add notes about jit to claude.md

CLAUDE.md

@@ -34,6 +34,35 @@ result = graph_rewrite(uop, pm)
 ### Schedule Cache
 Schedules are cached by graph structure. BIND nodes (variables with bound values) are unbound before cache key computation so different values hit the same cache.
 
+### TinyJit Behavior
+TinyJit captures a schedule on the second call (cnt=1) and replays it on subsequent calls. **Critical**: The Python code inside a jitted function only runs during warmup (cnt=0,1). After that, only the captured schedule executes.
+
+**Side effects and assigns**: If a tensor is modified via `.assign()` inside a jitted function but not included in the `realize()` call, those assigns won't be captured in the schedule. This is especially important for:
+- **BatchNorm running stats** (`running_mean`, `running_var`) - These are updated via `.assign()` during forward pass but are NOT dependencies of the loss
+- Any stateful tensor updated as a side effect
+
+```python
+# ❌ BROKEN with JIT - BatchNorm stats only update during warmup (2 iterations)
+@TinyJit
+def train_step():
+    loss = model(x).mean().backward()
+    Tensor.realize(loss, grads)  # running_mean.assign() not captured!
+
+# ✅ CORRECT - explicitly realize buffers so assigns are in the schedule
+@TinyJit
+def train_step():
+    loss = model(x).mean().backward()
+    Tensor.realize(*params, *buffers, loss, grads)  # buffers includes running stats
+```
+
+**Debugging JIT issues**: If training works with `JIT=0` but fails with JIT, check if stateful tensors are being realized. You can verify ASSIGN chains:
+```python
+def count_assign_chain(uop, depth=0):
+    if uop.op.name != 'ASSIGN': return depth
+    return count_assign_chain(uop.src[0], depth+1)
+print(count_assign_chain(bn.running_mean.uop))  # Should increase each step, not plateau at 2
+```
+
 ## Directory Structure
 
 ```
@@ -84,6 +113,7 @@ VIZ=1 python -c "from tinygrad import Tensor; Tensor.ones(10).sum().realize()"
 - `SPEC=1` - Enable UOp spec verification
 - `NOOPT=1` - Disable optimizations
 - `DEVICE=CPU/CUDA/AMD/METAL` - Set default device
+- `JIT=0` - Disable JIT (useful for debugging JIT-related issues)
 
 ## Debugging Tips
 
@@ -91,6 +121,8 @@ VIZ=1 python -c "from tinygrad import Tensor; Tensor.ones(10).sum().realize()"
 2. **Check schedule**: `tensor.schedule()` returns list of ScheduleItems
 3. **Trace graph rewrites**: Use `VIZ=1` or add print in PatternMatcher callbacks
 4. **Find UOps by type**: `[u for u in uop.toposort() if u.op is Ops.SOMETHING]`
+5. **JIT vs non-JIT**: If something works with `JIT=0` but not with JIT, the issue is likely unrealized side-effect tensors (see TinyJit Behavior above)
+6. **Check tensor state**: `tensor.uop.op` shows current state - `Ops.BUFFER` means realized, `Ops.ASSIGN` means pending write
 
 ## Style Notes