JMIR Publications

ABSTRACT

Background:

Consumer weight-management tools prescribe daily calorie targets open-loop: a population prediction equation estimates energy expenditure, an intended deficit is subtracted, and the number is rarely checked against what happens to the individual. Self-reported energy intake carries a large, stable, person-specific under-reporting bias, so a weight-loss stall presents two indistinguishable failure modes — a wrong target or an incomplete log — that demand opposite interventions.

Objective:

To describe the design of the deficit loop, a deterministic closed-loop calorie-target controller operating inside per-user large language model (LLM) coaching agents over consumer messaging (SMS and WhatsApp), and to report engineering constraints and field observations from its first 7 weeks of production operation.

Methods:

The controller maintains two energy-expenditure estimates in deliberately different units: an apparent expenditure back-solved from the user's own logged meals and weigh-ins, which inherits the user's reporting bias by construction, and an anthropometric prediction in physiological units, used exclusively for safety bounds. Their ratio routes each weekly run between re-deriving the target and repairing the measurement. An absolute deficit applied in the user's own logging units yields a provable fixed-point property: the steady-state true deficit equals the intended deficit for any stable multiplicative reporting bias. All arithmetic is computed outside the generative layer, and estimator internals are structurally excluded from user-facing messages. Observations are retrospective, de-identified aggregates from production snapshots (July and September 2026) of a commercial service; there was no control group.

Results:

Across users with at least one closed-loop control window (n=29), measured expenditure ran a median of approximately 284 kcal/day below the plan's textbook-formula prediction (24/29 below) and approximately 511 kcal/day below a consumer-calculator recommendation (22/24 below) — for the median user, roughly half of the formula-promised weekly progress. On 28-day forward weight-change prediction (57 windows, 19 users), the loop nearly eliminated the formula baseline's systematic bias (−0.02 vs −0.15 kg/week) and improved median absolute error (0.26 vs 0.36 kg/week). Over 7 weeks the controller landed 65 target movements (35 down, 30 up; median absolute change 100 kcal/day), and sub-floor detection reclassified roughly half of the recently active fleet (19/36) as not having a calorie-target problem. In a scan of 3,345 outbound coaching messages, 725 (21%) "room to eat" encouragements were sent while the user's standing target exceeded measured expenditure by at least 150 kcal/day, motivating the paper's central architectural argument: in an LLM-mediated coach, the dominant harm of an over-estimated target is behavioral.

Conclusions:

Closing the loop on the prescription itself — while routing between "fix the target" and "fix the measurement" under self-report bias — is feasible at production scale inside LLM-mediated coaching, with all numbers kept outside the generative layer. This is an observational systems report from a self-selected commercial cohort, not a clinical-efficacy claim; controlled evaluation is future work.