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5ff8ce1 140ce5b 5ff8ce1 140ce5b 5ff8ce1 140ce5b 5ff8ce1 140ce5b 5ff8ce1 140ce5b 5ff8ce1 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 | # ALSA.py
# ============================================================
# ALSA = NLSAEncoder + GPLM baseline + in-context attention residual mixing
#
# Key idea:
# ALSA = global predictor + analog/attention-like correction in diffusion coords ψ
#
# Behavior:
# - if prefix length ell == L: baseline-only AR rollout (NLSA+GPLM)
# - if ell > L: ALSA correction enabled:
# E_ctx = Y_true - Y_glob
# p(q,b) ∝ exp(-||ψ_q-ψ_b||^2 / (2 ell_attn^2))
# y = y_glob + gamma_ctx * Σ_b p(q,b) E_ctx[b]
#
# This is a "Markovian" IC method because p(q,·) is a probability distribution.
#
# Repo expectations:
# - NLSAEncoder provides:
# .L, .K_, .psi_, .mu_ and .encode_window(window_LD)->(r,)
# - GPLM provides:
# GPLM(X_latent, Y_ambient, center_X=False, ...) and callable predict
#
# Dependencies:
# numpy (scipy optional for pdist if you want it, but not required)
# ============================================================
from __future__ import annotations
from dataclasses import dataclass
from typing import Any, Dict, Optional, Tuple, Union
import numpy as np
from numpy.lib.stride_tricks import sliding_window_view
# ------------------------------------------------------------
# Imports from your repo (robust fallbacks)
# ------------------------------------------------------------
# NLSA encoder
try:
from .nlsa_encoder import NLSA # type: ignore
except Exception:
try:
from nlsa_encoder import NLSA # type: ignore
except Exception:
# if you named the file NLSA.py and class NLSAEncoder lives there
from NLSA import NLSA # type: ignore
# GPLM decoder
try:
from .gplm import GPLM # type: ignore
except Exception:
try:
from gplm import GPLM # type: ignore
except Exception:
from GPLM import GPLM # type: ignore
Array = np.ndarray
# ============================================================
# Small utilities
# ============================================================
def _as_2d(X: Array) -> Array:
X = np.asarray(X, dtype=float)
if X.ndim == 1:
X = X[:, None]
return X
def _sliding_windows(F_tD: Array, L: int) -> Array:
"""
Return windows W (K,L,D) from F (N,D) with K=N-L+1.
Handles numpy stride ordering differences.
"""
F = _as_2d(F_tD)
W = sliding_window_view(F, window_shape=int(L), axis=0)
# W can be (K,L,D) or (K,D,L)
a, b = W.shape[1], W.shape[2]
if (a, b) == (L, F.shape[1]):
return np.ascontiguousarray(W)
if (a, b) == (F.shape[1], L):
return np.ascontiguousarray(np.transpose(W, (0, 2, 1)))
raise ValueError(f"Unexpected window shape {W.shape} for L={L}, D={F.shape[1]}.")
def _sample_pairwise_d2(X: Array, m: int = 1024, seed: int = 0) -> Array:
"""
Sample pairwise squared distances for bandwidth estimation.
Returns 1D array of sampled d^2 values.
"""
X = np.asarray(X, dtype=np.float64)
n = X.shape[0]
if n <= 1:
return np.array([1.0], dtype=np.float64)
rng = np.random.default_rng(int(seed))
idx = rng.choice(n, size=min(int(m), n), replace=False)
Xs = X[idx]
# Sample random pairs among Xs
ns = Xs.shape[0]
M = min(20000, ns * (ns - 1) // 2)
ii = rng.integers(0, ns, size=M)
jj = rng.integers(0, ns, size=M)
mask = ii != jj
ii, jj = ii[mask], jj[mask]
if ii.size == 0:
return np.array([1.0], dtype=np.float64)
diff = Xs[ii] - Xs[jj]
return np.sum(diff * diff, axis=1)
def _median_ell_from_d2(d2: Array, q: float = 0.5, eps: float = 1e-12) -> float:
"""
If kernel is exp(-||x-y||^2/(2 ell^2)), heuristic:
ell^2 ≈ quantile(d^2)/2
"""
d2 = np.asarray(d2, dtype=np.float64)
if d2.size == 0:
return 1.0
v = float(np.quantile(d2, float(q)))
return float(np.sqrt(max(v / 2.0, eps)))
def _softmax_weights_from_d2(d2: Array, ell: float, eps: float = 1e-18) -> Array:
"""
p_i ∝ exp(-0.5 * d2_i / ell^2)
"""
d2 = np.asarray(d2, dtype=np.float64)
ell2 = float(ell) * float(ell) + 1e-18
logits = -0.5 * d2 / ell2
logits -= float(np.max(logits))
w = np.exp(logits)
s = float(np.sum(w))
return w / (s + eps)
# ============================================================
# ALSA config (sister to LISAConfig)
# ============================================================
@dataclass
class ALSAConfig:
# Encoder (NLSA)
L: int = 128
rank: int = 32
beta: Optional[float] = None
alpha: float = 1.0
center: bool = True
drop_first: bool = True
max_K_dense: int = 6000
seed: int = 0
# Baseline GPLM decoder psi->next sample
gplm_kwargs: Optional[Dict[str, Any]] = None
# psi preprocessing
whiten_psi: bool = True
# In-context attention correction
min_ctx_windows: Optional[int] = None # default r+1
ctx_k0: float = 10.0 # gamma_ctx = K_ctx/(K_ctx + ctx_k0)
attn_topk: Optional[int] = 64 # None = dense over all context
attn_ell: Optional[float] = None # if None -> estimate from training ψ geometry
attn_ell_q: float = 0.5 # quantile used for attn_ell estimation
# ============================================================
# ALSA main class
# ============================================================
class ALSA:
"""
ALSA = NLSAEncoder + GPLM baseline + attention-like (Markov) IC correction.
Training:
1) Fit NLSAEncoder on training series
2) Fit GPLM baseline on diffusion coords:
ψ_train(window) -> next sample
Inference:
- If prefix length ell == L: baseline-only AR rollout
- If ell > L:
build context windows within prefix
residual table E_ctx = Y_true - Y_glob
attention weights p(q,ctx) from ψ-distances
correction = Σ p * E_ctx
y = y_glob + gamma_ctx * correction
"""
def __init__(self, F_train: Array, *, config: Optional[ALSAConfig] = None, **kwargs: Any):
if config is None:
config = ALSAConfig(**kwargs)
self.cfg = config
F_train = _as_2d(F_train)
self.D = int(F_train.shape[1])
self.L = int(self.cfg.L)
# ---- 1) Encoder ----
self.enc = NLSA(
F_train,
L=int(self.cfg.L),
rank=int(self.cfg.rank),
beta=self.cfg.beta,
alpha=float(self.cfg.alpha),
center=bool(self.cfg.center),
drop_first=bool(self.cfg.drop_first),
max_K_dense=int(self.cfg.max_K_dense),
seed=int(self.cfg.seed),
)
self.r = 0 if self.enc.psi_ is None else int(self.enc.psi_.shape[1])
if self.r <= 0:
raise ValueError("NLSA produced r=0 diffusion dims. Increase rank or set drop_first=False.")
# Output mean from encoder centering
self.center = bool(self.cfg.center)
self.mu_X = self.enc.mu_.reshape(-1).astype(np.float64) if self.center else np.zeros((self.D,), dtype=np.float64)
# ---- 2) Baseline GPLM: psi -> next sample (centered space) ----
K = int(self.enc.K_)
n_pairs = K - 1
Psi_tr = np.asarray(self.enc.psi_[:n_pairs, :], dtype=np.float64) # (K-1, r)
# Targets in centered space
F_centered = F_train - self.mu_X[None, :] if self.center else F_train
Y_tr = np.asarray(F_centered[self.L : self.L + n_pairs, :], dtype=np.float64) # (K-1, D)
# Optional whitening of psi for both:
# - baseline decoder geometry
# - attention geometry
self.whiten_psi = bool(self.cfg.whiten_psi)
if self.whiten_psi:
self.psi_mu = Psi_tr.mean(axis=0, keepdims=True)
self.psi_sd = Psi_tr.std(axis=0, keepdims=True) + 1e-12
Psi_tr_w = (Psi_tr - self.psi_mu) / self.psi_sd
else:
self.psi_mu = np.zeros((1, self.r), dtype=np.float64)
self.psi_sd = np.ones((1, self.r), dtype=np.float64)
Psi_tr_w = Psi_tr
gkw = {} if self.cfg.gplm_kwargs is None else dict(self.cfg.gplm_kwargs)
# Critical: outputs already centered -> don't recenter in GPLM
gkw.setdefault("center_X", False)
gkw.setdefault("seed", int(self.cfg.seed))
gkw.setdefault("sigma2", 1e-4)
gkw.setdefault("jitter", 1e-8)
gkw.setdefault("m", min(1024, n_pairs))
gkw.setdefault("inducing", "kmeans_medoids")
self.baseline = GPLM(Psi_tr_w, Y_tr, **gkw)
# Attention hyperparams
self.attn_topk = None if self.cfg.attn_topk is None else int(self.cfg.attn_topk)
if self.cfg.min_ctx_windows is None:
self.min_ctx_windows = max(1, self.r + 1)
else:
self.min_ctx_windows = int(self.cfg.min_ctx_windows)
self.ctx_k0 = float(self.cfg.ctx_k0)
# Pick attention ell if not provided (based on training psi geometry)
if self.cfg.attn_ell is None:
d2 = _sample_pairwise_d2(Psi_tr_w, m=1024, seed=int(self.cfg.seed) + 123)
self.attn_ell = _median_ell_from_d2(d2, q=float(self.cfg.attn_ell_q))
else:
self.attn_ell = float(self.cfg.attn_ell)
# -------------------------
# psi processing
# -------------------------
def _psi_whiten(self, psi: Array) -> Array:
psi = np.asarray(psi, dtype=np.float64)
if psi.ndim == 1:
psi = psi[None, :]
if self.whiten_psi:
return (psi - self.psi_mu) / self.psi_sd
return psi
# -------------------------
# baseline step
# -------------------------
def predict_one_step_baseline(self, W_LD: Array) -> Array:
"""
Baseline one-step prediction:
window (L,D) -> psi -> GPLM -> next sample (D)
"""
W = np.asarray(W_LD, dtype=float)
if W.ndim == 1:
W = W[:, None]
if W.shape != (self.L, self.D):
raise ValueError(f"Expected window shape {(self.L, self.D)}, got {W.shape}")
psi = self.enc.encode_window(W) # (r,)
psi_w = self._psi_whiten(psi)[0] # (r,)
y_c = np.asarray(self.baseline(psi_w), dtype=np.float64).reshape(-1) # centered
return (y_c + self.mu_X) if self.center else y_c
# -------------------------
# main IC rollout
# -------------------------
def __call__(self, prefix: Array, steps: int = 1) -> Array:
"""
Forecast from prefix.
prefix: (ell,D), ell >= L
steps: horizon H
Returns:
(H,D) (or (D,) if H==1)
"""
prefix = _as_2d(prefix)
ell, D = prefix.shape
if D != self.D:
raise ValueError(f"ALSA trained with D={self.D}, got prefix D={D}.")
if ell < self.L:
raise ValueError(f"Need prefix length ell >= L={self.L}.")
H = int(steps)
if H <= 0:
return np.zeros((0, self.D), dtype=np.float64)
# Seed window is always last L
cur = prefix[-self.L :, :].copy()
# ----------------------------------------------------
# If no context (ell == L), run baseline-only rollout
# ----------------------------------------------------
if ell == self.L:
out = self._rollout_baseline(cur, H)
return out[0] if H == 1 else out
# ----------------------------------------------------
# Build context windows and residual table from prefix
# ----------------------------------------------------
W_all = _sliding_windows(prefix, self.L) # (K_n, L, D)
K_n = int(W_all.shape[0])
K_ctx = K_n - 1
# If too little context, baseline-only
if K_ctx < self.min_ctx_windows:
out = self._rollout_baseline(cur, H)
return out[0] if H == 1 else out
W_ctx = np.ascontiguousarray(W_all[:K_ctx, :, :]) # (K_ctx,L,D)
Y_true = np.asarray(prefix[self.L : self.L + K_ctx, :], float) # (K_ctx,D)
# Center targets
Y_true_c = (Y_true - self.mu_X[None, :]) if self.center else Y_true
# Encode context psi
Psi_ctx = np.zeros((K_ctx, self.r), dtype=np.float64)
for i in range(K_ctx):
Psi_ctx[i] = self.enc.encode_window(W_ctx[i])
Psi_ctx_w = self._psi_whiten(Psi_ctx) # (K_ctx,r)
# Baseline on context
Y_glob_ctx_c = np.asarray(self.baseline(Psi_ctx_w), dtype=np.float64) # (K_ctx,D)
# Residual table
E_ctx = Y_true_c - Y_glob_ctx_c # (K_ctx,D)
# Context gate gamma in [0,1]
gamma_ctx = float(K_ctx) / float(K_ctx + self.ctx_k0) if self.ctx_k0 > 0 else 1.0
# ----------------------------------------------------
# Rollout with attention residual correction
# ----------------------------------------------------
out = np.zeros((H, self.D), dtype=np.float64)
for h in range(H):
psi_q = self.enc.encode_window(cur) # (r,)
psi_q_w = self._psi_whiten(psi_q)[0] # (r,)
# Baseline prediction
y_glob_c = np.asarray(self.baseline(psi_q_w), dtype=np.float64).reshape(-1) # (D,)
# Attention weights on psi distances (Markov weights)
diff = Psi_ctx_w - psi_q_w[None, :] # (K_ctx,r)
d2 = np.einsum("kr,kr->k", diff, diff, optimize=True)
if self.attn_topk is not None and self.attn_topk < K_ctx:
k = int(self.attn_topk)
idx = np.argpartition(d2, kth=k - 1)[:k]
w = _softmax_weights_from_d2(d2[idx], self.attn_ell)
e_hat = w @ E_ctx[idx] # (D,)
else:
w = _softmax_weights_from_d2(d2, self.attn_ell)
e_hat = w @ E_ctx # (D,)
# Combine
y_c = y_glob_c + gamma_ctx * e_hat
y = (y_c + self.mu_X) if self.center else y_c
out[h] = y
# Advance window
if self.L > 1:
cur[:-1] = cur[1:]
cur[-1] = y
return out[0] if H == 1 else out
def _rollout_baseline(self, seed_LD: Array, H: int) -> Array:
"""
Baseline-only AR rollout (no IC correction).
"""
cur = np.asarray(seed_LD, dtype=float).copy()
out = np.zeros((int(H), self.D), dtype=np.float64)
for h in range(int(H)):
y = self.predict_one_step_baseline(cur)
out[h] = y
if self.L > 1:
cur[:-1] = cur[1:]
cur[-1] = y
return out
def __repr__(self) -> str:
return (
f"ALSA(L={self.L}, D={self.D}, r={self.r}, "
f"center={self.center}, whiten_psi={self.whiten_psi}, "
f"attn_topk={self.attn_topk}, attn_ell={self.attn_ell:.4g})"
)
__all__ = ["ALSA", "ALSAConfig"]
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