ImpRIF: Stronger Implicit Reasoning Leads to Better Complex Instruction Following

Chao Tong; Haihua Yang; Lin Yang; Xu Wang; Yuancheng Yang

arxiv: 2602.21228 · v2 · submitted 2026-02-04 · 💻 cs.CL · cs.AI

ImpRIF: Stronger Implicit Reasoning Leads to Better Complex Instruction Following

Yuancheng Yang , Lin Yang , Xu Wang , Chao Tong , Haihua Yang This is my paper

Pith reviewed 2026-05-16 07:56 UTC · model grok-4.3

classification 💻 cs.CL cs.AI

keywords implicit reasoningcomplex instruction followingreasoning graphsLLM trainingfine-tuningreinforcement learningchain-of-thought

0 comments

The pith

Formalizing implicit reasoning in instructions as verifiable graphs and training on them improves LLMs' complex instruction following.

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

The paper argues that LLMs often fail on complex instructions because they overlook the hidden logical structure and constraints embedded in them. It proposes representing those instructions as verifiable reasoning graphs that capture the latent steps, dependencies, and logic. From the graphs the authors generate large synthetic single-turn and multi-turn datasets, then train models first with supervised fine-tuning on graph-driven chain-of-thought reasoning and second with reinforcement learning that rewards adherence to the graph structure. On five benchmarks the resulting models show clear gains over their base versions. A reader would care because the work offers a concrete route to making language models more reliable when users give detailed, multi-part requests.

Core claim

Complex instructions that embed implicit reasoning, logical relations, and multi-constraint dependencies can be formalized as verifiable reasoning graphs; synthesizing data from these graphs and training models to reason explicitly along them via fine-tuning and reinforcement learning produces stronger implicit-reasoning ability and measurably better instruction following.

What carries the argument

Verifiable reasoning graphs that encode the latent logical structure of an instruction, enabling programmatic verification, data synthesis, and graph-guided chain-of-thought reasoning during training and inference.

If this is right

Models trained this way outperform base models on five complex instruction following benchmarks.
Both single-turn and multi-turn synthetic data generated from the graphs improve handling of intricate dependencies.
Explicit reinforcement on graph adherence reduces errors that arise from missed implicit logic or constraints.

Where Pith is reading between the lines

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

The same graph synthesis pipeline could be used to create training data for other reasoning-heavy tasks such as planning or multi-step problem solving.
If the graphs encode general reasoning patterns, the trained models may generalize to instruction types never seen during synthesis.
The verification step built into the graphs offers a route to automated checking or correction of model outputs during deployment.

Load-bearing premise

Instructions that require implicit reasoning can be reliably turned into verifiable reasoning graphs whose structure matches genuine user intent and whose synthetic data will transfer to natural-language instructions.

What would settle it

A controlled experiment in which models trained with the graph-based method show no gain, or a loss, on a benchmark of real-world complex instructions whose structure was not derived from the same graph formalism.

Figures

Figures reproduced from arXiv: 2602.21228 by Chao Tong, Haihua Yang, Lin Yang, Xu Wang, Yuancheng Yang.

**Figure 2.** Figure 2: Overview of the proposed pipeline. The top depicts the generation process of implicit reasoning data, the [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Figure 3: The performance of frontier models and our trained ImpRIF-32B on our internal test set and open [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

**Figure 4.** Figure 4: The performance of our model on LogicBench. [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗

**Figure 5.** Figure 5: Reward curves during RL training. We com [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗

**Figure 6.** Figure 6: Distribution of Multi-Turn Dialogue Rounds [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗

read the original abstract

As applications of large language models (LLMs) become increasingly complex, the demand for robust complex instruction following capabilities is growing accordingly. We argue that a thorough understanding of the instruction itself, especially the latent reasoning structure embedded between the lines, is crucial for improving instruction following. Therefore we target complex instructions that involve implicit reasoning, intricate logical relations, and multi-constraint dependencies. We propose ImpRIF, a method to enhance LLMs' understanding of implicit reasoning instructions, thereby improving its ability to follow complex instructions. We formalize such instructions as verifiable reasoning graphs, enabling programmatic verification and graph-driven chain-of-thought reasoning. Based on this formulation, we synthesize large-scale single- and multi-turn data, propose fine-tuning with graph reasoning, and apply reinforcement learning to explicitly train models to reason along the graph. On five complex instruction following benchmarks, our models substantially outperform their base models. These results demonstrate that enhancing implicit reasoning capabilities can significantly improve complex instruction following.

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

ImpRIF shows benchmark gains from graph-synthesized data and RL for implicit reasoning in instructions, but the transfer story from synthetic graphs to natural cases needs tighter checks.

read the letter

The core claim here is that formalizing complex instructions as verifiable reasoning graphs, synthesizing single- and multi-turn data from them, and training with graph-driven chain-of-thought plus RL produces clear improvements on instruction-following benchmarks. That pipeline is the main new piece: the graphs enable programmatic verification and structure the reasoning steps during both data creation and optimization, which the authors tie directly to handling implicit logical relations and multi-constraint dependencies. The results section reports substantial outperformance over base models across five benchmarks, which is the strongest part of the work and gives it practical relevance for agentic settings. The approach is straightforward to understand and the empirical thread from graphs to final scores is laid out without obvious circularity. The soft spots sit in the data side. The gains could stem from the scale or cleanliness of the synthetic examples rather than the implicit-reasoning enhancement itself, especially if graph construction adds artifacts that do not match real user intent. The abstract and methods summary do not include ablations that isolate the graph component or quantitative checks on how well the synthesized data matches natural instruction distributions. Those gaps make it hard to rule out simpler explanations like generic instruction tuning effects. This paper is aimed at groups working on LLM reasoning and complex instruction following. It has enough concrete results and a reproducible-sounding pipeline to merit a serious referee, even though revisions on validation and transfer experiments would be expected. I would send it to peer review.

Referee Report

3 major / 2 minor

Summary. The paper proposes ImpRIF, which formalizes complex instructions involving implicit reasoning as verifiable reasoning graphs. These graphs enable synthesis of large-scale single- and multi-turn training data, graph-driven chain-of-thought reasoning during fine-tuning, and reinforcement learning to train models to follow the graph structure. Experiments show that models trained this way substantially outperform their base models on five complex instruction following benchmarks, supporting the claim that stronger implicit reasoning improves complex instruction following.

Significance. If the transfer from graph-synthesized data to natural instructions is robust, the work offers a concrete mechanism for targeting latent logical structure in instructions rather than relying solely on scale or generic tuning. The use of programmatically verifiable graphs and graph-driven RL is a strength that could be extended to other reasoning-heavy tasks, provided the fidelity claims hold.

major comments (3)

[§3] §3 (Graph Construction): The central claim that verifiable reasoning graphs faithfully capture latent structure in real user instructions lacks a quantitative fidelity check (e.g., human agreement rates or distribution-shift metrics between synthetic graphs and natural instructions). Without this, gains on the five benchmarks could stem from data scale or generic instruction tuning rather than implicit-reasoning enhancement.
[§4.3] §4.3 (Ablation Studies): No ablation isolates the graph component from standard fine-tuning or CoT; the reported improvements cannot be attributed specifically to the verifiable-graph formulation versus other training choices.
[§5] §5 (Benchmark Results): The paper reports substantial outperformance but provides no error analysis or case studies showing that failures on natural instructions are reduced precisely because of better implicit-reasoning-graph adherence.

minor comments (2)

[Abstract] The abstract and introduction should explicitly name the five benchmarks and provide basic statistics (e.g., average instruction length, number of constraints) to allow readers to assess task difficulty.
[§3] Notation for the reasoning graph (nodes, edges, verification predicates) should be introduced with a small illustrative example in §3 rather than only in prose.

Simulated Author's Rebuttal

3 responses · 0 unresolved

Thank you for the constructive feedback on our work. We appreciate the referee's insights and address each major comment below, outlining specific revisions to strengthen the manuscript.

read point-by-point responses

Referee: [§3] §3 (Graph Construction): The central claim that verifiable reasoning graphs faithfully capture latent structure in real user instructions lacks a quantitative fidelity check (e.g., human agreement rates or distribution-shift metrics between synthetic graphs and natural instructions). Without this, gains on the five benchmarks could stem from data scale or generic instruction tuning rather than implicit-reasoning enhancement.

Authors: We agree that a quantitative fidelity validation is needed to strengthen the claim. In the revision, we will add a human evaluation on 100 sampled natural instructions from the benchmarks. Three annotators will rate graph fidelity on a 1-5 scale for implicit reasoning capture, reporting inter-annotator agreement (Cohen's kappa) and average fidelity scores. We will also include distribution-shift metrics (e.g., KL divergence on reasoning depth, constraint count, and logical relation types) between synthetic graphs and natural instructions to help rule out scale-only explanations. revision: yes
Referee: [§4.3] §4.3 (Ablation Studies): No ablation isolates the graph component from standard fine-tuning or CoT; the reported improvements cannot be attributed specifically to the verifiable-graph formulation versus other training choices.

Authors: We acknowledge the current ablations do not fully isolate the graph structure. We will expand §4.3 with new controlled experiments: (1) standard CoT fine-tuning without graph guidance, (2) plain instruction tuning, and (3) graph-driven training. These will report performance deltas attributable to the verifiable-graph formulation. We will include these results with statistical significance tests to directly address attribution. revision: yes
Referee: [§5] §5 (Benchmark Results): The paper reports substantial outperformance but provides no error analysis or case studies showing that failures on natural instructions are reduced precisely because of better implicit-reasoning-graph adherence.

Authors: We will add an error analysis subsection to §5. This will categorize errors (e.g., missed constraints, incorrect implicit inferences) on the five benchmarks for base vs. ImpRIF models, showing reduced rates in graph-related categories. We will also include 6 detailed case studies contrasting base-model failures with ImpRIF successes, explicitly tracing improvements to graph adherence during reasoning. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical pipeline with independent benchmark validation

full rationale

The paper proposes an empirical method: formalizing instructions as verifiable reasoning graphs, synthesizing single-/multi-turn data from them, fine-tuning with graph-driven CoT, and applying RL. Gains are measured on five external complex-instruction benchmarks against base models. No equations appear that reduce final performance numbers to quantities defined inside the method itself. No self-citations are invoked as load-bearing uniqueness theorems. The central claim rests on experimental transfer rather than definitional equivalence or fitted-input renaming.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The approach rests on the assumption that natural-language instructions can be losslessly converted into checkable graphs; this is treated as a domain modeling choice rather than derived from first principles.

axioms (1)

domain assumption Complex instructions contain latent reasoning structures that can be represented as directed graphs with verifiable nodes and edges.
Stated in the abstract as the basis for formalization and data synthesis.

invented entities (1)

verifiable reasoning graph no independent evidence
purpose: Explicit representation of implicit reasoning and constraints inside an instruction for programmatic verification and graph-guided training.
Introduced as the central modeling device; no independent evidence outside the paper is provided in the abstract.

pith-pipeline@v0.9.0 · 5470 in / 1168 out tokens · 24563 ms · 2026-05-16T07:56:57.996190+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

?

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

We formalize such instructions as verifiable reasoning graphs, enabling programmatic verification and graph-driven chain-of-thought reasoning... R_single(a) = 1/n Σ 1(a |= c_i)
IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking unclear

?

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

nodes denote concrete actions (conditional judgments, knowledge inference, mathematical computation) and edges encode dependency relations

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

15 extracted references · 15 canonical work pages

[1]

Scaling reasoning, losing control: Evaluating instruction following in large reasoning models.arXiv preprint arXiv:2505.14810,

Self-play with Execution Feedback: Improv- ing Instruction-following Capabilities of Large Lan- guage Models. InThe Thirteenth International Con- ference on Learning Representations. Tingchen Fu, Jiawei Gu, Yafu Li, Xiaoye Qu, and Yu Cheng. 2025. Scaling Reasoning, Losing Control: Evaluating Instruction Following in Large Reasoning Models.Preprint, arXiv:...

work page arXiv 2025
[2]

Deepseekmath-v2: Towards self-verifiable mathematical reasoning

Step-by-Step Mastery: Enhancing Soft Con- straint Following Ability of Large Language Models. InFindings of the Association for Computational Linguistics: ACL 2025, pages 19581–19596, Vienna, Austria. Association for Computational Linguistics. Zhihong Shao, Yuxiang Luo, Chengda Lu, Z. Z. Ren, Jiewen Hu, Tian Ye, Zhibin Gou, Shirong Ma, and Xi- aokang Zhan...

work page arXiv 2025
[3]

Conifer: Improving Complex Constrained Instruction-Following Ability of Large Language Models.Preprint, arXiv:2404.02823. Kimi Team, Yifan Bai, Yiping Bao, Guanduo Chen, Jia- hao Chen, Ningxin Chen, Ruijue Chen, Yanru Chen, Yuankun Chen, Yutian Chen, Zhuofu Chen, Jialei Cui, Hao Ding, Mengnan Dong, Angang Du, Chen- zhuang Du, Dikang Du, Yulun Du, Yu Fan, ...

work page arXiv 2025
[4]

thinking-process reward

LlamaFactory: Unified efficient fine-tuning of 100+ language models. InProceedings of the 62nd Annual Meeting of the Association for Compu- tational Linguistics (Volume 3: System Demonstra- tions), Bangkok, Thailand. Association for Computa- tional Linguistics. Tao Zou, Xinghua Zhang, Haiyang Yu, Minzheng Wang, Fei Huang, and Yongbin Li. 2025. EIF- BENCH:...

work page arXiv 2025
[5]

logicality

evaluates LLMs on following instructions that contain multiple interacting constraints. It pro- poses a hierarchical taxonomy with 4 constraint types, 19 dimensions, and 4 composition types, and builds a high-quality dataset based on this structure. Its evaluation combines rule-augmented LLM judg- ing with composition-aware scoring. The bench- mark reveal...

work page 2024
[6]

Reason through the constraints

work page
[7]

Lay out an execution plan

work page
[8]

How should shared resources be prioritized to avoid prioritization-related issues in embedded systems where resources are highly competitive?

Validate the result Your thought process must be detailed. System Prompt: ERG CoT Thinking Note that the thinking process needs to be structured and logical. The analysis of instruction constraints in the thinking process can refer to the following chain of thought prompts: {ERG_CoT} H Thinking Pattern Example For the same problem, different thinking patt...

work page
[9]

Scope Definition (12 chars)

work page
[10]

Stakeholder Needs (15)

work page
[11]

Functional Requirements (19)

work page
[12]

Non-functional Requirements (22)

work page
[13]

Constraints and Assumptions (23)

work page
[14]

Success Criteria (13)

work page
[15]

What key issues should be addressed in a requirements document?

Risk Management (13) Wait, but 13 is a prime number. Wait, the list items are just text, but the count of characters per item is important for ordering. Let me check the character counts: ... (Iterative fine-tuning and retrying) Wait, but need to make sure they are not repeated. Let me count: that's 9 words. Now, check if they are unique. Yes. Now, the to...

work page

[1] [1]

Scaling reasoning, losing control: Evaluating instruction following in large reasoning models.arXiv preprint arXiv:2505.14810,

Self-play with Execution Feedback: Improv- ing Instruction-following Capabilities of Large Lan- guage Models. InThe Thirteenth International Con- ference on Learning Representations. Tingchen Fu, Jiawei Gu, Yafu Li, Xiaoye Qu, and Yu Cheng. 2025. Scaling Reasoning, Losing Control: Evaluating Instruction Following in Large Reasoning Models.Preprint, arXiv:...

work page arXiv 2025

[2] [2]

Deepseekmath-v2: Towards self-verifiable mathematical reasoning

Step-by-Step Mastery: Enhancing Soft Con- straint Following Ability of Large Language Models. InFindings of the Association for Computational Linguistics: ACL 2025, pages 19581–19596, Vienna, Austria. Association for Computational Linguistics. Zhihong Shao, Yuxiang Luo, Chengda Lu, Z. Z. Ren, Jiewen Hu, Tian Ye, Zhibin Gou, Shirong Ma, and Xi- aokang Zhan...

work page arXiv 2025

[3] [3]

Conifer: Improving Complex Constrained Instruction-Following Ability of Large Language Models.Preprint, arXiv:2404.02823. Kimi Team, Yifan Bai, Yiping Bao, Guanduo Chen, Jia- hao Chen, Ningxin Chen, Ruijue Chen, Yanru Chen, Yuankun Chen, Yutian Chen, Zhuofu Chen, Jialei Cui, Hao Ding, Mengnan Dong, Angang Du, Chen- zhuang Du, Dikang Du, Yulun Du, Yu Fan, ...

work page arXiv 2025

[4] [4]

thinking-process reward

LlamaFactory: Unified efficient fine-tuning of 100+ language models. InProceedings of the 62nd Annual Meeting of the Association for Compu- tational Linguistics (Volume 3: System Demonstra- tions), Bangkok, Thailand. Association for Computa- tional Linguistics. Tao Zou, Xinghua Zhang, Haiyang Yu, Minzheng Wang, Fei Huang, and Yongbin Li. 2025. EIF- BENCH:...

work page arXiv 2025

[5] [5]

logicality

evaluates LLMs on following instructions that contain multiple interacting constraints. It pro- poses a hierarchical taxonomy with 4 constraint types, 19 dimensions, and 4 composition types, and builds a high-quality dataset based on this structure. Its evaluation combines rule-augmented LLM judg- ing with composition-aware scoring. The bench- mark reveal...

work page 2024

[6] [6]

Reason through the constraints

work page

[7] [7]

Lay out an execution plan

work page

[8] [8]

How should shared resources be prioritized to avoid prioritization-related issues in embedded systems where resources are highly competitive?

Validate the result Your thought process must be detailed. System Prompt: ERG CoT Thinking Note that the thinking process needs to be structured and logical. The analysis of instruction constraints in the thinking process can refer to the following chain of thought prompts: {ERG_CoT} H Thinking Pattern Example For the same problem, different thinking patt...

work page

[9] [9]

Scope Definition (12 chars)

work page

[10] [10]

Stakeholder Needs (15)

work page

[11] [11]

Functional Requirements (19)

work page

[12] [12]

Non-functional Requirements (22)

work page

[13] [13]

Constraints and Assumptions (23)

work page

[14] [14]

Success Criteria (13)

work page

[15] [15]

What key issues should be addressed in a requirements document?

Risk Management (13) Wait, but 13 is a prime number. Wait, the list items are just text, but the count of characters per item is important for ordering. Let me check the character counts: ... (Iterative fine-tuning and retrying) Wait, but need to make sure they are not repeated. Let me count: that's 9 words. Now, check if they are unique. Yes. Now, the to...

work page