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# PID Control

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arXiv Nov 6, 2026
MoE load balancing recast as feedback control: PID (I) holds the busiest expert lower across a data-mixture switch
Data-mixture changes during mixture-of-experts (MoE) training disrupt the per-expert load a router had converged to, yet existing balancing methods were evaluated only on stationary data. This work formulates load balancing as feedback control: each expert's deviation from an equal share is the control error, a per-expert bias added to router scores is the control input, and the auxiliary loss and ALF-LB correspond to a proportional term and a sign-based integral term. Keeping only the integral term, PID (I) attains lower MaxVio than the compared methods before and after a mid-run mixture switch in OLMoE pretraining and in continual pretraining of OLMoE-1B-7B, at comparable perplexity.
Data-mixture changes during mixture-of-experts (MoE) training disrupt the per-expert load a router had converged to, yet existing balancing methods were evaluated only on stationary data. This work formulates load balancing as feedback control: each expert's deviation from an equal share is the control error, a per-expert bias added to router scores is the control input, and the auxiliary loss and ALF-LB correspond to a proportional term and a sign-based integral term. Keeping only the integral term, PID (I) attains lower MaxVio than the compared methods before and after a mid-run mixture switch in OLMoE pretraining and in continual pretraining of OLMoE-1B-7B, at comparable perplexity.
Yikun Hou（First author）
PID-Balancer MoE Load Balancing PID Control
researchsquare.com Oct 27, 2026
Recursive training gets a thermostat: closed-loop control cuts collapse risk from 2.67 to 0.48 and keeps 97.4% of the tail
Generative models retrained on their own output narrow their distribution and lose the tails first, and training pipelines have lacked a way to correct this while they run. HOMEOSTASIS fuses signed, hash-chained provenance records with three model vital signs, predictive entropy, calibration error and representational drift, into a Lyapunov-style collapse-risk score, and a PID controller adjusts the human-data mixing ratio and quarantine decisions. On a five-dimensional Gaussian recursion over 30 seeds and 20 generations, closed-loop control lowered final collapse risk from 2.67 to 0.48 and held tail coverage at 97.4% against 66.2% without control, while provenance-gated quarantine showed no detectable benefit beyond control alone.
Generative models retrained on their own output narrow their distribution and lose the tails first, and training pipelines have lacked a way to correct this while they run. HOMEOSTASIS fuses signed, hash-chained provenance records with three model vital signs, predictive entropy, calibration error and representational drift, into a Lyapunov-style collapse-risk score, and a PID controller adjusts the human-data mixing ratio and quarantine decisions. On a five-dimensional Gaussian recursion over 30 seeds and 20 generations, closed-loop control lowered final collapse risk from 2.67 to 0.48 and held tail coverage at 97.4% against 66.2% without control, while provenance-gated quarantine showed no detectable benefit beyond control alone.
University of Liberal Arts Bangladesh
Maruf Sharker Munna（First author, Corresponding author）
HOMEOSTASIS Model Collapse PID Control Watermarking

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