Title: Textual Equilibrium Propagation for Deep Compound AI Systems
Primary area: foundation or frontier models, including LLMs
Keywords: Compound AI System

Abstract: Large language models (LLMs) increasingly operate as components of compound AI systems which coordinate multiple modules (e.g., LLMs, retrievers, tools, verifiers) over long-horizon workflows. Although recent frameworks that propagate textual feedback globally (e.g., TextGrad) enable optimization of such pipelines, we identify two depth-scaling failure modes in long-horizon agentic workflows: 1) \emph{exploding textual gradient}, where textual feedback accumulates exponentially across layers, resulting in increasingly lengthy feedback that becomes computationally prohibitive and amplifies evaluation biases; and 2) \emph{vanishing textual gradient}, where limited long-context ability causes models to overemphasize recent or early portions, while compression of lengthy feedback causes downstream messages to lose specificity as they propagate many hops upstream. To address these issues, we introduce \textbf{Textual Equilibrium Propagation (TEP)}, a local learning principle inspired by Equilibrium Propagation in energy-based models. TEP operates in two phases: 1) a free phase where a local LLM critics iteratively refine prompts until reaching equilibrium (no further improvements suggested); and 2) a nudged phase which leverages proximal prompt edits with bounded modification intensity, guided by task-level objectives propagated through forward signaling rather than backward feedback chains. This design enables 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 suites, TEP consistently improves accuracy and efficiency over global propagation methods such as TextGrad, with larger gains at greater depths. TEP preserves the practicality of black-box LLM components, while enabling robust optimization of long-horizon compound systems.