Add memory coach, transformer recall model, and training FAB.

Introduce Q/K/V memory dialogue with coach APIs, a lightweight NumPy
transformer for per-word forgetting prediction, and a floating training
menu linking daily quiz, spell, and coach flows.

Co-authored-by: Cursor <cursoragent@cursor.com>

backend/services/memory_transformer/encoding.py

@@ -0,0 +1,106 @@
+"""将 QuizRecord 序列编码为 Transformer 输入特征。"""
+
+import math
+from datetime import datetime, timezone
+from typing import Optional
+
+from models import QuizRecord, Word
+
+FEATURE_DIM = 16
+MAX_SEQ_LEN = 32
+
+QUESTION_TYPES = ("en_to_zh", "zh_to_en", "spell", "memory_coach")
+STATUS_ORDER = ("new", "learning", "mastered", "weak")
+
+
+def parse_iso(s: str) -> datetime:
+    s = s.replace("Z", "+00:00")
+    try:
+        return datetime.fromisoformat(s)
+    except ValueError:
+        return datetime.strptime(s[:19], "%Y-%m-%dT%H:%M:%S").replace(tzinfo=timezone.utc)
+
+
+def word_en(w: Word) -> str:
+    return w.target_text if w.source_lang == "zh" else w.source_text
+
+
+def _log_hours(delta_hours: float) -> float:
+    return math.log1p(max(0.0, delta_hours)) / math.log1p(24 * 30)
+
+
+def _one_hot(index: int, size: int) -> list[float]:
+    v = [0.0] * size
+    if 0 <= index < size:
+        v[index] = 1.0
+    return v
+
+
+def _pad_features(feats: list[float]) -> list[float]:
+    row = feats[:FEATURE_DIM]
+    while len(row) < FEATURE_DIM:
+        row.append(0.0)
+    return row
+
+
+def word_static_features(word: Word) -> list[float]:
+    en = word_en(word)
+    status_idx = STATUS_ORDER.index(word.status) if word.status in STATUS_ORDER else 1
+    feats = [
+        word.mastery_score / 100.0,
+        min(word.consecutive_correct_count, 10) / 10.0,
+        min(word.correct_count, 50) / 50.0,
+        min(word.wrong_count, 50) / 50.0,
+        min(len(en), 24) / 24.0,
+    ]
+    feats.extend(_one_hot(status_idx, len(STATUS_ORDER)))
+    return _pad_features(feats)
+
+
+def event_features(
+    record: QuizRecord,
+    prev_at: Optional[datetime],
+    at: datetime,
+) -> list[float]:
+    q_idx = (
+        QUESTION_TYPES.index(record.question_type)
+        if record.question_type in QUESTION_TYPES
+        else 0
+    )
+    if prev_at is None:
+        delta_h = 0.0
+    else:
+        delta_h = max(0.0, (at - prev_at).total_seconds() / 3600.0)
+    dur = min(record.duration_seconds or 0, 600) / 600.0
+    feats = [
+        1.0 if record.is_correct else 0.0,
+        _log_hours(delta_h),
+        dur,
+    ]
+    feats.extend(_one_hot(q_idx, len(QUESTION_TYPES)))
+    return _pad_features(feats)
+
+
+def build_sequence_matrix(
+    word: Word,
+    records: list[QuizRecord],
+    now: Optional[datetime] = None,
+) -> tuple[list[list[float]], int]:
+    """
+    返回 (seq_features, valid_len)。
+    第 0 位为词项 CLS（静态），其后为按时间排序的练习事件（最多 MAX_SEQ_LEN-1）。
+    """
+    now = now or datetime.now(timezone.utc)
+    ordered = sorted(records, key=lambda r: r.created_at)
+    seq: list[list[float]] = [word_static_features(word)]
+
+    prev_at: Optional[datetime] = parse_iso(word.created_at)
+    for r in ordered[-(MAX_SEQ_LEN - 1) :]:
+        at = parse_iso(r.created_at)
+        seq.append(event_features(r, prev_at, at))
+        prev_at = at
+
+    valid_len = len(seq)
+    while len(seq) < MAX_SEQ_LEN:
+        seq.append([0.0] * FEATURE_DIM)
+    return seq, valid_len