arxiv: 2604.05404 · v2 · submitted 2026-04-07 · 💻 cs.PF · cs.SE

Recognition: no theorem link

Beyond Accuracy: Unveiling Inefficiency Patterns in Tool-Integrated Reasoning

Qisheng Su , Shiting Huang , Zhen Fang , Ziyan Chen , Zehui Chen , Feng Zhao

Authors on Pith no claims yet

Pith reviewed 2026-05-10 19:19 UTC · model grok-4.3

classification 💻 cs.PF cs.SE

keywords tool-integrated reasoningefficiency metricKV cacheinference latencyLLM tool callingperformance evaluationreasoning correctnessinefficiency patterns

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The pith

PTE metric predicts LLM tool-use latency better than token counts

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

In tool-integrated reasoning, where language models call external tools, each tool call pauses the model and evicts its key-value cache, requiring recomputation of prior context. Tool responses can also be very long, further slowing down the generation process as the cache grows. Standard metrics based on token or toolcall counts do not reflect these actual inference times. The paper proposes Prefill Token Equivalents (PTE) to measure efficiency by converting all operations into equivalent prefill costs while accounting for cache waste and long responses. Tests in industrial settings show PTE matches wall-clock time more closely than token counts, and across benchmarks, higher PTE use correlates with poorer reasoning accuracy.

Core claim

The central discovery is that Prefill Token Equivalents (PTE) provides a hardware-aware way to quantify the total computational cost in tool-integrated reasoning by unifying internal model computations with external tool interactions, specifically adjusting for the recomputation costs from KV-Cache evictions during tool calls and the increased per-step latency from lengthy tool outputs. This metric aligns more closely with measured wall-clock latency in high-concurrency environments than conventional token counts, maintains consistent model efficiency orderings across varied hardware, and reveals that reasoning trajectories with elevated PTE expenditures are associated with reduced correct

What carries the argument

Prefill Token Equivalents (PTE), a metric that estimates the equivalent amount of prefill token processing required, including penalties for non-reusable cache segments caused by tool call interruptions and the decode overhead from extended tool responses.

Load-bearing premise

The five chosen benchmarks together with the industrial high-concurrency tests sufficiently represent the range of typical tool-integrated reasoning applications.

What would settle it

A controlled experiment on additional TIR tasks or different model families where standard token counts show stronger correlation with measured latency than PTE, or where no negative relationship appears between PTE cost and answer correctness.

Figures

Figures reproduced from arXiv: 2604.05404 by Feng Zhao, Qisheng Su, Shiting Huang, Zehui Chen, Zhen Fang, Ziyan Chen.

**Figure 2.** Figure 2: Overview of the four inefficiency patterns in Tool-Integrated Reasoning. [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 3.** Figure 3: Correlation analysis between real-world la [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

**Figure 4.** Figure 4: PTE (Prefill-Token Equivalents) versus Average Score on five benchmarks. The bubble size represents the scale of active parameters. Models in the bottom-right region exhibit better trade-offs between efficiency and accuracy. Note the logarithmic scale on the y-axis. – Llama-3.1 series are pure instruct models. Internal thinking tokens are negligible on every task, yielding high efficiency and medium accur… view at source ↗

**Figure 5.** Figure 5: Distribution of average PTE per reasoning step across five benchmarks. The cost per step escalates as the context length grows, contrasting with the token-based "front-loading" trend. 10 20 30 40 Average Score (%) 10 3 10 4 Average PTE (Log Scale) Qwen2.5-7B Qwen2.5-32B Qwen2.5-72B Qwen3-32B Qwen-235B-Instruct Qwen-235B-Thinking Ty-Deepresearch GLM-4.5 GLM-4.5-Air Llama3.1-8B Llama3.1-70B Dv3.1-terminus GP… view at source ↗

**Figure 6.** Figure 6: Visualization of tool-mixing behavior on WebInstruct-Verified. Point color indicates the ratio of mixed-tool trajectories, with lighter colors (yellow) representing higher mixing frequencies. 6.2 Analysis of TIR Inefficiency Patterns Building on these results, this section provides a deeper analysis of their implications. We evaluate four inefficiency patterns in Tool-Integrated Reasoning through the lens… view at source ↗

**Figure 7.** Figure 7: Distribution of PTEs for correct and incorrect [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗

**Figure 8.** Figure 8: Distribution of Average Assistamt Response Tokens Across Reasoning Steps. The figure illustrates the response length for each step in a reasoning trajectory. The phenomenon is described as "first-step effect" where models tend to "front-load" their computational budget. System Prompt For Webinstruct-Verified You are an Expert Problem Solver. Your mission is to accurately solve problems by skillfully integ… view at source ↗

**Figure 9.** Figure 9: System Prompt Example System Prompt For LLM Judge Predicted Answer: predicted answer Expected Answer: ground truth Determine if the predicted answer is semantically correct (case-insensitive). Reply only a JSON object in the format: {"correct": 0} or {"correct": 1} Do not include any additional text or markdown formatting [PITH_FULL_IMAGE:figures/full_fig_p014_9.png] view at source ↗

**Figure 10.** Figure 10: Answer Verify Prompt 14 [PITH_FULL_IMAGE:figures/full_fig_p014_10.png] view at source ↗

**Figure 11.** Figure 11: Comparison of PTE between Correct(red) and Incorrect(blue) Reasoning Trajectories. Incorrect reasoning is consistently associated with higher PTE across models and tasks. cial pricing strategies. Its hardware-adaptive design ensures robustness across any deployment scenario. 18 [PITH_FULL_IMAGE:figures/full_fig_p018_11.png] view at source ↗

**Figure 12.** Figure 12: Pattern I: Confirmatory Tool Usage. An example from AIME24 where Qwen3-235B-Thinking solves the problem internally first, arriving at the correct answer. However, it subsequently invokes the Python tool solely to verify this known result. This "Think-then-Verify" behavior unnecessarily inflates the context length and PTE cost without contributing new information to the solution [PITH_FULL_IMAGE:figures/f… view at source ↗

**Figure 13.** Figure 13: Pattern II: Tool-Mixing. An example from WebInstruct-Verified where DeepSeek-V3.1-Terminus fragmentally alternates between Search and Python tools. This behavior accumulates context of intermediate outputs and inflates the PTE cost, yet yields no obvious accuracy improvement compared to single-toolset strategies (as evidenced in Fig. 4e). 20 [PITH_FULL_IMAGE:figures/full_fig_p020_13.png] view at source ↗

**Figure 14.** Figure 14: Pattern III: Lack of Tool Priors. An example from AIME24 where Qwen-2.5-7B-Instruct fails to utilize the Python tool effectively. The model invokes the code interpreter but forgets to include a print statement, resulting in an empty output. This suggests a lack of pretraining exposure to the tool environment, leading to wasted inference steps [PITH_FULL_IMAGE:figures/full_fig_p021_14.png] view at source ↗

**Figure 15.** Figure 15: Pattern IV: Tool Format Collapse. An example from SimpleQA illustrating model brittleness. Tongyi-Deepresearch fails to adhere to the predefined tool schema, hallucinating a search tool format that differs syntactically from the system prompt (likely reverting to its training data format). This mismatch causes immediate parsing error and recurring failures in the following steps despite the semantic inten… view at source ↗

read the original abstract

In real-world Tool-Integrated Reasoning (TIR) scenarios, where LLMs interleave reasoning with external tool calls, a major source of inefficiency is that the toolcalls create pauses between LLM requests and cause KV-Cache eviction, forcing recomputation. Also, the long, unfiltered response returned by external tools inflates the KV-Cache, so each decode step spends more time loading the growing cache and thus becomes steadily slower as context length increases. However, existing efficiency metrics like token counts and toolcall counts fail to capture the real model inference latency. To address this, we introduce PTE (Prefill Token Equivalents), a hardware-aware TIR-efficiency metric that unifies internal reasoning and external tool-use costs while explicitly accounting for non-reusable KV-Cache and long-tool-response scenarios. Validation in a high-concurrency industrial setting indicates that PTE aligns significantly better with wall-clock latency than standard token counts, while maintaining consistent efficiency rankings across diverse hardware profiles. We conduct extensive experiments across five TIR benchmarks, quantify their PTE costs, and identify four inefficiency patterns that appear in TIR. We also discover that trajectories with higher PTE costs tend to have lower reasoning correctness, indicating that simply using more tools does not improve the quality of the answer.

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 introduces PTE as a metric that better tracks real latency in tool-using LLMs by including KV-cache eviction and long responses, with industrial tests showing improved alignment over token counts.

read the letter

The paper's main contribution is defining PTE to capture the real costs in tool-integrated reasoning, where tool calls cause KV-cache eviction and long responses slow down later steps. Their high-concurrency industrial validation shows PTE lines up better with wall-clock time than standard token counts and gives consistent rankings across hardware. They also run experiments on five benchmarks, list four inefficiency patterns, and report that higher-PTE trajectories tend to have lower correctness scores. That last point is a straightforward observation worth checking further in practice. The work does a solid job calling out the mismatch between existing metrics and actual deployment latency, and the hardware consistency check adds some credibility to the claims. The patterns they identify could help engineers spot issues in their own setups without needing new code right away. The soft spots are the missing details on how PTE is calculated exactly and the absence of statistical tests or error bars around the latency correlations. The abstract leaves open whether the five benchmarks cover enough variety in tool response lengths or task types, so the negative link to correctness might not hold outside those specific cases. If the benchmarks share unstated similarities, the results could be narrower than they appear. This is useful for people building or tuning production systems that interleave LLM reasoning with external tools. A reader focused on inference efficiency would pick up concrete ways to think about latency beyond raw token counts. It deserves a serious referee because the underlying problem is common in deployed systems and the metric offers a practical alternative, even if revisions will need to add more rigorous checks on the correlations and broader testing.

Referee Report

3 major / 2 minor

Summary. The paper argues that standard metrics such as token counts and tool-call counts fail to capture real inference latency in Tool-Integrated Reasoning (TIR) because tool calls trigger KV-cache evictions and long tool responses inflate the cache, slowing decode steps. It introduces PTE (Prefill Token Equivalents), a hardware-aware metric that unifies reasoning and tool-use costs while accounting for non-reusable KV-cache. Industrial high-concurrency validation shows PTE aligns better with wall-clock latency than token counts and yields consistent efficiency rankings across hardware; experiments on five TIR benchmarks identify four inefficiency patterns and report that higher-PTE trajectories exhibit lower reasoning correctness.

Significance. If the empirical claims hold after proper statistical controls and generalizability checks, PTE could serve as a practical replacement for token-based efficiency measures in TIR system design and benchmarking, directly linking efficiency to latency and correctness. The negative correlation finding would highlight a previously under-quantified trade-off in tool usage. The industrial validation and cross-hardware consistency are strengths, but the absence of derivation details, statistical tests, and ablation studies limits the immediate adoption potential.

major comments (3)

[PTE definition (abstract and §3)] The definition and derivation of PTE are presented without explicit equations or parameter-free claims in the abstract and methods; it is therefore impossible to verify how the metric converts tool-response lengths and KV-cache eviction events into prefill equivalents or why it is hardware-aware rather than fitted to the specific industrial traces.
[Industrial validation (§4)] The central claim that PTE 'aligns significantly better' with wall-clock latency than token counts rests on industrial validation but reports no correlation coefficients, p-values, confidence intervals, or error bars; without these, the strength of the alignment and the cross-hardware ranking consistency cannot be assessed.
[Benchmark experiments and correlation analysis (§5)] The reported negative correlation between PTE cost and reasoning correctness, as well as the four inefficiency patterns, are derived from five unspecified benchmarks without controls for task difficulty, statistical significance tests, or cross-benchmark ablation; this leaves open whether the patterns and correlation are general properties of TIR or artifacts of the chosen task distributions and tool-response lengths.

minor comments (2)

[Abstract] The abstract would benefit from a one-sentence mathematical sketch of how PTE is computed from KV-cache state and tool-response length.
[Experiments] No mention is made of whether the five benchmarks and industrial traces are publicly available or whether code for PTE computation will be released, which affects reproducibility.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We are grateful to the referee for their constructive comments, which have helped us identify areas for improvement in clarity and rigor. We address each major comment below, indicating the revisions we will make to the manuscript.

read point-by-point responses

Referee: [PTE definition (abstract and §3)] The definition and derivation of PTE are presented without explicit equations or parameter-free claims in the abstract and methods; it is therefore impossible to verify how the metric converts tool-response lengths and KV-cache eviction events into prefill equivalents or why it is hardware-aware rather than fitted to the specific industrial traces.

Authors: We thank the referee for pointing this out. In the revised manuscript, we will include the explicit mathematical definition of PTE in the abstract and provide a detailed derivation in §3, including the formulas that map tool-response lengths and KV-cache eviction events to prefill token equivalents. The hardware-awareness stems from incorporating hardware-specific factors such as memory bandwidth and cache eviction costs, which are not fitted to traces but derived from first principles of transformer inference. We will also clarify that PTE is parameter-free in its core formulation. revision: yes
Referee: [Industrial validation (§4)] The central claim that PTE 'aligns significantly better' with wall-clock latency than token counts rests on industrial validation but reports no correlation coefficients, p-values, confidence intervals, or error bars; without these, the strength of the alignment and the cross-hardware ranking consistency cannot be assessed.

Authors: We agree that additional statistical details are necessary. In the revision, we will add Pearson and Spearman correlation coefficients, associated p-values, 95% confidence intervals, and error bars for the comparisons between PTE and token counts against wall-clock latency. We will also include statistical tests confirming the consistency of efficiency rankings across hardware profiles. revision: yes
Referee: [Benchmark experiments and correlation analysis (§5)] The reported negative correlation between PTE cost and reasoning correctness, as well as the four inefficiency patterns, are derived from five unspecified benchmarks without controls for task difficulty, statistical significance tests, or cross-benchmark ablation; this leaves open whether the patterns and correlation are general properties of TIR or artifacts of the chosen task distributions and tool-response lengths.

Authors: We will specify the five TIR benchmarks explicitly in the revised text. We will perform and report statistical significance tests (e.g., t-tests or Wilcoxon tests) for the negative correlation and for differences in correctness across PTE levels. For controls, we will add an analysis stratifying by task difficulty where possible. However, a full cross-benchmark ablation may require additional experiments; we will include partial ablations on benchmark subsets and discuss generalizability limitations. The patterns were observed consistently across the benchmarks, supporting their generality. revision: partial

Circularity Check

0 steps flagged

No circularity: PTE is a new definition validated empirically against external latency measurements.

full rationale

The paper defines PTE as a hardware-aware metric that accounts for KV-Cache eviction and long tool responses in TIR scenarios. It then reports empirical validation showing better alignment with wall-clock latency than token counts, plus observed patterns from five benchmarks. No equations, fitted parameters, or self-citations are presented that reduce the metric or the inefficiency patterns to tautological inputs by construction. The alignment and correlation findings are data-driven observations, not self-referential derivations. The derivation chain is self-contained as an empirical metric proposal plus measurement.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 1 invented entities

Based solely on the abstract, the central addition is the PTE metric itself. No free parameters, standard mathematical axioms, or other invented entities are described.

invented entities (1)

PTE (Prefill Token Equivalents) no independent evidence
purpose: Hardware-aware efficiency metric unifying reasoning and tool-use costs while accounting for KV-cache effects
Newly defined construct introduced to address limitations of token counts in TIR scenarios

pith-pipeline@v0.9.0 · 5530 in / 1227 out tokens · 61997 ms · 2026-05-10T19:19:54.964758+00:00 · methodology

discussion (0)

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\ n \ nprobability = grand / prize \ n \ nBut since we need the fraction , it's grand / prize = 1 / 115.\ n \ nLet's code it using math . comb ( since Python 3.10+ has math . comb , but if not , we can define it ) .\ n \ nWait , in Python , math . comb is available from 3.8 onwards . Let's assume the environment supports it .\ n \ nCode :\ n \ nimport mat...
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[ Organic vs . Conventional Farming ]..." Assistant:(usevisittool) Now let me visit the most relevant USDA page to get detailed information about what organic agriculture excludes : " tool_calls ": {" arguments ": "{\" url \": \" https :// www . usda . gov / about - usda / news / blog / organic -101 - what - organic - farming - and - processing ...\" , \"...

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