code/codec.py

"""Sub-2-bit weight codec: randomised Hadamard incoherence processing followed by
multi-stage residual vector quantisation on a shared (amortised-free) codebook.

Rate is controlled in 0.5 bit/weight steps by the number of residual stages:
each stage codes a d=16 subvector with an 8-bit index -> 0.5 bit/weight/stage.
"""
import math
import torch

D_SUB = 16          # subvector dimension
CB_BITS = 8         # bits per stage index
CB_SIZE = 1 << CB_BITS
BITS_PER_STAGE = CB_BITS / D_SUB   # 0.5 bit/weight


# ---------------------------------------------------------------- Hadamard
def _fwht(x):
    """In-place fast Walsh-Hadamard transform over the last dim (power of 2)."""
    n = x.shape[-1]
    assert n & (n - 1) == 0, f"dim {n} not a power of two"
    h = 1
    orig = x.shape
    x = x.reshape(-1, n).clone()
    while h < n:
        x = x.view(-1, n // (2 * h), 2, h)
        a = x[:, :, 0, :].clone()
        b = x[:, :, 1, :].clone()
        x[:, :, 0, :] = a + b
        x[:, :, 1, :] = a - b
        x = x.view(-1, n)
        h *= 2
    return (x / math.sqrt(n)).reshape(orig)


def _signs(n, seed, device, dtype):
    g = torch.Generator(device="cpu").manual_seed(seed)
    return (torch.randint(0, 2, (n,), generator=g).to(device=device,
            dtype=dtype) * 2 - 1)


def rht_forward(W, seed):
    sr = _signs(W.shape[1], seed, W.device, W.dtype)
    sl = _signs(W.shape[0], seed + 1, W.device, W.dtype)
    X = _fwht(W * sr)                    # right transform
    X = _fwht((X * sl.unsqueeze(1)).t().contiguous()).t().contiguous()
    return X


def rht_inverse(X, seed):
    sr = _signs(X.shape[1], seed, X.device, X.dtype)
    sl = _signs(X.shape[0], seed + 1, X.device, X.dtype)
    W = _fwht(X.t().contiguous()).t().contiguous() * sl.unsqueeze(1)
    W = _fwht(W) * sr
    return W


# ---------------------------------------------------------------- codebook
_CN = {}


def _cnorm(C):
    k = id(C)
    if k not in _CN or _CN[k][0] is not C:
        _CN[k] = (C, (C * C).sum(1).unsqueeze(0))
    return _CN[k][1]


def _assign(X, C, chunk=1 << 20):
    if X.shape[0] <= chunk:
        return (_cnorm(C) - 2.0 * (X @ C.t())).argmin(1)
    out = torch.empty(X.shape[0], dtype=torch.long, device=X.device)
    Cn = _cnorm(C)
    for s in range(0, X.shape[0], chunk):
        e = min(s + chunk, X.shape[0])
        out[s:e] = (Cn - 2.0 * (X[s:e] @ C.t())).argmin(1)
    return out


def rht_hessian(H, seed):
    """Transform an input-side Hessian into the RHT basis: H' = T^T H T with
    T = diag(s_r) * Hadamard (orthogonal, symmetric Hadamard)."""
    s = _signs(H.shape[0], seed, H.device, H.dtype)
    A = H * s.unsqueeze(0) * s.unsqueeze(1)
    A = _fwht(A)
    A = _fwht(A.t().contiguous()).t().contiguous()
    return A


# ---------------------------------------------------------------- quantiser
def vq(V, codebooks, stages, refine=1):
    """Multi-stage residual VQ of [N, D_SUB] rows, with optional coordinate
    refinement: each stage index is re-solved against the residual left by all
    the other stages, which recovers part of the greedy-encoding loss."""
    Q = torch.zeros_like(V)
    parts = []
    for s in range(stages):
        C = codebooks[s]
        idx = _assign(V - Q, C)
        p = C[idx]
        parts.append(p)
        Q = Q + p
    for _ in range(refine):
        for s in range(stages):
            Q = Q - parts[s]
            idx = _assign(V - Q, codebooks[s])
            parts[s] = codebooks[s][idx]
            Q = Q + parts[s]
    return Q


def _block_ldl(H, blk):
    """H = L D L^T with L block-unit-lower-triangular (blocks of size blk).

    The per-block inverses are batched into a single call rather than looped.
    """
    n = H.shape[0]
    C = torch.linalg.cholesky(H)
    K = n // blk
    diag = torch.stack([C[k * blk:(k + 1) * blk, k * blk:(k + 1) * blk]
                        for k in range(K)])
    dinv = torch.linalg.inv(diag)
    Binv = torch.zeros_like(C)
    idx = torch.arange(blk, device=H.device)
    for k in range(K):
        Binv[k * blk + idx[:, None], k * blk + idx[None, :]] = dinv[k]
    return C @ Binv


def prepare_hessian(H, seed, rht_on=True, blk=D_SUB, damp=0.01):
    """Rotate, damp and block-LDL-factorise a Hessian once, so that every linear
    sharing this input reuses the factorisation."""
    dev = H.device
    Hf = H.float().clone()
    dead = torch.diag(Hf) <= 0
    if dead.any():
        Hf[dead, dead] = 1.0
    Hf += torch.eye(Hf.shape[0], device=dev) * (damp * torch.diag(Hf).mean())
    Hr = rht_hessian(Hf, seed) if rht_on else Hf
    return _block_ldl(Hr, blk), dead


def ldlq_quantize(W, L, dead, codebooks, stages, seed=1234, rht_on=True,
                  blk=D_SUB, refine=0):
    """Hessian-aware quantisation: minimise ||(W-What) X||_F with H = X X^T,
    by block-LDL error feedback over blk-column groups, each group coded by the
    residual VQ. `L`/`dead` come from `prepare_hessian` and are shared by all
    linears reading the same input."""
    dt = W.dtype
    Wf = W.float()
    if dead is not None and dead.any():
        Wf = Wf.clone()
        Wf[:, dead] = 0.0

    X = rht_forward(Wf, seed) if rht_on else Wf
    scale = X.pow(2).mean(dim=1, keepdim=True).sqrt().clamp_min(1e-8)
    Xn = X / scale

    o, i = Xn.shape
    K = i // blk
    Q = torch.zeros_like(Xn)
    E = torch.zeros_like(Xn)
    for k in range(K - 1, -1, -1):
        s = slice(k * blk, (k + 1) * blk)
        tgt = Xn[:, s]
        if k + 1 < K:
            tgt = tgt + E[:, (k + 1) * blk:] @ L[(k + 1) * blk:, s]
        Q[:, s] = vq(tgt.reshape(-1, D_SUB), codebooks, stages,
                     refine).reshape(o, blk)
        E[:, s] = Xn[:, s] - Q[:, s]

    Xq = Q * scale
    What = rht_inverse(Xq, seed) if rht_on else Xq
    bits = stages * BITS_PER_STAGE + 16.0 / i
    return What.to(dt), dict(bits=bits, stages=stages)


def quantize(W, codebooks, stages, seed=1234, rht_on=True, refine=1):
    """Quantise [out,in] weight matrix at `stages`*0.5 bits/weight, ignoring
    activation statistics (the data-free ablation of `ldlq_quantize`)."""
    Wf = W.float()
    X = rht_forward(Wf, seed) if rht_on else Wf
    o, i = X.shape
    scale = X.pow(2).mean(dim=1, keepdim=True).sqrt().clamp_min(1e-8)
    Xn = X / scale
    Q = vq(Xn.reshape(-1, D_SUB), codebooks, stages, refine).reshape(o, i)
    Xq = Q * scale
    What = rht_inverse(Xq, seed) if rht_on else Xq
    bits = stages * BITS_PER_STAGE + 16.0 / i          # + fp16 row scale
    return What.to(W.dtype), dict(bits=bits, stages=stages)


def build_codebooks(max_stages=6, device="cpu", seed=0):
    """Stage-0 codebook on Gaussian data; each later stage on the residual
    distribution produced by the preceding stages (so shapes adapt)."""
    g = torch.Generator(device="cpu").manual_seed(seed)
    X = torch.randn(400_000, D_SUB, generator=g).to(device)
    cbs, R = [], X.clone()
    for s in range(max_stages):
        C = _kmeans(R, CB_SIZE, iters=35, seed=seed + s, device=device)
        cbs.append(C)
        R = R - C[_assign(R, C)]
    return cbs


def _kmeans(X, size, iters, seed, device):
    g = torch.Generator(device="cpu").manual_seed(seed)
    n = X.shape[0]
    C = X[torch.randperm(n, generator=g)[:size]].clone()
    for _ in range(iters):
        idx = _assign(X, C)
        C_new = torch.zeros_like(C)
        cnt = torch.zeros(size, device=device)
        C_new.index_add_(0, idx, X)
        cnt.index_add_(0, idx, torch.ones(n, device=device))
        dead = cnt == 0
        C_new[~dead] /= cnt[~dead].unsqueeze(1)
        if dead.any():
            C_new[dead] = X[torch.randint(0, n, (int(dead.sum()),),
                                          generator=g)]
        C = C_new
    return C


# ---------------------------------------------------------------- baseline
def rtn(W, bits, group=128):
    """Round-to-nearest uniform baseline with per-group asymmetric scales."""
    o, i = W.shape
    Wf = W.float().reshape(o, i // group, group)
    mn = Wf.amin(-1, keepdim=True)
    mx = Wf.amax(-1, keepdim=True)
    n = 2 ** bits - 1
    s = ((mx - mn) / n).clamp_min(1e-9)
    q = ((Wf - mn) / s).round().clamp(0, n)
    Wq = (q * s + mn).reshape(o, i)
    eff = bits + 2 * 16.0 / group
    return Wq.to(W.dtype), dict(bits=eff)