scripts/rdpg_core.py

"""Core routines for reproducing arXiv:2601.06014 (Taing & Levin, ICML 2026):
"On the Effect of Misspecifying the Embedding Dimension in Low-rank Network Models".

Model: A = P + E with P = rho * X X^T, X in R^{n x r}.
ASE:   Xhat_{1:d} = Uhat_{1:d} |Shat|^{1/2}_{1:d}, eigenpairs sorted by |eigenvalue| desc.

Backend: torch CUDA eigh when available (float64), else numpy.
"""
import csv
import json
import math
import os
import time
import zlib

import numpy as np

try:
    import torch

    HAS_TORCH = True
    HAS_CUDA = torch.cuda.is_available()
except Exception:
    HAS_TORCH = False
    HAS_CUDA = False

R_TRUE = 5  # true latent dimension used throughout the paper's experiments


def seed_for(*parts):
    """Stable 32-bit seed from string parts."""
    return zlib.crc32("|".join(str(p) for p in parts).encode()) & 0xFFFFFFFF


def rng_for(*parts):
    return np.random.default_rng(seed_for(*parts))


# ---------------------------------------------------------------- sampling

def dirichlet_latent(n, r, rng):
    return rng.dirichlet(np.ones(r), size=n)  # rows on the simplex


def sym_noise(n, dist, rng, sigma=1.0):
    """Symmetric mean-zero noise matrix. dist in {normal, laplace, exp, poisson, t2.5}.
    sigma scales the base distribution (base variances: normal 1, laplace 2, exp 1,
    poisson 1, t2.5 = 5)."""
    if dist == "normal":
        M = rng.standard_normal((n, n))
    elif dist == "laplace":
        # Paper item (b) says "E_ij + 1 ~ Laplace(0,1)", but Laplace(0,1) is already
        # mean-zero, so the +1 shift would violate the paper's own mean-zero
        # requirement; we read it as E_ij ~ Laplace(0,1) (variance 2).
        M = rng.laplace(0.0, 1.0, size=(n, n))
    elif dist == "exp":
        M = rng.exponential(1.0, size=(n, n)) - 1.0
    elif dist == "poisson":
        M = rng.poisson(1.0, size=(n, n)).astype(np.float64) - 1.0
    elif dist == "t2.5":
        M = rng.standard_t(2.5, size=(n, n))  # infinite 4th moment: violates A7
    else:
        raise ValueError(dist)
    if sigma != 1.0:
        M *= sigma
    U = np.triu(M, 1)
    return U + U.T + np.diag(np.diag(M))


def weighted_rdpg(n, r, dist, rng, rho=1.0, sigma=1.0):
    """Returns (A, Xs, lam_pop) with Xs = sqrt(rho)*X the estimand and lam_pop the
    non-zero eigenvalues of P (descending), computed exactly via the r x r Gram trick."""
    X = dirichlet_latent(n, r, rng)
    Xs = math.sqrt(rho) * X
    P = Xs @ Xs.T
    A = P + sym_noise(n, dist, rng, sigma=sigma)
    lam_pop = np.linalg.eigvalsh(Xs.T @ Xs)[::-1].copy()  # eigs of P via Gram
    return A, Xs, lam_pop


def binary_dirichlet_rdpg(n, r, rng, rho=1.0):
    """Sparse binary RDPG with Dirichlet latents. A_ij ~ Bern(rho x_i^T x_j), diag 0."""
    X = dirichlet_latent(n, r, rng)
    Xs = math.sqrt(rho) * X
    P = Xs @ Xs.T
    U = rng.random((n, n))
    A = (np.triu(U, 1) < np.triu(P, 1)).astype(np.float64)
    A = A + A.T
    lam_pop = np.linalg.eigvalsh(Xs.T @ Xs)[::-1].copy()
    return A, Xs, lam_pop


def sbm_binary(n, r, rng, p_in=0.9, p_out=0.1):
    """SBM per paper Section 4.2: pi ~ Dir(1_r), z ~ Cat(pi), B = 0.1 + 0.8 I.
    Latent truth X = U_{1:r} S^{1/2}_{1:r} from P = Z B Z^T (exact via r x r trick)."""
    B = np.full((r, r), p_out) + (p_in - p_out) * np.eye(r)
    while True:
        pi = rng.dirichlet(np.ones(r))
        z = rng.choice(r, size=n, p=pi)
        counts = np.bincount(z, minlength=r)
        if counts.min() >= 1:
            break
    C = np.diag(np.sqrt(counts.astype(np.float64)))
    K = C @ B @ C  # r x r, same non-zero spectrum as P
    lam, Q = np.linalg.eigh(K)
    lam = lam[::-1].copy()
    Q = Q[:, ::-1].copy()
    Z = np.zeros((n, r))
    Z[np.arange(n), z] = 1.0
    U = Z @ np.diag(1.0 / np.sqrt(counts)) @ Q  # orthonormal columns
    X = U @ np.diag(np.sqrt(np.maximum(lam, 0.0)))
    P = X @ X.T
    Urand = rng.random((n, n))
    A = (np.triu(Urand, 1) < np.triu(P, 1)).astype(np.float64)
    A = A + A.T
    return A, X, lam


# ---------------------------------------------------------------- spectral

def full_eigh(A):
    """Full symmetric eigendecomposition, float64. Returns (w, V) ascending, numpy."""
    t0 = time.time()
    if HAS_CUDA:
        T = torch.from_numpy(np.ascontiguousarray(A)).cuda()
        w, V = torch.linalg.eigh(T)
        w = w.cpu().numpy()
        V = V.cpu().numpy()
        del T
        torch.cuda.empty_cache()
    else:
        w, V = np.linalg.eigh(A)
    return w, V, time.time() - t0


def spectral_norm_sym(E):
    """||E|| for symmetric E (largest |eigenvalue|)."""
    if HAS_CUDA:
        T = torch.from_numpy(np.ascontiguousarray(E)).cuda()
        w = torch.linalg.eigvalsh(T)
        out = float(torch.max(torch.abs(w)).cpu())
        del T
        torch.cuda.empty_cache()
        return out
    w = np.linalg.eigvalsh(E)
    return float(np.max(np.abs(w)))


def ase_decompose(A, r=R_TRUE, max_dim=45):
    """One eigh, reused across embedding dimensions.

    Returns dict with:
      order      : indices of eigenpairs sorted by |eigenvalue| descending
      w          : all eigenvalues (ascending, as returned by eigh)
      V          : all eigenvectors
      abs_w_desc : |eigenvalues| descending
      max_abs_trail_full : max_{alpha>r} max_j |u_hat_{j,alpha}|  (ALL trailing pairs)
      max_abs_trail_win  : same but only over trailing pairs r+1..max_dim (used in ASE)
      eigh_s     : eigh wall seconds
    """
    w, V, eigh_s = full_eigh(A)
    order = np.argsort(-np.abs(w), kind="stable")
    abs_w_desc = np.abs(w)[order]
    trail = order[r:]
    max_abs_trail_full = float(np.max(np.abs(V[:, trail]))) if trail.size else float("nan")
    win = order[r:max_dim]
    max_abs_trail_win = float(np.max(np.abs(V[:, win]))) if win.size else float("nan")
    return dict(order=order, w=w, V=V, abs_w_desc=abs_w_desc,
                max_abs_trail_full=max_abs_trail_full,
                max_abs_trail_win=max_abs_trail_win, eigh_s=eigh_s)


def ase_embed(dec, d):
    """d-dimensional ASE from a decomposition."""
    idx = dec["order"][:d]
    return dec["V"][:, idx] * np.sqrt(np.abs(dec["w"][idx]))[None, :]


def trailing_block_2inf(dec, r, d):
    """||Xhat_{r+1:d}||_{2,inf}: max row norm of the extra-dimension block (d>r)."""
    if d <= r:
        return 0.0
    idx = dec["order"][r:d]
    blk = dec["V"][:, idx] * np.sqrt(np.abs(dec["w"][idx]))[None, :]
    return float(np.max(np.linalg.norm(blk, axis=1)))


# ---------------------------------------------------------------- alignment

def pad_cols(M, d):
    n, c = M.shape
    if c >= d:
        return M[:, :d]
    return np.hstack([M, np.zeros((n, d - c))])


def procrustes(Xhat, Xtrue):
    """W = argmin_W ||Xhat W - Xtrue||_F over O_d (Eq. 18 in the paper)."""
    M = Xhat.T @ Xtrue
    U, s, Vt = np.linalg.svd(M)
    W = U @ Vt
    return W, s


def errors_at_dim(dec, Xs, d, r=R_TRUE):
    """Paper's evaluation: pad, Frobenius-Procrustes align, report norms.

    Returns (err2inf, errF, trail2inf, min_frob_sq) where min_frob_sq is the exact
    closed-form min over W of ||Xhat W - Xtrue||_F^2 (from the Procrustes SVD)."""
    Xhat = ase_embed(dec, d)
    if d >= r:
        Xt = pad_cols(Xs, d)
        Xh = Xhat
    else:
        Xh = pad_cols(Xhat, r)  # Xhat^circ per Eq. (def:Xcirc)
        Xt = Xs
    W, s = procrustes(Xh, Xt)
    D = Xh @ W - Xt
    err2inf = float(np.max(np.linalg.norm(D, axis=1)))
    errF = float(np.linalg.norm(D))
    min_frob_sq = float((Xh * Xh).sum() + (Xt * Xt).sum() - 2.0 * s.sum())
    return err2inf, errF, trailing_block_2inf(dec, r, d), min_frob_sq


def min_2inf_over_W(Xh, Xt, iters=300, seed=0):
    """Approximately minimize ||Xh W - Xt||_{2,inf} over orthogonal W (subgradient
    descent + polar retraction, multi-start). Returns achieved value (upper bound on
    the true min)."""
    rng = np.random.default_rng(seed)
    d = Xh.shape[1]
    W0, _ = procrustes(Xh, Xt)
    best = np.inf
    for start in range(3):
        W = W0.copy()
        if start > 0:
            Q, _ = np.linalg.qr(W0 + 0.05 * rng.standard_normal((d, d)))
            W = Q
        step = 0.1
        for it in range(iters):
            D = Xh @ W - Xt
            rown = np.linalg.norm(D, axis=1)
            i = int(np.argmax(rown))
            best = min(best, float(rown[i]))
            if rown[i] < 1e-15:
                break
            g = np.outer(Xh[i], D[i] / rown[i])  # d x d subgradient wrt W
            W = W - step * g
            U, _, Vt = np.linalg.svd(W)  # polar retraction to O_d
            W = U @ Vt
            step *= 0.985
    return best


# ---------------------------------------------------------------- output

class ResultSink:
    """Appends rows to a local CSV and periodically pushes it to a HF dataset repo."""

    def __init__(self, fname, fieldnames, repo_id="visv-Bro/rdpg-misspec-results"):
        self.fname = fname
        self.fieldnames = fieldnames
        self.repo_id = repo_id
        self.rows_since_push = 0
        new = not os.path.exists(fname)
        self.fh = open(fname, "a", newline="")
        self.writer = csv.DictWriter(self.fh, fieldnames=fieldnames)
        if new:
            self.writer.writeheader()
            self.fh.flush()

    def add(self, **row):
        self.writer.writerow(row)
        self.fh.flush()
        self.rows_since_push += 1

    def push(self, force=False):
        if os.environ.get("NO_PUSH", "0") == "1":
            return
        if self.rows_since_push == 0 and not force:
            return
        try:
            from huggingface_hub import HfApi

            HfApi().upload_file(
                path_or_fileobj=self.fname,
                path_in_repo=os.path.basename(self.fname),
                repo_id=self.repo_id,
                repo_type="dataset",
            )
            print(f"[push] {self.fname} -> {self.repo_id} ok", flush=True)
            self.rows_since_push = 0
        except Exception as e:  # keep computing even if a push fails
            print(f"[push] FAILED ({e}); will retry later", flush=True)


def log(msg):
    print(f"[{time.strftime('%H:%M:%S')}] {msg}", flush=True)