Appendix 2A: Output Verbosity Reduction and Resource Efficiency

Token-Delta Distribution and Deployment-Scale Estimates

Author: Leonard Rojas

Date: 2026-07-07

Status: Current (token-delta dataset spans 26 fine-tuning runs across seven model families, through Qwen2.5-Coder-14B v2.0F, 2026-07-06)

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Abstract

This appendix extracts and extends the output-verbosity result reported in Appendix 2 (Section 7.5, addressing secondary research question 4) into a resource-efficiency analysis. It consolidates the IFEval [3] token-delta measurements across 26 fine-tuning runs spanning seven model families, characterizes their distribution, and estimates the deployment-scale energy and water implications of the observed reduction. Across instruct-tuned models, Framework compliance training reduces output verbosity by a median of 36.7% and a mean of 39.0% (IFEval word-count proxy, 541 prompts), with 19 of 26 runs falling in the 30% to 70% reduction band and a maximum single-run reduction of 71.8%. Because autoregressive inference energy scales with the number of tokens processed, and inference accounts for an estimated 80% to 90% of total AI energy use [1], a reduction in output length maps to a proportional reduction in per-query energy and its associated water and carbon footprints. The measured central tendency exceeds the reduction fractions assumed in both the Framework’s own pre-testing session efficiency thesis (Chapter 11) and a subsequent 2026 United Nations University report [1], which serves as independent corroboration. Limitations, including the word-count proxy and the Jevons rebound effect, are stated in Section 7.

1. Scope and Relationship to Appendix 2

Appendix 2 reports a multi-experiment fine-tuning study in which the Four Laws of Instanced AI and WCAG 2.2-AA [5] accessibility principles are embedded into open-weight language models via QLoRA [6]. Its secondary research question 4 asks whether that training produces a measurable change in output verbosity, and Section 7.5 answers in the affirmative: instruct models trained on the Framework curriculum become consistently terser.

This appendix does not repeat the training methodology or the per-experiment results. It has a narrower purpose: to consolidate the verbosity measurements into a single distribution, and to quantify what that reduction implies for energy and water demand when a compliant model is deployed at scale. The verbosity reduction is a behavioral side effect established in Appendix 2; the resource implication is the corollary developed here and in Chapter 11.

The framing is a direct consequence of the Framework’s design goals. Compliance training suppresses two verbosity sources at once: decorative structure rejected on WCAG grounds (enumerated markup, repeated content, filler placeholders), and meta-commentary suppressed by the conditional-activation curriculum. The terser output is simply the model responding to the input without embellishment and stopping.

2. Measurement Method

The verbosity metric is the IFEval token delta: the change in mean response length between a base model and its Framework-trained adapter, measured over the 541 prompts of the Google Research IFEval benchmark [3]. Length is reported as a word-count proxy rather than literal tokenizer tokens, computed identically for the base and trained runs so the delta is internally consistent.

For each model, the delta is defined as:

delta_percent = (aisf_mean_words - base_mean_words) / base_mean_words

A negative value indicates the trained model is less verbose than its base. Base-model response sets are cached artifacts and are not re-generated between adapter versions; the trained adapter is the only variable in each pair. Word counts are a proxy for tokens (a word corresponds to roughly 1.3 tokens for these tokenizers), so the reported percentages are directional and order-of-magnitude with respect to token count. The measurement is taken only on an instruction-following benchmark. Billed production traffic would produce different results; Section 7 states the consequences of both approximations.

3. Token-Delta Distribution

Twenty-six runs were measured across seven model families: Mistral 7B base and Instruct, Llama 3.1 8B, Gemma 2 9B, Qwen3-8B, Qwen2.5-Coder-14B, Mistral Nemo 12B, and Ministral 3 3B, including intermediate training iterations retained for the record.

Table 1. Summary statistics (26 runs).

The distribution is skewed toward reduction: 19 of 26 runs fall in the 30% to 70% band, with a pronounced cluster in the 30% to 40% sub-band and a thin tail of deep reducers. Two runs became more verbose; both are noted in Table 3.

Table 2. Distribution by 10-point bin (signed delta).

The -40% to -30% bin holds 9 of 26 runs and the -70% to -40% span holds 10 more: 19 of 26 runs fall in the 30% to 70% reduction band, a clear majority above the fractions the deployment estimates assume.

Table 3. Full token-delta results, greatest reduction first. Base and AISF columns are mean words per response over 541 IFEval prompts.

The two increases (rows 25 and 26) are the only runs in which Framework training raised verbosity. Row 25 is a base (non-instruct) checkpoint whose untrained baseline is already extreme (587 words per response); row 26 is a single Gemma 2 iteration. Every other instruct run reduced verbosity. Duplicate-looking Mistral rows are distinct runs measured against different base references (212.2 versus 228.3 base words); the base column disambiguates them and they are not merged.

4. Per-Query Energy Basis

The resource relevance of output length follows from where AI spends energy. Model training is a recurring cost rather than a one-time outlay, since models are retrained on a regular cadence to stay current. The continuous inference phase that serves billions of interactions is the larger share, at an estimated 80% to 90% of total AI energy use [1]. Inference energy is dominated by autoregressive decoding, which processes tokens sequentially, so per-query energy rises with the number of tokens generated.

Output length is therefore a first-order determinant of per-query cost. A typical conversational language-model response uses roughly 200 times the energy of a text classification, and long or elaborate responses reach 500 to 1,000 times [1]. Within text-only tasks, model choice combined with response length can drive differences of up to two orders of magnitude. Table 4 gives representative per-query electricity figures.

Table 4. Mean electricity per query by task (UNU-INWEH Figure 11) [1].

A typical response at 0.420 Wh is roughly nine times a short-text answer, and a long response at 1.900 Wh is roughly four times a typical one. Reducing output length moves a query down this ladder. A verbosity reduction of the magnitude in Table 1 therefore reduces per-query energy by a comparable fraction, before any change in query volume.

5. Deployment-Scale Resource Estimates

Two preliminary estimates translate a token reduction into resource savings. They scope different denominators, so their absolute magnitudes are not directly comparable, but both rest on a reduction fraction that the measured distribution supports.

Table 5. Preliminary resource-scaling estimates.

The UNU-INWEH figure is equivalent to the annual residential electricity use of 672,000 to 756,000 people in Sub-Saharan Africa (at 130 kWh per person per year) [1]. The whitepaper figure of roughly 27 TWh per year is comparable to the residential electricity of every home in Los Angeles plus half of Chicago. The associated water saving, computed at an industry water usage effectiveness of about 1.8 liters per kWh [4], is roughly 48.6 billion liters per year, comparable to about 39,600 Olympic-sized pools or one Caesar Creek Lake.

The two figures differ by roughly three orders of magnitude (GWh versus TWh) because one counts a single platform’s queries and the other counts all AI data-center electricity. Both are order-of-magnitude estimates. The focus of this appendix is on the empirical reduction fraction those estimates assume.

6. Independent Corroboration and Precedence

Table 5’s two estimates each assume a reduction fraction (30% and 33%). The token-delta distribution is the measurement of that fraction. Table 6 places the preliminary assumptions beside the measured results.

Table 6. Preliminary versus measured token reduction.

The measured central tendency exceeds both assumed values. The independence of the United Nations University Institute for Water, Environment and Health’s estimate is the point of interest. That 2026 publication from UNU-INWEH arrives at a message-level efficiency argument, that reducing verbosity yields material savings at platform scale, through an entirely separate line of analysis, and selects a 30% reduction as its illustrative case.

The Framework’s session-efficiency thesis (Chapter 11) and the token-delta measurements reported here predate that report by many months. The report is independent later corroboration of a position the Framework already held and had measured. Two distinctions follow. First, the direction of dependence: the UNU report independently converged on the Framework’s figures. Second, the epistemic status of the numbers: the report’s 30% is a stipulated illustration, whereas the 36.7% median reported here is an empirical result across 26 runs. An external body independently reasoning to the same conclusion, and to a more conservative figure than the Framework had already demonstrated, strengthens the claim.

7. Limitations

Proxy metric. The delta is a word-count proxy over 541 IFEval prompts. Literal tokenizer tokens and real-world tasks would yield different results. Words approximate tokens (about 1.3 tokens per word, or about 1 token per 4 characters), so the percentages are directional with respect to token count. The reduction is measured only on an instruction-following benchmark.

Rebound effect. Lower per-use energy does not automatically lower total impact. When a service becomes cheaper or faster, usage tends to rise, a pattern often described as the Jevons Paradox [1]. A verbosity-reduction lever should be paired with resource budgets (e.g. token, GPU-hour, or kilowatt-hour caps) rather than treated as an automatic net saving. The Framework’s enforcement posture, which applies the constraint at every session rather than depending on user initiative, is consistent with that pairing.

Grid and hardware dependence. Absolute energy, water, and carbon depend on hardware, batching, data-center efficiency, and grid mix. The same watt-hour carries different carbon and water footprints by location. The scaling estimates in Section 5 are illustrative at the global-average level and are not site-specific predictions.

8. Conclusions

Framework compliance training produces a consistent, cross-architecture reduction in output verbosity: a 36.7% median across 26 runs and seven model families, with only two explicable exceptions. The practical consequence is a model that costs less to run. Because inference dominates AI energy use and per-query energy scales with token count, a terser model is proportionally cheaper to operate in electricity, water, and carbon at every query it serves.

At deployment scale the two preliminary estimates place that saving between tens of gigawatt-hours and tens of terawatt-hours per year, and the measured reduction exceeds the fractions both assume. That the Framework reached this result before the 2026 UNU-INWEH report independently converged on it establishes the efficiency corollary as a demonstrated property of the trained models, subject to the rebound caveat in Section 7.

References

[1] M. Aczel, S. Chamanara, M. Matin, A. Farsi, T. Marwala, and K. Madani, Environmental Cost of AI’s Energy Use: Carbon, Water and Land Footprints, United Nations University Institute for Water, Environment and Health (UNU-INWEH), Richmond Hill, Ontario, Canada, 2026. doi:10.53328/INR26RMA002

[2] International Energy Agency, Energy and AI, IEA, 2025. https://www.iea.org/reports/energy-and-ai

[3] J. Zhou, T. Lu, S. Mishra, S. Brahma, S. Basu, Y. Luan, D. Zhou, and L. Hou, “Instruction-Following Evaluation for Large Language Models,” 2023. arXiv:2311.07911

[4] AKCP, “Data Center Water Usage Effectiveness (WUE),” 2021. https://www.akcp.com/index.php/2021/01/14/data-center-water-usage-effectiveness-wue/

[5] World Wide Web Consortium, Web Content Accessibility Guidelines (WCAG) 2.2, W3C Recommendation, Oct. 2023. https://www.w3.org/TR/WCAG22/

[6] T. Dettmers, A. Pagnoni, A. Holtzman, and L. Zettlemoyer, “QLoRA: Efficient Finetuning of Quantized LLMs,” Advances in Neural Information Processing Systems (NeurIPS), 2023. arXiv:2305.14314