Localizing Prompt Ambiguity in Large Language Models with Probe-Targeted Attribution

# Localizing Prompt Ambiguity in Large Language Models with Probe-Targeted Attribution
Source: [https://arxiv.org/html/2606.05486](https://arxiv.org/html/2606.05486)
Govind Ramesh Georgia Institute of Technology govind\.ramesh@gatech\.edu&Yao Dou Georgia Institute of Technology douy@gatech\.edu&Wei Xu Georgia Institute of Technology wei\.xu@cc\.gatech\.edu

###### Abstract

Prompt ambiguity is a common source of failure in large language models, but is difficult to localize because it is a latent property of the prompt, while existing attribution methods are designed to explain observable outputs such as logits or generated tokens\. We introduce PRIG, a gradient attribution method that uses a probe logit to attribute latent ambiguity to token positions\. Specifically, PRIG trains a linear probe to distinguish clear prompts from ambiguous prompts and attributes the probe score to earlier token representations in the residual stream\. To enable token\-level evaluation, we construct synthetic ambiguity datasets across coding, math, and writing by rewriting one task\-critical sentence per prompt, and complement them with a human\-written gold benchmark\. In this setting, PRIG localizes ambiguous spans substantially better than gradient attribution baselines, achieving 0\.840 AUROC on the combined synthetic benchmark and 0\.891 AUROC on the gold set\. It also outperforms GPT\-5\.4 on sentence\-level ambiguity identification and retains useful signal out\-of\-domain\. These results establish PRIG as a practical tool for identifying which parts of a prompt are ambiguous\. More broadly, they suggest that latent prompt properties can be localized through intermediate representations, rather than through output\-level attribution\. Code is available[here](https://github.com/govindramesh/LLM-Ambiguity-Attribution)\.

## 1Introduction

Large language models \(LLMs\) are increasingly used in settings where they must follow complex natural language instructions, including question answering, coding generation, and open\-ended task execution\. LLM failures are often discussed as products of incorrect reasoning, planning, or factual recall, but many stem from ambiguity in the prompt rather than from a deficiency in reasoning or knowledge\(Minet al\.,[2020](https://arxiv.org/html/2606.05486#bib.bib1); Stelmakhet al\.,[2022](https://arxiv.org/html/2606.05486#bib.bib2)\)\. Prior work has shown that ambiguous questions are common in real\-world settings and that a meaningful fraction of downstream errors can be traced to ambiguity in the input itself rather than to missing model competence\(Minet al\.,[2020](https://arxiv.org/html/2606.05486#bib.bib1); Trienes and Balog,[2019](https://arxiv.org/html/2606.05486#bib.bib3); Stelmakhet al\.,[2022](https://arxiv.org/html/2606.05486#bib.bib2)\)\. This ambiguity can take several forms: a prompt may omit or underspecify constraints, contain multiple plausible semantic readings, or rely on vague or incomplete references\(Yanget al\.,[2025](https://arxiv.org/html/2606.05486#bib.bib47)\)\. Resulting failures are especially consequential in domains where even small specification gaps matter, such as coding, mathematical problem solving, and writing tasks\(Yanget al\.,[2025](https://arxiv.org/html/2606.05486#bib.bib47)\)\. In these settings, an LLM may respond confidently while having inferred the wrong task altogether, making ambiguity not only a usability problem, but also a reliability and trust problem, since models may hallucinate plausible but incorrect task assumptions\(Jiet al\.,[2023](https://arxiv.org/html/2606.05486#bib.bib4)\)\.

![Refer to caption](https://arxiv.org/html/2606.05486v1/x1.png)Figure 1:Our contributions include: synthetic data generation of ambiguous prompts from coding, writing, and math datasets; training of ambiguity probe to separate clear and ambiguous prompts; probe\-based gradient attribution of tokens for ambiguity\.Recent work has explored clarifying\-question generation, selective abstention, ambiguity benchmarks, and structure disambiguation, showing that even frontier LLMs struggle to resolve ambiguous instructions reliably on their own\(Kuhnet al\.,[2022](https://arxiv.org/html/2606.05486#bib.bib5); Krasheninnikovet al\.,[2022](https://arxiv.org/html/2606.05486#bib.bib6); Coleet al\.,[2023](https://arxiv.org/html/2606.05486#bib.bib7); Muet al\.,[2024](https://arxiv.org/html/2606.05486#bib.bib8); Saparina and Lapata,[2025](https://arxiv.org/html/2606.05486#bib.bib9)\)\. Thus, understandingwhereambiguity originates in the prompt is essential for debugging prompts, improving alignment, and building robust systems\. However, existing attribution methods are primarily designed to explain model outputs rather than latent properties of the input itself\(Sundararajanet al\.,[2017](https://arxiv.org/html/2606.05486#bib.bib12); Shrikumaret al\.,[2017](https://arxiv.org/html/2606.05486#bib.bib13); Abnar and Zuidema,[2020](https://arxiv.org/html/2606.05486#bib.bib14)\)\. Ambiguity presents a difficult attribution target for perturbation\-based and activation patching methods, since underspecification is often not locally removable\. That is, deleting an influential span may leave the prompt equally or more ambiguous instead of producing a clean counterfactual\. Attention\-based methods are also insufficient, since attention weights reflect where the model looks rather than which tokens causally determine behavior\(Jain and Wallace,[2019](https://arxiv.org/html/2606.05486#bib.bib15)\)\. Meanwhile, input\-level gradient attribution in deep autoregressive transformers can diffuse across long contexts and highly nonlinear token interactions\(Hookeret al\.,[2019](https://arxiv.org/html/2606.05486#bib.bib19); Zhao and Shan,[2024](https://arxiv.org/html/2606.05486#bib.bib17)\)\.

We approach prompt ambiguity as a latent property encoded in LLM hidden representations, which have previously been used to detect simple forms of ambiguity\(Zhanget al\.,[2025b](https://arxiv.org/html/2606.05486#bib.bib18); Skeanet al\.,[2025](https://arxiv.org/html/2606.05486#bib.bib40); Alain and Bengio,[2017](https://arxiv.org/html/2606.05486#bib.bib21)\)\. We train linear probes to distinguish clear prompts from ambiguous prompts, interpret the probe logit as an ambiguity score, and attribute that score to token positions\.

To do this, we construct synthetic ambiguity datasets spanning coding, math, and writing by rewriting a task\-critical span in each prompt to introduce ambiguity while preserving topic and structure\. We then apply integrated gradients over intermediate hidden states, rather than input embeddings, to attribute ambiguity scores to tokens\. Restricting attribution to a local layer span and using the probe logit as the target captures token contributions to downstream ambiguity features while reducing attribution diffusion\. The key contributions of this work are:

- •We introduce a problem class of feature\-level token attribution for a latent prompt property, specifically for identifying ambiguity\.
- •We construct synthetic task\-level ambiguity datasets across coding, math, and writing that support direct token\-level evaluation\.
- •We propose a probe\-targeted residual integrated gradients method for attributing a probe\-defined ambiguity signal to token positions through intermediate hidden states\.
- •We show that this approach localizes ambiguous regions accurately, transfers across domains, and improves substantially over standard gradient\-based token attribution baselines\.

## 2Problem Setup

Let a prompt be represented as a token sequencex=\(x1,…,xn\)x=\(x\_\{1\},\\dots,x\_\{n\}\)\. For a transformer withLLlayers, lethiℓ∈ℝdh\_\{i\}^\{\\ell\}\\in\\mathbb\{R\}^\{d\}denote the residual stream representation of token positioniiafter layerℓ\\ell\. We are interested in ambiguity as a latent property of the prompt at input, not as a property of any particular generated continuation\.

We assume that ambiguity is at least partially linearly decodable from internal representations\. Thus, for each layerℓ\\ell, we train a logistic regression probe on the residual activationshℓh^\{\\ell\}\. We collapsehℓh^\{\\ell\}across the sequence length dimension, either by taking the last tokenhnℓh\_\{n\}^\{\\ell\}, or taking the mean across tokens to get probeFℓF\_\{\\ell\}:

h¯ℓ​\(x\)=1n​∑i=1nhiℓ,Fℓ​\(x\)=wℓ⊤​h¯ℓ​\(x\),\\bar\{h\}^\{\\ell\}\(x\)=\\frac\{1\}\{n\}\\sum\_\{i=1\}^\{n\}h\_\{i\}^\{\\ell\},\\quad F\_\{\\ell\}\(x\)=w\_\{\\ell\}^\{\\top\}\\bar\{h\}^\{\\ell\}\(x\),\(1\)wherewℓ∈ℝdw\_\{\\ell\}\\in\\mathbb\{R\}^\{d\}is the probe weight vector at layerℓ\\ell\. In this current setup the probe is trained without an intercept, so the scalarFℓ​\(x\)F\_\{\\ell\}\(x\)is exactly the probe logit before the logistic nonlinearity\.

This gives us a differentiable ambiguity functional:

Fℓ​\(x\)=1n​∑i=1n⟨wℓ,hiℓ​\(x\)⟩\.F\_\{\\ell\}\(x\)=\\frac\{1\}\{n\}\\sum\_\{i=1\}^\{n\}\\langle w\_\{\\ell\},h\_\{i\}^\{\\ell\}\(x\)\\rangle\.\(2\)The attribution objective is then to assign a scoreaia\_\{i\}to each token position, whereaia\_\{i\}measures how much positioniicontributes toFℓ​\(x\)F\_\{\\ell\}\(x\)\.

This setup is different from standard token attribution in that we do not attribute an output logit to input embeddings\. Here, we attribute a probe\-based internal feature to token representations\. Therefore, our problem is feature\-level attribution in representation space\.

## 3Method

### 3\.1Background

Gradient\-based attribution methods estimate how sensitive a scalar target is to small changes in the input or in an internal representation\. Saliency maps and Gradient×\\timesInput are computationally efficient, but their reliance on local first\-order information makes them sensitive to saturation, sharp nonlinearities, and local instabilities in deep networks\(Shrikumaret al\.,[2017](https://arxiv.org/html/2606.05486#bib.bib13); Hookeret al\.,[2019](https://arxiv.org/html/2606.05486#bib.bib19)\)\. Integrated Gradients \(IG\) was introduced to address these issues by integrating gradients along a path from a baselinex′x^\{\\prime\}to the inputxx\(Sundararajanet al\.,[2017](https://arxiv.org/html/2606.05486#bib.bib12)\):

IGi​\(x;x′\)=\(xi−xi′\)​∫01∂F​\(x′\+α​\(x−x′\)\)∂xi​𝑑α\.\\mathrm\{IG\}\_\{i\}\(x;x^\{\\prime\}\)=\(x\_\{i\}\-x^\{\\prime\}\_\{i\}\)\\int\_\{0\}^\{1\}\\frac\{\\partial F\(x^\{\\prime\}\+\\alpha\(x\-x^\{\\prime\}\)\)\}\{\\partial x\_\{i\}\}\\;d\\alpha\.\(3\)
IG satisfies sensitivity and implementation invariance in the standard setting and is typically more stable than raw gradients\(Sundararajanet al\.,[2017](https://arxiv.org/html/2606.05486#bib.bib12)\)\. However, applying IG directly in embedding space still has issues due to choice of baseline, interpolation paths traversing regions that do not correspond to valid tokens, and attribution diffusing across long contexts or many weakly relevant positions\(Kapishnikovet al\.,[2021](https://arxiv.org/html/2606.05486#bib.bib31); Gohet al\.,[2021](https://arxiv.org/html/2606.05486#bib.bib32); Mersha and Kalita,[2026](https://arxiv.org/html/2606.05486#bib.bib33)\)\. These concerns have motivated both smoothing variants and layer\-wise extensions of IG in transformer models\(Gohet al\.,[2021](https://arxiv.org/html/2606.05486#bib.bib32); Mersha and Kalita,[2026](https://arxiv.org/html/2606.05486#bib.bib33)\)\.

### 3\.2Probe\-Targeted Residual Integrated Gradients

Our method consists of three coupled components: tokenwise probe score at layerℓ\\ell, integrated gradients over a truncated residual\-stream subgraph from layermmto layerℓ\\ell, and a Gaussian smoothing step applied to the resulting token scores\.

Standard probing mean\-pools the token representations and then applies the probe weight vector as seen in Equation[1](https://arxiv.org/html/2606.05486#S2.E1)\. For classification, this is sufficient\. For attribution, however, we derive a feature logit at layerℓ\\ellas:

Fℓ​\(x\)=1n​∑i=1n⟨wℓ,hiℓ​\(x\)⟩,F\_\{\\ell\}\(x\)=\\frac\{1\}\{n\}\\sum\_\{i=1\}^\{n\}\\langle w\_\{\\ell\},h\_\{i\}^\{\\ell\}\(x\)\\rangle,\(4\)an aggregation of a tokenwise dot\-product\. This operates under the assumption that a probe learns a particular direction in representation space, so the dot\-product with each token representation quantifieshow muchthe token represents that direction\. Because the probe is linear, Equations[1](https://arxiv.org/html/2606.05486#S2.E1)and[4](https://arxiv.org/html/2606.05486#S3.E4)are numerically equivalent when residual activationshℓh^\{\\ell\}are mean\-pooled, but would not be equivalent if the probe is trained on the last token representation,hnℓh\_\{n\}^\{\\ell\}\.

Letℓ\\ellbe the layer at which the ambiguity probe is evaluated, and letm<ℓm<\\ellbe the layer at which attribution is performed\. Write

Rm​\(x\)=\[h1m​\(x\),…,hnm​\(x\)\]∈ℝn×dR^\{m\}\(x\)=\[h\_\{1\}^\{m\}\(x\),\\dots,h\_\{n\}^\{m\}\(x\)\]\\in\\mathbb\{R\}^\{n\\times d\}\(5\)for the matrix of residual representations at layermm\. Define the residual\-space function

Gℓ,m​\(R\)=Fℓ​\(fℓ:m​\(R\)\),G\_\{\\ell,m\}\(R\)=F\_\{\\ell\}\(f\_\{\\ell:m\}\(R\)\),\(6\)wherefℓ:mf\_\{\\ell:m\}denotes the forward computation from layermmto layerℓ\\ell\. Intuitively,Gℓ,mG\_\{\\ell,m\}treats the residual stream at layermmas the input and the probe logit at layerℓ\\ellas the scalar output\.

We use a zero baseline in residual space\. For interpolation parameterα∈\[0,1\]\\alpha\\in\[0,1\], the path is

Rαm=α​Rm​\(x\)\.R\_\{\\alpha\}^\{m\}=\\alpha R^\{m\}\(x\)\.\(7\)Integrated gradients on this path yield a dimension\-wise attribution

Ai,jℓ,m​\(x\)=hi,jm​\(x\)​∫01∂Gℓ,m​\(Rαm\)∂hi,jm​𝑑α,A\_\{i,j\}^\{\\ell,m\}\(x\)=h\_\{i,j\}^\{m\}\(x\)\\int\_\{0\}^\{1\}\\frac\{\\partial G\_\{\\ell,m\}\(R\_\{\\alpha\}^\{m\}\)\}\{\\partial h\_\{i,j\}^\{m\}\}\\;d\\alpha,\(8\)wherehi,jmh\_\{i,j\}^\{m\}is dimensionjjof token positioniiat layermm\. In practice, we approximate the integral with a Riemann sum over 50 points\. The final score per\-token is obtained by summing over residual dimensions:

aiℓ,m​\(x\)=∑j=1dAi,jℓ,m​\(x\)\.a\_\{i\}^\{\\ell,m\}\(x\)=\\sum\_\{j=1\}^\{d\}A\_\{i,j\}^\{\\ell,m\}\(x\)\.\(9\)Instead of propagating attribution through the full path of embeddings to feature logit, we restrict the backward graph to the layers that immediately precede the probe layer\. We treat the sequence positions ofhmh\_\{m\}as equivalent to the token positions of the input\. This is done under the intuition that, in transformer computation, each token position retains a corresponding residual\-stream vector, and successive attention and MLP blocks update that vector while preserving positional alignment in the sequence\. Although the representation at a position gradually incorporates contextual information from other tokens, the residual stream remains indexed by token position throughout the network\. We therefore treat mid\-layer residual states as contextual token representations that remain meaningfully aligned to token positions in the original sequence\. Now, we are analyzing how residual states at token positions in layermmcontribute to the ambiguity feature decoded at layerℓ\\ell\. For our problem, this helps reduce the diffusion that often appears in full input\-space attribution for long transformer contexts\.

Raw token\-level attribution scores can still be noisy because subword tokenization can split semantically coherent phrases and because local gradient estimates may vary sharply across neighboring positions\. To reduce these artifacts, we smooth the raw token scores with a one\-dimensional Gaussian kernel:

a~i=∑j=1nKσ​\(i−j\)​aj,\\tilde\{a\}\_\{i\}=\\sum\_\{j=1\}^\{n\}K\_\{\\sigma\}\(i\-j\)\\,a\_\{j\},\(10\)whereKσK\_\{\\sigma\}is a discrete Gaussian kernel\. In all reported experiments, we useσ=3\\sigma=3\. Furthermore, since we are evaluating the more complex task task\-level ambiguity rather than word\-level ambiguity, isolated token spikes are rarely the meaningful object of interest; that is, task\-level ambiguity more often occurs when a small set of nearby tokens jointly obscures the underlying task\.

We refer to this full procedure as PRIG\. The method is*probe\-targeted*as defined in the objective in Equation[4](https://arxiv.org/html/2606.05486#S3.E4), and it is*residual*because attribution is performed on residual stream states rather than input embeddings\.

Truncating attribution to a residual\-space subgraph changes the axioms expected from Integrated Gradients\. The global completeness guarantee of IG no longer applies with respect to the original embedding\-to\-feature computation\. In that sense, PRIG gives up global completeness in exchange for a more local view of how ambiguity is assembled between layersmmandℓ\\ell\.

## 4Data Construction

### 4\.1Base datasets

We study three domains in which prompt ambiguity is common but semantically different:

- •Coding:LeetCodeDataset\(Xiaet al\.,[2025](https://arxiv.org/html/2606.05486#bib.bib23)\)
- •Math:MATH Dataset\(Hendryckset al\.,[2021](https://arxiv.org/html/2606.05486#bib.bib24)\)
- •Writing:PromptTensor Prompt Bank\(PromptTensor,[2026](https://arxiv.org/html/2606.05486#bib.bib25)\)

### 4\.2Dataset Processing

Processing for each dataset:

- •Coding:we keep only problems labeledharddifficulty with at least five sentences and remove any examples from the prompts\.
- •Math:we keep only problems with at least four sentences and discard prompts containing drawings\.
- •Writing:we keep only prompts with intent labelsplanningorgenerationwith at least four sentences and remove near\-duplicates that have the same instructions\.

After filtering, thecoding,math, andwritingdatasets have 501, 357, and 385 prompts respectively, with 25% of each dataset held\-out for use in evaluating of probes and PRIG\.

#### Synthetic ambiguity generation

For each prompt, we generate exactly one ambiguous counterpart by instructing GPT\-5\.4 to rewrite a sentence such that the underlying task of the prompt becomes unclear \(see Appendix[A](https://arxiv.org/html/2606.05486#A1)\)\. This construction creates a binary classification signal for probe training, with original prompts labeled as clear and rewritten prompts labeled as ambiguous\. Furthermore, since one sentence is rewritten to contain the ambiguity, each prompt has a token\-span target for evaluation\.

#### Ground\-truth labeling

Each ambiguous prompt is paired with a binary token mask\. Tokens that fall inside the rewritten ambiguous sentence are labeled positive, and all other tokens are labeled negative\. The evaluation task is therefore to recover the ambiguous sentence as a token\-level positive region from continuous attribution scores\.

### 4\.3Gold Dataset

In addition to the synthetic data, we construct a human\-writtengoldset of 12 ambiguous prompts, with 4 from each domain\. The math problems in thegoldset come from AIME exams and the coding problems come from SWE\-Bench Pro\(Denget al\.,[2025](https://arxiv.org/html/2606.05486#bib.bib26)\)\. Thus, at least for coding and math, thegoldset is different in that it is not synthetically generated and comes from different datasets within the same topic\. This set is used only for evaluation, and provides signal on whether the method transfers beyond the exact GPT\-generated perturbation distribution used to create the synthetic training data\.

## 5Experiments and Results

### 5\.1Experimental Setup

All experiments useLlama\-3\.1\-8B\-Instruct\(Dubey and others,[2024](https://arxiv.org/html/2606.05486#bib.bib27)\)\. The chat template is applied to each prompt, with a generation prompt, to replicate how prompts are processed by an LLM\. For evaluation, metrics are calculated on the tokens corresponding to the original prompt without the chat template\.

#### Probe Quality

We extract residual stream representations at every layer and train a separate logistic regression probe at each layer using mean\-pooled residual states\. Implementation details are provided in Appendix[C](https://arxiv.org/html/2606.05486#A3)\. Figure[2](https://arxiv.org/html/2606.05486#S5.F2)plots probe accuracy over layers when trained on each of thecoding,math,writing, andcombineddatasets\. We observe that accuracy rises sharply over the first 5–6 layers, peaks around layer 15, and then plateaus or decreases slightly\. This suggests that ambiguity becomes progressively more linearly accessible through the middle of the network and remains relatively stably represented in later layers\.

![Refer to caption](https://arxiv.org/html/2606.05486v1/figures/probe_plot.png)Figure 2:Probe performance over layers for probes trained on thecoding,math,writing, andcombineddatasets\.
#### Attribution Layer Configuration

Each attribution method requires a probe layerℓ\\ell, and PRIG additionally requires an attribution layermm, as described in Section[3\.2](https://arxiv.org/html/2606.05486#S3.SS2)\. For each domain, we select the attribution layer or interval from a set of candidate values using training\-set performance, to be used for downstream evaluation\. Appendix[D](https://arxiv.org/html/2606.05486#A4)reports the results of varying the attribution layer choices\.

#### Metrics

On ambiguous prompts, the target span is the single rewritten sentence, so evaluation reduces to a token\-level ranking problem: tokens inside the ambiguous sentence should receive higher scores than tokens outside it\. We report Area Under the Receiver Operating Characteristic curve \(AUROC\) and Area Under the Precision\-Recall Gain curve \(AUPRG\)\.

AUROC measures the probability that a randomly chosen positive token is ranked above a randomly chosen negative token\. In this setting, it captures whether the attribution map broadly separates the ambiguous span from the rest of the prompt\. AUPRG is also reported since only one sentence in each prompt is ambiguous, and therefore the positive class is a small fraction of the total sequence, making the task imbalanced\. Precision\-Recall Gain\(Flach and Kull,[2015](https://arxiv.org/html/2606.05486#bib.bib28)\)adjusts for the base rate of the positive class, which makes performance above random interpretable and comparable across prompt samples with different amounts of ambiguous tokens\.

### 5\.2Baselines

We compare PRIG against three baselines:

#### Gradient×\\timesInput from the probe logit\.

We compute the gradient of the probe logit with respect to input embeddings and multiply by the embeddings\. This is the most direct embedding\-space baseline for the same probe target\.

#### Integrated Gradients from the probe logit\.

We compute standard Integrated Gradients from a baseline in embedding space to the actual prompt embeddings, using the probe logit as the scalar target\. We compute IG using 50 steps\.

#### LLM sentence selection\.

We use GPT\-5\.4 as a zero\-shot sentence\-level baseline\. It is prompted to identify the ambiguous sentence if one exists, or returnNoneif no sentence in the prompt is ambiguous\.

### 5\.3Results

#### Prompt Ambiguity Localization

For each domain in the dataset, we evaluate PRIG using a probe trained on that domain’s held\-out evaluation set\. This experiment measures how well PRIG can localize ambiguity to the ground\-truth sentence span\. Table[1](https://arxiv.org/html/2606.05486#S5.T1)shows that PRIG substantially outperforms both gradient attribution baselines on all three domains\. These results align with the hypothesis that the sequence positions of a residual state can represent the original tokens in the same position for the purposes of attribution, and that attributing to residual\-space provides better localization than embedding\-space\.

In addition to the single\-domain probes, acombinedprobe trained on the union of thecoding,math, andwritingsynthetic datasets performs strongly on thecombinedevaluation set\.

![Refer to caption](https://arxiv.org/html/2606.05486v1/x2.png)Figure 3:Token attribution maps for a prompt from the human\-writtengoldset\. Darker red indicates higher attribution, and the bold underlined text marks the ambiguous span\.Table 1:Attribution results using a probe trained on each dataset and evaluated on in\-domain ambiguous prompts\. Each entry reports AUROC \| AUPRG\.Table 2:Cross\-domain attribution results for PRIG\. Rows indicate the domain used to train the probe, and columns indicate the evaluation domain for attribution\. Each entry reports AUROC \| AUPRG\.
#### Human\-Written Gold Set

We evaluate PRIG on thegoldset to measure generalization beyond synthetic rewrites\. We evaluate thegoldset using thecombinedprobe\. Table[1](https://arxiv.org/html/2606.05486#S5.T1)shows that this probe transfers strongly to the benchmark with 0\.891 AUROC and 0\.870 AUPRG\. These results suggest that the probe ambiguity feature learned from the synthetic data generalizes beyond the GPT\-generated rewrite distribution and the particular datasets used for training\.

Figure[3](https://arxiv.org/html/2606.05486#S5.F3)compares token attribution maps on an ambiguous prompt from thegoldset for each gradient attribution method\. The bold underlined span marks the ambiguous sentence\.

#### Cross\-Domain Generalization

Cross\-domain experiments test whether the ambiguity feature represented by the probes can generalize beyond the task it was trained on to attribute ambiguity for other tasks\. We train probes on one domain and apply PRIG to the other domains\. High out\-of\-domain performance would suggest that the probe is detecting a shared ambiguity direction rather than memorizing domain\-specific surface patterns\.

The results in Table[2](https://arxiv.org/html/2606.05486#S5.T2)show that out\-of\-domain performance remains strong overall\. The average in\-domain performance across the three domains is 0\.870 AUROC and 0\.821 AUPRG; average out\-of\-domain performance decreases to 0\.805 AUROC and 0\.688 AUPRG\. Performance degrades out of domain, which is expected given the differences between coding, math, and writing prompts\. Even so, the off\-diagonal results remain far above random performance and the baselines in Table[1](https://arxiv.org/html/2606.05486#S5.T1)\.

#### Sentence Attribution Against GPT Baseline

To compare PRIG against GPT\-5\.4, we define a sentence\-level ambiguity identification task\. Each prompt is either a positive example, containing exactly one ambiguous sentence, or a negative example, containing no ambiguous sentence\. For negative examples, the ground truth label isNone; a prediction is correct if and only if the model returnsNone\. For positive examples, the ground truth label is the unique ambiguous sentence; a prediction is correct if and only if the model returns that sentence\. PredictingNoneon a positive example, or predicting the wrong sentence, is counted as incorrect\.

GPT\-5\.4 is evaluated on this setup to either identify the ambiguous sentence or returnNone\(see Appendix[B](https://arxiv.org/html/2606.05486#A2)\)\. For PRIG, however, the raw output is a token\-level attribution map\. We therefore aggregate token scores within each sentence by taking the mean attribution over the sentence’s tokens\. The predicted sentence is the one with the highest aggregated score\. To allow the attribution model to abstain on clear prompts, we introduce a thresholdτ\\tau: if the highest\-scoring sentence has score belowτ\\tau, the prediction is changed toNone\. We selectτ\\tauby 5\-fold cross validation on the held\-outcombineddataset, which contains 305 ambiguous prompts and 305 clear prompts, and report the mean and standard deviation of F1, precision, and recall across folds in Table[3](https://arxiv.org/html/2606.05486#S5.T3)\.

PRIG outperforms GPT\-5\.4 on all three aggregate metrics\. In particular, PRIG achieves higher precision while also improving F1, indicating that the attribution\-based decision rule is substantially less likely to hallucinate ambiguity on clear prompts while providing similar performance in recall\.

Table 3:Sentence\-level ambiguity identification on the held\-outcombineddataset for GPT\-5\.4 and PRIG\. Reported PRIG values are mean±\\pmstandard deviation over the 5\-fold cross\-validation used to select the abstention threshold\.The specified version of thecombineddataset provides a token\-level check on false positives\. In this evaluation, the mask marks the sentence that would have been rewritten if the specified prompt had been turned into an ambiguous one\. Low scores suggest that when the prompt is fully specified, PRIG does not spuriously attribute ambiguity on that sentence\. Using thecombinedprobe, PRIG produces near\-random attribution scores of0\.4520\.452AUROC and0\.1950\.195AUPRG on fully\-specified prompts\. These results suggests that PRIG is better calibrated than GPT\-5\.4 to abstain from ambiguity claims when no ambiguous sentence is present\.

## 6Related Work

#### Prompt Ambiguity

Studies on ambiguity in LLM prompts cover clarifying\-question generation, selective abstention, ambiguity benchmarks, and controlled tests of alternative semantic readings\(Kuhnet al\.,[2022](https://arxiv.org/html/2606.05486#bib.bib5); Krasheninnikovet al\.,[2022](https://arxiv.org/html/2606.05486#bib.bib6); Coleet al\.,[2023](https://arxiv.org/html/2606.05486#bib.bib7); Muet al\.,[2024](https://arxiv.org/html/2606.05486#bib.bib8); Saparina and Lapata,[2025](https://arxiv.org/html/2606.05486#bib.bib9)\)\. A prompt may be underspecified because it omits a necessary constraint, multiple semantic interpretations exist, or key references are too vague\(Yanget al\.,[2025](https://arxiv.org/html/2606.05486#bib.bib47)\)\. Recent work shows that even strong models can be highly sensitive to such underspecification, with substantial changes in behavior under small rephrasings or missing pieces of task information\(Kamathet al\.,[2024](https://arxiv.org/html/2606.05486#bib.bib10); Saparina and Lapata,[2024](https://arxiv.org/html/2606.05486#bib.bib11)\)\.

#### Token Attribution

Methods for token attribution in neural networks are commonly divided into perturbation\-based, gradient\-based, and attention\-based methods\(Ribeiroet al\.,[2016](https://arxiv.org/html/2606.05486#bib.bib29); Lundberg and Lee,[2017](https://arxiv.org/html/2606.05486#bib.bib30); Abnar and Zuidema,[2020](https://arxiv.org/html/2606.05486#bib.bib14); Jain and Wallace,[2019](https://arxiv.org/html/2606.05486#bib.bib15); Zhao and Shan,[2024](https://arxiv.org/html/2606.05486#bib.bib17)\)\. Perturbation methods estimate importance by observing how model behavior changes when tokens are masked, deleted, or replaced, but struggle in discrete text domains\(Lundberg and Lee,[2017](https://arxiv.org/html/2606.05486#bib.bib30); Zhao and Shan,[2024](https://arxiv.org/html/2606.05486#bib.bib17); Xiaoet al\.,[2025](https://arxiv.org/html/2606.05486#bib.bib46)\)\. Related intervention\-based methods in mechanistic interpretability, such as activation patching and attribution patching, attempt to localize behavior by swapping internal activations between runs\(Kramáret al\.,[2024](https://arxiv.org/html/2606.05486#bib.bib48); Rezaei Jafariet al\.,[2025](https://arxiv.org/html/2606.05486#bib.bib49)\)\. These methods benefit from a clean contrast between a feature\-present and a feature\-absent execution\. Attention\-based attributions trace which tokens attend to others\. Early approaches treated raw attention as an explanation signal, while later work introduced attention rollout, attention flow, and more elaborate graph\-based schemes to track information transport through many layers\(Abnar and Zuidema,[2020](https://arxiv.org/html/2606.05486#bib.bib14); Azarkhalili and Libbrecht,[2025](https://arxiv.org/html/2606.05486#bib.bib36); Qianget al\.,[2022](https://arxiv.org/html/2606.05486#bib.bib37)\)\. Findings suggest that attention weights are not equivalent to causal importance after information has mixed through residual connections and MLP blocks\(Jain and Wallace,[2019](https://arxiv.org/html/2606.05486#bib.bib15); Abnar and Zuidema,[2020](https://arxiv.org/html/2606.05486#bib.bib14)\)\.

#### Linear Probing and Latent Representations

Feature probing identifies what information has become linearly accessible inside the model\. Linear probes were introduced as layer\-wise diagnostic tools for intermediate representations\(Alain and Bengio,[2017](https://arxiv.org/html/2606.05486#bib.bib21)\)and later became a standard method for studying language\-model structure\. Probing shows that hidden states can encode syntactic relations, hierarchical structure, and other abstract linguistic properties\(Hewitt and Manning,[2019](https://arxiv.org/html/2606.05486#bib.bib38); Diego\-Simónet al\.,[2025](https://arxiv.org/html/2606.05486#bib.bib39)\)\. More recent work has extended probing to epistemic and behavioral states, including answerability, confidence, calibration, and hallucination\(Moreno Cencerradoet al\.,[2025](https://arxiv.org/html/2606.05486#bib.bib41); Berkowitzet al\.,[2025](https://arxiv.org/html/2606.05486#bib.bib42); Wanget al\.,[2026](https://arxiv.org/html/2606.05486#bib.bib43); Brinket al\.,[2026](https://arxiv.org/html/2606.05486#bib.bib44); Zhanget al\.,[2025a](https://arxiv.org/html/2606.05486#bib.bib45)\)\.

## 7Conclusion

We introduce PRIG, a method for localizing prompt ambiguity in large language models by attributing a probe\-based feature through a local residual\-stream subgraph\. Across coding, math, and writing tasks, PRIG consistently outperforms other gradient attribution baselines and performs better sentence\-level ambiguity identification than GPT\-5\.4\. These results suggest that latent features in prompts, such as ambiguity, can be attributed to a input tokens through probe\-targeted representation\-space attribution\.

## Limitations

PRIG assumes prompt ambiguity is linearly decodable from internal LLM representations\. We do not evaluate whether the same attribution setup transfers to other latent properties, model families, or LLM scales\. The probe is trained primarily on LLM\-generated synthetic ambiguity\. While the human\-writtengoldset evaluates generalization beyond the rewrite distribution, the learned feature may still reflect biases of the generation pipeline\. We also define the ground\-truth ambiguity span as the rewritten sentence, but ambiguity may depend on broader context and may be less cleanly localized in real\-world prompts\. Future work could study whether ambiguity localization improves prompt repair and downstream model performance\. PRIG is also sensitive to probing and attribution layer selection\. Reported results use the best\-performing local interval selected on the training set for each domain rather than a single universal configuration\. Performance differences across layer choices are reported in Appendix[D](https://arxiv.org/html/2606.05486#A4)\.

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- Z\. Zhang, J\. Duan, E\. Kim, and K\. Xu \(2025b\)Sparse neurons carry strong signals of question ambiguity in llms\.InProceedings of the 2025 Conference on Empirical Methods in Natural Language Processing,pp\. 16092–16110\.Cited by:[§1](https://arxiv.org/html/2606.05486#S1.p3.1)\.
- Z\. Zhao and B\. Shan \(2024\)ReAGent: towards a model\-agnostic feature attribution method for generative language models\.CoRRabs/2402\.00794\.External Links:[Document](https://dx.doi.org/10.48550/arXiv.2402.00794),[Link](https://arxiv.org/abs/2402.00794)Cited by:[§1](https://arxiv.org/html/2606.05486#S1.p2.1),[§6](https://arxiv.org/html/2606.05486#S6.SS0.SSS0.Px2.p1.1)\.

## Appendix ASynthetic Ambiguity Generation Prompts

The synthetic rewrite prompt used in dataset construction is:

Synthetic Data Generation Prompt[⬇](data:text/plain;base64,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)Youaregivena\{domain\}promptconsistingofmultiplesentences\.Yourtaskhastwosteps:1\.Identifythesentenceinthepromptthatismostcriticaltounderstandingwhatthe\{domain\}questionisasking\.Thisshouldbethesentencewhoseremovalorcorruptionwouldmostseverelyimpaircomprehensionofthetask\.2\.Forthissentence,producean\*\*obscuredversion\*\*thatobfuscatestheunderlyingmeaningsuchthat,ifsubstitutedbackintotheprompt,theoverallmeaningoftheproblemwouldbecomeunclear\.Youmustobscurethesentenceenoughthatthe\{domain\}problemisnolongerunderstandablelogicallyifsubstitutedin\.AnLLMshouldnotrespondtothemodifiedpromptbecauseofhowunclearitis\.Note:\*\*DONOT\*\*onlycreateambiguitythroughscopeambiguousvocabulary/quantifiers\(wordslike"maybe","sometimes","vaguely"or"random"\)orwordssynonymouswith’vague’\(wordslike"mystery","random","something","however","any","may","specified"\)fortheobfuscation\.Instead,considerusingtechniqueslikeaddingrandominformation,deletingkeyinformation,andreplacingwords\.Justmakesurethemeaningisobfuscatedenoughthatthewholepromptbecomesunclearandunanswerable\.\#\#\#\#\#Hereareexamplesofgoodobfuscations:\{examples\}NOTES:\-Thechangedsentencestillhasasimilarmeaningastheoriginal,butismorevague\.\-Thechangedsentencewouldmaketheoverallpromptunclearifsubstitutedin\.\-Everypartofthechangedsentenceismorevaguethantheoriginal,sothewholenewsentenceisambiguous\.\-Thechangedsentenceshouldbeunclearonitsown\.\#\#\#\#\#OutputInstructions:Youmustoutput\*\*only\*\*thefollowingJSON\-likeobject,withnoextratextbeforeorafter:\{\*\*originalsentence\*\*:\*\*obscuredversion\*\*,\}Importantconstraints:\-Chooseonly1sentencetoobfuscatethatwouldmostimpaircomprehensionofthetaskifchanged\.\-Theobscuredversionshouldnotbelongerthantheoriginalsentence\.\-Thekeymustbeanexactsentencecopiedverbatimfromtheprompt\.\-Thevaluemustbeanchangedversionofonlythatsentence\.\-Donotparaphrasetheoriginaltextinthekeys\.\-Donotincludeexplanations,bulletpoints,orformattingoutsidetheschema\.Hereisthe\{domain\}prompt:"\{prompt\}"

The placeholder\{domain\}is populated with the domain of the prompt,\{example\_string\}is populated with a concatenated block of the gold set examples for the domain, and\{prompt\}is populated with the clear prompt\.

## Appendix BGPT\-5\.4 Ambiguity Sentence\-Selection Prompt

The zero\-shot GPT\-5\.4 baseline for sentence\-level ambiguity identification used the following prompt:

GPT Sentence\-Level Ambiguity Identification Prompt[⬇](data:text/plain;base64,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)Youaregivenapromptbelow\.Yourtaskistoidentifywhichpartoftheprompt,ifany,isambiguous\.\#\#\#\#\#OutputInstructions:\-Youmustoutput\*\*only\*\*thesentencethatyouhaveidentifiedasambiguous,ortheword"NONE"ifthereisnoambiguoussentence\.\-Ifasentenceischosen,itmustbecopiedverbatimfromtheprompt\.\-Donotincludeexplanations,bulletpoints,orotherformatting\.Hereistheprompttoanalyze:"\{prompt\}"

## Appendix CProbe Training Details

Questions are first wrapped with the Llama\-3\.1\-Instruct chat template before activations are extracted\. The text prompt is formatted as:

Llama\-3\.1\-Instruct Prompt Template[⬇](data:text/plain;base64,PHxiZWdpbl9vZl90ZXh0fD48fHN0YXJ0X2hlYWRlcl9pZHw+c3lzdGVtPHxlbmRfaGVhZGVyX2lkfD4KCjx8ZW90X2lkfD48fHN0YXJ0X2hlYWRlcl9pZHw+dXNlcjx8ZW5kX2hlYWRlcl9pZHw+Cgp7cHJvbXB0fTx8ZW90X2lkfD48fHN0YXJ0X2hlYWRlcl9pZHw+YXNzaXN0YW50PHxlbmRfaGVhZGVyX2lkfD4=)<\|begin\_of\_text\|\><\|start\_header\_id\|\>system<\|end\_header\_id\|\><\|eot\_id\|\><\|start\_header\_id\|\>user<\|end\_header\_id\|\>\{prompt\}<\|eot\_id\|\><\|start\_header\_id\|\>assistant<\|end\_header\_id\|\>

#### Generating Activations

We loadmeta\-llama/Llama\-3\.1\-8B\-Instructthrough TransformerLens and cachehook\_resid\_postactivations at every layer\.

#### Train/Test Split

For each layer, probe training uses a stratified random 75/25 split viatrain\_test\_split\(X, y, test\_size=0\.25, stratify=y\)\. To prevent contamination, a prompt’s original and ambiguous versions cannot end up in different splits, and attribution experiments are run only on the same held\-out prompts\.

#### Probe Model

At every layer we train an independent binary logistic\-regression probe with

sklearn\.linear\_model\.LogisticRegression\(max\_iter=5000,fit\_intercept=False\)

Under the standard scikit\-learn defaults used by this constructor, the model uses L2 regularization withC=1\.0,dual=False, tolerance1e\-4, and thelbfgsoptimizer unless a different solver is specified\. For binary labels, the fitted classifier learns a single coefficient vectorcoef\_of shape\(1, d\)and, becausefit\_intercept=False, the intercept is fixed to zero\.

## Appendix DAttribution Results Across Probe Layers

This appendix shows the results of attributions when changing probe layers/intervals\. All values are mean held\-out performance, reported as AUROC \| AUPRG\.

PRIG attribution results across a set of layer intervals for the coding, math, andwritingprobes:

Gradient attribution baseline results across probe layers, where rows correspond to the probe layerℓ\\ellused for attribution:

All experiments were conducted using an NVIDIA A40 GPU, with each layer/interval evaluation on one dataset taking <30 minutes\.

## Appendix EAdditional Qualitative Examples

The following heatmaps show two additional examples from the gold set, specifically from the math and coding domains\.

Math Example:

![[Uncaptioned image]](https://arxiv.org/html/2606.05486v1/x3.png)

Coding Example:

![[Uncaptioned image]](https://arxiv.org/html/2606.05486v1/x4.png)

## Appendix FHuman\-Written Gold Set Prompts

The gold set contains 12 prompt pairs, consisting of four prompts from each of the writing, math, and coding domains\. For each pair below, the clear prompt is the original version and the ambiguous prompt is the edited version used for evaluation\.

Writing Prompt 1Clear Prompt[⬇](data:text/plain;base64,RGVzaWduIGEgc2l4LW1vbnRoIHN5c3RlbWF0aWMgcmV2aWV3IHdvcmtmbG93IGZvciBlcGlnZW5ldGljIHRyYXVtYSBtYXJrZXJzIHJlc2VhcmNoLiBPdXRsaW5lIGZvdXIgZGlzdGluY3QgcGhhc2VzIHdpdGggc3BlY2lmaWMgZGVsaXZlcmFibGVzLCBxdWFsaXR5IGFzc2Vzc21lbnQgcHJvdG9jb2xzIGZvciBpbmNsdWRlZCBzdHVkaWVzLCBhbmQgaGV0ZXJvZ2VuZWl0eSBldmFsdWF0aW9uIGNyaXRlcmlhLiBJbmNsdWRlIHRpbWVsaW5lIG1pbGVzdG9uZXMsIHRlYW0gcm9sZSBhc3NpZ25tZW50cywgYW5kIGRvY3VtZW50YXRpb24gc3RhbmRhcmRzIGZvciByZXByb2R1Y2liaWxpdHkgYWNyb3NzIG11bHRpZGlzY2lwbGluYXJ5IGNvbGxhYm9yYXRvcnMu)Designasix\-monthsystematicreviewworkflowforepigenetictraumamarkersresearch\.Outlinefourdistinctphaseswithspecificdeliverables,qualityassessmentprotocolsforincludedstudies,andheterogeneityevaluationcriteria\.Includetimelinemilestones,teamroleassignments,anddocumentationstandardsforreproducibilityacrossmultidisciplinarycollaborators\.Ambiguous Prompt[⬇](data:text/plain;base64,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)Designasix\-monthsystematicreviewworkflowforepigenetictraumamarkersresearch\.Chooseanamountoftimeandsplititup,whereeachhasitsowntasks,rulesforensuringhighscores,andpointsthatquantifyhowdifferenteachis\.Includetimelinemilestones,teamroleassignments,anddocumentationstandardsforreproducibilityacrossmultidisciplinarycollaborators\.

Writing Prompt 2Clear Prompt[⬇](data:text/plain;base64,RGV2ZWxvcCBhIHByZS1yZWdpc3RyYXRpb24gcHJvdG9jb2wgZm9yIGEgbXVsdGktc2l0ZSBjbGluaWNhbCB0cmlhbCBvbiBkZXByZXNzaW9uIHRyZWF0bWVudC4gU3BlY2lmeSBwcmltYXJ5IGFuZCBzZWNvbmRhcnkgZW5kcG9pbnRzLCBzdG9wcGluZyBydWxlcyBmb3IgZWZmaWNhY3kgYW5kIGZ1dGlsaXR5LCBhbmFseXNpcyBwbGFuIGluY2x1ZGluZyBtaXNzaW5nIGRhdGEgaGFuZGxpbmcsIGFuZCBkYXRhIHNoYXJpbmcgY29tbWl0bWVudHMuIEluY2x1ZGUgcG93ZXIgYW5hbHlzaXMgYW5kIHNlbnNpdGl2aXR5IGFuYWx5c2VzLg==)Developapre\-registrationprotocolforamulti\-siteclinicaltrialondepressiontreatment\.Specifyprimaryandsecondaryendpoints,stoppingrulesforefficacyandfutility,analysisplanincludingmissingdatahandling,anddatasharingcommitments\.Includepoweranalysisandsensitivityanalyses\.Ambiguous Prompt[⬇](data:text/plain;base64,TWFrZSBhIGd1aWRlIGZvciB0aGUgZHVyYXRpb24gYmVmb3JlIG9mZmljaWFsIHJlZ2lzdHJhdGlvbiB0aGF0IGNvbnRhaW5zIHJ1bGVzIGZvciB0ZXN0aW5nIHJlbGF0ZWQgdG8gc29sdmluZyBzdHJvbmcgbmVnYXRpdmUgZW1vdGlvbiBhY3Jvc3MgbWFueSBvZmZpY2lhbCBsb2NhdGlvbnMuIFNwZWNpZnkgcHJpbWFyeSBhbmQgc2Vjb25kYXJ5IGVuZHBvaW50cywgc3RvcHBpbmcgcnVsZXMgZm9yIGVmZmljYWN5IGFuZCBmdXRpbGl0eSwgYW5hbHlzaXMgcGxhbiBpbmNsdWRpbmcgbWlzc2luZyBkYXRhIGhhbmRsaW5nLCBhbmQgZGF0YSBzaGFyaW5nIGNvbW1pdG1lbnRzLiBJbmNsdWRlIHBvd2VyIGFuYWx5c2lzIGFuZCBzZW5zaXRpdml0eSBhbmFseXNlcy4=)Makeaguideforthedurationbeforeofficialregistrationthatcontainsrulesfortestingrelatedtosolvingstrongnegativeemotionacrossmanyofficiallocations\.Specifyprimaryandsecondaryendpoints,stoppingrulesforefficacyandfutility,analysisplanincludingmissingdatahandling,anddatasharingcommitments\.Includepoweranalysisandsensitivityanalyses\.

Writing Prompt 3Clear Prompt[⬇](data:text/plain;base64,Q3JpdGlxdWUgYW4gZXhwZXJpbWVudGFsIGRlc2lnbiBmb3IgY29uZm91bmQgdnVsbmVyYWJpbGl0eSwgZGVtYW5kIGNoYXJhY3RlcmlzdGljcywgYW5kIGVjb2xvZ2ljYWwgdmFsaWRpdHkgdGhyZWF0cy4gSWRlbnRpZnkgZG91YmxlLWJsaW5kIGZhaWx1cmVzLCBzb2NpYWwgZGVzaXJhYmlsaXR5IGNvbnRhbWluYXRpb24sIGFuZCBhcnRpZmljaWFsIHRhc2sgY29uc3RyYWludHMuIFN1Z2dlc3QgZGVzaWduIG1vZGlmaWNhdGlvbnMgc3RyZW5ndGhlbmluZyBpbnRlcm5hbCBhbmQgZXh0ZXJuYWwgdmFsaWRpdHkuIFByb3ZpZGUgdGhlIHJlc3BvbnNlIGFzIGEgYnVsbGV0IGxpc3Qgd2l0aCBjbGVhciBzZWN0aW9uIGhlYWRlcnMu)Critiqueanexperimentaldesignforconfoundvulnerability,demandcharacteristics,andecologicalvaliditythreats\.Identifydouble\-blindfailures,socialdesirabilitycontamination,andartificialtaskconstraints\.Suggestdesignmodificationsstrengtheninginternalandexternalvalidity\.Providetheresponseasabulletlistwithclearsectionheaders\.Ambiguous Prompt[⬇](data:text/plain;base64,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)Critiqueanexperimentaldesignforconfoundvulnerability,demandcharacteristics,andecologicalvaliditythreats\.Identifydouble\-blindfailures,socialdesirabilitycontamination,andartificialtaskconstraints\.Suggestdesignmodificationsstrengtheninginternalandexternalvalidity\.Whencreatingtheresponse,formatthepointsseparatelyandstacked,withdescriptionsofsimilarpointstogroupthem\.

Writing Prompt 4Clear Prompt[⬇](data:text/plain;base64,U3ludGhlc2l6ZSBhIHNjb3BpbmcgcmV2aWV3IG9uIGRlY2VudHJhbGl6ZWQgYXV0b25vbW91cyBvcmdhbml6YXRpb25zIGluIGdvdmVybmFuY2UgY29udGV4dHMuIE1hcCBkaXNjaXBsaW5hcnkgY29udHJpYnV0aW9ucyBmcm9tIHBvbGl0aWNhbCBzY2llbmNlLCBjb21wdXRlciBzY2llbmNlLCBhbmQgb3JnYW5pemF0aW9uYWwgdGhlb3J5LiBJZGVudGlmeSBkZWZpbml0aW9uYWwgYW1iaWd1aXRpZXMsIGVtcGlyaWNhbCBldmlkZW5jZSBnYXBzLCBhbmQgbm9ybWF0aXZlIGFzc3VtcHRpb25zIGVtYmVkZGVkIGluIHRoZSBsaXRlcmF0dXJlLg==)Synthesizeascopingreviewondecentralizedautonomousorganizationsingovernancecontexts\.Mapdisciplinarycontributionsfrompoliticalscience,computerscience,andorganizationaltheory\.Identifydefinitionalambiguities,empiricalevidencegaps,andnormativeassumptionsembeddedintheliterature\.Ambiguous Prompt[⬇](data:text/plain;base64,V3JpdGUgYWJvdXQgZXhpc3RpbmcgY29udGVudCBvbiB0b3BpY3Mgb2Ygb3JnYW5pemF0aW9ucyB0aGF0IGRpc3RyaWJ1dGUgYXV0aG9yaXR5IGF1dG9tYXRpY2FsbHksIGVzcGVjaWFsbHkgZm9yIG9mZmljaWFsIGNhc2VzLiBNYXAgZGlzY2lwbGluYXJ5IGNvbnRyaWJ1dGlvbnMgZnJvbSBwb2xpdGljYWwgc2NpZW5jZSwgY29tcHV0ZXIgc2NpZW5jZSwgYW5kIG9yZ2FuaXphdGlvbmFsIHRoZW9yeS4gSWRlbnRpZnkgZGVmaW5pdGlvbmFsIGFtYmlndWl0aWVzLCBlbXBpcmljYWwgZXZpZGVuY2UgZ2FwcywgYW5kIG5vcm1hdGl2ZSBhc3N1bXB0aW9ucyBlbWJlZGRlZCBpbiB0aGUgbGl0ZXJhdHVyZS4=)Writeaboutexistingcontentontopicsoforganizationsthatdistributeauthorityautomatically,especiallyforofficialcases\.Mapdisciplinarycontributionsfrompoliticalscience,computerscience,andorganizationaltheory\.Identifydefinitionalambiguities,empiricalevidencegaps,andnormativeassumptionsembeddedintheliterature\.

Math Prompt 1Clear Prompt[⬇](data:text/plain;base64,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)Triangle$\\triangleABC$liesinplane$\\mathcal\{P\}$with$AB=6$,$AC=4$,and$\\angleBAC=90^\{\\circ\}$\.Let$D$bethereflectionacross$\\overline\{BC\}$ofthecentroidof$\\triangleABC$\.Fourspheres,allonthesamesideof$\\mathcal\{P\}$,haveradii$1$,$2$,$3$,and$r$andaretangentto$\\mathcal\{P\}$atpoints$A$,$B$,$C$,and$D$,respectively\.Thefourspheresarealsoeachtangenttoasecondplane$\\mathcal\{T\}$andareallonthesamesideof$\\mathcal\{T\}$\.Thevalueof$r$canbewrittenas$\\frac\{m\}\{n\}$,where$m$and$n$arerelativelyprimepositiveintegers\.Find$m\+n$\.Ambiguous Prompt[⬇](data:text/plain;base64,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)Triangle$\\triangleABC$liesinplane$\\mathcal\{P\}$with$AB=6$,$AC=4$,and$\\angleBAC=90^\{\\circ\}$\.Let$D$bethereflectionacross$\\overline\{BC\}$ofthecentroidof$\\triangleABC$\.Theshapesarearoundtheareaof$\\mathcal\{P\}$,haveinternallengthsofintegervaluesandaretouching$\\mathcal\{P\}$atindividuallocations\.Thefourspheresarealsoeachtangenttoasecondplane$\\mathcal\{T\}$andareallonthesamesideof$\\mathcal\{T\}$\.Thevalueof$r$canbewrittenas$\\frac\{m\}\{n\}$,where$m$and$n$arerelativelyprimepositiveintegers\.Find$m\+n$\.

Math Prompt 2Clear Prompt[⬇](data:text/plain;base64,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)Astandardfairsix\-sideddieisrolledrepeatedly\.Eachtimethediereads1or2,Alicegetsacoin;eachtimeitreads3or4,Bobgetsacoin;andeachtimeitreads5or6,Carolgetsacoin\.TheprobabilitythatAliceandBobeachreceiveatleasttwocoinsbeforeCarolreceivesanycoinscanbewrittenas$\\tfracmn,$where$m$and$n$arerelativelyprimepositiveintegers\.Find$100m\+n\.$Ambiguous Prompt[⬇](data:text/plain;base64,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)Astandardfairsix\-sideddieisrolledrepeatedly\.WhenthediehasanumberrelatedtoAlice,sheisrewardedandsimilarly,BobandCarolgetrewardedwhenthedieisrolledinafavorablewaytothem\.TheprobabilitythatAliceandBobeachreceiveatleasttwocoinsbeforeCarolreceivesanycoinscanbewrittenas$\\tfracmn,$where$m$and$n$arerelativelyprimepositiveintegers\.Find$100m\+n\.$

Math Prompt 3Clear Prompt[⬇](data:text/plain;base64,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)EdandSuebikeatequalandconstantrates\.Similarly,theyjogatequalandconstantrates,andtheyswimatequalandconstantrates\.Edcovers$74$kilometersafterbikingfor$2$hours,joggingfor$3$hours,andswimmingfor$4$hours,whileSuecovers$91$kilometersafterjoggingfor$2$hours,swimmingfor$3$hours,andbikingfor$4$hours\.Theirbiking,jogging,andswimmingratesareallwholenumbersofkilometersperhour\.FindthesumofthesquaresofEd’sbiking,jogging,andswimmingrates\.Ambiguous Prompt[⬇](data:text/plain;base64,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)Therearetwopeoplethatbikeatsimilarpace,andonewhichdoesnotchangeovertime\.Similarly,theyjogatequalandconstantrates,andtheyswimatequalandconstantrates\.Edcovers$74$kilometersafterbikingfor$2$hours,joggingfor$3$hours,andswimmingfor$4$hours,whileSuecovers$91$kilometersafterjoggingfor$2$hours,swimmingfor$3$hours,andbikingfor$4$hours\.Theirbiking,jogging,andswimmingratesareallwholenumbersofkilometersperhour\.FindthesumofthesquaresofEd’sbiking,jogging,andswimmingrates\.

Math Prompt 4Clear Prompt[⬇](data:text/plain;base64,QSBsYXJnZSBjYW5kbGUgaXMgJDExOSQgY2VudGltZXRlcnMgdGFsbC4gSXQgaXMgZGVzaWduZWQgdG8gYnVybiBkb3duIG1vcmUgcXVpY2tseSB3aGVuIGl0IGlzIGZpcnN0IGxpdCBhbmQgbW9yZSBzbG93bHkgYXMgaXQgYXBwcm9hY2hlcyBpdHMgYm90dG9tLiBTcGVjaWZpY2FsbHksIHRoZSBjYW5kbGUgdGFrZXMgJDEwJCBzZWNvbmRzIHRvIGJ1cm4gZG93biB0aGUgZmlyc3QgY2VudGltZXRlciBmcm9tIHRoZSB0b3AsICQyMCQgc2Vjb25kcyB0byBidXJuIGRvd24gdGhlIHNlY29uZCBjZW50aW1ldGVyLCBhbmQgJDEwayQgc2Vjb25kcyB0byBidXJuIGRvd24gdGhlICRrJC10aCBjZW50aW1ldGVyLiAoVGhlIGNhbmRsZSBidXJucyBkb3duIGVhY2ggaW5kaXZpZHVhbCBjZW50aW1ldGVyIGF0IGEgZml4ZWQgcmF0ZS4pIFN1cHBvc2UgaXQgdGFrZXMgJFQkIHNlY29uZHMgZm9yIHRoZSBjYW5kbGUgdG8gYnVybiBkb3duIGNvbXBsZXRlbHkuIENvbXB1dGUgdGhlIGNhbmRsZSdzIGhlaWdodCBpbiBjZW50aW1ldGVycyAkXHRmcmFje1R9ezJ9JCBzZWNvbmRzIGFmdGVyIGl0IGlzIGxpdC4=)Alargecandleis$119$centimeterstall\.Itisdesignedtoburndownmorequicklywhenitisfirstlitandmoreslowlyasitapproachesitsbottom\.Specifically,thecandletakes$10$secondstoburndownthefirstcentimeterfromthetop,$20$secondstoburndownthesecondcentimeter,and$10k$secondstoburndownthe$k$\-thcentimeter\.\(Thecandleburnsdowneachindividualcentimeteratafixedrate\.\)Supposeittakes$T$secondsforthecandletoburndowncompletely\.Computethecandle’sheightincentimeters$\\tfrac\{T\}\{2\}$secondsafteritislit\.Ambiguous Prompt[⬇](data:text/plain;base64,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)Alargecandleis$119$centimeterstall\.Itisdesignedtoburndownmorequicklywhenitisfirstlitandmoreslowlyasitapproachesitsbottom\.Specifically,thecandletakes$10$secondstoburndownthefirstcentimeterfromthetop,$20$secondstoburndownthesecondcentimeter,and$10k$secondstoburndownthe$k$\-thcentimeter\.\(Thecandleburnsdowneachindividualcentimeteratafixedrate\.\)Supposeittakes$T$secondsforthecandletoburndowncompletely\.FigureouthowmuchofthecandleisleftintermsofitsheightincentimetersafterithasbeenburningforadurationoftimerelatedtoT\.

Coding Prompt 1Clear Prompt[⬇](data:text/plain;base64,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)\#Consolidate‘ListMixin‘into‘List‘toSimplifyListModelStructureandMaintenanceThe‘ListMixin‘classwasusedtoprovidesupplementalmethodsfor‘/type/list‘objectsinOpenLibrary,butitsexistenceresultedincodeduplicationandfragmentedlogicacrossmultiplemodules\.Thecurrentstructurerequireddeveloperstounderstandandmaintainboththe‘List‘classanditsseparate‘ListMixin‘,increasingcognitiveloadandcreatingpotentialinconsistenciesinobjectbehavior\.Moreover,testdefinitionsfor‘List‘werescatteredacrossunrelatedtestfiles\.Thelisttypeshouldregisteras‘/type/list’withtheapplication’smodelregistryandexposelistbehaviordirectlyonthe‘List’model\.The‘"lists"’changesetmustberegisteredandavailablevia‘ListChangeset’\.Anycoderesolvingalist’sownershouldworkviathe‘List’modelforpersonkeysusingletters,hyphens,orunderscores,yieldingthecorrectownerforeach\.Ambiguous Prompt[⬇](data:text/plain;base64,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)\#Consolidate‘ListMixin‘into‘List‘toSimplifyListModelStructureandMaintenanceThe‘ListMixin‘classwasusedtoprovidesupplementalmethodsfor‘/type/list‘objectsinOpenLibrary,butitsexistenceresultedincodeduplicationandfragmentedlogicacrossmultiplemodules\.Thecurrentstructurerequireddeveloperstounderstandandmaintainboththe‘List‘classanditsseparate‘ListMixin‘,increasingcognitiveloadandcreatingpotentialinconsistenciesinobjectbehavior\.Moreover,testdefinitionsfor‘List‘werescatteredacrossunrelatedtestfiles\.Thestructureshouldbeenteredwithanewnameintheprogrammodeldirectoryandshowlistcharacteristicsforthatmodel\.The‘"lists"‘changesetmustberegisteredandavailablevia‘ListChangeset‘\.Anycoderesolvingalist’sownershouldworkviathe‘List‘modelforpersonkeysusingletters,hyphens,orunderscores,yieldingthecorrectownerforeach\.

Coding Prompt 2Clear Prompt[⬇](data:text/plain;base64,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)\#‘getOpenSubsonicExtensions‘EndpointRequiresAuthenticationDespiteIntendedPublicAccess\*\*The‘getOpenSubsonicExtensions‘endpointiscurrentlypartoftheprotectedroutegroupintheSubsonicAPI\.Asaresult,itrequiresuserauthenticationtoaccess,eventhoughthedataitreturnsisnotintendedforpublicuse\.Thisendpointshouldbepubliclyaccessiblewithoutrequiringauthentication\.AnyclientorapplicationshouldbeabletocallittodeterminewhichOpenSubsonicextensionstheserversupports\.Ambiguous Prompt[⬇](data:text/plain;base64,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)\#‘getOpenSubsonicExtensions‘EndpointRequiresAuthenticationDespiteIntendedPublicAccess\*\*The‘getOpenSubsonicExtensions‘endpointiscurrentlypartoftheprotectedroutegroupintheSubsonicAPI\.Asaresult,itrequiresuserauthenticationtoaccess,eventhoughthedataitreturnsisnotintendedforpublicuse\.Thisendpointshouldbepubliclyaccessiblewithoutrequiringauthentication\.Thefunctionalityshouldbecapableofbeingusedbyotherprogramstofindwhatfeaturesaresupportedontheserver\.

Coding Prompt 3Clear Prompt[⬇](data:text/plain;base64,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)\#\#Title:‘RoomHeaderButtons‘cancrashwhenthreadnotificationsareunsupportedorwhenthe‘room‘propismissing\.Wheninteractingwithhomeserversthatdon’tsupportthreadnotifications,thecomponentstillattemptstoaccessthread\-relatedstateandtoopenthethreadspanel,whichcantriggerruntimeerrors\.Additionally,ifthe‘room‘propisnullorundefined,thecomponentperformsunsafepropertyaccessonroom\-specificfields,whichcanleadtopotentialcrashes\.Thecomponentshouldguardallthread\-relatedaccessesandactionswhenthehomeserverdoesnotsupportthreadnotifications,avoidinganyattempttoopenthethreadspanelinthatscenario\.Itshouldalsosafelyhandleamissing‘room‘prop\.Inbothsituations,renderingshouldcompletewithoutexceptions\.Ambiguous Prompt[⬇](data:text/plain;base64,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)\#\#Title:‘RoomHeaderButtons‘cancrashwhenthreadnotificationsareunsupportedorwhenthe‘room‘propismissing\.Wheninteractingwithhomeserversthatdon’tsupportthreadnotifications,thecomponentstillattemptstoaccessthread\-relatedstateandtoopenthethreadspanel,whichcantriggerruntimeerrors\.Whena‘room‘objectdoesn’thaverealvalues,thecontrollingelementdoesimproperactionsontherelevantcontentwhichcouldresultinfunctionalitybreaking\.Thecomponentshouldguardallthread\-relatedaccessesandactionswhenthehomeserverdoesnotsupportthreadnotifications,avoidinganyattempttoopenthethreadspanelinthatscenario\.Itshouldalsosafelyhandleamissing‘room‘prop\.Inbothsituations,renderingshouldcompletewithoutexceptions\.

Coding Prompt 4Clear Prompt[⬇](data:text/plain;base64,KipBZGQgYSBjb25jdXJyZW50IHF1ZXVlIHV0aWxpdHkgdG8gc3VwcG9ydCBjb25jdXJyZW50IHByb2Nlc3NpbmcgaW4gVGVsZXBvcnQqKgoKKipEZXNjcmlwdGlvbioqCgpUZWxlcG9ydCBjdXJyZW50bHkgbGFja3MgYSByZXVzYWJsZSBtZWNoYW5pc20gdG8gcHJvY2VzcyBpdGVtcyBjb25jdXJyZW50bHkgd2l0aCBhIHdvcmtlciBwb29sIHdoaWxlIHByZXNlcnZpbmcgdGhlIG9yZGVyIG9mIHJlc3VsdHMgYW5kIGFwcGx5aW5nIGJhY2twcmVzc3VyZSB3aGVuIGNhcGFjaXR5IGlzIGV4Y2VlZGVkLiBBIHNvbHV0aW9uIHNob3VsZCBhbGxvdyBzdWJtaXR0aW5nIGl0ZW1zIGZvciBwcm9jZXNzaW5nLCByZXRyaWV2aW5nIHJlc3VsdHMgaW4gaW5wdXQgb3JkZXIsIGFuZCBjb250cm9sbGluZyBjb25jdXJyZW5jeSBhbmQgYnVmZmVyaW5nLgoKVGhlcmUgaXMgY3VycmVudGx5IG5vIGdlbmVyYWwtcHVycG9zZSBjb25jdXJyZW50IHF1ZXVlIGluIHRoZSBjb2RlYmFzZSBmb3IgbWFuYWdpbmcgY29uY3VycmVudCBkYXRhIHByb2Nlc3NpbmcgdGFza3Mgd2l0aCB3b3JrZXIgcG9vbHMgYW5kIG9yZGVyLXByZXNlcnZpbmcgcmVzdWx0IGNvbGxlY3Rpb24uIFRoaXMgdXRpbGl0eSBhZGRyZXNzZXMgdGhlIG5lZWQgZm9yIGEgcmV1c2FibGUsIGNvbmZpZ3VyYWJsZSBtZWNoYW5pc20gdG8gcHJvY2VzcyBhIHN0cmVhbSBvZiB3b3JrIGl0ZW1zIGNvbmN1cnJlbnRseSB3aGlsZSBtYWludGFpbmluZyByZXN1bHQgb3JkZXIgYW5kIHByb3ZpZGluZyBiYWNrcHJlc3N1cmUgd2hlbiBjYXBhY2l0eSBpcyBleGNlZWRlZC4=)\*\*AddaconcurrentqueueutilitytosupportconcurrentprocessinginTeleport\*\*\*\*Description\*\*Teleportcurrentlylacksareusablemechanismtoprocessitemsconcurrentlywithaworkerpoolwhilepreservingtheorderofresultsandapplyingbackpressurewhencapacityisexceeded\.Asolutionshouldallowsubmittingitemsforprocessing,retrievingresultsininputorder,andcontrollingconcurrencyandbuffering\.Thereiscurrentlynogeneral\-purposeconcurrentqueueinthecodebaseformanagingconcurrentdataprocessingtaskswithworkerpoolsandorder\-preservingresultcollection\.Thisutilityaddressestheneedforareusable,configurablemechanismtoprocessastreamofworkitemsconcurrentlywhilemaintainingresultorderandprovidingbackpressurewhencapacityisexceeded\.Ambiguous Prompt[⬇](data:text/plain;base64,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)\*\*AddaconcurrentqueueutilitytosupportconcurrentprocessinginTeleport\*\*\*\*Description\*\*Teleportcurrentlylacksareusablemechanismtoprocessitemsconcurrentlywithaworkerpoolwhilepreservingtheorderofresultsandapplyingbackpressurewhencapacityisexceeded\.Changescouldincludeawaytogiveitemstohandle,gettingresultsinacertainorder,anddealingwithmanyprocessesatoncewithdelaying\.Thereiscurrentlynogeneral\-purposeconcurrentqueueinthecodebaseformanagingconcurrentdataprocessingtaskswithworkerpoolsandorder\-preservingresultcollection\.Thisutilityaddressestheneedforareusable,configurablemechanismtoprocessastreamofworkitemsconcurrentlywhilemaintainingresultorderandprovidingbackpressurewhencapacityisexceeded\.