/**
 * splat-train-backward.parity.ts
 *
 * JavaScript port of the WGSL kernel in `splat-train-backward.wgsl`. Exists so the GPU trainer
 * backward can be exercised in Node (no WebGPU adapter there) and compared against the
 * gradient-checked CPU reference GaussianTrainer2D.backward2D.
 *
 * It mirrors the kernel EXACTLY, including the fixed-point round-trip: gradients are quantized via
 * `toFixed(v) = round(v * SCALE)` (matching `i32(round(...))` in WGSL), accumulated as integers
 * (the atomic<i32> scatter), then dequantized by `/ SCALE`. The only twin↔WGSL difference is
 * round-half tie-breaking (JS half-up vs WGSL half-to-even), which is measure-zero on real data.
 *
 * Parity chain (mirrors splat-shared-sort): WGSL ↔ this twin is STRUCTURAL (the test regexes the
 * .wgsl for the load-bearing ops); this twin ↔ backward2D is BEHAVIORAL (numeric, within the
 * fixed-point tolerance). backward2D ↔ true gradients is already proven by finite differences.
 *
 * If splat-train-backward.wgsl is edited, this twin MUST be updated in lockstep.
 *
 * @see splat-train-backward.wgsl
 * @see ../GaussianTrainer2D.ts (backward2D — the CPU reference)
 */
import type { Gaussian2D, Gaussian2DGrad } from '../GaussianTrainer2D';
/** Fixed-point scale — MUST equal FIXED_POINT_SCALE in splat-train-backward.wgsl. */
export declare const FIXED_POINT_SCALE = 65536;
/** Per-pixel hit cap — MUST equal MAX_HITS in the .wgsl. */
export declare const MAX_HITS = 256;
/**
 * Parity twin of the WGSL alpha-blend backward. Returns dequantized per-gaussian gradients
 * (same shape as backward2D). Uses the production cutoffs (clip=true): sigma<0 skip,
 * alpha<1/255 skip, 0.999 clamp — matching the kernel.
 */
export declare function trainBackwardParity(g: Gaussian2D, W: number, H: number, dLimg: Float64Array | Float32Array, bg?: readonly [number, number, number], scale?: number): Gaussian2DGrad;
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