Annealing in variational inference mitigates mode collapse: A theoretical study on Gaussian mixtures

2026-02-16 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics · Depth: Expert, extended

Summary

A theoretical study investigates annealing-based strategies to mitigate mode collapse in variational inference (VI), a critical challenge when approximating multimodal distributions. The research provides a mathematical analysis in a tractable setting: learning a Gaussian mixture. By leveraging a low-dimensional summary statistics description, the authors precisely characterize the interplay between initial temperature and annealing rate, deriving a sharp formula for the probability of mode collapse. The analysis demonstrates that an appropriately chosen annealing scheme can robustly prevent mode collapse. Numerical evidence, including experiments with neural network-based RealNVP normalizing flows in 128 dimensions, qualitatively extends these theoretical trade-offs, offering guidance for designing effective annealing strategies in practical VI pipelines. The study used a bimodal Gaussian target distribution with parameters like R=3, w*=0.8, and w1=0.5, and an exponential annealing schedule.

Key takeaway

Research Scientists working with variational inference on multimodal distributions should carefully tune annealing schedules, recognizing the critical trade-off between initial temperature and annealing rate. To reliably avoid mode collapse, you must ensure that increasing the initial temperature is accompanied by a proportional increase in annealing duration ($t_0$), thereby maintaining a sufficiently slow annealing rate. This strategy is crucial even when the true mode separation is unknown, as it ensures the system remains in a high-temperature regime long enough for modes to separate.

Key insights

Annealing in variational inference can robustly prevent mode collapse by balancing initial temperature and annealing rate.

Principles

• Mode collapse arises from reverse KL's strong penalty on low-probability regions.
• High temperature promotes exploration, mitigating mode collapse.
• Optimal annealing balances modal resolution with convergence speed.

Method

The method involves minimizing the reverse Kullback-Leibler divergence between a variational distribution and a tempered target distribution, progressively lowering the temperature from $\beta<1$ to $\beta=1$ using a spherical gradient flow.

In practice

• Increase annealing duration ($t_0$) with initial temperature to maintain a small annealing rate.
• Monitor sample variance projected onto target modes to detect mode collapse in flows.
• Use exponential annealing schedules for predictable behavior.

Topics

• Variational Inference
• Mode Collapse
• Annealing Strategies
• Gaussian Mixtures
• Normalizing Flows

Code references

• Luijios/annealed_vi_gmms

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.