Instruction Boundary in LLMs

• Instruction Boundary is a measure of how the completeness and structure of prompt instructions shape LLM reasoning, highlighting biases beyond mere knowledge limitations.
• BiasDetector quantifies these biases by evaluating performance under complete, redundant, and insufficient prompt scenarios using metrics like accuracy, generalization rate, and stability rate.
• Empirical studies reveal that even advanced LLMs can exhibit significant output biases and instability when prompt instructions are misaligned, stressing the need for refined prompt engineering.

Instruction Boundary refers to a fundamental vulnerability in LLM reasoning that arises from the degree and nature of prompt coverage—that is, how completely, redundantly, or insufficiently a user’s instructions capture the full intent or possible options of a task. Even when LLMs exhibit high headline accuracy, their outputs can be significantly biased by the boundaries set by prompt design, leading to risks in both everyday and high-stakes applications. This concept shifts focus from the well-studied knowledge boundary (limitations in a model’s internal knowledge or ability to self-diagnose uncertainty) to the subtler but equally impactful ways that prompt formulation and coverage can systematically bias LLM outputs (Ling et al., 24 Sep 2025).

1. Theoretical Foundation and Definition

Instruction Boundary characterizes the extent to which LLM reasoning is subject to the constraints and signals embedded in prompt instructions. It is formally defined as the model's subjective reasoning capability as constrained by the prompt's description, task coverage, and explicitness of guidance. Crucially, biases under the instruction boundary can manifest even upstream of the model’s factual knowledge limitations, arising from the coverage, redundancy, or insufficiency in the instructions given to the system.

The paper distinguishes Instruction Boundary from knowledge boundary: whereas knowledge boundary deals with the LLM’s ability to avoid hallucinations or self-diagnose uncertainty, Instruction Boundary concerns itself with prompt-induced reasoning biases that are directly linked to input design, not just the factual knowledge internal to the model.

Typical manifestations include a tendency for LLMs to overuse labels such as "Unknown" or "True" in well-covered prompts, or produce unstable/hallucinated outputs when key details are omitted or irrelevant information is included.

2. BiasDetector: Framework for Quantitative Evaluation

BiasDetector is introduced as a unified, systematic framework for measuring the influence of Instruction Boundary using three prompt scenarios:

• Complete Instructions: Prompts with a full, unbiased set of options and explicit guidance (vanilla scenario, used as the baseline).
• Redundant Instructions: Prompts containing additional, potentially distracting or conformity-inducing information.
• Insufficient Instructions: Prompts that are missing critical options or detailed guidance, simulating under-specified real-world queries.

BiasDetector evaluates reasoning on eight distilled facets and applies a collection of mathematical metrics:

• Vanilla Accuracy: $$\operatorname{Acc} = \frac{1}{|D|}\sum \mathbb{I}(y_i = \hat{y}_i)$$
• Generalization Rate (GR) and Stability Rate (SR):
  • $$GR = \frac{1}{|D|}\sum \mathbb{I}(y_i = \hat{y}_b\,\,\wedge\,\,y_i \in D_S)$$
  • $$SR = \frac{1}{|D|} \sum \mathbb{I}(y_i = \hat{y}_b)$$
• Additional robustness, instability, and harmonic robustness scores (RS) are provided in LaTeX in the paper.

These metrics capture not only gross accuracy, but also the degree to which reasoning is robust or unstable under perturbations by redundant or insufficient instruction coverage.

3. Empirical Observations and Analysis

Experimental evaluation covers prominent LLMs (e.g., GPT-3.5-turbo, GPT-4o, LLaMA-3.1-8B-Instruct, Claude-3.7-Sonnet, Gemini-2.0-Flash) across multiple settings and task formats. Salient findings include:

• Even when full information is provided (Complete instructions), LLMs nonetheless exhibit answer biases, such as a favoritism for "Unknown" or "True" labels.
• Introducing redundant elements into prompts (Redundant instructions) leads to shifts in output distributions—often a conformity or output-shift effect, where the model echoes the distractor label.
• In Insufficient instruction settings (missing detail or options), models see large accuracy drops (sometimes by tens of percentage points) and increased divergence between GR and SR, reflecting greater output instability or hallucination.
• Multi-turn dialogue or self-reflection can modestly narrow the gap between SR and GR, but does not fully eliminate reasoning biases when prompt coverage is suboptimal.
• Prompt-polishing mechanisms may worsen biases if critical options are omitted during automatic rewriting.

These empirical results demonstrate that LLM output is far more sensitive to prompt design than headline accuracy suggests, particularly when tested on task formats with varying degrees of instruction coverage.

4. Mitigation Strategies and Recommendations

Mitigating the risks associated with Instruction Boundary requires both technical and human-in-the-loop measures:

• Prompt Engineering: Users should frame possible actions or options as “choices,” reducing the model’s propensity for overconfidence or spurious certainty. Careful formulation can mediate instruction-induced biases.
• Macroscopic Modeling: Expanded experimentation with “LLM Judge” paradigms, particularly in high-risk domains, helps to uncover context-dependent biases and to calibrate system behavior appropriately.
• Cautious Use of Prompt-Polishing: Developers should monitor whether automatic prompt rewriting omits key information, potentially introducing additional bias.
• Dialogue-based Self-Reflection: Enabling the model to revisit or reconsider its prior outputs in multi-turn interactions provides a modest buffer against some types of reasoning bias.
• Bias-Aware Evaluation: Applying frameworks like BiasDetector to benchmark and monitor LLM robustness under varying degrees of prompt coverage should become standard practice in high-stakes deployments.

The use of granular, label-sensitive metrics also helps developers identify where models are robust (e.g., for “tense” vs “sparse” label categories) and target mitigation accordingly.

5. Practical Impact and Risk Profile

Instruction Boundary biases have significant implications:

• Low-risk Contexts: In ordinary or educational applications, non-expert users are vulnerable to overconfident or misleading outputs if their prompts are incomplete or distracting.
• High-risk Domains: In critical domains (e.g., legal, medical, financial), prompt-bound reasoning biases may have severe consequences, as models may err confidently when key options are omitted or presented with misleading details.
• The observed decoupling of headline accuracy and robust downstream performance underlines that existing metrics alone do not provide sufficient assurance of reliability under real-world operational conditions.

This effect underscores a new category of risk for LLM-based tools, where reasoning can appear robust in benchmark settings but degrade sharply due to incomplete or misaligned prompt coverage.

6. Future Directions

Research and practical deployment must address several fronts:

• Prompt Design Best Practices: Exploration into prompt structuring and coverage optimization is needed to mitigate instruction-induced reasoning biases.
• Expanded Benchmarks: Combining knowledge boundary (uncertainty estimation) with instruction boundary (coverage sensitivity) in a unified evaluation is necessary for comprehensive trustworthiness assessment.
• Label Sensitivity: Further exploration of how label sparsity or semantic complexity influences robustness will guide model and dataset improvements.
• Dynamic Prompt Adaptation: Development of adaptive mechanisms that signal uncertainty or recommend clarification to users may reduce overconfident or biased outputs.

Ultimately, instruction boundary effects point to the critical importance of prompt engineering and bias-aware evaluation in both research and deployment of LLMs. Addressing these issues is necessary to make progress towards fair, robust, and trustworthy reasoning in both high- and low-stakes real-world scenarios (Ling et al., 24 Sep 2025).