Forward: compare via matrix relative error (max abs error / max|ref|)
instead of a per-element ratio, so near-zero outputs where two correct
f32 GEMMs differ only in rounding order don't inflate the metric.
Backward: L = sum(W∘C) is bilinear, so central differences are
truncation-free — use eps=1e-2 (sharper f32 resolution of the
difference) and atol=1e-3 to floor near-zero-gradient subtraction noise.
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
Forward: hand-written tiled GEMM vs cuBLAS sgemm on random matrices
(square / non-tile-aligned rect / 256³), max relative error < 1e-3, using
the row-major⟺col-major identity to drive cuBLAS without explicit
transposes. Backward: scalar loss L = sum(W∘C) (so dC = W), dA/dB from
matmul_backward checked against the finite-diff harness. Gated behind
not(no_cuda).
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
New xtrain-tensor crate: DType (F32), shape/stride helpers, Arc-counted
host/device Storage with CPU↔CUDA copy, and a contiguous Tensor with
creation, host↔device transfer, and a scale() op driving the elementwise
kernel. GPU integration tests (host↔device roundtrip + scale correctness)
gated behind not(no_cuda); a thin build.rs emits the no_cuda cfg so the
kernel call sites compile out locally.
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
