SIGNALAI·Jul 2, 2026, 4:00 AMSignal75Medium term

Zeroth-Order Optimization at the Edge of Stability

Source: arXiv cs.LG

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Zeroth-Order Optimization at the Edge of Stability

arXiv:2604.14669v2 Announce Type: replace Abstract: Zeroth-order (ZO) methods are widely used when gradients are unavailable or prohibitively expensive, including black-box learning and memory-efficient fine-tuning of large models, yet their optimization dynamics in deep learning remain underexplored. In this work, we provide an explicit step size condition that exactly captures the (mean-square) linear stability of a family of ZO methods based on the standard two-point estimator. Our characterization reveals a sharp contrast with first-order (FO) methods: whereas FO stability is governed sole

Why this matters
Why now

The continuous push for more efficient and scalable AI models, especially in resource-constrained environments, makes advancements in optimization techniques particularly relevant now.

Why it’s important

This research provides a deeper understanding of zeroth-order optimization stability, critical for black-box learning and efficient fine-tuning of large AI models, potentially unlocking new applications and reducing computational costs.

What changes

Our understanding of the stability characteristics of zeroth-order methods is now more explicit, revealing a sharp contrast with first-order methods that could lead to more robust and performant learning algorithms.

Winners
  • · AI researchers and developers
  • · Companies utilizing black-box AI systems
  • · Developers of memory-efficient AI applications
Losers
  • · Inefficient AI optimization methods
  • · Systems highly reliant on first-order methods for all tasks
Second-order effects
Direct

Improved stability and efficiency in zeroth-order optimization methods for AI.

Second

Broader adoption of zeroth-order methods in scenarios where gradients are inaccessible or costly, such as edge AI or privacy-preserving learning.

Third

Acceleration of AI model development and deployment in diverse, resource-constrained environments, leveling the playing field for smaller developers or specific industrial applications.

Editorial confidence: 90 / 100 · Structural impact: 55 / 100
Original report

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Read at arXiv cs.LG
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