# Depth as a Candidate Source: Portfolio Allocation for Recurrent Test-Time Scaling in Large Language Models

**Authors:** Chaoyuan Hao, Wentao Yue, Yanyan Wu, Boyuan Gao, Tianyou Lai, Maolin Wang, Yongxin Ni, Hanwen Du, Youhua Li  
**Published:** 9 Nov 2026  
**Links:** [arXiv](https://arxiv.org/abs/2611.12293) · [PDF](https://arxiv.org/pdf/2611.12293) · [This page](https://omen-bit.github.io/ai-paper-daily/paper/2611.12293.html)

## Abstract

Recurrent latent reasoning in large lanugage models (LLMs) scales test-time computation by increasing recurrent depth, naturally framing inference as a problem of deciding when to stop. We identify a previously overlooked limitation of this single-depth view through systematic preliminary analysis: deeper recurrence can lose correct solutions found at shallower depths, while depth-specific success sets remain broadly non-nested even after controlling for marginal accuracy. This suggests that depth determines not only computation cost, but also access to distinct candidate solutions. Motivated by this finding, we propose Depth Portfolio Allocation (DPA), which reformulates recurrent test-time scaling as budgeted allocation across depth-specific candidate sources. DPA supports both fixed portfolios and feedback-guided sequential allocation under a shared inference budget. Experiments on GSM8K, SVAMP, MultiArith, and MBPP show that mixed-depth portfolios expand oracle coverage under matched candidate counts and nominal costs, while feedback-guided allocation generally matches or improves uniform allocation and can reduce computation in high-budget settings. Code and data are avaible at : https://anonymous.4open.science/r/LLM-latent-B7BC/.

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