Textual Equilibrium Propagation for Deep Compound AI Systems

Authors: Minghui Chen, Wenlong Deng, James Zou, Han Yu, Xiaoxiao Li

Published in: Accepted to The Fourteenth International Conference on Learning Representations (ICLR 2026)

Abstract

Large language models (LLMs) are increasingly deployed as part of compound AI systems that coordinate multiple modules, such as retrievers, tools, and verifiers, over long-horizon workflows. Recent approaches that propagate textual feedback globally, such as TextGrad, make it feasible to optimize such pipelines, but we find that performance degrades as system depth grows.

In particular, long-horizon agentic workflows exhibit two depth-scaling failure modes: 1) exploding textual gradient, where textual feedback grows exponentially with depth, leading to prohibitively long messages and amplified evaluation biases; and 2) vanishing textual gradient, where limited long-context ability causes models to overemphasize partial feedback, and compression of lengthy feedback causes downstream messages to gradually lose specificity as they propagate many hops upstream.

To mitigate these issues, we introduce Textual Equilibrium Propagation (TEP), a local learning principle inspired by Equilibrium Propagation in energy-based models. TEP includes two phases: 1) a free phase where local LLM critics iteratively refine prompts until reaching equilibrium, with no further improvements suggested; and 2) a nudged phase that applies proximal prompt edits with bounded modification intensity, using task-level objectives that propagate via forward signaling rather than backward feedback chains.

This design supports local prompt optimization followed by controlled adaptation toward global goals without the computational burden and signal degradation of global textual backpropagation. Across long-horizon QA benchmarks and multi-agent tool-use datasets, TEP consistently improves accuracy and efficiency over global propagation methods such as TextGrad. The gains grow with depth while preserving the practicality of black-box LLM components in deep compound AI systems.