Per-(batch, horizon) softmax + cross-entropy loss + gradient w.r.t.
the 21 atom logits. First of three backward stages — F.3b adds layer-2
weight grads (dW2, db2, dhidden), F.3c adds layer-1 weight grads
(dW1, db1, dh_t with ReLU mask).
Kernel `cuda/rl_frd_softmax_ce_grad.cu`:
* grid_dim = (B, FRD_N_HORIZONS, 1), block_dim = (FRD_N_ATOMS=21, 1, 1)
— one block per (batch, horizon) pair, threads cooperate over the
21 atoms via shared mem
* Standard numerically-stable softmax: shift by row_max, exponentiate,
normalize by row_sum (thread 0 does the serial reductions — 21
atoms is small enough warp-shuffle overhead isn't worth it)
* Gradient: (p[a] - 1{a==label}) / B at the source per v_head_bwd
convention (mean-reduce over batch)
* Loss: -log(p[label]) with 1e-30 floor against log(0)
* Sentinel label (-1) zeros both gradient row and loss — for the
missing-horizon case at the rightmost edge of the snapshot stream
(forward returns at h=300 ticks aren't realized for the last
300 snapshots; loader marks those labels with -1)
* Per feedback_no_atomicadd: per-(b, h, a) sole-writer pattern
Rust wiring `src/rl/frd.rs::FrdHead::softmax_ce_grad`:
* Second cubin loaded alongside fwd (separate module per the
aux_heads pattern; small handle, no impact on init time)
* Caller provides labels_d [B, FRD_N_HORIZONS] of i32 and gets back
grad_logits + per-(b, h) raw CE; sum + λ_frd scaling left to the
caller (F.4 will hook this into stats.l_total + Adam step)
Tests `tests/frd_head.rs` — 3 new GPU-oracle tests (6/6 file total),
all PASS on RTX 3050 Ti:
1. frd_softmax_ce_grad_uniform_logits_match_log_n_atoms — for any
label, uniform logits → CE = ln(FRD_N_ATOMS) = ln(21) ≈ 3.0445.
Also asserts per-row Σ grad_logits = 0 (softmax-CE invariant).
2. frd_softmax_ce_grad_sentinel_label_zeros_row — label=-1 with
non-trivial random logits produces exactly zero loss + grad
for every row (no leak through the sentinel path).
3. frd_softmax_ce_grad_finite_diff_matches_analytical — perturbs
one logit slot by ±ε=1e-3, compares (L(+ε) - L(-ε))/(2ε) to
the kernel's analytical gradient. rel_err ≈ 1.3e-3 (fp32
finite-diff is rounding-error-limited at this ε; tolerance
set to 5e-3 with explanatory comment).
The first two tests provide strong analytical oracles (no CPU
reference impl per feedback_no_cpu_test_fallbacks). The finite-diff
test cross-validates the full softmax+CE chain via a numerical
gradient — the standard ground-truth for autodiff kernels.
6cfd7e6691