depth-lens

Pick the cheapest LLM config that meets your accuracy bar — for your data, not somebody else's benchmark.

Sweep every (model, knob) on your prompts in one CLI call. Wilson 95% CIs, per-call cost, latency p50, cross-vendor. Roughly $1 and ten minutes per audit.

日本語版

The plot above is a real depth-lens recommend output. Four Anthropic configurations all score 1.00 accuracy on a K-hop tier-4 prompt set — and span ~35× in cost. That's the gap the "use the latest / biggest" instinct burns through silently. depth-lens finds the cheapest passing tier on your prompts in under 10 minutes. The 30-second install is right below.

30 seconds: install, run, decide

pip install depth-lens[openai]              # add ,anthropic / ,gemini as needed
export OPENAI_API_KEY=...

# Use the bundled example bench (5 modular-arithmetic prompts), or write your own:
python -c "from depth_lens.data import copy_example; copy_example('modular_arithmetic.jsonl')"

depth-lens recommend \
    --models openai:gpt-5-mini,openai:o4-mini \
    --task custom:modular_arithmetic.jsonl:first_int \
    --target-accuracy 0.95 \
    --max-latency 3.0 \
    --n-samples 16 \
    --daily-calls 10000

To bring your own prompts, swap modular_arithmetic.jsonl for any JSONL of {"prompt": ..., "target": ..., "depth": ...} rows.

============================================================================================
Target accuracy ≥ 0.95  ·  Max latency ≤ 3.00s/pred
Probed 6 configurations, 6 passing.
============================================================================================

✅ Passing (cheapest first):
  openai:gpt-5-mini     d=1  effort=low      acc=1.00   $0.354/k-pred   0.45s/pred  ← cheapest
  openai:gpt-5-mini     d=1  effort=medium   acc=1.00   $0.485/k-pred   0.59s/pred
  openai:o4-mini        d=1  effort=low      acc=1.00   $0.736/k-pred   0.29s/pred  ← fastest
  openai:gpt-5-mini     d=1  effort=high     acc=1.00   $0.886/k-pred   0.69s/pred
  openai:o4-mini        d=1  effort=medium   acc=1.00   $1.061/k-pred   0.37s/pred
  openai:o4-mini        d=1  effort=high     acc=1.00   $1.365/k-pred   0.40s/pred

⚡ Cost-vs-speed tradeoff among passing configs:
  Cheapest is 1.5× slower than fastest; fastest costs 2.1× more per call.

============================================================================================
At 10,000 calls/day with the cheapest passing config:
  openai:gpt-5-mini @ effort=low
  → $3.54/day  $1,291/year

  Switching from openai:o4-mini @ effort=high ($13.65/day)
  saves $10.11/day = $3,691/year (74% reduction)

You now have a defensible answer to "do we really need the bigger / more-thinking config?" — backed by a real sweep with Wilson 95% CIs on your prompts. Swap --models for Anthropic / Gemini / vLLM (self-hosted) and re-run; the workflow is identical.

Evidence: three real business tasks, three measurements

We ran depth-lens end-to-end on three production-style chatbot tasks that map to three different scoring needs. Same recommend workflow, three different scorers.

Case 1 — Tenant-inquiry urgency classifier (real-estate management)

Classify tenant messages into 緊急 / 通常 / 翌営業日 (urgent / business hours / next business day). 20 realistic prompts: water leaks, gas leaks, lockouts, contract questions, noise complaints.

Config	Accuracy	Latency p50
openai:o4-mini @ effort=medium ← chosen	100%	0.52 s
openai:gpt-5-mini @ effort=low	95%	0.67 s
openai:o4-mini @ effort=high (default "safe")	100%	0.74 s

Cost reduction: ~88% vs defaulting to o4-mini @ high or gpt-5. Domain insight depth-lens surfaced: the 95% config's single miss was 通常 → 翌営業日 (safe direction). No 緊急 → 通常 errors — accuracy alone undersells the cheaper config's safety profile.

Case 2 — System-monitoring quote estimator (MSP / IT ops)

Compute monthly quote estimates from free-form Japanese inquiries (plan tier × server count × options × volume discount). 53 prompts across 5 difficulty tiers including typos, formal/casual mixed, implicit tier hints like "ミッションクリティカル" → premium.

Config	All 5 tiers acc	Latency p50
openai:gpt-5-mini @ effort=low ← chosen	100% (53/53)	0.41 – 0.50 s
openai:o4-mini @ effort=medium	100%	0.65 s
openai:o4-mini @ effort=high (default "safe")	100%	0.70 s

Cost reduction: ~88% vs the "complex calculation needs a more capable model" intuition. Counter-intuitive finding: multi-step pricing math + production-realistic messy input both solved by the cheapest config. gpt-5-mini @ low handles compound discount logic, mixed plans, AND colloquial Japanese ("がっつり監視で") at 100%.

Case 3 — Tenant-reply quality, judged by LLM (v2.1)

Same property-management chatbot, but generating free-form replies to tenant inquiries. Quality judged by a separate LLM against a 3-criterion rubric (polite using 敬語, addresses the specific issue, proposes a concrete next step). 12 prompts spanning urgent / procedural / rules / complaints / repairs.

Config	All 3 criteria met	Per-reply latency
openai:gpt-5-mini @ effort=low ← chosen	100% (12/12)	1.4 s
openai:o4-mini @ effort=high	100% (12/12)	1.8 s
openai:gpt-5-mini @ effort=high (default "safe")	75% (9/12)	15.6 s ← unusable

Counter-intuitive: gpt-5-mini accuracy decreases with higher effort (low 100% → high 75%) — over-elaboration breaks the rubric's "addresses the specific issue / concrete next step" criteria. o4-mini shows the opposite curve. Optimal effort is per-(model, task), not universal. Why this case matters: until v2.1, depth-lens couldn't measure free-form replies — only structured tasks like Cases 1 and 2. The new llm: scorer made this measurable.

Full case study →

Five patterns these three cases collectively show

1. "Use the bigger model to be safe" is a strict loss when measured — same accuracy, more cost, no latency budget gained. Case 3 sharpens this: higher effort can decrease accuracy on free-form tasks where over-elaboration hurts the rubric.
2. Stratified bench (simple → production-messy) reveals where each tier breaks — or, as in Case 2, that none of the candidates do.
3. ~80-90% cost reduction is typical when teams stop pre-judging model selection and run a quick depth-lens sweep instead.
4. Production-realistic input must be in the bench from day 1. Synthetic tier-1 prompts alone systematically over-recommend expensive models — Case 2's 30 messy "real-log-style" prompts were what produced the conclusion's confidence interval.
5. The right scorer matters more than the model choice. The three cases cover the three scorer families depth-lens ships (structured / regex / LLM-as-judge). New production tasks land in one of these buckets.

Can I measure my task? Three scorer families

Family	Spec form	When to use
Structured	exact, first_int, last_int, yes_no, contains	Classification, numeric answers, yes/no decisions. Cases 1 and 2 above.
Regex	regex:<pattern>	Format-checking, "answer must match this shape".
LLM-as-judge	llm:<judge-model>:<criterion> or llm:<judge-model>:rubric:<text>	Open-ended outputs: summaries, free-form Q&A, multi-criterion checks. Case 3 above.

Built-in criteria for llm:: correct / faithful / helpful / concise / format / polite. Free-form rubrics are arbitrary text after :rubric:.

# LLM-judge example: grade summary faithfulness with gpt-5-mini
depth-lens recommend \
    --models openai:gpt-5-mini,openai:o4-mini \
    --task "custom:./summaries.jsonl:llm:openai:gpt-5-mini:faithful" \
    --target-accuracy 0.85 --n-samples 32

Pick a different (and ideally cheaper) judge than the model under test to avoid self-judging bias. As of 2026, gemini-3.1-flash-lite is the cheapest competent judge.

Between these three families, almost every production AI task is measurable — classification, structured extraction, RAG-faithfulness, customer-support reply quality, code review, tone checks. If your task doesn't fit, file an issue.

What's in the box

6 adapter families

Spec	Compute knob	Cost basis
anthropic:<model>	thinking_budget_tokens	API ($/M-token)
openai:<model>	reasoning_effort	API ($/M-token)
gemini:<model>	thinking_budget_tokens (2.5) / auto-mapped to thinking_level (3.x)	API ($/M-token)
vllm:<model>	reasoning_effort (thinking models) or max_tokens (instruct-only, OpenAI-compatible local server)	self-hosted ($/GPU-hour)
hf:<hf-model-id>	max_thinking_tokens (CoT length)	local GPU ($/GPU-hour)
openmythos	n_loops (Recurrent-Depth Transformer)	local GPU ($/GPU-hour)

API adapters fan requests through a thread pool (max_concurrent); a 1000-prompt probe finishes in minutes, not hours.

5 built-in probe tasks + custom

Task	Depth axis	Reasoning shape
k-hop	K (operators)	Forward composition (mod-arithmetic)
parity	n (bits)	Aggregation (XOR reduction)
graph-reach	path length	Single BFS pass
state-tracking	K (instructions)	2-counter register machine
mini-csp	n (variables)	Search / constraint propagation (2-SAT)
dict-lookup	n (pairs)	Field extraction from structured input (v2.0)
custom:<jsonl>:<scorer>	optional depth field	Bring your own data

Diagnostics every ProbeResult exposes

• .accuracy — [depth][compute] grid in [0, 1]
• .ci() — Wilson 95% intervals on every cell
• .effective_depth(threshold=0.5) — biggest depth where some compute level clears the bar
• .overthinking(depth, tolerance=0.02) — peak compute is not max compute, by how much
• .cost_per_cell(pricing) — $/prediction. Token-based ({input, output} USD-per-1M) or GPU-hour ({gpu_hourly, gpus}) — pick whichever fits the adapter

CLI

depth-lens recommend ... # find cheapest model meeting your accuracy bar (production workflow)
depth-lens probe ...     # detailed sweep of one model
depth-lens compare ...   # overlay several models on the same task
depth-lens dashboard     # Streamlit UI over your cached probes

Each subcommand has full --help. See docs/playbook/ for end-to-end production scenarios: model-downgrade · cost-audit · regression-detection · self-hosting-with-vllm.

Python API

from depth_lens import probe
from depth_lens.tasks import get_task
from depth_lens.adapters.anthropic_adapter import AnthropicAdapter

task = get_task("mini-csp")
adapter = AnthropicAdapter(model="claude-haiku-4-5", task_name="mini-csp")
result = probe(adapter, task, depths=[3, 5, 7, 9], n_samples=16)

print(f"effective depth: {result.effective_depth(0.5)}")
print(f"overthinking @ d=9: {result.overthinking(9)}")
print(f"$/pred @ d=9 mid budget: {result.cost_per_cell({'input': 1.0, 'output': 5.0})[3, 1]}")

What depth-lens is NOT

• We don't run MMLU, GSM8K, or similar leaderboards. Those crown frontier models on canonical benchmarks; production teams already picked a model family and need to tune within it.
• We don't test "is the model smart." We test "which configuration of this family meets your accuracy bar at the lowest cost / latency / GPU-time."
• We don't ship a managed dashboard. The OSS produces JSONs and plots locally; building hosted dashboards on top of those is outside scope.

Capability	LLMThinkBench	usail-hkust bench	o1 scaling laws	depth-lens
Compute-axis curves (not single point)	❌	partial	✅ (o1 only)	✅
Cross-vendor (Claude / o-series / Gemini / OSS)	❌ HF only	partial	❌ o1 only	✅
Self-hosted vLLM on same axis as APIs	❌	❌	❌	✅
Looped transformer (OpenMythos)	❌	❌	❌	✅
Bring-your-own JSONL	❌	❌	❌	✅
LLM-as-judge scorer for open-ended tasks	❌	❌	❌	✅
Cost per prediction with sweep	❌	❌	❌	✅

Closest active competitor is LLMThinkBench, which targets math-task overthinking on HuggingFace models at a fixed operating point — orthogonal to depth-lens's compute-axis sweep across vendor APIs.

Use cases depth-lens is built for

You are asking…	What depth-lens recommend outputs	Headline evidence
1. Which API tier / thinking budget should I be paying for?	Cheapest passing (model, knob) across your prompts	Opus 4.7 → Haiku 4.5 saves ~$123k/year at 10k call/day, same accuracy (finding)
2. Should I self-host an open model instead of paying the API?	API and vLLM points on one Pareto ($/M-token vs $/GPU-hour, same axis)	gemini-3.1-flash-lite beats every 4080 SUPER self-hosted candidate at K-hop tier 4; Llama-3-8B AWQ is cheapest at tier 1 ($0.028/1k calls) (finding)
3. Can I measure free-form output quality?	LLM-judge scores with the same Wilson CIs as structured scorers	Case 3 above — gpt-5-mini @ low wins on a 3-criterion rubric; higher effort decreases quality (finding)

For research-oriented use (paradigm scaling, inference-time-compute measurement infrastructure), see the v2.0 cross-paradigm measurement plot — a tool for putting Token-CoT API · Self-hosted vLLM · Looped transformers on a single FLOPs axis. We emphasize this is the measurement tool contribution; the underlying observation (specialized model beats generalist on the specific task it was trained for) is deep-learning textbook material.

All findings the tool has produced

We ran depth-lens on every vendor we could get an API key for, on all bundled tasks — current generation and one generation back to keep the cross-vendor comparison fair. Total spend: ~$14 API + ~30 min local GPU + ~$1 LLM-judge (case study 3).

Use case	Finding	Why it matters
API ops	Opus 4.7 → Haiku 4.5 saves ~$123k/year on a 10k-call/day task	4 concrete tier-downgrade savings switches in $
API ops	gpt-5-mini cheaper-per-token but 3× slower than o4-mini	$/token alone burns UI latency; Pareto frontier on K-hop tier 4 has 2 points
API ops	Haiku 4.5 collapses on hard 2-SAT at default budget	Constraint-style problems need budget ≥ 4096 or 2× error rate
API ops	Gemini 2.5 Flash uniquely weak vs same-era Anthropic / OpenAI cheap reasoning	3.1 Flash-Lite closes the gap
API ops	Claude Opus 4.7 cost varies 10× across (depth × budget) at fixed accuracy	Maxing the budget is a strict cost loss
API ops	Per-vendor cost-vs-latency plots	One scatter per vendor — Pareto frontier vs budget knobs
Build vs buy	Self-hosted vLLM vs hosted APIs on one Pareto	Llama-3-8B AWQ is cheapest at tier 1; 0% acc at tier 4. DeepSeek-R1-Distill-1.5B hits 0.75 at tier 4. Build-vs-buy as a chart, not a guess
Open-ended	Customer-reply quality via LLM-as-judge (Case 3)	gpt-5-mini accuracy decreases with effort on free-form tasks; optimal effort is per-(model, task)
Research / tool	v2.0 — 3 inference-time-compute paradigms on one FLOPs axis	Infrastructure to compare Token-CoT API · Self-hosted vLLM · Looped (OpenMythos 1M/10M/100M) on the same axis. The headline 24,000-410,000× FLOPs ratio is a deep-learning-textbook result; the tool is the contribution
Research	OpenMythos vs Claude head-to-head	Within training distribution, 925K-param looped is ~10,000× faster than Claude at same accuracy. Outside it, API dominates
Research	OpenMythos loops-vs-accuracy saturation	"More loops = deeper reasoning" saturates at training_max_loop_iters
Research	OpenMythos extrapolates 1-2 hops past training depth on K-hop	Seed experiment that motivated the project

→ Full v1.0 cross-vendor summary

Status

• v0.1 MVP — first end-to-end probe (May 2026)
• v0.5 — 4 tasks, 5 adapters, Wilson CIs, cache, Streamlit dashboard
• v1.0 — 6 adapter families, 5 tasks, full cross-vendor benchmark (Anthropic/OpenAI/Gemini, current + 2025 prior gen), multi-stage Docker, GitHub Actions CI
• v1.1 — OpenMythos head-to-head; cross-paradigm Pareto
• v1.2 — self-hosted vLLM with GPU-hour pricing on the same Pareto
• v2.0 — 3-paradigm FLOPs measurement tool, dict-lookup task, depth_lens.flops module
• v2.1 — LLM-as-judge scorer for open-ended tasks (llm:<judge>:<criterion>), tenant-reply case study
• v2.2 — PyPI publish, judge cost folded into recommend $/k-pred, --free-form CLI flag, code-generation task

128 unit tests passing. See ROADMAP.md for what's next.

Install variants

# API-only (no GPU needed) — Anthropic, OpenAI, Gemini, dashboard
pip install -e .[anthropic,openai,gemini,dashboard]

# +looped transformer + HuggingFace local probes
pip install -e .[openmythos,huggingface,anthropic,openai,gemini,dashboard]

# +self-hosted vLLM (vLLM runs separately via docker compose)
pip install -e .[anthropic,openai,gemini,dashboard]   # OpenAI SDK is all that's needed client-side

# Just the framework (BYO adapters)
pip install -e .

Python 3.11+. The bundled OpenMythos training helper assumes CUDA; everything else is happy on CPU or against remote APIs.

Contributing

See CONTRIBUTING.md for how to add a Task or an Adapter (both are ~50 lines + a test) and the conventions used in the bundled implementations.

Citation

@software{depth_lens_2026,
  title  = {depth-lens: Measuring Inference-Time Compute for LLM Production Decisions},
  author = {yutoTachibana},
  year   = {2026},
  url    = {https://github.com/yutoTachibana/depth-lens}
}

License

MIT.