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)
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 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)
Measured on GPU pod
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)
Measured on GPU pod
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).)
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).
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
Citation
@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.
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