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: [R] Sinc Reconstruction for LLM Prompts: Applying Nyquist-Shannon to the Specification Axis (275 obs, 97% cost reduction, open source)

Reddit r/MachineLearning / 3/22/2026

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Key Points

  • The study applies the Nyquist-Shannon sampling theorem to LLM prompt engineering, showing a raw prompt acts as one sample of a six-band specification signal, and missing reconstruction leads to aliasing such as hallucination, hedging, and structural incoherence.
  • In 275 production observations, the CONSTRAINTS band accounts for about 42.7% of output quality.
  • The approach yields a dramatic improvement in signal-to-noise ratio, from 0.003 to 0.92.
  • API costs drop by 97% (roughly $1,500 to $45 per month) with open-source code and implementation available.

I applied the Nyquist-Shannon sampling theorem to LLM prompt engineering. The core finding: a raw prompt is 1 sample of a 6-band specification signal, producing aliasing (hallucination, hedging, structural incoherence).

Key results from 275 production observations:

- CONSTRAINTS band carries 42.7% of output quality

- SNR improvement from 0.003 to 0.92

- 97% API cost reduction ($1,500 to $45/month)

- All 4 optimized agents converge to identical zone allocation

Paper: https://doi.org/10.5281/zenodo.19152668

Code: https://github.com/mdalexandre/sinc-llm

pip install sinc-llm

submitted by /u/Financial_Tailor7944
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