//  [python]
def lut_m_step(self, Q_orig, groupsize, quantizer, scale=None, svd_rank=None):
        with torch.enable_grad():
            W = self.layer.weight.data.clone().float()
            G = self.G
            del self.G
            if scale is not None:
                scale.detach()

            offset = (W.mm(G) * W).sum()

            all_centroids = quantizer.all_centroids
            all_assignments = self.assignments
            vq_dim = quantizer.vq_dim

            if svd_rank is not None:
                assert vq_dim == 1, "In this implementation, SVD only works on 1D VQ"
                r = int(all_centroids[0].shape[1] * svd_rank)
                print(f"Effective SVD rank: {r}")
                Groups = all_centroids[0].shape[0]

                C = torch.concat(all_centroids, dim=0).squeeze()  # G x K
                C, new_idx = torch.sort(C, dim=1)
                new_idx = torch.argsort(new_idx, dim=1).split(Groups)

                U, S, V = torch.svd(C)
                all_centroids, V = (U * S[:, None])[:, :r].split(Groups), V[:r]

                new_assignments = []
                for idx, a in zip(new_idx, all_assignments):
                    new_assignments.append([])
                    for a_ in a:
                        remapped_a = torch.gather(idx, dim=1, index=a_)
                        new_assignments[-1].append(remapped_a)
                all_assignments = new_assignments

            def make_quantized_weight(centroids, assignments, scale=None):
                all_values = []
                for c, a in zip(centroids, assignments):
                    if svd_rank is not None:
                        c = (c @ V).unsqueeze(-1)
                    for a_ in a:
                        values = torch.gather(
                            c, dim=1, index=a_.unsqueeze(-1).expand(-1, -1, vq_dim)
                        )
                        all_values.append(values.view(W.shape[0], -1))
                Q = torch.concat(all_values, dim=1)
                if scale is not None:
                    Q = torch.mul(Q, scale)
                return Q

            with torch.no_grad():
                Q = make_quantized_weight(all_centroids, all_assignments, scale)

                orig_loss = quad_loss_2(W, Q, G)
                snr_before = 10 * np.log10(offset.item() / orig_loss.item())

            must_restart = True
            lr = 1e-3

            while must_restart:
                orig_centroids = [c.data.clone() for c in all_centroids]
                [c.requires_grad_() for c in all_centroids]
                param_list = list(all_centroids) + ([] if svd_rank is None else [V])
                o = torch.optim.Adam(param_list, lr=lr)
                for _ in range(25):
                    must_restart = False
                    o.zero_grad()
                    Q = make_quantized_weight(all_centroids, all_assignments, scale)
                    loss = quad_loss_2(W, Q, G)
                    if loss > orig_loss or torch.isnan(loss):
                        lr *= 1e-1
                        print(f"Inner loop: Restarting M-step with lr={lr:.2e}")
                        must_restart = True
                        all_centroids = orig_centroids
                        break
                    loss.backward()
                    o.step()

                if not must_restart:
                    if quantizer.codebook_bitwidth is not None:
                        new_all_centroids = [
                            quantize_centroids(
                                c.requires_grad_(False),
                                quantizer.codebook_bitwidth,
                                per_codebook=quantizer.quantize_per_codebook,
                            )
                            for c in all_centroids
                        ]
                    else:
                        new_all_centroids = all_centroids
                    Q = make_quantized_weight(new_all_centroids, all_assignments, scale)
                    loss = quad_loss_2(W, Q, G)
                    if torch.isnan(loss):
                        lr *= 1e-1
                        print(f"Outer loop: Restarting M-step with lr={lr:.2e}")
                        must_restart = True
                        all_centroids = orig_centroids
                        continue

                    del orig_centroids
                    print(
                        f"time M-step SGD {(time.time() - self.tick):.2f}; final loss: {loss.item():.4f}"
                    )
                    orig_loss = quad_loss_2(W, Q, G)
                    snr_after = 10 * np.log10(offset.item() / orig_loss.item())

                    print(f"improvement: {snr_before:.2f} -> {snr_after:.2f}")

        return Q