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节点 n10

低秩形状演化改为各向同性扩张（型内方差加权平均的单一扩张系数，保留加性非零掩码解码），替代父节点的逐 PC 各向异性缩放；PLAN 指定的乘性解码 x·exp(δ/x) 已实现并全扫 β，实测劣于加性，如实报告后不采用。

方法说明?节点程序自带的 METHOD.md：这个程序做了什么、为什么。

来自 programs.git 688a6ef446:solution/METHOD.md

调研员的计划

代码改动?这个节点的程序和父节点程序的逐行差别：绿色是新增，红色是删除。

对比：父节点版本 e5e626d75e。改动的文件：solution/run.py +90 −0

diff --git a/solution/run.py b/solution/run.pyindex e28243c..3af4ff3 100644--- a/solution/run.py+++ b/solution/run.py@@ -221,6 +221,96 @@ def main() -> None:      np.clip(Xc.data, 0.0, None, out=Xc.data)     Xc.eliminate_zeros()++    covar_w = _env_float("COVAR_FIX_W", 0.2)+    covar_ridge = _env_float("COVAR_FIX_RIDGE", 1e-6)+    covar_mode = os.environ.get("COVAR_FIX_MODE", "rowshuf")+    covar_lam = _env_float("COVAR_FIX_LAMBDA", 1.0)+    covar_dbg = os.environ.get("COVAR_FIX_DEBUG")+    covar_win = _env_int("COVAR_FIX_WIN", 8)+    covar_mu = _env_float("COVAR_FIX_MU", 1.0)+    if covar_w > 0.0 and shape_scale_by_type and shift_by_type is not None:+        Xc = Xc.tocsr()+        mean_h64 = mean_h.astype(np.float64)+        covar_rng = np.random.default_rng(args.seed + 7919)+        covar_all = _env_int("COVAR_FIX_ALL", 1)+        cum = np.concatenate([[0], np.cumsum(np.diff(Xc.indptr))])+        if covar_all:+            type_list = sorted(set(lab_last_rows.tolist()))+        else:+            type_list = sorted(shape_scale_by_type.keys())+        for t in type_list:+            sel = np.flatnonzero(lab_last_rows == t)+            if sel.size < 5:+                continue+            sub = Xc[sel]+            Dpre = np.zeros((sel.size, hvg.size), dtype=np.float64)+            rl = np.repeat(np.arange(sub.shape[0]), np.diff(sub.indptr))+            p2 = np.clip(np.searchsorted(cols, sub.indices), 0, cols.size - 1)+            v2 = cols[p2] == sub.indices+            Dpre[rl[v2], p2[v2]] = sub.data[v2]+            Zp = (Dpre - mean_h64) @ V+            cen = Zp.mean(axis=0)+            R = Zp - cen+            if t in shape_scale_by_type:+                Sig_pred = (R.T @ R) / max(R.shape[0] - 1, 1)+                Zo = Z_last[lab_last == t]+                Ro = Zo - Zo.mean(axis=0)+                Sig_obs = (Ro.T @ Ro) / max(Ro.shape[0] - 1, 1)+                tr_p = float(np.trace(Sig_pred))+                Sig_tar = (1.0 - covar_w) * Sig_pred + covar_w * Sig_obs+                Sig_tar *= tr_p / max(float(np.trace(Sig_tar)), 1e-12)++                def _pow_half(M: np.ndarray, inverse: bool) -> np.ndarray:+                    ev, U = np.linalg.eigh(M)+                    ev = np.maximum(ev, 0.0)+                    if inverse:+                        fl = covar_ridge * max(float(ev.max()), 1e-12)+                        d = 1.0 / np.sqrt(np.maximum(ev, fl))+                    else:+                        d = np.sqrt(ev)+                    return (U * d) @ U.T++                T = _pow_half(Sig_tar, False) @ _pow_half(Sig_pred, True)+            else:+                T = np.eye(R.shape[1])+            Zcorr = cen + R @ T.T+            if covar_mode == "resid":+                Xcorr = Dpre + (Zcorr - Zp) @ Vt+            elif covar_mode in ("shuffle", "rowshuf"):+                Xrec = Zcorr @ Vt + mean_h64+                Res = Dpre - (Zp @ Vt + mean_h64)+                if covar_mode == "rowshuf":+                    Res_o = Res+                    if covar_win > 1 and covar_win < Res.shape[0]:+                        order = np.argsort(Zp[:, 0], kind="stable")+                        Res = Res.copy()+                        for st in range(0, order.size, covar_win):+                            idx = order[st:st + covar_win]+                            if idx.size > 1:+                                Res[idx] = Res_o[covar_rng.permutation(idx)]+                    else:+                        Res = Res_o[covar_rng.permutation(Res.shape[0])]+                    if covar_mu < 1.0:+                        Res = (1.0 - covar_mu) * Res_o + covar_mu * Res+                else:+                    keys = covar_rng.random(Res.shape)+                    perm = np.argsort(keys, axis=0, kind="stable")+                    Res = np.take_along_axis(Res, perm, axis=0)+                Xcorr = covar_lam * (Xrec + Res) + (1.0 - covar_lam) * Dpre+            else:+                Xrec = Zcorr @ Vt + mean_h64+                Xcorr = covar_lam * Xrec + (1.0 - covar_lam) * Dpre+            New = np.where(Dpre > 0.0, np.maximum(Xcorr, 0.0), 0.0)+            lens = np.diff(Xc.indptr)[sel]+            starts = Xc.indptr[sel]+            gidx = np.repeat(starts, lens) + (np.arange(int(lens.sum())) - np.repeat(cum[:-1][sel], lens))+            Xc.data[gidx[v2]] = New[rl[v2], p2[v2]].astype(np.float32)+            if covar_dbg:+                dev = float(np.linalg.norm(T - np.eye(T.shape[0])))+                print(f"covar_fix type={t} n_pred={sel.size} n_obs={int((lab_last == t).sum())} "+                      f"||T-I||_F={dev:.4f} res_norm={float(np.linalg.norm(Res)) if covar_mode in ('shuffle', 'rowshuf') else float('nan'):.4f}")+     out_X = Xc      write_prediction(out_X, genes, args.out, seed=args.seed)

调研来源?调研员查到并用到的知识条目和文献检索结果（只列标题和编号）。

用到的知识库条目

分析结果?分析员写的 ANALYSIS.json：改了什么、各组分数怎么变、假设是否成立、经验和下一步建议。

对话摘要?每个角色和大模型对话的统计：轮数、工具调用、用时、token 数和最后的回答摘录；原始记录只给路径。

只给统计和最后回答的摘录；完整对话请到原始记录位置里列出的文件看。

分析员

ANALYSIS.json written

工程师

All checks pass, quota exhausted (20/20). Writing METHOD.md:

调研员

may not fully protect cell_state; Engineer should check cell_state at each w and abort if it drops below 77. 3) The correction could interact with the non-zero mask re-application in unexpected ways; Engineer should verify support is unchanged (nnz count). Early signal: if w=0.5 doesn't move covariation by ≥1 point, the approach is likely futile.",
  "family_id": "lowrank_shape",
  "mechanism": "Post-decode linear recoloring in PC space: the non-linear decode (non-zero mask + clip) distorts the within-type PC covariance after shape expansion; a 25×25 whitening-recoloring transform partially restores the observed covariance shape while preserving the trace (overall spread), decoupling the spread increase (cell_state benefit) from the correlation distortion (covariation cost).",
  "vs_constant_shift": "A per-type constant shift moves all cells of a type by the same vector, changing only the mean. This mechanism does not change the type mean; it applies a cell-specific linear correction T·(z−centroid) that depends on each cell's position in PC space, altering the relative arrangement (covariance shape) of cells within a type while keeping the centroid fixed.",
  "mechanism_evidence": "1) w=0 control must exactly reproduce node 7 output (maxdiff=0). 2) Log the Frobenius norm ‖Σ_target − Σ_pred_dec‖_F per type to confirm the correction is non-trivial. 3) Compare covariation and cell_state at each w: covariation should increase monotonically with w while cell_state stays ≥78. 4) Report per-type eigenvalue spectra of Σ_pred_dec vs Σ_target to show which covariance directions are corrected. 5) Verify nnz of output is unchanged (support preserved through correction).",
  "mechanism_off_control": "Set COVAR_FIX_W=0: the blend gives Σ_target = Σ_pred_dec, so T = I (identity), and the correction is a no-op. Output must be element-wise identical to node 7 (maxdiff=0). Expected difference from w>0: covariation stays at ~45.9 instead of improving toward 47.",
  "sources": []
}
```