convergence-monitoring（收敛监控）

Convergence Monitoring

Convergence monitoring answers the most important question in iterative AI development: when should you stop iterating? The answer is not a fixed number of iterations or a time limit -- it is convergence. Convergence means the agent's output is stabilizing; each iteration produces fewer and smaller changes than the last.

Core insight: You don't need a zero-diff -- you need the remaining modifications to be inconsequential.

1. What Is Convergence?

Convergence appears as a rapid, consistent decline in the volume of changes from one iteration to the next:

Iteration 1:  ████████████████████████████████████████  300 lines changed
Iteration 2:  ████████████████                          120 lines changed
Iteration 3:  ██████                                     40 lines changed
Iteration 4:  ██                                         10 lines changed (cosmetic only)
              ^--- Convergence reached: the diff shrinks each pass until only cosmetic changes remain

Convergence indicators

What convergence looks like in git

# Check lines changed per iteration
git log --oneline --stat

# Iteration 5: trivial changes
abc1234 Iteration 5: formatting and comment fixes
 3 files changed, 8 insertions(+), 6 deletions(-)

# Iteration 4: minor adjustments
def5678 Iteration 4: edge case handling
 5 files changed, 22 insertions(+), 8 deletions(-)

# Iteration 3: moderate changes
ghi9012 Iteration 3: complete API integration
 12 files changed, 85 insertions(+), 31 deletions(-)

# Iteration 2: significant changes
jkl3456 Iteration 2: implement core features
 18 files changed, 156 insertions(+), 42 deletions(-)

# Iteration 1: major initial work
mno7890 Iteration 1: initial implementation
 25 files changed, 312 insertions(+), 15 deletions(-)

2. What Is a Ceiling?

A ceiling is when the agent cannot make further progress due to external constraints. Like convergence, it produces small diffs -- but for fundamentally different reasons.

Convergence:  Agent is DONE      -> small diffs because work is complete
Ceiling:      Agent is STUCK     -> small diffs because agent cannot proceed

Ceiling causes

How to tell them apart

How to distinguish them

Check 1: Are tests passing?
  YES, and improving -> Convergence
  NO, stuck at same failures -> Ceiling

Check 2: Is the agent trying new approaches?
  NO, just polishing -> Convergence
  YES, but they all fail similarly -> Ceiling

Check 3: Are there BLOCKED tasks in impl tracking?
  NO -> Convergence
  YES -> Ceiling (read the blockers)

Check 4: Is the agent producing meaningful error messages?
  NO, just minor changes -> Convergence
  YES, about dependencies/tools/access -> Ceiling

3. Non-Convergence Signals

Non-convergence means the agent is making changes, but they are NOT decreasing. The system is not stabilizing.

Non-convergence:
Iteration 1:  ████████████████████████████████████████  250 lines changed
Iteration 2:  ██████████████████████████████████████    230 lines changed
Iteration 3:  ████████████████████████████████████████  260 lines changed
Iteration 4:  ██████████████████████████████████        220 lines changed
              ^--- NOT converging: changes are flat/oscillating

Root causes of non-convergence

The critical rule

When the loop isn't stabilizing, the problem is upstream -- fix the specifications, validation, or coordination rather than adding more passes.

Running more iterations when the system is not converging wastes time and compute. Instead:

1. Stop the iteration loop
2. Analyze the non-convergence pattern
3. Fix the root cause (usually specs or validation)
4. Resume the iteration loop

4. Test Pass Rate as Convergence Signal

Test pass rate is the most reliable quantitative convergence signal. Track these metrics:

Metrics to monitor

| Iteration | Tests | Pass | Fail | Skip | Pass Rate | Delta |
|-----------|-------|------|------|------|-----------|-------|
| 1         | 45    | 30   | 15   | 0    | 66.7%     | --    |
| 2         | 62    | 50   | 12   | 0    | 80.6%     | +13.9 |
| 3         | 78    | 70   | 8    | 0    | 89.7%     | +9.1  |
| 4         | 85    | 82   | 3    | 0    | 96.5%     | +6.8  |
| 5         | 88    | 87   | 1    | 0    | 98.9%     | +2.4  |

What to look for

Automated convergence check

# After each iteration, check convergence signals
echo "=== Convergence Check ==="

# 1. Lines changed (should be decreasing)
git diff --stat HEAD~1

# 2. Test results (should be improving)
{TEST_COMMAND} 2>&1 | tail -5

# 3. Build health (should always pass)
{BUILD_COMMAND} 2>&1 | tail -3

# 4. Files changed (should be decreasing)
git diff --name-only HEAD~1 | wc -l

5. Forward Progress Metrics

For large projects where full convergence takes many iterations, track forward progress toward eventual convergence.

Spec requirement coverage

The percentage of spec requirements with passing tests:

Spec Requirements Coverage:
  spec-auth.md:     ██████████████████████████████████████  95% (19/20 requirements)
  spec-data.md:     ████████████████████████████████        80% (16/20 requirements)
  spec-ui.md:       ██████████████████████                  55% (11/20 requirements)
  spec-api.md:      ████████████████████████████            70% (14/20 requirements)
  ─────────────────────────────────────────────────────
  Overall:          ████████████████████████████            75% (60/80 requirements)

Forward progress signals

Iteration velocity

Track how much progress each iteration makes:

| Iteration | Requirements Met | New This Iteration | Velocity |
|-----------|-----------------|-------------------|----------|
| 1         | 15/80           | 15                | 15       |
| 2         | 30/80           | 15                | 15       |
| 3         | 48/80           | 18                | 18       |
| 4         | 60/80           | 12                | 12       |
| 5         | 68/80           | 8                 | 8        |
| 6         | 73/80           | 5                 | 5        |
| 7         | 76/80           | 3                 | 3        |

Velocity should decrease over time (easy requirements first, hard ones last), but should never hit zero. Zero velocity = ceiling.

6. When to Stop Iterating

Stop conditions (convergence reached)

Stop the iteration loop when ANY of these are true:

1. Completion signal emitted: Agent outputs <all-tasks-complete>
2. Changes are trivial: Last iteration changed fewer than ~20 lines, all formatting/comments
3. Test pass rate is stable: Pass rate has been 95%+ for 2+ consecutive iterations
4. All exit criteria met: Every [] in the exit criteria checklist is [x]
5. Forward progress stalled positively: All spec requirements have passing tests

Continue conditions (not yet converged)

Continue iterating when ALL of these are true:

1. Changes are still substantial (behavior changes, not just formatting)
2. Test pass rate is still improving
3. There are still TODO or IN_PROGRESS tasks in impl tracking
4. The iteration count is under the maximum

Investigate conditions (possible ceiling)

Pause and investigate when ANY of these are true:

1. Changes are small but tests are NOT passing
2. Agent is retrying the same approach repeatedly
3. BLOCKED tasks are accumulating in impl tracking
4. Test pass rate is oscillating (up-down-up-down)
5. Agent is producing error messages about dependencies or tooling

7. Monitoring During Iteration Loops

What to monitor in real time

+------------------------------------------------------+
| Convergence Dashboard                                |
+------------------------------------------------------+
| Iteration: 4/10                                      |
| Lines changed: 45 (prev: 112, trend: decreasing)    |
| Files changed: 3 (prev: 8, trend: decreasing)       |
| Test pass rate: 94.2% (prev: 87.1%, trend: up)      |
| Tests: 82 total (prev: 75, trend: up)               |
| BLOCKED tasks: 0 (prev: 1, trend: down)             |
| Status: CONVERGING                                   |
+------------------------------------------------------+

Monitoring commands

# Quick convergence check after each iteration
echo "--- Lines changed ---"
git diff --stat HEAD~1 | tail -1

echo "--- Files changed ---"
git diff --name-only HEAD~1 | wc -l

echo "--- Test results ---"
{TEST_COMMAND} --summary 2>&1 | tail -3

echo "--- Impl tracking status ---"
grep -c "BLOCKED\|IN_PROGRESS\|TODO\|DONE" context/impl/impl-*.md

Automated alerts

Set up alerts for non-convergence signals:

8. Non-Convergence Recovery

When you detect non-convergence, follow this recovery process:

Step 1: Stop the iteration loop

Do not keep running. More iterations will not help.

Step 2: Diagnose the root cause

## Non-Convergence Diagnosis

### Symptoms
- [ ] Changes are flat (not decreasing)
- [ ] Changes are oscillating (up-down-up-down)
- [ ] Agent is retrying failed approaches
- [ ] Tests are oscillating (passing then failing)
- [ ] Multiple agents changing the same files

### Root Cause Analysis
1. Check specs: Are requirements clear and unambiguous?
2. Check validation: Can the agent verify correctness?
3. Check file ownership: Are agents conflicting?
4. Check scope: Is the prompt trying to do too much?
5. Check dependencies: Are external resources available?

Step 3: Fix the root cause

Step 4: Resume the iteration loop

After fixing the root cause, resume from where you stopped. Do NOT restart from scratch -- git history preserves all progress.

# Resume with the same prompt, possibly fewer remaining iterations
iteration-loop context/prompts/003-generate-impl-from-plans.md -n 5 -t 1h

9. Convergence and Revision

Revision directly improves convergence by making specs more complete:

Without revision:
  Iteration 1: 200 lines, 5 manual fixes -> specs unchanged
  Iteration 2: 180 lines, 4 manual fixes -> specs unchanged
  Iteration 3: 170 lines, 4 manual fixes -> NOT converging

With revision:
  Iteration 1: 200 lines, 5 manual fixes -> specs updated with 5 new requirements
  Iteration 2: 100 lines, 2 manual fixes -> specs updated with 2 new requirements
  Iteration 3: 50 lines, 0 manual fixes  -> CONVERGING

Frequent manual fixes without revision = non-convergence. The iteration loop keeps producing the same bugs because nothing in the specs prevents them.

Cross-References

• Convergence patterns reference: See references/convergence-patterns.md for the complete convergence pattern catalog with examples.
• Revision: See ck:revision skill for how tracing bugs to specs improves convergence.
• Prompt pipeline: See ck:prompt-pipeline skill for designing prompts with proper exit criteria and completion signals.
• Validation-first design: See ck:validation-first skill for building validation gates that provide convergence signals.
• Impl tracking: See ck:impl-tracking skill for tracking progress and detecting ceiling conditions.