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MarkovScale: Towards Optimal Sequential Scaling at Inference Time

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 6.0Download Report PDF
Inference-time ScalingMarkov Decision ProcessEfficiency OptimalityProbabilistic FrameworkLLM Reasoning
Abstract:

Sequential scaling is a prominent inference-time scaling paradigm, yet its performance improvements are typically modest and not well understood, largely due to the prevalence of heuristic, non-principled approaches that obscure clear optimality bounds. To address this, we introduce a principled framework that models sequential scaling as a two-state Markov process, uncovering its fundamental properties and providing closed-form expressions for key aspects, including the conditions under which sequential scaling enhances accuracy, the theoretical accuracy upper bound, and the convergence rate. Leveraging this formulation, we develop MarkovScale, a practical system that applies these optimality criteria to achieve a theoretically grounded balance between accuracy and efficiency. Comprehensive experiments across 3 backbone LLMs and 5 benchmarks show that MarkovScale consistently outperforms state-of-the-art parallel and sequential scaling methods, representing a significant step toward optimal and resource-efficient inference in LLMs. The source code will be open upon acceptance at https://open-upon-acceptance.

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This report is AI-GENERATED using Large Language Models and WisPaper (A scholar search engine). It analyzes academic papers' tasks and contributions against retrieved prior work. While this system identifies POTENTIAL overlaps and novel directions, ITS COVERAGE IS NOT EXHAUSTIVE AND JUDGMENTS ARE APPROXIMATE. These results are intended to assist human reviewers and SHOULD NOT be relied upon as a definitive verdict on novelty.
NOTE that some papers exist in multiple, slightly different versions (e.g., with different titles or URLs). The system may retrieve several versions of the same underlying work. The current automated pipeline does not reliably align or distinguish these cases, so human reviewers will need to disambiguate them manually.
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Overview

Overall Novelty Assessment

The paper proposes a Markov process framework for sequential scaling in LLM inference, providing closed-form expressions for optimality conditions, accuracy bounds, and convergence rates. It resides in the 'Principled Sequential Optimization' leaf, which contains only two papers including this one. This is a notably sparse research direction within the broader taxonomy, suggesting that theoretically grounded sequential scaling remains relatively underexplored compared to heuristic refinement methods or parallel sampling strategies. The sibling paper in this leaf represents the only other work attempting formal optimality guarantees in sequential scaling.

The taxonomy reveals that most sequential scaling research falls into 'Heuristic Sequential Refinement' (two papers) or migrates toward 'Parallel and Hybrid Scaling' (four papers across two leaves). Neighboring branches include 'Compute-Optimal Allocation' (four papers) and 'Uncertainty-Guided Termination' (two papers), which address related but distinct problems: budget distribution across heterogeneous strategies and adaptive stopping based on confidence signals. The paper's Markov formulation bridges these areas by providing a principled stopping criterion within a sequential framework, positioning it at the intersection of formal optimization and adaptive control.

Among thirty candidates examined, the Markov formulation contribution shows one refutable candidate out of ten examined, while the closed-form conditions and MarkovScale system contributions each found zero refutable candidates among ten examined. This suggests that the theoretical framework and practical system design appear relatively novel within the limited search scope, though the core Markov modeling approach has at least one overlapping prior work. The analysis does not claim exhaustive coverage; these statistics reflect top-K semantic matches and citation expansion, not a comprehensive field survey.

Based on the limited literature search, the work appears to occupy a sparsely populated research direction with modest prior overlap. The taxonomy structure indicates that principled sequential optimization remains less developed than parallel or heuristic approaches, and the contribution-level statistics suggest the theoretical bounds and system design may offer incremental advances. However, the restricted search scope (thirty candidates) and single-sibling leaf context limit definitive claims about field-wide novelty.

Taxonomy

Core-task Taxonomy Papers
47
3
Claimed Contributions
30
Contribution Candidate Papers Compared
1
Refutable Paper

Research Landscape Overview

Core task: sequential scaling optimization for large language model inference. The field addresses how to allocate computational resources during inference to improve output quality, speed, or both. The taxonomy reveals several major branches: Test-Time Compute Scaling Strategies explore methods that adaptively invest more computation at inference time, often through sequential refinement or search; Speculative and Parallel Decoding focuses on accelerating generation via draft-and-verify schemes such as Lookahead Decoding[1] and Cascade Speculative Drafting[12]; Inference Scaling Laws and Empirical Analysis investigates how performance scales with compute budgets, exemplified by Inference Scaling Laws[5] and Beyond Chinchilla-Optimal[6]; Architectural Efficiency and System Optimization targets hardware-aware scheduling and pipeline improvements; Training-Based Optimization and Model Compression reduces model size or training overhead; Adaptive and Dynamic Inference Control adjusts generation strategies on-the-fly; Meta-Analysis and Survey Studies synthesize findings across methods; and Auxiliary Applications and Extensions apply these ideas to domains like multimodal or edge deployment. Within Test-Time Compute Scaling, a particularly active line of work examines principled sequential optimization, where models iteratively refine outputs or explore multiple reasoning paths. MarkovScale[0] sits in this cluster, emphasizing a Markov decision process framework for allocating compute across sequential steps. Nearby, Particle Monte Carlo[26] employs particle-based sampling to explore solution spaces, while Optimal Test-Time Compute[3] and Compute-Optimal Inference[17] study how to optimally distribute a fixed budget over samples or iterations. These approaches contrast with verifier-guided methods like Verifier-Guided Scaling[25] and adaptive termination schemes such as Adaptive Termination[31], which dynamically halt computation based on confidence signals. MarkovScale[0] distinguishes itself by framing the allocation problem as a sequential decision task, offering a formal lens on when to continue refining versus when to stop, a trade-off central to balancing quality gains against computational cost in modern LLM inference.

Claimed Contributions

Principled Markov formulation for sequential scaling

The authors model sequential scaling as a two-state Markov process where transitions represent the LLM amending answers between correct and incorrect states. This formulation enables closed-form solutions for performance bounds and reveals fundamental properties such as convergence behavior that can be analytically predicted in advance.

10 retrieved papers
Can Refute
Closed-form conditions for beneficial scaling and performance bounds

The framework establishes explicit mathematical criteria (Theorem 3.1) that determine when sequential scaling improves or degrades performance, based on zero-shot accuracy and transition probabilities. It also provides closed-form expressions for theoretical upper, neutral, and lower performance bounds that can be computed before experimentation.

10 retrieved papers
MarkovScale system with optimal stopping criteria

The authors implement a practical system that operationalizes the theoretical framework through gating strategies and optimal stopping criteria. MarkovScale determines when to terminate scaling iterations to achieve a theoretically grounded balance between accuracy and token efficiency, with variants including training-based and training-free implementations.

10 retrieved papers

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

Principled Markov formulation for sequential scaling

The authors model sequential scaling as a two-state Markov process where transitions represent the LLM amending answers between correct and incorrect states. This formulation enables closed-form solutions for performance bounds and reveals fundamental properties such as convergence behavior that can be analytically predicted in advance.

Contribution

Closed-form conditions for beneficial scaling and performance bounds

The framework establishes explicit mathematical criteria (Theorem 3.1) that determine when sequential scaling improves or degrades performance, based on zero-shot accuracy and transition probabilities. It also provides closed-form expressions for theoretical upper, neutral, and lower performance bounds that can be computed before experimentation.

Contribution

MarkovScale system with optimal stopping criteria

The authors implement a practical system that operationalizes the theoretical framework through gating strategies and optimal stopping criteria. MarkovScale determines when to terminate scaling iterations to achieve a theoretically grounded balance between accuracy and token efficiency, with variants including training-based and training-free implementations.

Table of Contents