Exp Lens Variance Stability

Variance Stability Experimental Design Lens

Philosophical Mode: Stability Primary Question: "Is the signal larger than the noise?" Focus: Run-to-Run Variance, Seed Sensitivity, Nondeterminism Sources, Confidence Intervals, Noise Floor

When to Use

• ML experiments with high variance across seeds
• Systems benchmarks with environmental noise
• Results where small differences are claimed as improvements
• User invokes /exp-lens-variance-stability or /make-experiment-diag variance

Critical Constraints

NEVER:

• Modify any source code files
• Do not litter the codebase with useless comments, TODO markers, or explanatory annotations — the skill output and diagram speak for themselves

ALWAYS:

• Count the actual number of independent runs — single-run results must be flagged prominently
• Assess whether claimed improvements exceed the observed standard deviation
• Identify all sources of nondeterminism, not just random seeds
• Report when confidence intervals are absent — absence is a finding, not an omission
• BEFORE creating any diagram, LOAD the /mermaid skill using the Skill tool - this is MANDATORY

Analysis Workflow

Step 1: Launch Parallel Exploration Subagents

Spawn Explore subagents to investigate:

Random Seed Management

• Find how seeds are set and varied
• Look for: seed, random_state, torch.manual_seed, np.random, set_seed, PYTHONHASHSEED

Nondeterminism Sources

• Find sources of nondeterminism beyond seeds
• Look for: cudnn, benchmark, deterministic, parallel, async, thread, race, order, nondeterministic

Multiple Run Protocol

• Find how many runs are performed per condition
• Look for: n_runs, trials, repeat, replicate, mean, std, confidence, interval, aggregate

Variance Reporting

• Find how variance is reported (if at all)
• Look for: std, stderr, confidence, interval, range, median, quartile, bootstrap, error_bar

Signal-to-Noise Assessment

• Find whether claimed improvements exceed observed variance
• Look for: significant, difference, improvement, margin, effect_size, gap, overlap

Step 2: Build Variance Profile

For each reported result:

1. How many independent runs?
2. What is the standard deviation across runs?
3. Does the claimed improvement exceed the noise floor?
4. Are confidence intervals reported?
5. What sources of nondeterminism exist beyond seeds?

Build the variance profile.

Step 3: Analyze Signal vs Noise

CRITICAL — Analyze Signal vs Noise: For every claimed improvement:

• Is the improvement magnitude larger than the run-to-run standard deviation?
• Could the ranking of methods change under reruns?
• Are the "best" results cherry-picked from multiple seeds?

Step 4: Create the Diagram

Use the mermaid skill conventions to create a stochasticity diagram with:

Direction: TB (nondeterminism sources flow down through aggregation to reported results)

Subgraphs:

• NONDETERMINISM SOURCES
• VARIANCE AGGREGATION
• REPORTED RESULTS

Node Styling:

• stateNode class: Nondeterminism sources
• handler class: Aggregation methods
• output class: Reported results
• gap class: Unreported variance or single-run results
• detector class: Confidence intervals and statistical tests
• cli class: Seed management

Step 5: Write Output

Write the diagram to: temp/exp-lens-variance-stability/exp_diag_variance_stability_{YYYY-MM-DD_HHMMSS}.md

Output Template

# Variance Stability Analysis: {Experiment Name}

**Lens:** Variance Stability (Stability)
**Question:** Is the signal larger than the noise?
**Date:** {YYYY-MM-DD}
**Scope:** {What was analyzed}

## Variance Profile

| Experiment | N Runs | Mean | Std | CI | Signal > Noise? |
|------------|--------|------|-----|----|-----------------|
| {experiment} | {n} | {mean} | {std} | {CI or "Not reported"} | {Yes/No/Unclear} |

## Nondeterminism Inventory

| Source | Type | Controlled? | Impact |
|--------|------|-------------|--------|
| {source} | {seed/hardware/async/etc} | {Yes/No/Partial} | {Low/Medium/High} |

## Stochasticity Diagram

```mermaid
%%{init: {'flowchart': {'nodeSpacing': 50, 'rankSpacing': 60, 'curve': 'basis'}}}%%
graph TB
    %% CLASS DEFINITIONS %%
    classDef cli fill:#1a237e,stroke:#7986cb,stroke-width:2px,color:#fff;
    classDef stateNode fill:#004d40,stroke:#4db6ac,stroke-width:2px,color:#fff;
    classDef handler fill:#e65100,stroke:#ffb74d,stroke-width:2px,color:#fff;
    classDef phase fill:#6a1b9a,stroke:#ba68c8,stroke-width:2px,color:#fff;
    classDef newComponent fill:#2e7d32,stroke:#81c784,stroke-width:2px,color:#fff;
    classDef output fill:#00695c,stroke:#4db6ac,stroke-width:2px,color:#fff;
    classDef detector fill:#b71c1c,stroke:#ef5350,stroke-width:2px,color:#fff;
    classDef gap fill:#ff6f00,stroke:#ffa726,stroke-width:2px,color:#000;
    classDef integration fill:#c62828,stroke:#ef9a9a,stroke-width:2px,color:#fff;

    subgraph NDSources ["NONDETERMINISM SOURCES"]
        direction TB
        SEED["Random Seed<br/>━━━━━━━━━━<br/>Controlled via<br/>seed management"]
        HW["Hardware Variance<br/>━━━━━━━━━━<br/>GPU/CPU ordering<br/>differences"]
        ASYNC["Async Operations<br/>━━━━━━━━━━<br/>Thread/process<br/>race conditions"]
    end

    subgraph Aggregation ["VARIANCE AGGREGATION"]
        direction TB
        MULTI["Multiple Runs<br/>━━━━━━━━━━<br/>N independent<br/>repetitions"]
        CI["Confidence Interval<br/>━━━━━━━━━━<br/>Statistical bounds<br/>on estimates"]
    end

    subgraph Results ["REPORTED RESULTS"]
        direction TB
        RESULT["Reported Result<br/>━━━━━━━━━━<br/>Mean ± std<br/>with CI"]
        SINGLE["Single-Run Result<br/>━━━━━━━━━━<br/>No variance<br/>reported"]
    end

    SEED --> MULTI
    HW --> MULTI
    ASYNC --> MULTI
    MULTI --> CI
    CI --> RESULT
    MULTI --> SINGLE

    %% CLASS ASSIGNMENTS %%
    class SEED cli;
    class HW,ASYNC stateNode;
    class MULTI handler;
    class CI detector;
    class RESULT output;
    class SINGLE gap;

Seed Sensitivity Assessment

Reporting Completeness Checklist

• Number of runs reported per condition
• Standard deviation or standard error reported
• Confidence intervals reported
• All seeds or seed range disclosed
• Nondeterminism sources acknowledged

Key Findings

• {Description of whether signals exceed noise and reporting completeness}

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## Pre-Diagram Checklist

Before creating the diagram, verify:

- [ ] LOADED `/mermaid` skill using the Skill tool
- [ ] Using ONLY classDef styles from the mermaid skill (no invented colors)
- [ ] Diagram will include a color legend table

---

## Related Skills

- `/make-experiment-diag` - Parent skill for lens selection
- `/mermaid` - MUST BE LOADED before creating diagram
- `/exp-lens-reproducibility-artifacts` - For environment and artifact reproducibility
- `/exp-lens-error-budget` - For systematic error and bias analysis