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/routers/coach_router.py

@@ -0,0 +1,35 @@
+from fastapi import APIRouter, Depends
+from sqlalchemy.orm import Session
+
+from auth import get_current_user
+from database import get_db
+from models import User
+from schemas import CoachSessionResponse, CoachTurnRequest, CoachTurnResponse
+from services.memory_coach_service import memory_coach_service
+
+router = APIRouter(prefix="/api/coach", tags=["coach"])
+
+
+@router.get("/session", response_model=CoachSessionResponse)
+def coach_session(
+    db: Session = Depends(get_db),
+    current_user: User = Depends(get_current_user),
+):
+    return memory_coach_service.start_session(db, current_user)
+
+
+@router.post("/turn", response_model=CoachTurnResponse)
+def coach_turn(
+    data: CoachTurnRequest,
+    db: Session = Depends(get_db),
+    current_user: User = Depends(get_current_user),
+):
+    return memory_coach_service.handle_turn(
+        db,
+        current_user,
+        data.word_id,
+        data.stage,
+        data.user_message,
+        data.hints_used,
+        data.duration_seconds or 0,
+    )

backend/routers/word_router.py

@@ -7,12 +7,14 @@ from auth import get_current_user
 from database import get_db
 from models import User
 from schemas import (
+    MemoryTransformerPredictResponse,
     MemoryVisualizationResponse,
     WordCreate,
     WordMemoryDetailResponse,
     WordOut,
     WordUpdate,
 )
+from services.memory_transformer import memory_transformer_service
 from services.memory_visual_service import memory_visual_service
 from services.word_service import word_service
 
@@ -55,6 +57,16 @@ def word_memory(
     return memory_visual_service.get_word_memory(db, current_user, word_id)
 
 
+@router.get("/{word_id}/memory-model", response_model=MemoryTransformerPredictResponse)
+def word_memory_model(
+    word_id: int,
+    db: Session = Depends(get_db),
+    current_user: User = Depends(get_current_user),
+):
+    word = word_service.get_word(db, current_user, word_id)
+    return memory_transformer_service.predict_for_word(db, current_user, word)
+
+
 @router.get("/{word_id}", response_model=WordOut)
 def get_word(
     word_id: int,