Forward-Return-Distribution head per SP20 §3 P3. Supervised forecaster
over 3 horizons × 21 return-bucket atoms — replaces the survivor-biased
checklist head per CRIT-1.
Architecture (2-layer MLP):
hidden [B, 64] = ReLU(h_t [B, 128] @ W1 [128, 64] + b1)
logits [B, 63] = hidden @ W2 [64, 63] + b2 // 63 = 3 × 21
Softmax + CE happen in the backward kernel (F.3). The forward kernel
caches the post-ReLU hidden buffer to avoid recomputing the W1 product
+ ReLU mask on backward.
Kernel `cuda/rl_frd_fwd.cu` — 1 block per batch, 64 threads:
* Phase 1 (tid < 64): each thread computes one hidden activation,
stages into shared mem, writes the cached `hidden_out[b, tid]`
* Phase 2 (tid < 63): each thread computes one output logit by
reading the shared hidden vector
* No atomicAdd (per-batch, per-output sole-writer pattern)
* No host branches in the launch (graph-capture safe)
Rust head module `src/rl/frd.rs`:
* `FrdHead::new(dev, cfg)` — Xavier × 0.1 init for W1/W2 (small enough
to keep initial softmax near-uniform), zero biases. Scoped-init-seed
guard per pearl_scoped_init_seed_for_reproducibility.
* `forward(h_t_d, hidden_out_d, logits_out_d, b_size)` — single
kernel launch via the cached `fwd_fn` handle.
* Public weight buffers (w1_d, b1_d, w2_d, b2_d) for the upcoming
bwd kernel + test harnesses.
* `pub const FRD_OUT_DIM = FRD_N_HORIZONS × FRD_N_ATOMS = 63` — single
canonical reference for the per-batch output width.
Tests `tests/frd_head.rs` — 3 GPU-oracle tests, all PASS on RTX 3050 Ti:
1. frd_forward_zero_input_emits_zero_logits — h_t=0 with default
b1=b2=0 must produce exactly zero logits AND zero cached hidden.
Unambiguous analytical oracle for the full matmul + ReLU + matmul
chain.
2. frd_forward_shape_matches_spec — random h_t produces correctly
shaped output [B × 63] with per-horizon softmax sums = 1.0
within 1e-5 (numerical-stable log-sum-exp).
3. frd_forward_relu_mask_consistent_with_cached_hidden — strictly
negative h_t input → ≥50% of cached hidden slots must be exactly
zero (ReLU fires). Empirically 128/256 zeros on the seeded init.
Per feedback_isv_for_adaptive_bounds: bucket-range σ stays in ISV
(slot 503, seeded ±3σ); only the 21-atom count is structural
compile-time per SP20 §0.1.
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