/**
 * cpu_ops.ts — the small set of exact CPU primitives the reference forward and
 * backward passes share (linear, RMSNorm, SiLU, softplus).
 *
 * Each one mirrors a WGSL kernel exactly, so a gradient computed here is the
 * gradient of the function the GPU actually evaluates. They are deliberately
 * plain loops over `Float32Array`: correctness first, and small enough that the
 * finite-difference check in `tests/backprop.test.ts` is meaningful.
 */
/** Epsilon used by `rmsnorm_forward` in `ACTIVATIONS_WGSL`. */
export declare const RMSNORM_EPS = 0.000001;
export declare function sigmoid(x: number): number;
/** SiLU(x) = x * sigmoid(x) — mirrors `silu_forward`. */
export declare function silu(x: number): number;
/** d/dx SiLU(x) = sigmoid(x) * (1 + x * (1 - sigmoid(x))). */
export declare function siluGrad(x: number): number;
/** Numerically stable softplus — mirrors the kernel's `max(x,0) + log1p(exp(-|x|))`. */
export declare function softplus(x: number): number;
/**
 * Y = X @ W^T + b, mirroring `linear_forward`.
 *
 * @param X   (M, K)
 * @param W   (N, K) row-major
 * @param b   (N,)
 * @param out (M, N) — written, not accumulated
 */
export declare function linearForward(X: Float32Array, W: Float32Array, b: Float32Array, M: number, K: number, N: number, out: Float32Array): void;
/**
 * Backward of {@link linearForward}. `dX` is written; `dW` and `db` are
 * ACCUMULATED into (so one parameter can collect gradient from several call
 * sites without a temporary).
 */
export declare function linearBackward(dY: Float32Array, X: Float32Array, W: Float32Array, M: number, K: number, N: number, dX: Float32Array, dW: Float32Array, db: Float32Array): void;
/**
 * RMSNorm forward — mirrors `rmsnorm_forward`:
 *   inv[r] = 1 / sqrt(mean(x[r]²) + eps);  y[r,i] = x[r,i] * inv[r] * w[i]
 */
export declare function rmsNormForward(x: Float32Array, w: Float32Array, M: number, D: number, out: Float32Array, inv: Float32Array, eps?: number): void;
/**
 * RMSNorm backward. `dx` and `dw` are ACCUMULATED into — `dx` in particular is
 * usually the residual path, which already carries a gradient.
 */
export declare function rmsNormBackward(dY: Float32Array, x: Float32Array, w: Float32Array, inv: Float32Array, M: number, D: number, dx: Float32Array, dw: Float32Array, _eps?: number): void;
//# sourceMappingURL=cpu_ops.d.ts.map