FLA KDA Skill

Use this skill for KDA-specific work under fla/ops/kda/** and tests that exercise KDA behavior.

Public code map

• Public API: fla.ops.kda.chunk_kda, fla.ops.kda.fused_recurrent_kda.
• Gate helpers: naive_kda_gate, naive_kda_lowerbound_gate, kda_gate_fwd, kda_gate_bwd, fused_kda_gate, kda_gate_chunk_cumsum in fla/ops/kda/gate.py.
• Chunk forward: chunk_kda_fwd in chunk_fwd.py.
• Intra/inter forward: chunk_kda_fwd_intra, chunk_kda_fwd_kernel_intra_sub_chunk, chunk_kda_fwd_kernel_inter_solve_fused in chunk_intra.py.
• Token-parallel non-safe path: chunk_kda_fwd_intra_token_parallel in chunk_intra_token_parallel.py.
• WY recompute: recompute_w_u_fwd and recompute_w_u_fwd_kda_kernel in wy_fast.py.
• Backward: chunk_kda_bwd, chunk_kda_bwd_intra, chunk_kda_bwd_wy_dqkg_fused.
• Backends: FlashKDABackend, KDATileLangBackend.

Gate modes

chunk_kda has two gate input contracts:

1. Pre-gated mode: use_gate_in_kernel=False.
   • g is already the log-space decay tensor.
   • A_log, dt_bias, and lower_bound are not part of the gate activation.
2. In-kernel mode: use_gate_in_kernel=True.
   • g is raw gate input.
   • A_log is required and dt_bias is optional.
   • Without safe_gate, activation is -exp(A_log) * softplus(g + dt_bias).
   • With safe_gate, activation is lower_bound * sigmoid(exp(A_log) * (g + dt_bias)).

safe_gate=True requires use_gate_in_kernel=True, lower_bound is not None, and -5 <= lower_bound < 0.

Safe gate numerical note

With lower_bound=-5, every per-token gate value is in [-5, 0) before the RCP_LN2 conversion used by chunk_kda_fwd. A 16-token sub-chunk can therefore accumulate -80 in natural-log units. Directly feeding the full span to exp2 would be larger in base-2 units, so the safe intra path relies on offsetting.

chunk_kda_fwd_kernel_intra_sub_chunk uses a midpoint offset before exponentiation:

• b_gm = b_g - b_gn;
• exp2(b_gm) and exp2(-b_gm).

With the midpoint offset, each exponent operand covers at most about half of the 16-token sub-chunk. Under lower_bound=-5, this is about 40 / ln(2), which is below the kernel's exp2 safety comment threshold. The important invariant is not the raw cumulative value alone; it is that each exponentiation uses a local offset rather than the full chunk cumsum directly.

For inter-subchunk work, chunk_kda_fwd_kernel_inter_solve_fused computes decay ratios with paired offsets such as:

• exp2(b_g1 - b_gn1) and exp2(b_gn1 - b_g0);
• exp2(b_g2 - b_gn2) and exp2(b_gn2 - b_g1).

Both terms are non-positive under monotonic accumulated decay, so the off-diagonal inter path avoids positive exponent growth. The triangular solve operates on masked lower-triangular blocks, so it does not introduce an unbounded exponent path.

Safe vs non-safe intra path

• Safe path: chunk_kda_fwd_intra(..., safe_gate=True) calls chunk_kda_fwd_kernel_intra_sub_chunk for 16-token diagonal blocks, then calls chunk_kda_fwd_kernel_inter_solve_fused with USE_SAFE_GATE=True.
• Non-safe path: safe_gate=False calls chunk_kda_fwd_intra_token_parallel for diagonal blocks, then calls the same inter/solve kernel with USE_SAFE_GATE=False.
• Do not change one path without checking the other path unless the contract is explicitly safe-only or non-safe-only.

Correctness checklist

Before finishing a KDA behavior change, use fla-correctness-coverage and cover only axes affected by the change:

• dense and varlen sequence layout;
• forward and backward if training path is touched;
• pre-gated, non-safe in-kernel, and safe in-kernel gate modes where supported;
• raw beta logits and post-sigmoid beta where supported;
• use_qk_l2norm_in_kernel=True/False where relevant;
• MHA and GVA (HV > H);
• D != Dv when value dimension is involved;
• initial/final state, return_intermediate_states, and CP paths when touched;
• backend verifier behavior for FlashKDA / TileLang changes.
• gate numerical extremes when gate math or intra/inter decay is touched: lower_bound=-5, a lower bound close to 0, large positive and negative g + dt_bias, extreme A_log, long-sequence cumulative decay, chunk boundaries, and ragged varlen boundaries.

Style constraints

• Use platform helpers from fla.utils (device, device_platform, IS_NVIDIA, IS_NVIDIA_HOPPER, IS_NVIDIA_BLACKWELL, IS_AMD, IS_INTEL) instead of adding new direct torch.cuda platform checks in tests or public code. If no helper covers the condition, add one in fla.utils first.
• Keep math derivations in operator docs or PR text; in Triton kernels, prefer compact shape comments and one-line rationale comments.
• Do not include internal-only paths, private model names, local machine paths, or private workload identifiers in public tests or skills.