Budget-Aware Anytime Reasoning with LLM-Synthesized Preference Data

Amir H. Rezaeian; Aziza Mirsaidova; Dan Roth; Lydia B. Chilton; Miguel Ballesteros; Shwan Ashrafi; Xuanming Zhang; Zhou Yu

arxiv: 2601.11038 · v2 · submitted 2026-01-16 · 💻 cs.CL

Budget-Aware Anytime Reasoning with LLM-Synthesized Preference Data

Xuanming Zhang , Shwan Ashrafi , Aziza Mirsaidova , Amir H. Rezaeian , Miguel Ballesteros , Lydia B. Chilton , Zhou Yu , Dan Roth This is my paper

Pith reviewed 2026-05-16 13:51 UTC · model grok-4.3

classification 💻 cs.CL

keywords anytime reasoningbudget-constrained inferenceLLM self-improvementpreference data synthesisinference-time optimizationtrip planningmath reasoningscience QA

0 comments

The pith

LLMs can generate better partial solutions under fixed token budgets by synthesizing preference data from their own reasoning comparisons.

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

Large language models must often stop reasoning early because extra tokens cost real money and time. The paper introduces an anytime framework that measures how solution quality improves as more reasoning tokens are spent, plus an inference-time method where the model generates multiple reasoning paths, compares them internally, and synthesizes preference data to favor stronger paths. This self-generated preference signal is then used at inference to steer toward higher-quality intermediate answers without any extra training or external labels. Experiments on trip-planning, AIME math problems, and GPQA science questions show the approach lifts quality at every budget level for models ranging from LLaMA to GPT-4o.

Core claim

The central claim is that an inference-time self-improvement loop, in which an LLM synthesizes preference pairs by comparing its own reasoning traces, produces measurably stronger intermediate solutions at any given computation budget, as quantified by the Anytime Index on NaturalPlan trip-planning, AIME, and GPQA tasks across Grok-3, GPT-4.1/4o, and LLaMA families.

What carries the argument

Inference-time self-improvement via LLM-synthesized preference data, where the model compares its own reasoning paths to create training signals that guide better partial outputs, paired with the Anytime Index that tracks quality gains against increasing token counts.

If this is right

Solution quality improves more steeply with each additional reasoning token.
The gains appear across model families without requiring fine-tuning or human labels.
Anytime behavior strengthens on both planning and multi-step math or science problems.
Models can deliver usable outputs earlier in the reasoning process, reducing average inference cost.

Where Pith is reading between the lines

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

Deployed systems could allocate smaller per-query budgets while preserving acceptable answer quality.
The same internal-comparison loop might be applied to agentic or tool-using workflows that require sequential decisions.
Combining the method with light external verification could further strengthen the preference signals.

Load-bearing premise

The model's internal comparisons of reasoning paths it generated itself are reliable enough to identify genuinely better paths without external verification or task-specific tuning.

What would settle it

If, on a fresh held-out task, the synthesized preferences produce no improvement or a drop in solution quality at intermediate token budgets relative to the base model, the effectiveness of the self-improvement loop would be falsified.

read the original abstract

We study the reasoning behavior of large language models (LLMs) under limited computation budgets. In such settings, producing useful partial solutions quickly is often more practical than exhaustive reasoning, which incurs high inference costs. Many real-world tasks, such as trip planning, require models to deliver the best possible output within a fixed reasoning budget. We introduce an anytime reasoning framework and the Anytime Index, a metric that quantifies how effectively solution quality improves as reasoning tokens increase. To further enhance efficiency, we propose an inference-time self-improvement method using LLM-synthesized preference data, where models learn from their own reasoning comparisons to produce better intermediate solutions. Experiments on NaturalPlan (Trip), AIME, and GPQA datasets show consistent gains across Grok-3, GPT-oss, GPT-4.1/4o, and LLaMA models, improving both reasoning quality and efficiency under budget constraints.

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 anytime framework and self-improvement via internal preferences look practical on paper but rest on unverified assumptions about the quality of LLM-generated comparisons.

read the letter

The main things here are an anytime reasoning setup that tracks how solution quality improves with more tokens, plus an inference-time method where the model generates its own preference pairs from reasoning traces to refine intermediate outputs. That combination is new enough to stand out from standard chain-of-thought or budget-constrained decoding work. The experiments report gains on NaturalPlan trip planning, AIME, and GPQA across several models including Grok-3 and GPT variants, which suggests the approach can deliver better partial answers when compute is capped. The Anytime Index metric is a straightforward way to quantify the efficiency curve, and the self-improvement step avoids needing external labels, which is a real plus for deployment settings. That said, the abstract gives no baselines, error bars, or statistical details, so it is hard to judge whether the gains are robust or just within noise. The bigger concern is whether the model's own comparisons reliably pick better paths on hard problems; on AIME or GPQA, where partial correctness is not obvious, self-preferences could reinforce common mistakes rather than fix them. Without external validation or ablation on preference accuracy, the consistent gains across models feel under-supported. This is the kind of work that would interest people building cost-sensitive reasoning systems or anyone running LLMs in real-time applications. It deserves a serious referee because the core idea is grounded in a practical constraint and the method is reproducible in principle, even if the current evidence needs tightening on the self-improvement claims. I would send it out for review rather than desk reject.

Referee Report

2 major / 1 minor

Summary. The paper introduces an anytime reasoning framework for LLMs under limited computation budgets, along with the Anytime Index metric to quantify how solution quality improves with additional reasoning tokens. It proposes an inference-time self-improvement method that synthesizes preference data by having the LLM compare its own reasoning traces, enabling better intermediate solutions within token constraints. Experiments on NaturalPlan (Trip), AIME, and GPQA datasets report consistent gains in reasoning quality and efficiency across Grok-3, GPT-oss, GPT-4.1/4o, and LLaMA models.

Significance. If the self-improvement results hold under rigorous validation, the work could meaningfully advance practical LLM reasoning by improving performance under fixed budgets without external supervision or task-specific tuning. The Anytime Index provides a useful lens for efficiency analysis, and the approach's apparent model-agnostic nature strengthens its potential applicability to real-world tasks like planning and math reasoning.

major comments (2)

[Experiments] Experiments section: The abstract claims consistent gains across three datasets and multiple models, but supplies no details on baselines, statistical tests, error bars, or data exclusion rules. This absence is load-bearing because it prevents verification of whether the reported improvements in quality and efficiency are statistically reliable or artifactual.
[Method] Method section (self-improvement procedure): The core assumption that LLM internal comparisons of reasoning traces reliably identify superior paths lacks external validation or correlation analysis with ground-truth correctness. On hard tasks such as AIME and GPQA, where partial solution quality is non-obvious, this risks reinforcing common error patterns (e.g., calculation slips) rather than correcting them, directly undermining the generalization claim.

minor comments (1)

[Abstract] The abstract would benefit from briefly stating the magnitude of gains (e.g., token savings or quality deltas) to give readers an immediate sense of effect size.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on experimental details and validation of the self-improvement procedure. We address each major comment below and will incorporate revisions to improve rigor and transparency.

read point-by-point responses

Referee: [Experiments] Experiments section: The abstract claims consistent gains across three datasets and multiple models, but supplies no details on baselines, statistical tests, error bars, or data exclusion rules. This absence is load-bearing because it prevents verification of whether the reported improvements in quality and efficiency are statistically reliable or artifactual.

Authors: We agree that additional experimental details are necessary for verification. In the revised manuscript, we will expand the Experiments section to explicitly list all baselines (including chain-of-thought, tree-of-thoughts, and self-consistency variants), report error bars from multiple independent runs with different seeds, include statistical significance tests (paired t-tests and Wilcoxon signed-rank tests with p-values), and clarify any data exclusion or filtering rules applied to the NaturalPlan, AIME, and GPQA datasets. These changes will directly address concerns about reliability and artifactual results. revision: yes
Referee: [Method] Method section (self-improvement procedure): The core assumption that LLM internal comparisons of reasoning traces reliably identify superior paths lacks external validation or correlation analysis with ground-truth correctness. On hard tasks such as AIME and GPQA, where partial solution quality is non-obvious, this risks reinforcing common error patterns (e.g., calculation slips) rather than correcting them, directly undermining the generalization claim.

Authors: We acknowledge the limitation in validation. The revised manuscript will add a dedicated analysis subsection correlating LLM preference judgments with ground-truth final-answer correctness on subsets of AIME and GPQA where partial traces can be evaluated. We will also include qualitative examples of both successful corrections and potential failure modes (such as reinforcing calculation errors) and discuss this as a limitation. While full external validation for all partial solutions would require extensive human annotation beyond the paper's scope, the observed gains across multiple models provide supporting evidence; we will moderate generalization claims to reflect this. revision: partial

Circularity Check

0 steps flagged

No significant circularity in the derivation chain

full rationale

The paper defines an anytime reasoning framework and Anytime Index, then describes an inference-time self-improvement procedure that synthesizes preference pairs from the model's own reasoning traces to train better intermediate outputs. Experimental results are reported on external benchmarks (NaturalPlan Trip, AIME, GPQA) across multiple models, with gains measured against token budgets. No equations reduce a claimed prediction to a fitted input by construction, no load-bearing self-citations justify uniqueness or ansatzes, and the self-synthesized data is treated as a training signal whose quality is assessed via downstream task performance rather than assumed tautologically. The derivation therefore remains self-contained against the reported external metrics.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The central claim rests on the assumption that models can improve reasoning by comparing their own generated outputs and on the introduction of the Anytime Index as a new evaluation metric; no explicit free parameters are stated in the abstract.

axioms (1)

domain assumption LLMs can learn useful preferences from comparisons among their own reasoning traces without external supervision
This underpins the inference-time self-improvement method described in the abstract.

invented entities (1)

Anytime Index no independent evidence
purpose: Quantifies how solution quality improves as the number of reasoning tokens increases
New metric introduced to evaluate the anytime reasoning framework.

pith-pipeline@v0.9.0 · 5476 in / 1224 out tokens · 38310 ms · 2026-05-16T13:51:13.960925+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

We introduce an anytime reasoning framework and the Anytime Index, a metric that quantifies how effectively solution quality improves as reasoning tokens increase... using LLM-synthesized preference data
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

Experiments on NaturalPlan (Trip), AIME, and GPQA datasets show consistent gains

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