Metrics & Evaluations — All Variants & Tricks

Updated July 2026 with 2025–2026 SOTA additions — new entries marked ★. Algorithm names link to their papers (arXiv / project page).

April 2026 · Version 1.0


Contents

  1. Why Evaluation Is the Moat
  2. Foundations: Statistical Setup
  3. Image Quality Metrics
  4. Video Quality Metrics
  5. Audio / Speech Metrics
  6. LLM Quality Metrics
  7. LLM-as-Judge
  8. Human Evaluation
  9. Arena-Style Evaluation
  10. Multimodal / VLM Evaluation
  11. Agent and Code-Agent Evaluation
  12. Reasoning Evaluation
  13. Safety, Bias, Truthfulness
  14. Online / Production Evaluation
  15. Contamination and Cheating
  16. Reward Hacking and Goodharting
  17. Eval Harness Design
  18. Specialized Domains
  19. Multi-Aspect / Holistic Frameworks
  20. Eval at Different Stages
  21. Reporting and Communication
  22. Frontier 2025–2026
  23. Production Stack 2026

Appendix A: Twenty-Five Things to Know

Appendix B: Decision Tree — "Which Metric / Benchmark?"

Appendix C: Year-by-Year Eval Milestones

1. Why Evaluation Is the Moat

1.1 The thesis

Key

At the frontier, the team with the best continuous, contamination-free, human-grounded eval pipeline wins, regardless of architecture or data choices. Evals shape every other decision: model selection, hyperparameters, ablations, releases.

1.2 The Goodhart problem

"When a measure becomes a target, it ceases to be a good measure." Every benchmark gets gamed eventually:

1.3 Three eval phases

  1. Pre-launch: held-out benchmarks, ablations, internal vibes.
  2. Online: A/B, shadow, guardrails on production traffic.
  3. Post-launch: drift / regression detection, slice-based monitoring.

1.4 Eval design principles

1.5 The hierarchy of evidence

  1. Closed-loop downstream metric (deployed-system success).
  2. Calibrated human preference at scale (Arena Elo).
  3. Held-out human ratings on rubric.
  4. LLM-as-judge (calibrated).
  5. Automatic benchmarks.
  6. Self-eval / proxy.

Higher = more trustworthy + more expensive.

2. Foundations: Statistical Setup

2.1 Population vs sample

A benchmark is a sample from some implicit "task population." Sample size matters:

2.2 Confidence intervals

Wilson score for a proportion (e.g., accuracy):

\[p \pm z\sqrt{\frac{p(1-p)}{n}}.\]

\(z = 1.96\) for 95%. For \(n = 1000\), \(p = 0.5\): \(\pm 3.1\%\).

2.3 Bootstrap

Resample data with replacement; recompute metric; gives confidence bands. Standard for non-trivial metrics (FID, BLEU, etc.).

2.4 Significance testing

2.5 Reporting standards

2.6 Pearson / Spearman correlation

3. Image Quality Metrics

3.1 Pixel-level

3.2 Structural

SSIM (Wang et al.): structural similarity index in luminance, contrast, structure:

\[\mathrm{SSIM}(x,y) = \frac{(2\mu_x\mu_y + c_1)(2\sigma_{xy} + c_2)}{(\mu_x^2 + \mu_y^2 + c_1)(\sigma_x^2 + \sigma_y^2 + c_2)}.\]

MS-SSIM: multi-scale variant.

3.3 Perceptual: LPIPS

Learned Perceptual Image Patch Similarity: distance in deep network features (VGG / AlexNet). Strongly correlates with human similarity judgments. Standard since 2018.

3.4 Distributional: FID, KID

Fréchet Inception Distance:

\[\mathrm{FID} = \|\mu_r - \mu_g\|^2 + \mathrm{tr}\!\left(\Sigma_r + \Sigma_g - 2(\Sigma_r\Sigma_g)^{1/2}\right),\]

on Inception-V3 features. Standard for GANs / diffusion since 2017. Limitations: backbone choice matters; broken at high quality.

KID: kernel-based MMD; less biased at small sample.

IS (Inception Score): confidence + diversity; deprecated.

CMMD (CLIP MMD): replaces Inception with CLIP; better for modern generation.

3.5 Precision / Recall on manifold

Separate fidelity (precision) from diversity (recall). Useful when FID misleading.

3.6 Aesthetic predictors

3.7 Compositional / VQA-based

VQAScore: VLM-as-judge for compositional fidelity. "Is the cat sitting on the chair?" → probability "yes".

GenEval: object counting + attribute binding + spatial.

T2I-CompBench: multi-aspect compositional.

3.8 Detection / segmentation specific

IoU: \(|A \cap B|/|A \cup B|\). Generalized variants:

3.9 Mean Average Precision (mAP)

Sweep score threshold; compute precision-recall curve; AP = area under PR curve. COCO mAP: averaged over IoU \(\in \{0.50, 0.55, \ldots, 0.95\}\) and 80 classes. Standard for detection.

3.10 Segmentation: Dice / IoU / Panoptic Quality

Dice: \(2|A \cap B|/(|A| + |B|)\). Panoptic Quality (PQ): combined recognition + segmentation:

\[\mathrm{PQ} = \frac{\sum_{(p,g)\in \mathrm{TP}} \mathrm{IoU}(p,g)}{|\mathrm{TP}| + \tfrac{1}{2}|\mathrm{FP}| + \tfrac{1}{2}|\mathrm{FN}|}.\]

4. Video Quality Metrics

4.1 FVD (Fréchet Video Distance)

Same idea as FID with I3D / InternVideo features.

Standard for video generation since 2018.

Limitations: backbone choice; not perceptually well-calibrated.

4.2 KVD

Kernel variant of FVD.

4.3 VBench / VBench-2

Multi-axis benchmark with 16+ dimensions (subject consistency, motion smoothness, dynamic degree, scene transition, object class, temporal flicker, etc.). Aggregated score; standard for T2V comparison since 2024.

4.4 T2V-CompBench, EvalCrafter

Compositional + multi-aspect benchmarks. Counts, spatial relations, attribute binding, action over time.

4.5 VideoScore

Learned video reward model trained on human preferences. Used in alignment + filtering.

4.6 Motion-specific metrics

4.7 Identity preservation

4.8 Audio sync (for video+audio)

5. Audio / Speech Metrics

5.1 Speech recognition

5.2 Speech synthesis

5.3 Music / audio generation

5.4 Diarization

DER (Diarization Error Rate): speaker attribution accuracy.

5.5 TTS naturalness

Modern TTS evals: AB preference vs reference, MOS-N (naturalness), MOS-S (similarity to target speaker for cloning).

6. LLM Quality Metrics

6.1 Perplexity

\[\mathrm{PPL} = \exp\!\left(-\frac{1}{N}\sum_i \log p(x_i \mid x_{<i})\right).\]

Lower = better. Useful for training tracking; weak proxy for downstream quality. Comparable only at fixed tokenizer.

6.2 Cross-entropy in nats / bits-per-byte

Bits-per-byte normalizes across tokenizers (most fair cross-tokenizer comparison).

6.3 Classification-style benchmarks

6.4 Open-ended: BLEU, ROUGE, METEOR

6.5 Modern open-ended: LLM-as-judge

MT-Bench, AlpacaEval, AlpacaEval 2: pairwise comparison judged by GPT-4-class. Higher correlation with human preference than BLEU.

6.6 Math benchmarks

6.7 Code benchmarks

6.8 Reasoning benchmarks

6.9 pass@k

\[\mathrm{pass@}k = 1 - \prod_{i=1}^{k}(1 - p_i),\]

\(p_i\) = success probability of \(i\)-th independent sample. Standard for code; reported at \(k = 1, 5, 10, 100\).

7. LLM-as-Judge

7.1 The pattern

Use a strong LLM (GPT-4, Claude, Gemini) to rate / compare model outputs. Cheaper than human; biased.

7.2 Pairwise vs absolute

7.3 Known biases

7.4 Mitigations

7.5 LLM-as-judge benchmarks

7.6 Constitutional / rubric judges

7.7 Process Reward Models as judges

For step-level evaluation (math, agents): use PRM trained on per-step labels (PRM800K, Math-Shepherd).

★ 2026 SOTA update — Judge & reward-model benchmarks

8. Human Evaluation

8.1 Why human eval is gold

8.2 Side-by-side (SBS)

Show model A vs B; ask preference. Standard pattern.

8.3 Rating scales

8.4 Inter-annotator agreement

8.5 Calibration techniques

8.6 Cost

8.7 Common eval workflows

8.8 Vendors

Surge AI, Scale AI, Mercor, Outlier (formerly Scale's expert side), Snorkel, in-house at every frontier lab.

9. Arena-Style Evaluation

9.1 Chatbot Arena (LMSYS)

9.2 Bradley-Terry / Elo math

For pair \((i, j)\), \(P(i \succ j) = \dfrac{e^{r_i}}{e^{r_i} + e^{r_j}}\). Update via online estimator. Elo: same idea with K-factor.

9.3 Other arenas

9.4 Arena pros

9.5 Arena cons

9.6 Per-category breakdown

Arena-Hard, MT-Bench, others: per-task category breakdowns (math, coding, creative). Important; aggregate hides signals.

9.7 Style control

Arena Hard adds style control to remove length/markdown bias from preference. "Same length / structure" comparisons.

10. Multimodal / VLM Evaluation

10.1 General VLM benchmarks

10.2 Vision-only

10.3 Long-video

10.4 3D / spatial

10.5 Embodied / robotics

10.6 VBench / VBench-2 (video gen)

Already covered; standard for video gen.

10.7 Multimodal Arena

Vision Arena (LMSYS): pairwise comparison for VLMs.

★ 2026 SOTA update — Frontier VLM reasoning benchmark

11. Agent and Code-Agent Evaluation

11.1 Standard agent benchmarks

11.2 Trajectory evaluation

Beyond final success:

11.3 LLM-as-judge for agents

Strong LLM evaluates trajectories per rubric. Standard for free-form agent tasks.

11.4 Closed-loop downstream

For robotics / AV: real-world success rate is gold.

11.5 Agent leaderboards

★ 2026 SOTA update — Conversational & general agent benchmarks

★ 2026 SOTA update — Coding / CLI agent benchmarks

12. Reasoning Evaluation

12.1 Verifiable-reward benchmarks

Programmatic checking; un-gameable in principle.

12.2 Major benchmarks (April 2026)

12.3 Best-of-N / pass@k

For sampling-based reasoning:

\[\mathbb{E}\!\left[\max_{i\le N} r_i\right] \approx \mu + \sigma\sqrt{2 \ln N}.\]

Diminishing returns; reported as pass@1, pass@10, pass@100.

12.4 Self-consistency eval

Sample K reasoning chains; majority vote; report consistency. Useful for uncertainty quantification.

12.5 Process-level eval

Catches reasoning quality, not just final answer.

12.6 Token efficiency

Compute spent per problem solved. Important for cost-aware comparison: a model that solves at 10× token cost is often worse than one that solves at 1×.

13. Safety, Bias, Truthfulness

13.1 Refusal / harm

13.2 Truthfulness

13.3 Bias / fairness

13.4 Toxicity

13.5 Red-team metrics

13.6 Calibration

★ 2026 SOTA update — Grounding & factuality benchmarks

14. Online / Production Evaluation

14.1 A/B testing

14.2 Interleaving

Both models' outputs shown together; users pick. More efficient than A/B for ranking signal.

14.3 Shadow traffic

Route copy of production traffic to candidate model; compare offline. Lower risk than A/B.

14.4 Counterfactual eval

Compute candidate model's output on logged inputs; compare to logged response. Cheap; assumes input distribution stable.

14.5 Guardrail metrics

14.6 Drift detection

14.7 Per-segment dashboards

Slice metrics by:

Aggregate metrics hide regressions in slices.

14.8 Long-horizon retention

15. Contamination and Cheating

15.1 The problem

Models trained on internet may have seen eval examples. "Solving" may be memorization, not generalization.

15.2 Detecting contamination

15.3 Reducing contamination

15.4 LiveBench (continually updated)

15.5 Adversarial probes

15.6 Contamination-resistant patterns

16. Reward Hacking and Goodharting

16.1 The phenomenon

Models / teams optimize the metric instead of the underlying quality. Once a benchmark gets traction, gaming begins.

16.2 Common gaming patterns

16.3 Reward overoptimization

Gao et al. scaling law: true reward

\[R(\mathrm{KL}) \sim a\sqrt{\mathrm{KL}} - b\,\mathrm{KL}.\]

Proxy reward keeps rising while true quality declines past a peak.

16.4 Mitigations

16.5 Length-bias defenses

16.6 Sycophancy

Model agrees with user even when wrong. Test via deliberate-wrong prompts; track agreement rate.

17. Eval Harness Design

17.1 The eval harness

A reproducible system to run any benchmark on any model. Open-source standards:

17.2 Best practices

17.3 Prompt format issues

17.4 Eval configurations

17.5 Continuous eval during training

17.6 Eval-driven development

18. Specialized Domains

18.1 Medical

18.3 Financial

18.4 Scientific

18.5 Multilingual

18.6 Long-context

★ 2026 SOTA update — Long-context benchmarks (2025)

19. Multi-Aspect / Holistic Frameworks

19.1 HELM (Stanford)

Holistic Evaluation of Language Models. 16 core scenarios + 7 metrics dimensions (accuracy, calibration, robustness, fairness, bias, toxicity, efficiency). Mature open framework.

19.2 HELM Lite

Slim version for faster, frequent eval.

19.3 Big-Bench / Big-Bench Hard

Large collection of \(\sim\) 200 tasks contributed by community. BBH = 23-task hard subset.

19.4 MMLU-Pro / GPQA Diamond / Humanity's Last Exam

Frontier-level eval suites.

19.5 Evolve (HuggingFace) / Open LLM Leaderboard v2

Curated leaderboard with rigorous methodology. Common reference for open models.

19.6 Per-task breakdowns

Always required:

19.7 Composite scoring

20. Eval at Different Stages

20.1 Pretraining tracking

20.2 SFT / instruction-tuning

20.3 RLHF / DPO eval

20.4 Reasoning RL eval

20.5 Production eval

20.6 Cadence

21. Reporting and Communication

21.1 What a good eval report looks like

21.2 The bar for "new SOTA" claim

21.3 Dashboards

21.4 Warning signs in eval

21.5 Cherry-picking defenses

22. Frontier 2025–2026

22.2 Saturation crisis

22.3 New benchmark categories

22.4 Open research

23. Production Stack 2026

Use case Default approach Notes
LLM general quality MT-Bench / AlpacaEval 2 / Arena Elo + per-task
LLM frontier eval MMLU-Pro / GPQA / HLE / Math Frontier / uncontaminated
LLM reasoning AIME / Putnam / LiveCodeBench / ARC-AGI verifiable rewards
LLM code LiveCodeBench / SWE-bench-Verified / Codeforces post-cutoff
LLM safety HarmBench / JailbreakBench / XSTest + red-team
VLM / multimodal MMMU-Pro / MathVista / RealWorldQA / BLINK + Vision Arena
Long-context RULER / LongBench / ∞-Bench / LV-Eval multi-aspect
Image gen FID / CLIP-Score / HPSv3 / Image Arena VQAScore + human
Video gen FVD / VBench-2 / VideoScore / Video Arena + human
Audio gen FAD / CLAP-Score + MOS + human
Detection / segmentation COCO mAP / Cityscapes mIoU / PQ per-class
3D / NeRF / 3DGS PSNR / SSIM / LPIPS + Chamfer per-scene
Agent (general) GAIA / AgentBench / WebArena / OSWorld trajectory eval
Agent (SWE) SWE-bench-Verified + LiveCodeBench contamination-resistant
Robotics SimplerEnv / LIBERO / RoboCasa demos + real closed-loop
Eval harness lm-eval-harness / HELM / Open LLM Leaderboard v2 open standard
Online production A/B + interleave + guardrail drift metrics + continuous

Appendix A: Twenty-Five Things to Know

  1. Eval is the moat at frontier; design carefully.
  2. Goodhart's law: every metric gets gamed.
  3. Wilson confidence interval for proportions.
  4. Pearson vs Spearman: linear vs rank.
  5. PSNR / SSIM / LPIPS hierarchy.
  6. FID formula: \(\|\mu_r - \mu_g\|^2 + \mathrm{tr}(\Sigma_r + \Sigma_g - 2(\Sigma_r\Sigma_g)^{1/2})\).
  7. COCO mAP averages over IoU 0.50–0.95.
  8. BLEU / ROUGE / METEOR mostly weak for modern LLM open-ended.
  9. LLM-as-judge biases: position, length, self-preference.
  10. Order-swap + multi-judge + CoT-then-rate mitigations.
  11. Chatbot Arena Elo is closest to ground truth for LLMs.
  12. Bradley-Terry preference probability.
  13. pass@k formula: \(1 - \prod(1 - p_i)\).
  14. Best-of-N expected: \(\mathbb{E}[\max] \approx \mu + \sigma\sqrt{2 \ln N}\).
  15. Reward overoptimization scaling: \(a\sqrt{\mathrm{KL}} - b\,\mathrm{KL}\).
  16. KL anchor + RM ensemble for hacking defense.
  17. LiveCodeBench / current AIME / HLE for contamination-resistance.
  18. N-gram overlap detection for contamination check.
  19. HELM, lm-eval-harness, Open LLM Leaderboard v2 are open standards.
  20. RULER for long-context (better than NIAH alone).
  21. VBench-2 16+ axes for video gen.
  22. VQAScore / GenEval / T2I-CompBench for compositional T2I.
  23. Per-task breakdown + per-segment slicing always.
  24. Calibration: ECE, reliability diagrams.
  25. Closed-loop downstream metric > human > judge > automatic.

Appendix B: Decision Tree — "Which Metric / Benchmark?"

  1. LLM general quality? → MMLU-Pro + Arena Elo + MT-Bench / AlpacaEval 2.

  2. LLM frontier reasoning? → AIME / Putnam / FrontierMath / HLE / ARC-AGI.

  3. LLM code? → LiveCodeBench + SWE-bench-Verified.

  4. LLM safety? → HarmBench + JailbreakBench + XSTest + red-team.

  5. Multimodal VLM? → MMMU-Pro + MathVista + Vision Arena.

  6. Long-context? → RULER + LongBench + ∞-Bench Eval.

  7. Image generation? → HPSv3 + VQAScore + Image Arena + FID for legacy.

  8. Video generation? → VBench-2 + VideoScore + Video Arena + FVD.

  9. Detection / segmentation? → COCO mAP / Cityscapes mIoU / PQ.

  10. Agent task? → GAIA / WebArena / OSWorld / SWE-bench-Verified.

  11. Robotics? → SimplerEnv / LIBERO / real-world success rate.

  12. Production deployment? → A/B + interleave + guardrail drift metrics + continuous monitoring.

Appendix C: Year-by-Year Eval Milestones