multi_horizon_heads_backward: sigmoid + linear chain rule. One block,
HIDDEN_DIM=128 threads. Computes grad_w, grad_b, grad_h_in. No
atomicAdd; per-thread accumulation only.
cfc_step_backward: truncated K=1 BPTT through one CfC time step.
Forward pre/decay/tanh recomputed inside the kernel; emits grad_w_in,
grad_w_rec, grad_b, grad_h_old. tau is held frozen (structural
log-uniform init per Hasani 2022; backprop through tau deferred to
Phase A v2 if the gate needs it). Uses dynamic shared memory for the
d_pre relay between threads (size = 2 * n_hid * 4 bytes).
Tests (4/4 on sm_86) validate via on-GPU finite-difference:
- heads grad_h vs forward(h±eps) → matches at eps=1e-3, rel<=1%
- heads grad_b vs forward(b±eps) → matches at eps=1e-3, rel<=1%
- cfc grad_b vs forward(b±eps) → matches at eps=1e-3, rel<=5%
- cfc grad_h_old vs forward(h_old±eps) → matches at eps=1e-3, rel<=5%
CPU is not the reference (per feedback_no_cpu_test_fallbacks.md). The
kernel is the truth; numerical perturbation validates the analytic
gradient against the kernel's own forward.
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
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