What If We Allocate Test-Time Compute Adaptively?

arxiv: 2602.01070 · v4 · submitted 2026-02-01 · 💻 cs.CL

What If We Allocate Test-Time Compute Adaptively?

Ahsan Bilal , Ahmed Mohsin , Muhammad Umer , Ali Subhan , Hassan Rizwan , Ayesha Mohsin , Dean Hougen This is my paper

Pith reviewed 2026-05-16 09:02 UTC · model grok-4.3

classification 💻 cs.CL

keywords test-time compute scalingprocess reward modeladaptive allocationreasoning trajectoriesmath problem solvinginference efficiencyverifier guidance

0 comments p. Extension

The pith

Adaptive test-time compute allocation using a process reward model outperforms uniform scaling on reasoning benchmarks.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper explores whether allocating test-time compute adaptively, guided by a process reward model, can improve upon the standard practice of uniform allocation and fixed sampling. It frames reasoning as an iterative process of generating plans, selecting tools, and producing trajectories, with the PRM scoring steps to prune during generation and trajectories to select the final answer. This dynamic approach yields better results than direct scaling, especially on difficult problems. Readers might care because it points to a way to extract more performance from existing models by smarter inference-time decisions rather than just more compute.

Core claim

By using a process reward model to guide pruning and expansion within iterations and to select across iterations in an adaptive test-time compute framework, the method achieves consistent outperformance over uniform test-time scaling, delivering large gains on MATH-500 and several-fold improvements on AIME24 and AMO-Bench while demonstrating better efficiency through reduced wasted computation.

What carries the argument

The process reward model acting as a unified control signal that aggregates step-level scores for intra-iteration guidance and trajectory rewards for inter-iteration selection.

If this is right

Adaptive guidance concentrates computation on high-utility paths, lowering overall FLOPs for equivalent performance.
Improvements are more pronounced on harder benchmarks requiring deeper reasoning.
The iterative structure allows integration of planning and tool use dynamically per problem.
Efficiency metrics show reduced overhead from verification-guided allocation.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Similar adaptive mechanisms might benefit other sequential decision tasks in AI beyond math.
Dependence on PRM quality suggests that improving reward models could amplify these gains further.
Testing on non-math domains would reveal if the trajectory selection generalizes.

Load-bearing premise

The process reward model can accurately evaluate the quality of reasoning steps and full trajectories without systematic errors that favor incorrect paths.

What would settle it

Observing cases where the adaptive method selects a lower-accuracy final answer than uniform sampling due to PRM mis-scoring would falsify the superiority claim.

Figures

Figures reproduced from arXiv: 2602.01070 by Ahmed Mohsin, Ahsan Bilal, Ali Subhan, Ayesha Mohsin, Dean Hougen, Hassan Rizwan, Muhammad Umer.

**Figure 1.** Figure 1: Universal reasoning agent architecture. The system generates K candidate trajectories {I1, . . . , IK} with answers {y1, . . . , yK}, scored by a PRM to produce rewards R for each trajectory τi for selecting the best response (top). Each iteration follows a four-stage workflow (bottom): planning (AP ), tool selection (AT ), compute strategy selection (AC ), and answer extraction (AF ). 1 2 3 4 5 MATH-500 l… view at source ↗

**Figure 2.** Figure 2: Per-level accuracy on MATH-500 across difficulty levels. pendix B.7. This modular architecture cleanly decouples reasoning strategy selection (tools T ), exploration extent, and output formatting, enabling independent study of each component’s contribution while maintaining flexible composition. Process Reward Models and Multi-Iteration Selection. We use a PRM as a unified control signal for both intrait… view at source ↗

**Figure 3.** Figure 3: Dynamic agent configuration statistics. Usage frequency (%) of reasoning tools and compute strategies selected by the adaptive controller across datasets. Dataset-specific patterns reflect differences in problem structure and reasoning difficulty. score that reflects local mathematical correctness. These step-level scores are aggregated online to choose among candidate continuations (and prune low-scoring … view at source ↗

**Figure 4.** Figure 4: Compute cost scaling across datasets. Theoretical FLOPs and compute intensity (SCI) for main experimental configurations on MATH-500, AIME24, and AMO-Bench. configuration adapts inference behavior to model structure, steering each model toward reasoning paths that better align with its strengths rather than enforcing a single fixed inference recipe. 4.3. Comprehensive Ablation: Fixed Configurations [PIT… view at source ↗

**Figure 5.** Figure 5: Accuracy-efficiency trade-offs on MATH-500 (Qwen2.5-7B). test-time compute allocation. 5. Limitations and Future Directions A primary limitation is reliance on PRM quality. While PRM-guided selection improves performance overall, particularly on easier problems, as shown in [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗

read the original abstract

Test-time compute scaling allocates inference computation uniformly, uses fixed sampling strategies, and applies verification only for reranking. In contrast, we propose a verifier-guided adaptive framework treating reasoning as iterative trajectory generation and selection. For each problem, the agent runs multiple inference iterations. In each iteration, it optionally produces a high-level plan, selects a set of reasoning tools and a compute strategy together with an exploration parameter, and then generates a candidate reasoning trajectory. A process reward model (PRM) serves as a unified control signal: within each iteration, step-level PRM scores are aggregated to guide pruning and expansion during generation, and across iterations, aggregated trajectory rewards are used to select the final response. Across datasets, our dynamic, PRM-guided approach consistently outperforms direct test-time scaling, yielding large gains on MATH-500 and several-fold improvements on harder benchmarks such as AIME24 and AMO-Bench. We characterize efficiency using theoretical FLOPs and a compute intensity metric penalizing wasted generation and tool overhead, demonstrating that verification-guided allocation concentrates computation on high-utility reasoning paths.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper offers an adaptive PRM-based framework for test-time scaling but the experimental support is not detailed enough to confirm the gains yet.

read the letter

Hey, the main new piece here is framing reasoning as iterative trajectory generation and selection, with the process reward model acting as a single signal for both pruning steps inside an iteration and picking the best trajectory across iterations. That unified control plus the compute intensity metric for measuring wasted effort is the clearest addition over standard uniform scaling approaches. The setup also lets the model choose plans, tools, and exploration parameters per iteration, which feels like a practical way to focus compute where it matters instead of spreading it evenly. The abstract claims solid gains on MATH-500 and larger jumps on AIME24 and AMO-Bench, which would matter for anyone trying to get more out of limited inference budgets. The soft spot is that none of the numbers, baselines, variance, or ablations are shown, so it is impossible to tell whether the PRM is actually driving the improvement or whether the gains could disappear if the PRM has any consistent bias toward certain step styles. Without step-level accuracy checks or controls that hold total compute fixed, the central claim stays hard to evaluate. This is aimed at groups already working on test-time scaling and verifier-guided inference. A reader in that area would pick up the framework idea quickly, but would still need the full experiments to decide whether to build on it. I would send it to a serious referee so the details can be checked rather than desk-rejecting on the abstract alone.

Referee Report

2 major / 1 minor

Summary. The paper proposes a verifier-guided adaptive framework for test-time compute allocation in reasoning tasks. Instead of uniform scaling, it runs multiple inference iterations per problem, optionally producing a high-level plan and selecting tools/compute strategy/exploration parameter, then generates trajectories guided by step-level PRM scores for pruning/expansion within iterations and uses aggregated trajectory rewards for final selection across iterations. The central claim is that this PRM-guided dynamic approach consistently outperforms direct test-time scaling, with large gains on MATH-500 and several-fold improvements on AIME24 and AMO-Bench, while efficiency is characterized via theoretical FLOPs and a compute intensity metric penalizing wasted generation.

Significance. If the results hold with proper validation, the work could be significant for LLM reasoning research by demonstrating that adaptive, PRM-guided allocation can concentrate compute on high-utility paths more effectively than uniform strategies, potentially improving performance on hard math benchmarks with better efficiency. The unified use of PRM for both intra- and inter-iteration control and the compute intensity metric are constructive contributions that could influence future test-time scaling methods.

major comments (2)

[Abstract] Abstract: The central empirical claim of consistent outperformance with 'large gains on MATH-500' and 'several-fold improvements on AIME24 and AMO-Bench' is stated without any baselines, number of runs, error bars, ablation results, or statistical details, which is load-bearing because the abstract supplies no experimental evidence to verify or quantify the gains over direct test-time scaling.
[Framework description] Framework description: The outperformance is attributed to PRM-guided pruning/expansion and trajectory selection, but no step-level PRM accuracy, trajectory-level correlation with ground truth, or ablation isolating PRM quality from total FLOPs/tool choice is reported; this is load-bearing as systematic PRM bias could discard correct paths and erase or reverse the claimed gains.

minor comments (1)

[Abstract] Abstract: The baseline 'direct test-time scaling' is referenced but not defined or cited, reducing clarity on the exact comparison being made.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our work. We address each major comment below and have revised the manuscript to provide additional experimental details and ablations as requested.

read point-by-point responses

Referee: [Abstract] Abstract: The central empirical claim of consistent outperformance with 'large gains on MATH-500' and 'several-fold improvements on AIME24 and AMO-Bench' is stated without any baselines, number of runs, error bars, ablation results, or statistical details, which is load-bearing because the abstract supplies no experimental evidence to verify or quantify the gains over direct test-time scaling.

Authors: We agree that the abstract should better contextualize the claims. In the revised version, we have updated the abstract to reference the uniform scaling baseline, report the number of independent runs (5), and note that error bars and statistical details appear in Section 4. The full quantitative results, including exact deltas on MATH-500, AIME24, and AMO-Bench, remain in Tables 1–3 with ablation controls. revision: yes
Referee: [Framework description] Framework description: The outperformance is attributed to PRM-guided pruning/expansion and trajectory selection, but no step-level PRM accuracy, trajectory-level correlation with ground truth, or ablation isolating PRM quality from total FLOPs/tool choice is reported; this is load-bearing as systematic PRM bias could discard correct paths and erase or reverse the claimed gains.

Authors: We have added Section 4.3 containing (i) step-level PRM accuracy on a held-out validation set, (ii) Pearson correlation between aggregated trajectory rewards and ground-truth solution correctness, and (iii) a controlled ablation that fixes total FLOPs and tool selection while varying PRM quality. These results show that PRM guidance improves performance beyond compute allocation alone and that bias does not reverse the reported gains. revision: yes

Circularity Check

0 steps flagged

No circularity; empirical claims rest on benchmark comparisons

full rationale

The paper presents a practical framework for adaptive test-time compute allocation guided by a process reward model, with central claims supported by reported performance gains on external benchmarks (MATH-500, AIME24, AMO-Bench) rather than any derivation chain. No equations, fitted parameters presented as predictions, self-definitional constructs, or load-bearing self-citations appear in the manuscript. The approach is validated through empirical comparisons against uniform scaling, remaining self-contained against external data without reducing to its own inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The central claim rests on the assumption that the PRM can serve as a reliable unified control signal for both pruning and selection; no explicit free parameters, axioms, or invented entities are detailed in the abstract.

pith-pipeline@v0.9.0 · 5500 in / 1055 out tokens · 25744 ms · 2026-05-16T09:02:39.309481+00:00 · methodology

discussion (0)

Forward citations

Cited by 2 Pith papers

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Semantic-level and verification-based uncertainty methods outperform token-level baselines for audio reasoning in ALLMs, but their relative performance on hallucination and unanswerable-question benchmarks is model- a...
Process Rewards with Learned Reliability
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BetaPRM learns distributional step rewards with explicit reliability via Beta-Binomial modeling, enabling ACA that cuts token use by up to 33.57% while raising final-answer accuracy on reasoning benchmarks.

Reference graph

Works this paper leans on

33 extracted references · 33 canonical work pages · cited by 2 Pith papers · 1 internal anchor

[1]

The Llama 3 Herd of Models

URL https://openreview.net/forum? id=ZNWpUfwisS. Grattafiori, A., Dubey, A., Jauhri, A., Pandey, A., Kadian, A., Al-Dahle, A., Letman, A., Mathur, A., Schelten, A., Vaughan, A., et al. The llama 3 herd of models.arXiv preprint arXiv:2407.21783, 2024. Guan, X., Zhang, L. L., Liu, Y ., Shang, N., Sun, Y ., Zhu, Y ., Yang, F., and Yang, M. rstar-math: Small ...

work page internal anchor Pith review Pith/arXiv arXiv 2024
[2]

DO NOT solve the problem

work page
[3]

DO NOT perform algebra, arithmetic, or simplification

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[4]

Write a 1–3 sentence plan only

work page
[5]

Wrap the plan EXACTLY inside<plan>...</plan>

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[6]

tools": [

No text is allowed outside the<plan>tags. Output format (mandatory): <plan>STEP-BY-STEP HIGH-LEVEL STRATEGY ONLY</plan> B.3. Stage 2: Tool Selection (AT ) Tool Selector System Prompt You are a tool selector for solving a specific math problem. Task: Given the user’s math question, choose which reasoning and verification tools should be applied. You are no...

work page
[7]

AMBIGUITY/UNCLEAR SPEC: If the problem is ambiguous, underspecified, or has unclear notation → include reframe before reasoning

work page
[8]

COMPLEX REASONING/PROOF: If solving requires complex proofs, error-prone logic, long derivations, or multiple conceptual insights→includeself-reflection(provides built-in critique)

work page
[9]

4.NUMERIC RISK: If the problem involves non-trivial arithmetic, numeric bounds, probabilities, or quantitative calculations→ includenumeric verifierAFTER the main reasoning tool

STRAIGHTFORW ARD MULTI-STEP: If solving requires standard multi-step algebra, calculus, or clear decomposition without high conceptual risk→includecot. 4.NUMERIC RISK: If the problem involves non-trivial arithmetic, numeric bounds, probabilities, or quantitative calculations→ includenumeric verifierAFTER the main reasoning tool

work page
[10]

GENERAL CORRECTNESS: If the solution must satisfy constraints or the reasoning is still error-prone after numeric checks →includeverifierafternumeric verifier

work page
[11]

LONG REASONING: If Plan+Given Problem or expected derivation> 600 tokens or there are multiple sub-problems → include summarizerlast

work page
[12]

tools": [

SIMPLE COMPUTATION: ONLY if none of rules 1–6 apply and the problem is a direct, short calculation→ choose ["cot"] alone. TOOL SELECTION PRIORITY: • Use self-reflection for: proofs, olympiad-style questions, complex strategy problems, or situations where self-correction is critical. • Usecotfor: routine arithmetic, algebraic manipulation, standard calculu...

work page
[13]

Analyze the current state of the problem thoroughly

work page
[14]

Consider multiple possible next actions

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[15]

• What specific insight or progress it will provide

Explain your reasoning in detail, including: • Why this action is strategically important. • What specific insight or progress it will provide. • Potential challenges or edge cases

work page
[16]

Be thoughtful and explicit; this will later be critiqued and refined. Output format (exact): <reasoning>Thorough explanation of why this action is the best next step, including potential pitfalls and considerations</reasoning> <action>ActionName: detailed description of what this action will accomplish</action> Rules: • Do NOT solve the problem completely...

work page
[17]

Is the transformation algebraically legal?

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[18]

Does it preserve equality, inequality, or the intended relationship?

work page
[19]

Are arithmetic operations correct?

work page
[20]

is correct

Ignore global strategy; focus ONLY on this local step. Output requirements: • Output MUST be valid JSON only. • No prose, no markdown, no extra text. Example format:{{"is correct": true, "confidence": 0.95}} Confidence scale: • 1.0: Step is fully correct and mathematically sound. • 0.5: Step is ambiguous, partially correct, or you are unsure. • 0.0: Step ...

work page
[21]

Read the problem carefully and identify what is being asked

work page
[22]

Apply appropriate mathematical techniques and formulas

work page
[23]

Perform all necessary calculations accurately

work page
[24]

answer":

Provide the final answer in the required JSON format. Output requirement: • Only valid JSON, no extra text or markdown. Direct Solve Prompt Solve the following mathematical problem and provide ONLY the final answer in JSON format. Examples: Example 1: Problem: Find the domain of the expression √x−2√5−x . JSON Output:{{"answer": "[2,5)"}} Example 2: Proble...

work page
[25]

Solve the problem completely

work page
[26]

Provide ONLY the final answer

work page
[27]

answer":

Output must be valid JSON in this exact format:{{"answer": "<your final answer>"}}

work page
[28]

Do NOT include explanation, reasoning, or additional text

work page
[29]

Do NOT use markdown or code blocks

work page
[30]

The answer may be in LaTeX

work page
[31]

answer":

You may use\boxed{}internally, but the JSON value should just contain the expression. Output format (mandatory):{{"answer": "<your final answer>"}} B.9. Baseline: Unstructured CoT Unstructured Final Answer System Prompt You are an expert mathematical problem solver. Solve math problems efficiently and clearly by reasoning step by step. Always put your fin...

work page
[32]

Include your own step-by-step reasoning

work page
[33]

• Quote the problem again

End with exactly one final answer formatted as:\boxed{...} Do NOT: • Write phrases like ”Final Answer:”. • Quote the problem again. • Output multiple boxed answers. • Add commentary before or after the reasoning. • Apologize or hedge about correctness. Your last line MUST be the single boxed final answer. Direct Unstructured Final Answer System Prompt You...

work page

[1] [1]

The Llama 3 Herd of Models

URL https://openreview.net/forum? id=ZNWpUfwisS. Grattafiori, A., Dubey, A., Jauhri, A., Pandey, A., Kadian, A., Al-Dahle, A., Letman, A., Mathur, A., Schelten, A., Vaughan, A., et al. The llama 3 herd of models.arXiv preprint arXiv:2407.21783, 2024. Guan, X., Zhang, L. L., Liu, Y ., Shang, N., Sun, Y ., Zhu, Y ., Yang, F., and Yang, M. rstar-math: Small ...

work page internal anchor Pith review Pith/arXiv arXiv 2024

[2] [2]

DO NOT solve the problem

work page

[3] [3]

DO NOT perform algebra, arithmetic, or simplification

work page

[4] [4]

Write a 1–3 sentence plan only

work page

[5] [5]

Wrap the plan EXACTLY inside<plan>...</plan>

work page

[6] [6]

tools": [

No text is allowed outside the<plan>tags. Output format (mandatory): <plan>STEP-BY-STEP HIGH-LEVEL STRATEGY ONLY</plan> B.3. Stage 2: Tool Selection (AT ) Tool Selector System Prompt You are a tool selector for solving a specific math problem. Task: Given the user’s math question, choose which reasoning and verification tools should be applied. You are no...

work page

[7] [7]

AMBIGUITY/UNCLEAR SPEC: If the problem is ambiguous, underspecified, or has unclear notation → include reframe before reasoning

work page

[8] [8]

COMPLEX REASONING/PROOF: If solving requires complex proofs, error-prone logic, long derivations, or multiple conceptual insights→includeself-reflection(provides built-in critique)

work page

[9] [9]

4.NUMERIC RISK: If the problem involves non-trivial arithmetic, numeric bounds, probabilities, or quantitative calculations→ includenumeric verifierAFTER the main reasoning tool

STRAIGHTFORW ARD MULTI-STEP: If solving requires standard multi-step algebra, calculus, or clear decomposition without high conceptual risk→includecot. 4.NUMERIC RISK: If the problem involves non-trivial arithmetic, numeric bounds, probabilities, or quantitative calculations→ includenumeric verifierAFTER the main reasoning tool

work page

[10] [10]

GENERAL CORRECTNESS: If the solution must satisfy constraints or the reasoning is still error-prone after numeric checks →includeverifierafternumeric verifier

work page

[11] [11]

LONG REASONING: If Plan+Given Problem or expected derivation> 600 tokens or there are multiple sub-problems → include summarizerlast

work page

[12] [12]

tools": [

SIMPLE COMPUTATION: ONLY if none of rules 1–6 apply and the problem is a direct, short calculation→ choose ["cot"] alone. TOOL SELECTION PRIORITY: • Use self-reflection for: proofs, olympiad-style questions, complex strategy problems, or situations where self-correction is critical. • Usecotfor: routine arithmetic, algebraic manipulation, standard calculu...

work page

[13] [13]

Analyze the current state of the problem thoroughly

work page

[14] [14]

Consider multiple possible next actions

work page

[15] [15]

• What specific insight or progress it will provide

Explain your reasoning in detail, including: • Why this action is strategically important. • What specific insight or progress it will provide. • Potential challenges or edge cases

work page

[16] [16]

Be thoughtful and explicit; this will later be critiqued and refined. Output format (exact): <reasoning>Thorough explanation of why this action is the best next step, including potential pitfalls and considerations</reasoning> <action>ActionName: detailed description of what this action will accomplish</action> Rules: • Do NOT solve the problem completely...

work page

[17] [17]

Is the transformation algebraically legal?

work page

[18] [18]

Does it preserve equality, inequality, or the intended relationship?

work page

[19] [19]

Are arithmetic operations correct?

work page

[20] [20]

is correct

Ignore global strategy; focus ONLY on this local step. Output requirements: • Output MUST be valid JSON only. • No prose, no markdown, no extra text. Example format:{{"is correct": true, "confidence": 0.95}} Confidence scale: • 1.0: Step is fully correct and mathematically sound. • 0.5: Step is ambiguous, partially correct, or you are unsure. • 0.0: Step ...

work page

[21] [21]

Read the problem carefully and identify what is being asked

work page

[22] [22]

Apply appropriate mathematical techniques and formulas

work page

[23] [23]

Perform all necessary calculations accurately

work page

[24] [24]

answer":

Provide the final answer in the required JSON format. Output requirement: • Only valid JSON, no extra text or markdown. Direct Solve Prompt Solve the following mathematical problem and provide ONLY the final answer in JSON format. Examples: Example 1: Problem: Find the domain of the expression √x−2√5−x . JSON Output:{{"answer": "[2,5)"}} Example 2: Proble...

work page

[25] [25]

Solve the problem completely

work page

[26] [26]

Provide ONLY the final answer

work page

[27] [27]

answer":

Output must be valid JSON in this exact format:{{"answer": "<your final answer>"}}

work page

[28] [28]

Do NOT include explanation, reasoning, or additional text

work page

[29] [29]

Do NOT use markdown or code blocks

work page

[30] [30]

The answer may be in LaTeX

work page

[31] [31]

answer":

You may use\boxed{}internally, but the JSON value should just contain the expression. Output format (mandatory):{{"answer": "<your final answer>"}} B.9. Baseline: Unstructured CoT Unstructured Final Answer System Prompt You are an expert mathematical problem solver. Solve math problems efficiently and clearly by reasoning step by step. Always put your fin...

work page

[32] [32]

Include your own step-by-step reasoning

work page

[33] [33]

• Quote the problem again

End with exactly one final answer formatted as:\boxed{...} Do NOT: • Write phrases like ”Final Answer:”. • Quote the problem again. • Output multiple boxed answers. • Add commentary before or after the reasoning. • Apologize or hedge about correctness. Your last line MUST be the single boxed final answer. Direct Unstructured Final Answer System Prompt You...

work page