizer then sees batch-dependent gradients and the run diverges even though inference looked aligned. Backward invariance is a separate, explicit requirement, not something the forward checks cover. This issue makes "backward also invariant" a first-class, cross-op acceptance condition.

Scope

Make batch-invariant backward a required, tested property of every WS1 op.

• Define the backward-invariance check in the [WS1] Ground-truth harness + numerical contract for batch-invariant ops #108 harness (gradient outputs compared across batch configs, same tolerance policy as forward).
• Ensure each op's gradient reduction (dx, dweight, dW, etc.) uses a fixed, batch-shape-independent order — no atomicAdd in backward.
• Cover the most reduction-heavy backward first: RMSNorm dweight, GEMM dW/dX, attention backward, embedding-grad scatter.
• Validate gradients across batch=1/N, chunked-prefill on/off, and padding layouts.

Out of scope

• Re-implementing each op (each op issue owns its own backward kernel and fix; this issue owns the cross-cutting requirement, reusable gradient check, and status matrix).
• Optimizer / training-loop changes; multi-GPU gradient synchronization (WS2).
• FP8 backward.

Acceptance criteria

• The [WS1] Ground-truth harness + numerical contract for batch-invariant ops #108 harness has a reusable gradient-invariance assertion any op-issue can call.
• Each WS1 op with a backward passes gradient-invariance across the full sweep (bitwise or within [WS1] Ground-truth harness + numerical contract for batch-invariant ops #108 tolerance).
• No op uses atomicAdd or shape-dependent accumulation in its backward path.
• A short matrix records, per op, both forward-pass and backward-pass invariance status; gradient-drift reports include max abs diff, relative diff, tensor name, and first failing op.

Notes

• Depends on [WS1] Ground-truth harness + numerical contract for batch-invariant ops #108; cross-cuts every op issue (RMSNorm, matmul, attention, embedding / LM head, etc.).
• Best owned as a shared concern: this issue provides the gradient check and status matrix; each op issue is responsible for fixing its own backward path and passing the check.

Planned PRs

• Add a reusable gradient-invariance assertion to the [WS1] Ground-truth harness + numerical contract for batch-invariant ops #108 harness
• Per-op backward test requirements (RMSNorm dweight, GEMM dW/dX, attention backward first)
• Gradient-diff reporting utility (max abs / relative diff, tensor name, first failing op)
• Enforce no-atomicAdd / fixed-order accumulation in backward paths
• Per-op forward+backward invariance status matrix; wire full-chain backward into CI