RIMRULE: Improving Tool-Using Language Agents via MDL-Guided Rule Learning

# Improving Tool-Using Language Agents via MDL-Guided Rule Learning
Source: [https://arxiv.org/html/2601.00086](https://arxiv.org/html/2601.00086)
Xiang Gao1Yuguang Yao1Qi Zhang2Kaiwen Dong1 Avinash Baidya1Ruocheng Guo1Hilaf Hasson1Kamalika Das1

1

Intuit AI Research
2Temple University\{xiang\_gao, kamalika\_das\}@intuit\.com

###### Abstract

Large language models \(LLMs\) often struggle to use tools reliably in domain\-specific settings, where APIs may be idiosyncratic, under\-documented, or tailored to private workflows\. This highlights the need for effective adaptation to task\-specific tools\. We proposeRimRule, a neuro\-symbolic approach for LLM adaptation based on dynamic rule injection\. Compact, interpretable rules are distilled from failure traces and injected into the prompt during inference to improve task performance\. These rules are proposed by the LLM itself and consolidated using a Minimum Description Length \(MDL\) objective that favors generality and conciseness\. Each rule is stored in both natural language and a structured symbolic form, supporting efficient retrieval at inference time\. Experiments on tool\-use benchmarks show that this approach improves accuracy on both seen and unseen tools without modifying LLM weights\. It outperforms prompting\-based adaptation methods and complements finetuning\. Moreover, rules learned from one LLM can be reused to improve others, including long reasoning LLMs, highlighting the portability of symbolic knowledge across architectures\.111*Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics*\(Volume 1: Long Papers\), pages 34631–34646 July 2\-7, 2026 \(ACL 2026\)\. Copyright 2026 by the authors\.

RIMRULE: Improving Tool\-Using Language Agents via MDL\-Guided Rule Learning

Xiang Gao1Yuguang Yao1Qi Zhang2Kaiwen Dong1Avinash Baidya1Ruocheng Guo1Hilaf Hasson1Kamalika Das11Intuit AI Research2Temple University\{xiang\_gao, kamalika\_das\}@intuit\.com

## 1Introduction

Humans adapt by trying, erring, and compressing experience into reusable heuristics\(Kolb,[1984](https://arxiv.org/html/2601.00086#bib.bib172); Metcalfe,[2017](https://arxiv.org/html/2601.00086#bib.bib174); Gigerenzer and Gaissmaier,[2011](https://arxiv.org/html/2601.00086#bib.bib178)\)\. Such compact representation of regularities achieve cognitive economy—they preserve what matters for performance while discarding incidental detail, making knowledge easier to reuse across tasks and by other people\(Rosch,[1978](https://arxiv.org/html/2601.00086#bib.bib173)\)\.

![Refer to caption](https://arxiv.org/html/2601.00086v3/figures/intro.png)Figure 1:Learning reusable and interpretable rules from experienceLarge language models \(LLMs\)\(Brownet al\.,[2020](https://arxiv.org/html/2601.00086#bib.bib5); Baiet al\.,[2023](https://arxiv.org/html/2601.00086#bib.bib198); Team and others,[2023](https://arxiv.org/html/2601.00086#bib.bib94); Grattafioriet al\.,[2024](https://arxiv.org/html/2601.00086#bib.bib97)\)also require adaptation, especially when deployed in unfamiliar domains with specialized tools or under\-documented APIs\. However, the way LLMs adapt differs markedly from how humans do\. Today, adaptation typically takes one of three forms: \(i\) retrieved examples for few\-shot prompting\(Brownet al\.,[2020](https://arxiv.org/html/2601.00086#bib.bib5); Liuet al\.,[2021](https://arxiv.org/html/2601.00086#bib.bib123)\), \(ii\) globally tuned prompts\(Pryzantet al\.,[2023](https://arxiv.org/html/2601.00086#bib.bib96); Cuiet al\.,[2025](https://arxiv.org/html/2601.00086#bib.bib121)\), or \(iii\) fine\-tuned model weights\(Huet al\.,[2022](https://arxiv.org/html/2601.00086#bib.bib116)\)\. Each approach is powerful, but none supports abstraction, reuse, and interpretability in the way humans generalize from experience\. Few\-shot prompting reuses raw supervision but does not abstract—and LLMs often extract only shallow patterns from examples\(Weiet al\.,[2023](https://arxiv.org/html/2601.00086#bib.bib131)\); global prompts are static and brittle in interactive settings\(Vermaet al\.,[2024](https://arxiv.org/html/2601.00086#bib.bib199)\); and tuning model weights is costly, requiring retraining whenever the environment changes, and preventing easy sharing of acquired knowledge across models\(Yanget al\.,[2024](https://arxiv.org/html/2601.00086#bib.bib200)\)\.

We explore a fourth paradigm for adapting LLMs—one that mirrors how humans learn from failure, as illustrated in Fig\.[1](https://arxiv.org/html/2601.00086#S1.F1)\. Instead of tuning weights or retrieving demonstrations, we induce interpretable rules\. At training time, these rules are proposed in response to observed failures\. These rules are consolidated using the Minimum Description Length \(MDL\) principle\(Rissanen,[1978](https://arxiv.org/html/2601.00086#bib.bib40); Grunwald,[2007](https://arxiv.org/html/2601.00086#bib.bib14)\)and stored in a dual natural\-language and symbolic representation, enabling both principled compression and reliable retrieval\. At inference time, relevant rules are dynamically retrieved and injected into the prompt to improve LLM performance\. This constitutes a distinct adaptation paradigm: unlike few\-shot prompting, it emphasizes abstraction and compression over raw example replay; unlike finetuning, it produces interpretable artifacts\. Because these rules are both understandable to humans and legible to modern LLMs, they can be reused across different LLMs without retraining\.

We demonstrate this approach on two tool\-use benchmarks—ToolHop\(Yeet al\.,[2025](https://arxiv.org/html/2601.00086#bib.bib80)\)and BFCL\(Yanet al\.,[2024](https://arxiv.org/html/2601.00086#bib.bib81)\)—where LLMs must reason over tool descriptions and invoke them correctly\. Simple retry mechanisms based on tool error messages, or even the use of advanced long reasoning models, often fall short in reliably correcting systematic failures\. Our results highlight several key observations\.

- •First, inference\-time rule injection consistently improves performance, including on queries involving tools that never appear in training\.
- •Second, learned rules transfer across LLMs in both directions: rules distilled from weaker models improve stronger, long\-reasoning LLMs, and rules learned from stronger models can also benefit smaller or less capable ones\.
- •Third, our method outperforms prompting based adaptation approaches and complements finetuning, offering a distinct and synergistic axis of generalization\.

## 2Method

We introduceRimRule222Reusable,Interpretable, andMDL\-guided Rules, a scalable framework that equips LLM\-based agents with inference\-time intepretable rules distilled from failure traces\. Figure[2](https://arxiv.org/html/2601.00086#S2.F2)illustrates the overall architecture, and Table[1](https://arxiv.org/html/2601.00086#alg1)provides pseudocode\.

Instead of learning rules sequentially—an approach that is sensitive to data order and difficult to scale—RimRuledecouples rule induction into two phases\. In the first stage \(Section[2\.1](https://arxiv.org/html/2601.00086#S2.SS1)\), candidate rules are generated independently from individual failures, enabling parallel, order\-agnostic extraction across large interaction logs\. In the second stage \(Section[2\.2](https://arxiv.org/html/2601.00086#S2.SS2)\), these candidates are consolidated under an MDL objective, which prunes redundancy and selects a compact, high\-utility rule library\. This design avoids the path dependence of sequential rule learning while naturally supporting scalable rule discovery and reuse\.

![Refer to caption](https://arxiv.org/html/2601.00086v3/figures/system.png)Figure 2:The framework of our MDL\-guided rule learning\.### 2\.1Local Rule Generation

#### 2\.1\.1Experience Collection

We begin by running a zero\-shot LLM\-based agent over each sample in the training set and recording its execution trace\. When the resulting trace produces an incorrect answer or terminates prematurely due to tool\-calling errors, we retain it as experience for rule generation\. The collection of such failure traces constitutes the experience signal used for downstream rule induction\. Each training instance is represented as a tuple\(x,𝒮,τ−,τ∗\)\(x,\\mathcal\{S\},\\tau^\{\-\},\\tau^\{\*\}\), wherex∈𝒳x\\in\\mathcal\{X\}is the user query,𝒮\\mathcal\{S\}is the set of available tools,τ−\\tau^\{\-\}is the agent’s incorrect execution trace, andτ∗\\tau^\{\*\}is the corresponding ground\-truth trace\.333In settings without traces but with a reward function or score, the same mechanism can be adapted by proposing multiple candidate rules and selecting those that maximize observed reward on the instance; a full treatment is left to future work\.

#### 2\.1\.2Rule Generation via EBL

Given a failure traceτ−\\tau^\{\-\}and its ground\-truth counterpartτ∗\\tau^\{\*\}, the rule generator compares the two executions to identify a root\-cause*reasoning*failure, excluding downstream propagation effects, and proposes a compact ruler∈ℛ0r\\in\\mathcal\{R\}\_\{0\}to correct similar errors\. Each rule is tagged with an error typed​\(r\)∈\{dec,sel,arg\}d\(r\)\\in\\\{\\mathrm\{dec\},\\mathrm\{sel\},\\mathrm\{arg\}\\\}, corresponding to decomposition, tool selection, or argument construction\.

To abstract reusable rules, we follow*Explanation\-Based Learning*\(EBL\): a grounded explanation is generated and then generalized by removing instance\-specific details\(Mitchellet al\.,[1986](https://arxiv.org/html/2601.00086#bib.bib84); DeJong and Mooney,[1986](https://arxiv.org/html/2601.00086#bib.bib54)\)\. The generator is implemented as an LLM\-based function\.444See appendix for the prompt\.

Proposed rules are filtered by a*predictive check*, requiring improved performance on the same query when injected, and a*linguistic check*enforcing a clean*if–then*form and bounded length\. If a rule yields only partial improvement, the generator is re\-invoked to propose additional rules until the trace is corrected or no further atomic fixes are found\.

Algorithm 1RimRule1:Training failures

D=\{\(xi,𝒮i,τi−,τi∗\)\}i=1nD=\\\{\(x\_\{i\},\\mathcal\{S\}\_\{i\},\\tau\_\{i\}^\{\-\},\\tau\_\{i\}^\{\*\}\)\\\}\_\{i=1\}^\{n\}
2:Compact symbolic rule library

ℛ\\mathcal\{R\}
3:Stage 1: Rule Generation

4:for all

\(xi,𝒮i,τi−,τi∗\)∈D\(x\_\{i\},\\mathcal\{S\}\_\{i\},\\tau\_\{i\}^\{\-\},\\tau\_\{i\}^\{\*\}\)\\in Din paralleldo

5:

riNL←LLM\-Propose\-Rule​\(⋅\)r\_\{i\}^\{\\text\{NL\}\}\\leftarrow\\text\{LLM\-Propose\-Rule\}\(\\cdot\)
6:ifPasses checksthen

7:Add

riNLr\_\{i\}^\{\\text\{NL\}\}to pool

ℛ0\\mathcal\{R\}\_\{0\}
8:endif

9:endfor

10:Symbolic Translation

11:Induce vocabulary

𝒱\\mathcal\{V\}from

ℛ0\\mathcal\{R\}\_\{0\}
12:Translate

ℛ0\\mathcal\{R\}\_\{0\}to symbolic rules

ℛ\\mathcal\{R\}
13:Stage 2: MDL Consolidation

14:repeat

15:for all

r∈ℛr\\in\\mathcal\{R\}do

16:EvaluatePrune\(

rr\) andGeneralize\(

rr\)

17:if

Δ​LMDL<0\\Delta L\_\{\\text\{MDL\}\}<0then

18:Apply best edit

19:endif

20:endfor

21:untilno improvement

22:return

ℛ\\mathcal\{R\}

#### 2\.1\.3Symbolic Representation

Natural\-language renderings of the same rule often vary in phrasing, hindering both structural matching and consistent description\-length computation\. We therefore compile each rule into a symbolic representation with fixed fields and closed vocabularies, enabling principled MDL consolidation \(Section[2\.2\.2](https://arxiv.org/html/2601.00086#S2.SS2.SSS2)\) and efficient retrieval \(Section[2\.3](https://arxiv.org/html/2601.00086#S2.SS3)\)\.

The symbolic schema consists of five semantic fields:Domain\(broad topic\),Qualifier\(context\),Action\(prescribed operation\),Strength\(priority\), andToolCategory\(abstract tool type\)\. Each field draws values from a finite vocabulary\.

We construct these vocabularies by prompting an LLM \(see Appendix[A\.1](https://arxiv.org/html/2601.00086#A1.SS1)\) over batches of natural\-language rules and select the most compact vocabulary across randomized orderings\. Once fixed, each rule is translated into its symbolic form by assigning valid field values, yielding a deterministic and auditable rule set\.

### 2\.2Rule Consolidation

Rule generation typically produces a large set of overlapping and overly specific rules\. Consolidation is therefore required to select a compact subset that generalizes well\.

We consider two approaches: a prompt\-based heuristic that merges rules using an LLM, and a data\-driven alternative based on the Minimum Description Length \(MDL\) principle\.

#### 2\.2\.1Prompt\-Based

A simple consolidation strategy is to prompt an LLM to merge or rewrite candidate rules, as in AutoRule\(Wang and Xiong,[2025](https://arxiv.org/html/2601.00086#bib.bib32)\)\. While this can reduce redundancy at the textual level, it is heuristic and does not account for how rules affect agent behavior on actual failure cases\. This motivates a consolidation objective that explicitly trades off rule complexity against empirical effectiveness\.

#### 2\.2\.2MDL\-Guided

We adopt the*Minimum Description Length*\(MDL\) principle, which favors models that compress observed data while remaining concise\(Rissanen,[1978](https://arxiv.org/html/2601.00086#bib.bib40); Grunwald,[2007](https://arxiv.org/html/2601.00086#bib.bib14)\)\. In our setting, MDL provides a principled objective for selecting a compact rule set that corrects as many failures as possible without unnecessary complexity\.

##### Objective\.

LetH⊆ℛsymH\\subseteq\\mathcal\{R\}^\{\\text\{sym\}\}denote a candidate rule library\. We minimize

MDL​\(H\)=L​\(H\)\+L​\(D∣H\),\\mathrm\{MDL\}\(H\)=L\(H\)\+L\(D\\mid H\),whereL​\(H\)L\(H\)penalizes rule complexity andL​\(D∣H\)L\(D\\mid H\)measures how well the rules correct observed failures\.

##### Model Cost\.

We define a length\-based prior over rule libraries,

P​\(H\)∝exp⁡\(−α​∑r∈Hℓ​\(r\)\),P\(H\)\\propto\\exp\\\!\\Bigl\(\-\\alpha\\sum\_\{r\\in H\}\\ell\(r\)\\Bigr\),whereℓ​\(r\)\\ell\(r\)denotes thesymbolic token length555Symbolic token length provides a canonical measure of rule complexity by abstracting away incidental natural\-language phrasing\.of rulerrandα\>0\\alpha\>0controls the strength of regularization\. This corresponds to a maximum\-entropy prior under a constraint on expected total rule length\(Jaynes,[1957](https://arxiv.org/html/2601.00086#bib.bib43)\)\. Taking the negative log\-likelihood yields the model code length

L​\(H\)=−log⁡P​\(H\)=α​∑r∈Hℓ​\(r\)\+log⁡Z​\(α\),L\(H\)=\-\\log P\(H\)=\\alpha\\sum\_\{r\\in H\}\\ell\(r\)\+\\log Z\(\\alpha\),whereZ​\(α\)Z\(\\alpha\)is constant for a fixed candidate pool and is therefore omitted during optimization\.

##### Data Cost\.

Given failure casesD=\{\(xi,𝒮i,τi−,τi∗\)\}i=1nD=\\\{\(x\_\{i\},\\mathcal\{S\}\_\{i\},\\tau\_\{i\}^\{\-\},\\tau\_\{i\}^\{\*\}\)\\\}\_\{i=1\}^\{n\}, we defineai​\(H\)=1a\_\{i\}\(H\)=1if injectingHHcorrects failureii\. LetkH=∑iai​\(H\)k\_\{H\}=\\sum\_\{i\}a\_\{i\}\(H\)\. We model correction outcomes with a Bernoulli likelihood and use the refined MDL plug\-in code

L​\(D∣H\)=−\[kH​log⁡p^H\+\(n−kH\)​log⁡\(1−p^H\)\],L\(D\\mid H\)=\-\\bigl\[k\_\{H\}\\log\\hat\{p\}\_\{H\}\+\(n\-k\_\{H\}\)\\log\(1\-\\hat\{p\}\_\{H\}\)\\bigr\],wherep^H=kH/n\\hat\{p\}\_\{H\}=k\_\{H\}/n\. This term directly rewards rule sets that correct more failures\.

##### Greedy Consolidation\.

We minimizeMDL​\(H\)\\mathrm\{MDL\}\(H\)starting from the full rule pool and applying local edits that strictly reduce the objective\. We consider two operations:*pruning*a rule, and*generalizing*a tool\-specific rule to a category\-level rule\. Edits are accepted only when the reduction in model cost outweighs any increase in data cost\. This greedy procedure terminates when no local edit improves the MDL objective\.

In practice, consolidation scales linearly with the size of the candidate rule pool, as each iteration evaluates a constant set of local edits per rule\. While this greedy procedure does not guarantee a globally optimal solution and may miss beneficial non\-local edits, it follows standard practice in rule learning and MDL\-based pruning, where local edits are commonly used to remove redundancy and over\-specific rules and are empirically effective in improving generalization\(Quinlan,[1987](https://arxiv.org/html/2601.00086#bib.bib7); Fürnkranz,[1997](https://arxiv.org/html/2601.00086#bib.bib10); Grunwald,[2007](https://arxiv.org/html/2601.00086#bib.bib14)\)\. Exploring more global or approximate inference strategies for rule consolidation is an interesting direction for future work\.

##### MDL Behavior\.

Although the termL​\(D∣H\)L\(D\\mid H\)could be minimized by correcting no failures, this degenerate case is never reached in practice\. Consolidation proceeds greedily from a high\-performing initial rule set; in this regime, removing a rule that reduces the number of corrected failures sharply increasesL​\(D∣H\)L\(D\\mid H\), outweighing the modest reduction in model cost\. Such edits are therefore rejected\.

##### Choice ofα\\alpha\.

We select the regularization strengthα\\alphaby choosing the value that yields the best end\-to\-end accuracy after consolidation on the failure set\. Since each rule is evaluated on failures beyond its originating instance, this selection already reflects cross\-sample generalization\. Performance is stable across a wide range ofα\\alpha, indicating that MDL acts as a robust regularizer\.

### 2\.3Rule Retrieval

At inference time, injecting all learned rules is inefficient and noisy, making retrieval necessary to select only rules relevant to the current query and tool context\.

#### 2\.3\.1Natural language based

A simple baseline retrieves rules directly from their natural\-language form by encoding the query and available tools with an off\-the\-shelf sentence embedding model and selecting the top\-kkrules by cosine similarity\. While easy to implement, this approach relies on generic embeddings that struggle with lexical variability and fine\-grained rule semantics\. Finetuning a dedicated embedding model introduces additional complexity, including limited training data, the need for ground\-truth rule annotations, and reduced scalability\.

#### 2\.3\.2Symbolic\-based

To address these limitations, and inspired by prior work on structure\-aware retrieval\(Munikotiet al\.,[2023](https://arxiv.org/html/2601.00086#bib.bib203); Liet al\.,[2023](https://arxiv.org/html/2601.00086#bib.bib204)\), we perform retrieval over the symbolic representation of rules\. By structuring both rules and queries into shared semantic fields, symbolic matching is more efficient, interpretable, and more robust to incidental linguistic variation than retrieval over raw text\.

Given a queryxqx\_\{q\}and available tools𝒮q\\mathcal\{S\}\_\{q\}, we first convert the state into a symbolic representationzqz\_\{q\}\. Retrieval proceeds in two stages\. First, a coarse filter removes inapplicable rules: decomposition rules are always retained, while tool\-use rules are filtered based on whether their scope matches the available tools or tool categories\. Second, the remaining rules are ranked by semantic similarity between their symbolic fields and those ofzqz\_\{q\}, using a generic embedding model\. We retain the top\-kkrules and inject them into the prompt in natural\-language form\. Unlike retrieval over raw text, similarity is computed over a fixed symbolic vocabulary, where NL\-to\-symbolic conversion has already resolved much of the lexical and structural variation that generic embeddings struggle to capture\.

Table 1:Number of examples in each dataset split\.DatasetTrainTestRandUnseenToolHop3927051BFCL:Live\-Multiple735175143BFCL:Multi\-Turn\-Base906050Table 2:Accuracy \(±\\pmstandard deviation, in %\) and number of rules at each learning stage\. Rule consolidation improves performance while reducing rule count\.ToolHopBFCLTest\-randTest\-unseen\# RulesTest\-randTest\-unseen\# RulesInitial26\.5±1\.326\.5\\scriptstyle\\pm 1\.335\.1±1\.635\.1\\scriptstyle\\pm 1\.6050\.1±0\.950\.1\\scriptstyle\\pm 0\.945\.0±1\.045\.0\\scriptstyle\\pm 1\.00\+ Rule Gen\.27\.6±1\.327\.6\\scriptstyle\\pm 1\.342\.1±1\.642\.1\\scriptstyle\\pm 1\.67254\.8±1\.354\.8\\scriptstyle\\pm 1\.347\.6±1\.447\.6\\scriptstyle\\pm 1\.4151\+ Consolid\.31\.1±1\.3\\mathbf\{31\.1\}\\scriptstyle\\pm 1\.343\.1±1\.6\\mathbf\{43\.1\}\\scriptstyle\\pm 1\.66756\.6±1\.2\\mathbf\{56\.6\}\\scriptstyle\\pm 1\.248\.5±1\.4\\mathbf\{48\.5\}\\scriptstyle\\pm 1\.4121Table 3:Accuracy \(±\\pmstandard deviation\) of LLMs on Toolhop and BFCL, with and without rules\. Rules are learned once from Llama3\.2 and reused across models\.LearnedfromAppliedonToolHopBFCLNo RulesRimRuleNo RulesRimRuleLlama3\.2Llama3\.226\.5±1\.326\.5\\scriptstyle\\pm 1\.331\.1±1\.3\\mathbf\{31\.1\}\\scriptstyle\\pm 1\.350\.1±0\.950\.1\\scriptstyle\\pm 0\.956\.6±1\.2\\mathbf\{56\.6\}\\scriptstyle\\pm 1\.2GPT\-4o58\.1±1\.458\.1\\scriptstyle\\pm 1\.457\.4±1\.457\.4\\scriptstyle\\pm 1\.471\.6±0\.871\.6\\scriptstyle\\pm 0\.875\.6±1\.1\\mathbf\{75\.6\}\\scriptstyle\\pm 1\.1Llama473\.8±1\.273\.8\\scriptstyle\\pm 1\.276\.7±1\.2\\mathbf\{76\.7\}\\scriptstyle\\pm 1\.275\.8±0\.875\.8\\scriptstyle\\pm 0\.877\.5±1\.1\\mathbf\{77\.5\}\\scriptstyle\\pm 1\.1O153\.2±1\.453\.2\\scriptstyle\\pm 1\.457\.4±1\.4\\mathbf\{57\.4\}\\scriptstyle\\pm 1\.475\.6±0\.875\.6\\scriptstyle\\pm 0\.877\.6±1\.1\\mathbf\{77\.6\}\\scriptstyle\\pm 1\.1GPT\-4oLlama3\.226\.5±1\.326\.5\\scriptstyle\\pm 1\.331\.3±1\.3\\mathbf\{31\.3\}\\scriptstyle\\pm 1\.350\.1±0\.950\.1\\scriptstyle\\pm 0\.952\.4±1\.3\\mathbf\{52\.4\}\\scriptstyle\\pm 1\.3GPT\-4o58\.1±1\.458\.1\\scriptstyle\\pm 1\.460\.3±1\.4\\mathbf\{60\.3\}\\scriptstyle\\pm 1\.471\.6±0\.871\.6\\scriptstyle\\pm 0\.876\.4±1\.1\\mathbf\{76\.4\}\\scriptstyle\\pm 1\.1Llama473\.8±1\.273\.8\\scriptstyle\\pm 1\.277\.4±1\.2\\mathbf\{77\.4\}\\scriptstyle\\pm 1\.275\.8±0\.875\.8\\scriptstyle\\pm 0\.877\.7±1\.0\\mathbf\{77\.7\}\\scriptstyle\\pm 1\.0O153\.2±1\.453\.2\\scriptstyle\\pm 1\.456\.1±1\.2\\mathbf\{56\.1\}\\scriptstyle\\pm 1\.275\.6±0\.875\.6\\scriptstyle\\pm 0\.877\.9±1\.1\\mathbf\{77\.9\}\\scriptstyle\\pm 1\.1Table 4:Comparison of prompting\-based adaptation methods on ToolHop and BFCL\.ToolHopBFCLTest\-randTest\-unseenTest\-randTest\-unseenZero\-shot26\.5±1\.326\.5\\scriptstyle~\\pm 1\.335\.1±1\.635\.1\\scriptstyle\\pm 1\.650\.1±0\.950\.1\\scriptstyle~\\pm 0\.945\.0±1\.045\.0\\scriptstyle\\pm 1\.0Few\-shot\(Liuet al\.,[2021](https://arxiv.org/html/2601.00086#bib.bib123)\)29\.9±1\.429\.9\\scriptstyle~\\pm 1\.437\.9±1\.437\.9\\scriptstyle~\\pm 1\.454\.5±0\.954\.5\\scriptstyle~\\pm 0\.946\.6±1\.446\.6\\scriptstyle~\\pm 1\.4SEE\(Cuiet al\.,[2025](https://arxiv.org/html/2601.00086#bib.bib121)\)27\.6±1\.527\.6\\scriptstyle~\\pm 1\.535\.9±1\.535\.9\\scriptstyle~\\pm 1\.552\.2±1\.052\.2\\scriptstyle~\\pm 1\.045\.5±1\.045\.5\\scriptstyle~\\pm 1\.0RimRule\(Ours\)31\.1±1\.3\\mathbf\{31\.1\}\\scriptstyle\\pm 1\.343\.1±1\.6\\mathbf\{43\.1\}\\scriptstyle\\pm 1\.656\.6±1\.2\\mathbf\{56\.6\}\\scriptstyle\\pm 1\.248\.5±1\.4\\mathbf\{48\.5\}\\scriptstyle\\pm 1\.4Table 5:Performance with and withoutRimRulefor finetuned models\.ToolHopBFCLTest\-randTest\-unseenTest\-randTest\-unseenSFT \(Llama3\.2\)43\.8±1\.443\.8\\scriptstyle~\\pm 1\.438\.5±1\.538\.5\\scriptstyle~\\pm 1\.565\.0±0\.965\.0\\scriptstyle~\\pm 0\.958\.7±1\.458\.7\\scriptstyle~\\pm 1\.4\+RimRule50\.0±1\.4\\mathbf\{50\.0\}\\scriptstyle~\\pm 1\.445\.1±1\.6\\mathbf\{45\.1\}\\scriptstyle~\\pm 1\.668\.6±1\.2\\mathbf\{68\.6\}\\scriptstyle~\\pm 1\.262\.7±1\.3\\mathbf\{62\.7\}\\scriptstyle~\\pm 1\.3Function Calling \(GPT4o\)63\.8±1\.463\.8\\scriptstyle~\\pm 1\.483\.0±1\.283\.0\\scriptstyle~\\pm 1\.279\.6±0\.779\.6\\scriptstyle~\\pm 0\.777\.2±0\.877\.2\\scriptstyle~\\pm 0\.8\+RimRule66\.1±1\.4\\mathbf\{66\.1\}\\scriptstyle~\\pm 1\.485\.4±1\.1\\mathbf\{85\.4\}\\scriptstyle~\\pm 1\.181\.7±1\.0\\mathbf\{81\.7\}\\scriptstyle~\\pm 1\.079\.8±1\.0\\mathbf\{79\.8\}\\scriptstyle~\\pm 1\.0

## 3Experiments

### 3\.1Datasets

We evaluate our method on two tool\-use benchmarks:ToolHop666[https://hf\.co/datasets/bytedance\-research/ToolHop](https://hf.co/datasets/bytedance-research/ToolHop), CC BY 4\.0 licenseYeet al\.\([2025](https://arxiv.org/html/2601.00086#bib.bib80)\)andBFCL777[https://hf\.co/datasets/gorilla\-llm/Berkeley\-Function\-Calling\-Leaderboard](https://hf.co/datasets/gorilla-llm/Berkeley-Function-Calling-Leaderboard), Apache license 2\.0Yanet al\.\([2024](https://arxiv.org/html/2601.00086#bib.bib81)\)\. ToolHop consists of compositional, multi\-turn queries requiring multi\-step tool reasoning, while thelive\-multiplesubset of BFCL provides a complementary single\-step setting with a larger and more diverse tool set, making tool selection more challenging\.

For both datasets, we assume access to ground\-truth execution traces during training, but no ground\-truth rules are provided\. To evaluate generalization, we define two splits:test\-rand, a random in\-distribution split, andtest\-unseen, a held\-out split containing queries with tools not seen during training\. Dataset statistics are summarized in Table[1](https://arxiv.org/html/2601.00086#S2.T1)\.

### 3\.2Baselines

We compareRimRuleagainst several established adaptation paradigms:

- •Few\-shot in\-context learningretrieves top\-kktraining examples based on semantic similarity\(Liuet al\.,[2021](https://arxiv.org/html/2601.00086#bib.bib123)\)\.
- •Prompt optimizationwith SEE\(Cuiet al\.,[2025](https://arxiv.org/html/2601.00086#bib.bib121)\), which performs global prompt optimization by jointly evolving instructions and demonstrations\.
- •Finetuning, including supervised finetuning \(SFT\) of open\-source models using LoRA\(Huet al\.,[2022](https://arxiv.org/html/2601.00086#bib.bib116)\), as well as closed\-source models tuned for function calling\. For SFT, we construct training data from ground\-truth execution traces, training the model to generate correct tool selections and arguments conditioned on the query, available tools, and previous tool\-call results\.

All methods, including ours, use aReAct\-style prompting framework\(Yaoet al\.,[2023](https://arxiv.org/html/2601.00086#bib.bib19)\)for tool\-use reasoning, allowing agents to generate intermediate steps and tool calls interactively\. We permit agents to retry based on tool feedback or error messages, a common robustness mechanism that nonetheless struggles with systematic reasoning errors\. Our method builds on this setup by injecting explicit rules to prevent such failures\.

We use short names for evaluated models:Llama3\.2888meta\.llama3\-2\-3b\-instruct\-v1\-0,Llama4999meta\.llama4\-maverick\-17b\-instruct\-v1\-0,GPT\-4o101010gpt\-4o\-2024\-11\-20, andO1111111o1\-mini\-2024\-09\-12, whereO1is a long\-reasoning model\.

The symbolic representation supports rule consolidation and retrieval, not direct symbolic execution\. Because the tool\-use tasks we study involve noisy natural\-language queries and environments, purely symbolic rule application is brittle; accordingly, we do not compare against symbolic rule learners designed for clean, structured data\(Quinlan,[1990](https://arxiv.org/html/2601.00086#bib.bib27); Clark and Niblett,[1989](https://arxiv.org/html/2601.00086#bib.bib182); Cohen,[1995](https://arxiv.org/html/2601.00086#bib.bib8); Fürnkranz,[1997](https://arxiv.org/html/2601.00086#bib.bib10)\)\. Instead, rules are applied in natural\-language form to guide LLM reasoning\.

## 4Results and Discussion

### 4\.1Learning Process

Table[2](https://arxiv.org/html/2601.00086#S2.T2)illustrates the learning trajectory using Llama3\.2 as a representative example\. Other models exhibit similar trends\.

Starting from an empty rule library, we collect failure traces from a zero\-shot agent and generate candidate rules, yielding 72 rules on ToolHop and 151 on BFCL121212See Appendix for sample rules\. This initial rule set improves accuracy on both test\-rand and test\-unseen splits\.

Applying MDL\-guided consolidation further reduces the rule count \(by 7% on ToolHop and 20% on BFCL\) while improving performance on test\-rand and yielding smaller but consistent gains on test\-unseen\. Overall, the process produces a compact, interpretable rule library that improves both in\-distribution and out\-of\-distribution generalization\.

### 4\.2Case Study

Table[6](https://arxiv.org/html/2601.00086#S4.T6)shows a representative failure where the agent directly queries a complex familial relationship, leading to a tool error\.RimRuleidentifies the root cause as improper decomposition and induces a rule that enforces stepwise resolution of intermediate entities\. The resulting rule is abstract and reusable, and its symbolic form enables reliable retrieval for similar queries\. This example illustrates how failure traces are converted into compact rules that correct systematic reasoning errors beyond the original instance\.

Table 6:Case study illustrating failure\-driven rule induction and symbolic representation\.QueryHow many letters \(excluding the first and last\) are there in the first name of Viacheslav I of Kiev’s maternal grandfather?FailureThe agent directly queriesViacheslav I of Kiev’s maternal grandfather\. The tool returns an error:“no data found”\.Proposed RuleIf the user query involves identifying a specific familial relationship \(e\.g\., maternal grandfather\), then decompose the task by first resolving intermediate relationships \(e\.g\., mother, father\) sequentially\.Symbolic Formifdomain=FAMILIAL\_RELATIONSHIPortool\_category=GENEALOGY\_QUERY,then action=\[DECOMPOSE\_QUERY, RESOLVE\_INTERMEDIATE\_ENTITY, SEQUENCE\_SUBTASKS\]strength=MANDATORY
### 4\.3Re\-usability Across LLMs

Humans can share heuristics because they are interpretable across contexts\. By encoding adaptation as symbolic, human\-readable rules, our method enables knowledge to be reused across LLMs without retraining\.

We learn two rule libraries from failure traces produced byLlama3\.2andGPT\-4o, and apply them to models of varying size and reasoning strength, evaluating performance on the test\-rand split\. Table[3](https://arxiv.org/html/2601.00086#S2.T3)shows consistent gains in both directions:strong\-to\-weaktransfer improves smaller models, whileweak\-to\-strongtransfer benefits strong reasoning models such asO1andLlama4\. These results suggest that symbolic rules capture transferable failure patterns not resolved by scale alone\.

Table 7:Test\-rand accuracy \(±\\pmstandard deviation, in %\) comparing retrieval strategies\.MethodToolHopBFCLNat\. Lang\. based29\.4±1\.329\.4\\scriptstyle\\pm 1\.354\.1±1\.054\.1\\scriptstyle\\pm 1\.0Symbolic guided31\.1±1\.3\\mathbf\{31\.1\}\\scriptstyle\\pm 1\.356\.6±1\.2\\mathbf\{56\.6\}\\scriptstyle\\pm 1\.2
### 4\.4Performance on Small Dataset

We evaluateRimRulein a low\-resource setting on themulti\_turn\_basesplit of BFCL using only 90 training samples\. Despite limited supervision, the method learns just four rules \(Appendix[A\.2](https://arxiv.org/html/2601.00086#A1.SS2)\) yet achieves substantial gains: accuracy improves from55\.2%55\.2\\%to62\.1%62\.1\\%on test\-rand and from46\.0%46\.0\\%to60\.0%60\.0\\%on test\-unseen\. These results highlight the sample efficiency and practical applicability of rule\-based adaptation\.

### 4\.5Outperforming Prompting\-based Methods

We compareRimRuleagainst prompting\-based adaptation methods, including ReAct prompting\(Yaoet al\.,[2023](https://arxiv.org/html/2601.00086#bib.bib19)\), few\-shot in\-context learning\(Liuet al\.,[2021](https://arxiv.org/html/2601.00086#bib.bib123)\), and prompt optimization with SEE\(Cuiet al\.,[2025](https://arxiv.org/html/2601.00086#bib.bib121)\)\. As shown in Table[4](https://arxiv.org/html/2601.00086#S2.T4),RimRuleconsistently outperforms all prompting baselines on both ToolHop and BFCL, across test\-rand and test\-unseen splits, demonstrating stronger generalization than fixed\-prompt approaches\.

### 4\.6Complementing Finetuned Models

As shown in Table[5](https://arxiv.org/html/2601.00086#S2.T5), addingRimRuleto finetuned models yields consistent gains, especially on the test\-unseen split, indicating that symbolic rules correct residual systematic errors left by supervised training\. We observe similar improvements when applyingRimRuleto models with native function\-calling capabilities \(Table[5](https://arxiv.org/html/2601.00086#S2.T5)\), showing that rule\-based adaptation operates along an orthogonal axis of generalization\.

Table 8:Test\-rand accuracy \(±\\pmstandard deviation, in %\) comparing consolidation strategies\.MethodToolHopBFCLPrompt\-based27\.5±1\.427\.5\\scriptstyle\\pm 1\.452\.1±0\.952\.1\\scriptstyle\\pm 0\.9MDL\-guided31\.1±1\.3\\mathbf\{31\.1\}\\scriptstyle\\pm 1\.356\.6±1\.2\\mathbf\{56\.6\}\\scriptstyle\\pm 1\.2
### 4\.7Ablation Studies

##### Impact of retrieval method\.

Table[7](https://arxiv.org/html/2601.00086#S4.T7)shows that symbolic retrieval consistently outperforms retrieval based on raw natural\-language similarity on both datasets\.

##### Impact of consolidation method\.

As shown in Table[8](https://arxiv.org/html/2601.00086#S4.T8), MDL\-guided consolidation significantly outperforms prompt\-based rule merging\. Together, these results indicate that both symbolic retrieval and MDL\-based consolidation are essential to our approach\.

## 5Related Work

##### Rule Learning\.

Recent work studies rule learning with LLMs via prompting, extracting rules from demonstrationsGao and Das \([2024](https://arxiv.org/html/2601.00086#bib.bib167)\), graphsChenet al\.\([2024](https://arxiv.org/html/2601.00086#bib.bib72)\), or tracesZhanget al\.\([2024](https://arxiv.org/html/2601.00086#bib.bib56)\)to guide generationZhouet al\.\([2024](https://arxiv.org/html/2601.00086#bib.bib57)\); Wanget al\.\([2024b](https://arxiv.org/html/2601.00086#bib.bib58)\)\. Other approaches use rules at training time for synthetic supervisionMorishitaet al\.\([2024](https://arxiv.org/html/2601.00086#bib.bib69)\), reward modelingWang and Xiong \([2025](https://arxiv.org/html/2601.00086#bib.bib32)\), or distillationSadeqet al\.\([2025](https://arxiv.org/html/2601.00086#bib.bib98)\), or store rules in memoryWanget al\.\([2024c](https://arxiv.org/html/2601.00086#bib.bib70)\)\. In contrast to these largely static or training\-time uses, we learn and consolidate rules from failures for dynamic inference\-time reuse\.

##### Tool\-use Agents\.

Tool\-use agents often rely on retriever–generator pipelines or finetuning to select and call tools\(Qinet al\.,[2023](https://arxiv.org/html/2601.00086#bib.bib73); Patilet al\.,[2023](https://arxiv.org/html/2601.00086#bib.bib22)\), or train models to use tools via self\-supervision or agent tuning\(Schicket al\.,[2023](https://arxiv.org/html/2601.00086#bib.bib20)\)\. Recent work further explores reinforcement learning and agent\-centric optimization for tool use\(Leet al\.,[2025](https://arxiv.org/html/2601.00086#bib.bib206); Zhanget al\.,[2025](https://arxiv.org/html/2601.00086#bib.bib208)\), as well as generative approaches that tokenize tools for unified retrieval and calling\(Haoet al\.,[2023](https://arxiv.org/html/2601.00086#bib.bib201); Wanget al\.,[2024a](https://arxiv.org/html/2601.00086#bib.bib202)\)\. While effective, these approaches primarily encode adaptation in model parameters\. We instead externalize adaptation as a compact, interpretable rule library, enabling modular reuse across LLMs without retraining\.

## 6Conclusion

We proposeRimRule, an approach that adapts LLMs by distilling compact, interpretable rules from failure traces and applying them at inference time\. Without modifying model weights, our method improves both in\- and out\-of\-distribution performance, outperforms prompting\-based methods, and complements finetuned models\. These results position inference\-time rule learning as a practical path toward modular and interpretable LLM adaptation\.

## 7Limitations

Our approach assumes access to failure signals during training, such as execution traces or reliable performance feedback, which may not be available in all deployment settings\. Rule consolidation is performed using a greedy MDL\-based procedure; while efficient and effective at the scales studied, it does not guarantee a globally optimal rule set, and alternative optimization methods deserve future study\. In addition, the symbolic representation relies on a manually designed schema intended for noisy natural\-language tool\-use tasks; other domains may benefit from different symbolic abstractions\. Finally, the effectiveness of learned rules depends on the quality and diversity of observed failures, and gains may be smaller in domains with sparse or highly idiosyncratic errors\.

##### Potential Risks\.

As with any adaptive system, learned rules could overgeneralize or reflect biases present in observed failures if applied outside their intended scope\. We mitigate such risks by keeping rules interpretable and applied at inference time, enabling auditing, revision, or removal\. Future work may further explore safeguards for monitoring and validating rule usage in high\-stakes settings\.

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- Y\. Zhang, P\. Xiao, L\. Wang, C\. Zhang, M\. Fang, Y\. Du, Y\. Puzyrev, R\. Yao, S\. Qin, Q\. Lin,et al\.\(2024\)RuAG: learned\-rule\-augmented generation for large language models\.arXiv preprint arXiv:2411\.03349\.External Links:[Link](https://arxiv.org/abs/2411.03349)Cited by:[§5](https://arxiv.org/html/2601.00086#S5.SS0.SSS0.Px1.p1.1)\.
- P\. Zhou, J\. Pujara, X\. Ren, X\. Chen, H\. Cheng, Q\. V\. Le, E\. Chi, D\. Zhou, S\. Mishra, and H\. S\. Zheng \(2024\)Self\-discover: large language models self\-compose reasoning structures\.Advances in Neural Information Processing Systems37,pp\. 126032–126058\.External Links:[Link](https://arxiv.org/abs/2402.03620)Cited by:[§5](https://arxiv.org/html/2601.00086#S5.SS0.SSS0.Px1.p1.1)\.

## Appendix AAppendix

### A\.1Prompts

This section includes the prompts used throughout our pipeline: for generating rules from failure traces, discovering and updating the classification vocabulary, and translating rules into canonical form\. Prompts are shown as used, with placeholders for query, tools, and traces\.

YouareaseniorAIsystemsinstructortaskedwithhelpingatool\-usinglanguagemodel,referredtoastheToolAgent,improveitsabilitytousetoolsaccurately,efficiently,andreliably,evenwithnewtoolsandunseenqueriesthatarestructurallyand/orsemanticallysimilartopreviouslyseenexamples\.YourroleistoreviewincorrecttoolusagetracesproducedbytheToolAgent,comparethemagainstthecorrect\(groundtruth\)traces,andanalyzeanyembeddederrormessagestoreasonabouttheerror\.

Anincorrecttraceoccurswhenaquery’sexecutionbytheToolAgentdoesn’tmatchthegroundtruthanswer\.Incorrecttracesareeithercomplete\(finishedbutincorrect\)orincompleteduetounrecoverableexecutionerrors\.YouwillbeprovidedwiththeToolAgent’sfullexecutiontrace,includingembeddederrormessages\.

Therearetwotypesoferrors:

i\.Reasoningerrors\(toanalyzeandgeneraterulesfor\)

ii\.Propagationerrors\(toignore,astheyresultfrompriormistakes\)

Stepsmaycontain:

\(i\)noerrors,\(ii\)onlypropagationerrors,or\(iii\)oneormorereasoningerrors\.

Yourgoalistoextractgeneralizable,tool\-schema\-aware,andcontext\-sensitiverulesthatcanguidefuturetoolusage\-evenwithunseenqueriesandschemas\.Thinklikeameta\-cognitiveteacher:diagnoserootcausesandarticulateprecise,reusableabstractions\.

Youwillnowbegiven:

1\.Theuserquery\[INSERTUSERQUERY\]

2\.Theavailabletools\[INSERTTOOLSCHEMAJSON\]

3\.Theincorrecttrace\[INSERTTOOLAGENTTRACE\]

4\.Thegroundtruthtrace\[INSERTGROUNDTRUTHTRACE\]

Yourtaskistoidentifyreasoningerrorsbycomparingthetraces\.

Check:

\-Weresubtasksidentifiedcorrectly?

\-Werethecorrecttoolsselected?

\-Weretheargumentsconstructedcorrectly?

Guidelinesforrulegeneration:

\-Onlygeneraterulesforreasoningerrors

\-Identifyrootcauses,notsuperficialfixes

\-Rulesmustbegeneralizableandschema\-aware

\-Rulesmustnotcontainquery\-specificortool\-specifictokens

\-Eachrulemustbeatomicandclassifiableas:

a\.decompositionerror

b\.toolselectionerror

c\.toolargumentserror

\-Ifmultiplereasoningfailuresoccur,generatemultiplerulesunlessclarityispreserved

Rulesmustbesymbolic,composable,andconformtoastandardform\(e\.g\.,condition=\>action\)\.

Outputformat:

First,writeabriefanalysisexplainingtherootcauseanderrortype\.

Thenoutputoneruleonly,usingthisJSONstructure:

\{

"new\_rule":"<generalizedif\-thenrule\>",

"error\_type":"<decompositionerror/toolselectionerror/toolargumentserror\>"

\}

Listing 1:Prompt used to generate reasoning rules from failure traces\. Placeholders like user query and tool schemas are injected at runtime\.Youareanexpertruleclassificationspecialist\.

YourtaskistoCREATEtheinitialvocabularyforruleclassificationbasedontheprovidedfielddefinitions\.

Analyzetherulescarefullyandcreatecomprehensivecategoriesthatcoverallruletypes\.

Useonlyuppercaseletters,numbers,andunderscoresfortokennames\.

ReturnonlyvalidJSONformat\.

Createinitialvocabularyforruleclassificationbasedonthesedefinitions:

FIELDDEFINITIONS:

DOMAIN\(enum\):Broadtopicaldomain,inferredjointlyfromrulecontent\+toolcontext\+querycontext\.

QUALIFIER\(enum\):Fine\-grainedsituationaltagsthataremorespecificthandomain\.

ACTION\(enum\):Theaction\(s\)theruleprescribes,fromaclosedset\.

STRENGTH\(enum\):Ruleactionpriority\(must,may\)\.Samescope/domain/qualifier,higherpriorityshouldberetrievedratherthanlowpriority\.

Examples:MANDATORY,RECOMMENDED,OPTIONAL

TOOL\_CATEGORY\(enum\):Toolfunctionalcategorybasedontoolcapabilitiesandusagepatterns\.

Thisshouldrepresentbroadtooltypesthatcangroupsimilartoolstogether\.

Examples:DATA\_PROCESSING,SEARCH\_ENGINE,COMPUTATION,TEXT\_PROCESSING\.\.\.

Rulestoanalyze:

\[INSERT\_BULLETS\_HERE\]

Createacomprehensivevocabularycoveringallruletypesintheaboverules\.

Useonlyuppercaseletters,numbers,andunderscoresforcategorynames\.

ReturnJSON:

\{

"vocab\_version":"v1",

"domain":\[\.\.\.\],

"qualifier":\[\.\.\.\],

"action":\[\.\.\.\],

"strength":\[\.\.\.\],

"tool\_category":\[\.\.\.\]

\}

Listing 2:Prompt used to induce the rule classification vocabulary from a batch of rules\. Placeholders are filled dynamically\.Youareanexpertruleclassificationspecialist\.

YourtaskistoUPDATEandEXPANDanexistingvocabularybasedonnewrules\.

Reviewthecurrentvocabulary,identifymissingcategoriesfromnewrules,andreturnthecompleteupdatedvocabulary\.

Useonlyuppercaseletters,numbers,andunderscoresfortokennames\.

Avoidduplicatesandmaintainconsistencywithexistingcategories\.

ReturnonlyvalidJSONformat\.

Updateandexpandvocabularyforruleclassification\.

FIELDDEFINITIONS:

DOMAIN\(enum\):Broadtopicaldomain,inferredjointlyfromrulecontent\+toolcontext\+querycontext\.

QUALIFIER\(enum\):Fine\-grainedsituationaltagsthataremorespecificthandomain\.

ACTION\(enum\):Theaction\(s\)theruleprescribes,fromaclosedset\.

STRENGTH\(enum\):Ruleactionpriority\(must,may\)\.Samescope/domain/qualifier,higherpriorityshouldberetrievedratherthanlowpriority\.

TOOL\_CATEGORY\(enum\):Toolfunctionalcategorybasedontoolcapabilitiesandusagepatterns\.

Currentaccumulatedvocabulary:

DOMAIN:\[INSERTCURRENTDOMAINSOR’Noneyet’\]

QUALIFIER:\[INSERTCURRENTQUALIFIERSOR’Noneyet’\]

ACTION:\[INSERTCURRENTACTIONSOR’Noneyet’\]

STRENGTH:\[INSERTCURRENTSTRENGTHSOR’Noneyet’\]

TOOL\_CATEGORY:\[INSERTCURRENTTOOL\_CATEGORIESOR’Noneyet’\]

Newrulestoanalyze:

\[INSERTNEWRULEBULLETSHERE\]

Instructions:

1\.Reviewthecurrentvocabularyabove

2\.Analyzethenewrulestoidentifyanymissingcategories

3\.Addnewcategoriesifneeded,butavoidduplicates

4\.Keepexistingcategoriesthatarestillrelevant

5\.Returnthecompleteupdatedvocabulary

ReturnJSONwithallcategories\(existing\+new\):

\{

"domain":\["existing\_domains","new\_domains\_if\_any"\],

"qualifier":\["existing\_qualifiers","new\_qualifiers\_if\_any"\],

"action":\["existing\_actions","new\_actions\_if\_any"\],

"strength":\["existing\_strengths","new\_strengths\_if\_any"\],

"tool\_category":\["existing\_tool\_categories","new\_tool\_categories\_if\_any"\]

\}

Listing 3:Prompt used to update and expand the rule classification vocabulary using newly generated rules\.Youareanexpertruleclassificationspecialist\.

Yourtaskistoclassifyindividualrulesusingtheprovidedvocabulary\.

Analyzetherulecontent,toolcontext,andquerycontexttodeterminethemostappropriateclassification\.

Chooseonlyfromthegivenvocabularyoptions\.

ReturnonlyvalidJSONformat\.

Vocabenumerations:

\-domain:\[INSERTdomainlist\]

\-qualifier:\[INSERTqualifierlist\]

\-action:\[INSERTactionlist\]

\-strength:\[INSERTstrengthlist\]

\-tool\_category:\[INSERTtool\_categorylist\]

Ruletoclassify\(analyzeallfieldsforcontext\):

\[INSERTRULEOBJECTASJSON\]

ClassificationGuidelines:

DOMAIN:Inferfromrulecontent\+toolcontext\+querycontext\.Choosethebroadestapplicabledomainthatcoverstherule’stopic\.

QUALIFIER:Selectfine\-grainedsituationaltagsthataremorespecificthandomain\.Youcanselectmultiplequalifiersiftheruleappliestomultiplesituations\.Focusonconditions,constraints,orspecificcontextsmentionedintherule\.

ACTION:Identifythespecificaction\(s\)theruleprescribes\.Choosefromtheclosedsetofavailableactions\.Youcanselectmultipleactionsiftheruleprescribesmultiplesteps\.

STRENGTH:Determinerulepriority\(must,may\)\.MANDATORY=mustfollow,RECOMMENDED=shouldfollow,OPTIONAL=mayfollow\.Considertherule’slanguageandcontexttodeterminepriority\.

TOOL\_CATEGORY:Identifythefunctionalcategoryofthetool\(s\)usedinthisrule\.Choosefromtheavailabletoolcategoriesbasedonthetool’scapabilitiesandusagepattern\.Thisshouldrepresentthebroadfunctionaltypeofthetool\(e\.g\.,DATA\_PROCESSING,SEARCH\_ENGINE,COMPUTATION\)\.

ReturnONLYvalidJSONmatchingthisschema:

\{

"\_id":0,

"domain":"FAMILIAL\_RELATIONSHIPS",

"qualifier":\["SEQUENTIAL","MULTI\_STEP"\],

"action":\["DECOMPOSE","VALIDATE"\],

"strength":"MANDATORY",

"tool\_category":"DATA\_PROCESSING"

\}

Listing 4:Prompt used to classify individual rules using a fixed vocabulary\. Vocabulary values and rule content are injected at runtime\.
### A\.2Sample Rules

Below, we present a representative subset of learned rules\. Each rule is shown in natural language along with its corresponding symbolic representation\.

1\.Iftheuserqueryinvolvesidentifyingacomplexrelationship\(e\.g\.,step\-relative\)andtheavailabletoolsdonotdirectlysupporttherequestedrelationshiptype,thendecomposethequeryintointermediatesubtasksthatprogressivelyresolvetherelationshipthroughsimpler,directlysupportedrelationshiptypes\.

if\(domain=RELATIONSHIP\_RESOLUTIONandqualifier=\[RELATIONSHIP\_CHAIN

\_TRAVERSAL,INTERMEDIATE\_ENTITY\_IDENTIFICATION\]\)then\(action=\[DECOMPOSE\_QUERY,RESOLVE\_INTERMEDIATE\_ENTITY\]\)withstrength=MANDATORY

2\.Ifaqueryinvolvesdeterminingapropertyofanobjectderivedfromintermediatesteps\(e\.g\.,counting,analyzing,ortransforminganattributeofanentity\),thenthedecompositionmustexplicitlyincludeasubtasktoapplytheappropriateprocessortransformationtothederivedattribute\.

if\(domain=QUERY\_DECOMPOSITIONandqualifier=\[MULTI\_STEP\_REASONING,DERIVATIVE\_ENTITY\]\)then\(action=\[DECOMPOSE\_QUERY,TRANSFORM\_INPUT\]\)withstrength=MANDATORY

3\.Ifaqueryfailsduetoinsufficientorincompletedatareturnedbyatool,thenrefinetheinputargumentsbyincludingoptionalparametersthatprovideadditionalcontext\(e\.g\.,variantsofnames,timeperiods,regions,orotherapplicableconstraints\)toimprovedataretrievalaccuracy\.

if\(domain=TOOL\_ARGUMENT\_VALIDATIONandqualifier=\[INCOMPLETE\_DATA

\_REFINEMENT\]\)then\(action=\[REFINE\_INPUT\_ARGUMENTS,HANDLE\_INCOMPLETE\_DATA\]\)withstrength=RECOMMENDED

4\.Ifaqueryinvolvesdetermininganattribute\(e\.g\.,date,location,event\)ofanentitythatisrelatedtoanotherentity\(e\.g\.,familymember\),thendecomposethequerytofirstidentifytherelatedentitybeforeattemptingtodetermineitsattribute\.

if\(domain=QUERY\_DECOMPOSITIONandqualifier=\[RELATIONSHIP\_CHAIN\_

TRAVERSAL,INTERMEDIATE\_ENTITY\_IDENTIFICATION\]\)then\(action=\[DECOMPOSE\_QUERY,RESOLVE\_INTERMEDIATE\_ENTITY\]\)withstrength=MANDATORY

5\.Ifthesubtaskrequiresextractingaspecificsubsetofinformation\(e\.g\.,firstnamefromafullname\),thenconstructargumentsforthetooltorestricttheoutputtomatchtherequestedsubsetbyenablingrelevantoptionalparametersexplicitly,whileleavingunrelatedparametersattheirdefaults\.

if\(domain=NAME\_PROCESSINGandqualifier=\[NAME\_COMPONENT\_EXTRACTION\]\)then\(action=\[CONSTRUCT\_ARGUMENTS,REFINE\_INPUT\_ARGUMENTS\]\)withstrength=MANDATORY

6\.Iftheuserqueryinvolvesidentifyinginformationaboutaspecificfamilialrelationshipacrossmultiplegenerations\(e\.g\.,paternalgrandfather\),thendecomposethequerysuchthatthefamilialrelationshipisresolveddirectlyusingtoolsdesignedtoretrievegenealogicaldata,withoutredundantlyextractingunrelatedimmediaterelationships\.

if\(domain=RELATIONSHIP\_RESOLUTIONandqualifier=\[FAMILIAL\_RELATIONSHIP,RELATIONSHIP\_CHAIN\_TRAVERSAL\]\)then\(action=\[DECOMPOSE\_QUERY,IDENTIFY\_RELATIONSHIP\]\)withstrength=MANDATORY

7\.Ifaqueryinvolvesdeterminingtheancestryofapersonbasedonaspecificfamilialrelationship\(e\.g\.,maternalgrandfather\),thendecomposethetaskintosubtasksthatsequentiallyqueryeachfamiliallink\(e\.g\.,mother,mother’sfather\)andensureintermediateresultsareusedtorefinesubsequentsubtasks\.

if\(domain=HIERARCHICAL\_RELATIONSHIPSandqualifier=\[FAMILIAL\_RELATIONSHIP,RELATIONSHIP\_CHAIN\_TRAVERSAL,INTERMEDIATE\_ENTITY\_IDENTIFICATION\]\)then\(action=\[DECOMPOSE\_QUERY,SEQUENCE\_SUBTASKS,RESOLVE\_INTERMEDIATE\_ENTITY\]\)withstrength=MANDATORY

8\.Ifaqueryinvolvesidentifyinganentityindirectlyrelatedtoanother\(e\.g\.,thefounderofapoliticalpartyidentifiedinapreviousstep\),thenensurethatintermediatesubtaskschainoutputslogicallybyqueryingtherelationshipexplicitlyratherthanassumingassociationsprovidedinthequery\.

if\(domain=INDIRECT\_ENTITY

\_IDENTIFICATIONandqualifier=\[RELATIONSHIP\_CHAIN

\_TRAVERSAL,INTERMEDIATE\_ENTITY\_IDENTIFICATION\]\)then\(action=\[SEQUENCE\_SUBTASKS,RESOLVE\_INTERMEDIATE\_ENTITY\]\)withstrength=MANDATORY

9\.Ifaqueryinvolvesretrievinginformationaboutanindividual’srelative,thedecompositionmustincludeasubtasktoexplicitlyidentifytherelativebeforeretrievingspecificinformationaboutthem\.

if\(domain=RELATIONSHIP\_RESOLUTIONandqualifier=\[FAMILIAL\_RELATIONSHIP,RELATIONSHIP\_CHAIN\_TRAVERSAL\]\)then\(action=\[DECOMPOSE\_QUERY,RESOLVE\_INTERMEDIATE\_ENTITY\]\)withstrength=MANDATORY

10\.Ifthesubtaskinvolvesidentifyingafamilialorsocialrelationshipbetweenentities,thenselectatooldesignedtoqueryrelationships,anddonotselectatooldesignedforextractingnamecomponentsorparsingnames\.

if\(domain=RELATIONSHIP\_RESOLUTIONandqualifier=\[FAMILIAL\_RELATIONSHIP,RELATIONSHIP\_CHAIN\_TRAVERSAL\]\)then\(action=\[MATCH\_TOOL\_TO\_SUBTASK\]\)withstrength=MANDATORY

Listing 5:Sample rules learned from the ToolHop dataset1\.Ifareasoningprocessidentifiesasubtaskrequiringtool\-basedexecution,thenensurethetoolnamegeneratedintheoutputmatchesexactlywithoneoftheavailabletoolsintheschema\.Useschemavalidationtoconfirmthatthegeneratedtoolnameexistsbeforefinalizingtheresponse\.

if\(domain=TRANSPORTATIONandqualifier=\[SCHEMA\_VALIDATION,TOOL\_SELECTION\_ERROR\]\)then\(action=\[CONFIRM\_SCHEMA\_COMPLIANCE,SELECT\_TOOL\_BASED\_ON\_QUERY\]\)withstrength=MANDATORY

2\.IFthequeryinvolvesretrievinggeneralinformationaboutanentity,concept,oreventthatisnotexplicitlytiedtorecentupdatesortemporalrelevance,THENselectatooldesignedforgeneralwebsearchesinsteadofatoolspecializedforretrievingrecentnewsorupdates\.

if\(domain=GENERAL\_INFORMATION

\_RETRIEVALandqualifier=\[TOOL\_SELECTION\_ERROR\]\)then\(action=\[SELECT\_TOOL\_BASED\_ON\_QUERY\]\)withstrength=MANDATORY

3\.Ifthesubtaskrequirescheckingavailabilityorstocklevelsforspecificproductattributes\(e\.g\.,sizes,stockcount\),thenselectatoolwhoseschemaexplicitlysupportsinventory\-relatedoperations,ratherthanusingatooldesignedforgeneralproductdetails\.

if\(domain=INVENTORY\_MANAGEMENTandqualifier=\[TOOL\_SELECTION\_ERROR\]\)then\(action=\[SELECT\_TOOL\_BASED\_ON\_QUERY\]\)withstrength=MANDATORY

4\.Ifthesubtaskinvolvescheckingtheavailabilityofaspecificattribute\(e\.g\.,size,color,orstock\)foraproduct,thenselectatoolwhoseschemaexplicitlyincludesfunctionalityforqueryingavailabilityofattributesratherthanretrievinggeneralproductdetails\.

if\(domain=INVENTORY\_MANAGEMENTandqualifier=\[TOOL\_SELECTION\_ERROR\]\)then\(action=\[SELECT\_TOOL\_BASED\_ON\_QUERY\]\)withstrength=MANDATORY

5\.Ifauserqueryexplicitlyprovidesavalueforaparameter,regardlessofwhethertheparameterhasadefaultvalueintheschema,prioritizetheuser\-providedvalueoverthedefaultvaluewhenconstructingarguments\.

if\(domain=DATABASE\_MANAGEMENTandqualifier=\[USER\_QUERY\_VALUE\_PRIORITY,DEFAULT\_VALUE\_ASSIGNMENT\]\)then\(action=\[PRIORITIZE\_USER\_VALUE,CONSTRUCT\_TOOL\_ARGUMENTS\]\)withstrength=MANDATORY

6\.Iftheuserqueryexplicitlyrequestsunderstanding,explanation,orhelpaboutafunctionality,thenselectatooldesignedtoprovideinformationalassistanceratherthanoneintendedforoperationalexecution\.

if\(domain=GENERAL\_INFORMATION\_RETRIEVALandqualifier=\[TOOL\_SELECTION\_ERROR\]\)then\(action=\[SELECT\_TOOL\_BASED\_ON\_QUERY\]\)withstrength=MANDATORY

7\.Iftheintendedactionistoretrieveinformationbasedonuser\-specifiedfiltersorconstraints,thenselectatoolthatexplicitlysupportsfilteringorconstraint\-basedretrievalinitsschemadescription\.Ensurethesubtaskalignsdirectlywiththetool’sprimaryfunctionasspecifiedinitsschema\.

if\(domain=GENERAL\_INFORMATION\_RETRIEVALandqualifier=\[TOOL\_SELECTION\_ERROR\]\)then\(action=\[SELECT\_TOOL\_BASED\_ON\_QUERY\]\)withstrength=MANDATORY

8\.Ifasubtaskinvolvesidentifyingavailableoptionsorexploringpossiblechoicesforaresource\(e\.g\.,accommodations,flights,attractions\),thenselectatooldesignedforsearchingorbrowsingthoseresourcesratherthanatooldesignedforfinalizingorreservingthem\.

if\(domain=GENERAL\_INFORMATION\_RETRIEVALandqualifier=\[TOOL\_SELECTION\_ERROR\]\)then\(action=\[SELECT\_TOOL\_BASED\_ON\_QUERY\]\)withstrength=MANDATORY

9\.Iftheuserqueryspecifiesaconstraintrelatedtoanentity\(e\.g\.,actorname,directorname,genre,etc\.\),thenconstructthecorrespondingparametervaluebydirectlyextractingtheentitymentionedinthequery,insteadofusingdefaultorplaceholdervalues\.

if\(domain=GENERAL\_INFORMATION\_RETRIEVALandqualifier=\[REQUIRED\_PARAMETER

\_FORMATTING,USER\_QUERY\_VALUE\_PRIORITY\]\)then\(action=\[CONSTRUCT\_TOOL\_ARGUMENTS,PRIORITIZE\_USER\_VALUE\]\)withstrength=MANDATORY

10\.Ifaschemaexplicitlylimitsvalidvaluesforaninputparametertoapredefinedset,thenwhenconstructingarguments,mapuserpreferencestotheclosestvalidvaluewithinthisset,ordefaulttoaneutraloption\(e\.g\.,nofiltering\)whentheschemadisallowsexplicitpreferences\.

if\(domain=GENERAL\_INFORMATION\_RETRIEVALandqualifier=\[SCHEMA\_VALIDATION,DEFAULT\_VALUE\_ASSIGNMENT\]\)then\(action=\[CONSTRUCT\_TOOL\_ARGUMENTS,ASSIGN\_DEFAULT\_VALUE\]\)withstrength=MANDATORY

Listing 6:Sample rules learned from the BFCL: Live\-Multiple dataset1\.Ifasubtaskinvolvesinitiatingasystemorprocesswithpreconditions,thenidentifyandincludeallrequiredpreconditions\(e\.g\.,statevalidations,sequentialactions\)inthetaskdecomposition,ensuringthattheyareexecutedinthecorrectorderpriortoinvokingthemainaction\.Forexample,ifstartingaprocessrequirespreconditionsA,B,andC,verifyandsatisfyA,B,andCsequentiallybeforeinitiatingtheprocess\.

if\(domain=PROCESS\_MANAGEMENTandqualifier=\[PRECONDITION\_VALIDATION,TASK\_SEQUENCE\_VALIDATION\]\)then\(action=\[DECOMPOSE\_TASK,VALIDATE\_PRECONDITIONS,ENSURE\_SEQUENCE\]\)withstrength=MANDATORY

2\.Ifauserqueryinvolvesanactionthatrequiresspecificprerequisitestobemet\(e\.g\.,adependencybetweentasksorastaterequirement\),decomposethequeryintosubtasksthatexplicitlyaddresstheprerequisitesfirst\.Ensureeachprerequisitesubtaskisexecutedandvalidatedbeforeproceedingwiththedependentaction\.

if\(domain=PROCESS\_MANAGEMENTandqualifier=\[PREREQUISITE\_TASK,DEPENDENCY\_MANAGEMENT,TASK\_SEQUENCE\_VALIDATION\]\)then\(action=\[DECOMPOSE\_TASK,VALIDATE\_PRECONDITIONS,EXECUTE\_SUBTASK\]\)withstrength=MANDATORY

3\.Ifthetaskinvolvesconvertingamonetarytargetbetweentwocurrencies,thenensurethebasecurrencymatchesthesourceofthemonetarytargetandthetargetcurrencymatchesthedestinationspecifiedinthequerycontext\.Donotreversetheseroles,asitwillmisaligntheoutputwiththeintendedgoal\.

if\(domain=CURRENCY\_CONVERSIONandqualifier=\[CURRENCY\_CONSISTENCY,PRECONDITION\_VALIDATION\]\)then\(action=\[MATCH\_CURRENCY,VALIDATE\_PRECONDITIONS\]\)withstrength=MANDATORY

4\.Ifaqueryrequiresidentifyingentitiesfromacompleteset\(e\.g\.,allavailableoptions\),thenretrievethecomprehensivesetexplicitlyusingtoolsdesignedforglobalenumerationbeforeattemptingsubtasksthatdependonspecificentities\.Donotattempttoinferthesetbypiecemealorlocalizedretrievalfromindividualcomponents\.

if\(domain=ENTITY\_RETRIEVALandqualifier=\[GLOBAL\_ENUMERATION,DEPENDENCY\_MANAGEMENT\]\)then\(action=\[RETRIEVE\_GLOBAL\_SET,EXECUTE\_SUBTASK\]\)withstrength=MANDATORY

Listing 7:Sample rules learned from the BFCL: Multi\-Turn\-Base dataset
### A\.3Use of LLMs

ChatGPT131313[https://chatgpt\.com](https://chatgpt.com/)is used to polish the writing of this paper\.