---
license: cc-by-4.0
language:
  - en
tags:
  - llm-quantization
  - model-tier-routing
  - cost-quality-frontier
  - agentic-tool-calling
  - llm-cascade
  - nvfp4
  - self-hosted-serving
  - bfcl
pretty_name: >-
  The Precision Ladder: Measuring the Joint Model-Tier and Quantization-Precision Cost-Quality Frontier for Agentic Tool-Call Routing on Self-Hosted H200
viewer: false
---

# The Precision Ladder: Measuring the Joint Model-Tier and Quantization-Precision Cost-Quality Frontier for Agentic Tool-Call Routing on Self-Hosted H200

> **TL;DR** — Upgrades the one-dimensional FrugalGPT cascade to a two-dimensional (model-size x weight-precision) cost-quality frontier for self-hosted agentic tool-call routing, where one GPU-hour prices every grid cell. A closed-form crossing condition (rho^t * rho^Q > rho^l; shared-regime form D_c > xi/(1-xi)) predicts a category-inverted 'precision ladder' -- small full-precision on easy tasks, large low-bit on hard ones -- driven by byte parity (27B at 4.5 effective bits = 15.2 GB of weights vs 16.0 GB for 8B at 16 bits); a measured H100 NVL feasibility layer (BF16 peaks 7.5/15.3/27.5 GB of 93.6 GB, low-bit bitsandbytes paths unsupported) and a pre-registered R1-R4 protocol specify how the frontier cells will be settled.

**ThakiCloud AI Research** · 2026-09-27 · [📝 Tech blog (KO)](https://thakicloud.com/tech-blog/ko/research/precision-ladder-model-quant-routing/)

## Problem

For agentic tool-call tasks of graded difficulty (simple, parallel, agentic BFCL-style categories), a self-hosted operator must choose both the model tier (4B/8B/14B/27B dense Qwen3) and the weight precision (BF16/FP8/NVFP4). Under API pricing, FrugalGPT-style cascades optimize only the tier because the request price scales with it; on a single self-hosted GPU the price axis collapses (one GPU-hour covers any resident variant), the choice becomes two-dimensional, and it is open whether a quantized large model can beat a smaller full-precision model per successful task.

## Approach

Prices each (model, precision) cell by effective passing throughput E = tQ/l (passed tasks per GPU-second) under a judge-free BFCL-style code gate fixed at g = 0.85, so the cost per passed task is C = p_h/E and the routing entry is the gated argmax of E. The 2-D frontier is developed in closed form: it subsumes the 1-D cascade as its BF16-row projection (Theorem 1); the ladder-crossing condition rho^t * rho^Q > rho^l (Theorem 2) with the dividend-versus-cliff necessary form D_c > xi/(1-xi) (Corollaries 1-2); three category-inversion regimes (Proposition 1); and a hardware-transfer proposition (Proposition 2). Quality-decay inputs come from the measured tool-call cliff and the near-one throughput ratio from weights-only byte-parity arithmetic; a measured feasibility layer (checkpoint downloads, BF16 load and peak VRAM, low-bit stack compatibility) plus a pre-registered protocol with refutation criteria R1-R4 populate the cells.

## Key contributions

- System: a deployable per-category routing table ('precision ladder') for the ThakiCloud token factory -- the cheapest (model x precision) pair on the self-hosted fleet that passes the BFCL-style gate g = 0.85 -- composable with the zero-token skill router and queue-aware E-order tier fallback, and anchored by the 27B-NVFP4 production checkpoint at 89.6 percent overall on the 800-case BFCL-style suite.
- Society: a quantification of when a quantized large model beats a smaller full-precision model at equal task quality, giving self-hosted operators a concrete recipe to cut per-task inference spend and the energy behind it.
- Science: an upgrade of FrugalGPT-style 1-D cascades to the first joint 2-D (model-size x quantization-precision) cost-quality frontier for agentic tool-call workloads, with a closed-form crossing condition, a necessary dividend-versus-cliff inequality, category-structure regimes, a hardware-transfer proposition, and a pre-registered falsification protocol (P1-P3, R1-R4).

## Figures

![Measured BF16 Peak VRAM by Model Size](figures/fig1-bf16-vram.png)
*Measured BF16 peak VRAM of the 4B/8B/14B Qwen3 checkpoints on the 93.6 GB node: every variant fits with at least 70 percent headroom, so memory is not the binding constraint on the feasible set.  (Measured on GPU pod)*  
<sub>Measured on GPU pod</sub>

![Measured BF16 Checkpoint Load Time by Model Size](figures/fig2-bf16-load.png)
*Measured BF16 load time grows smoothly from 2.2 s (4B) to 5.0 s (14B) within a 189.8 s total feasibility wall on the 93.6 GB node.  (Measured on GPU pod)*  
<sub>Measured on GPU pod</sub>

![Weight Bytes per Variant: The Byte-Parity Mechanism](figures/fig3-byte-parity.png)
*Weights-only arithmetic at the crossing: 27B at 4.5 effective bits per weight (15.2 GB) reads slightly fewer bytes per forward pass than 8B at 16 bits (16.0 GB), keeping the throughput ratio near one; FP8 and BF16 27B are shown for scale.  (Analytical model (not measured): weights-only byte arithmetic as stated in the paper (BF16 = 2 bytes per weight, FP8 = 1 byte per weight, NVFP4 = 4.5 effective bits per weight).)*  
<sub>Analytical model (not measured): weights-only byte arithmetic as stated in the paper (BF16 = 2 bytes per weight, FP8 = 1 byte per weight, NVFP4 = 4.5 effective bits per weight).</sub>

## Results (as argued)

Analytical claims with a measured feasibility layer; no new per-cell quality or throughput measurements are reported. (i) The 2-D frontier weakly dominates the 1-D cascade, which is its BF16-row projection. (ii) In the byte-parity regime (27B NVFP4 15.2 GB vs 8B BF16 16.0 GB of weights, scenario rho^t = 0.95), the crossing flips by category: no crossing on simple (product 0.896 < 1) and crossing on agentic (product 1.064 > 1, about 6 percent lower cost per passed task) -- the predicted category-inverted routing table. (iii) Measured on the 93.6 GB H100 NVL node: BF16 4B/8B/14B peak at 7.5/15.3/27.5 GB (at least 70 percent headroom), load in 2.2/2.9/5.0 s, concurrent checkpoint downloads at about 171 s, total feasibility wall 189.8 s, and all six bitsandbytes 8/4-bit load attempts unsupported, so stack support -- not VRAM -- bounds the feasible set. (iv) The full 4x3 grid is memory-feasible on H100 NVL and a fortiori on the H200 deployment target.

## Limitations

No per-cell quality-throughput grid measurements are reported, so the regime of Proposition 1 (ladder, empty, or low-bit-dominated) is undetermined until R1-R4 run and the Section 5.3 illustration is a scenario, not data; the grid is a single model family (dense Qwen3); the measured feasibility layer is on H100 NVL while the deployment target is H200, with the transfer conditional on beta_c proxies guarded by R4 (20 percent bound); the gate is fixed at g = 0.85; the shared-regime corollaries assume rho^l = 1 and rho^r = 1, so low-bit token inflation or silent-error growth raises the required dividend; and p_h uses cited public on-demand list prices (H100 $2.50, H200 $3.50, B200 $5.00, RTX 5070 $0.60 per GPU-hour).

## Abstract

We upgrade the one-dimensional FrugalGPT cascade to a two-dimensional frontier over model tier and weight precision for self-hosted agentic serving, where the price axis collapses: one GPU serves one (model, precision) point at a fixed hourly rate. Per category, the cheapest gated pair is the argmax of effective passing throughput E = tQ/\ell under a judge-free BFCL-style code gate. A closed-form crossing condition, \rho_c^t\rho_c^Q>\rho_c^\ell, tests a larger low-bit challenger against a smaller full-precision incumbent per passed task (the per-true-task bill adds the success ratio \rho_c^r); in the shared regime its necessary form is the dividend-versus-cliff inequality D_c > \xi/(1-\xi). The predicted category-inverted routing table (small full-precision on easy, large low-bit on hard) is driven by byte parity: 15.2 GB of 27B weights at 4.5 effective bits versus 16.0 GB for 8B at 16 bits keeps the throughput ratio near one. The measured feasibility layer reports BF16 4B/8B/14B peaking at 7.5/15.3/27.5 GB on a 93.6 GB Hopper node, cited on-demand prices, an 89.6% BFCL-style anchor for the 27B-NVFP4 production checkpoint, and four pre-registered refutation criteria R1-R4. This is an analytical and positional study with a measured feasibility layer; no new per-cell quality or throughput measurements are reported.

## Files

- [📄 Paper (PDF)](paper.pdf)
- [LaTeX source](main.tex)
- [References (BibTeX)](refs.bib)

## Citation

```bibtex
@techreport{thaki_precision_ladder_model_quant_routing_2026,
  title  = {The Precision Ladder: Measuring the Joint Model-Tier and Quantization-Precision Cost-Quality Frontier for Agentic Tool-Call Routing on Self-Hosted H200},
  author = {ThakiCloud AI Research (Hyojung Han)},
  year   = {2026},
  institution = {ThakiCloud}, note = {thaki-AI/daily-paper-2026-09-27-precision-ladder-model-quant-routing}
}
```

---
*Generated by ThakiCloud nightly research pipeline. License: CC BY 4.0.*