Instruction Hierarchy in Systems

• Instruction hierarchy is a structured ordering of directives based on authority, abstraction, and priority across diverse systems.
• It enables detailed task decomposition and robust scheduling in domains such as real-time computing, compiler design, and AI planning.
• Empirical approaches using techniques like segment embeddings and intermediate representation augmentation significantly improve instruction compliance and safety.

Instruction hierarchy refers to any explicit or implicit structure in which instructions, tasks, or directives are ordered, layered, or prioritized according to authority, abstraction, privilege, granularity, or logical decomposition. The concept is critical across real-time systems, compiler and programming environments, AI planning, robotics, multi-agent natural language processing, and, more recently, in the alignment and safety of LLMs. This entry surveys technical definitions, underlying methodologies, and the state of empirical research on instruction hierarchies, spanning hardware, software, and AI systems.

1. Fundamental Concepts and Definitions

Instruction hierarchy can involve several, sometimes orthogonal, dimensions across systems:

• Privilege/Authority Level: Instructions are ordered according to trust, such as system, developer, user, and external tool inputs (Wallace et al., 19 Apr 2024, Wu et al., 9 Oct 2024, Zhang et al., 12 Feb 2025, Geng et al., 21 Feb 2025, Wan et al., 27 Sep 2025).
• Abstraction Granularity: High-level, abstract instructions decompose into finer-grained subtasks, procedures, or primitive actions (Arumugam et al., 2017, Köhn et al., 2020, Zhou et al., 2021).
• Structural Order or Priority: Within code, instructions or program components are arranged for maintainability and comprehension, either by convention or via machine-learned orderings (Reiss et al., 2017).
• Hardware and Execution Order: In processors and heterogeneous systems, hierarchical execution flows through pipelines, multi-level cache hierarchies, or dataflow graphs (0807.0993, Srivastava et al., 2016, Ausavarungnirun et al., 2018).
• Knowledge Hierarchies: In knowledge dissemination and instruction generation, hierarchy mirrors the progression from data, to information, to knowledge, to wisdom (DIKW) (Zhou et al., 2023).

A consistent theme is that the instruction hierarchy informs mechanisms for (a) ambiguity resolution, (b) conflict arbitration, and (c) efficient, modular decomposition of tasks.

2. Instruction Hierarchy in Hardware and Software Systems

2.1. Multi-Level Cache and Execution Hierarchies

In real-time embedded systems, evaluating worst-case execution time (WCET) requires instruction cache analyses that respect the multi-level set-associative and fully associative cache hierarchy (0807.0993). The hierarchical analysis is necessary since L1 and L2 caches differ in size and associativity, affecting hit/miss behavior and execution timing. Safe WCET estimation merges uncertain accesses at each level with formulations such as

$$\text{ACS}_{\text{out}} = \operatorname{Join}(\operatorname{Update}(\text{ACS}_{\text{in}}, r), \text{ACS}_{\text{in}})$$

and computes hit costs across the hierarchy:

$\text{COST}_\text{first}(r) = \sum_{\ell=1}^n T_\text{hit,\ell} \cdot \text{present}_\text{first,\ell}(r)$

allowing for tight yet safe WCET prediction.

2.2. Hierarchical Instruction Representation in Compilers

In systems targeting heterogeneous hardware (e.g., CPUs, GPUs), hierarchically-structured dataflow graphs (DFGs) are used to express parallel tasks at multiple granularities. HPVM, for instance, utilizes a virtual instruction set and intermediate representation that encode computation hierarchies through nodes and intrinsics in LLVM IR, supporting flexible mapping to hardware units and tiling for memory locality (Srivastava et al., 2016).

2.3. Program Order Hierarchies in Code Organization

A machine-learned instruction hierarchy model can be constructed to order program components (fields, methods, classes) via a region-based structure and decision tree classifiers, supporting project-specific conventions and facilitating automated code insertion, reordering, and maintainability (Reiss et al., 2017).

3. Hierarchical Planning and Abstraction in AI and Robotics

Hierarchical decomposition is foundational in planning and instruction interpretation.

3.1. Grounding Multi-Level Natural Language Instructions

Robotics frameworks achieve instruction hierarchy by inferring the appropriate abstraction (level $\ell$) and associated reward function ($m$):

$$(\hat{\ell}, \hat{m}) = \arg\max_{\ell, m} P(\ell, m \mid c)$$

mapping commands to a planning hierarchy structure. Statistical models (IBM Model 2) and deep neural architectures handle alignment and translation between language and reward representations, yielding efficiency and flexibility in human-robot interaction (Arumugam et al., 2017).

3.2. Hierarchical Task Networks in Instruction Generation

Hierarchical Task Network (HTN) planning is applied to instruction generation, decomposing complex tasks (e.g., building structures in Minecraft) into high-level and low-level actions according to

$\mathcal{P} = (F, C, A, M, I, s_0)$

where tasks $C$ and primitive actions $A$ are recursively expanded by decomposition methods $M$ until atomic steps are obtained. Cost functions over $(2^F, A)$ balance the granularity and efficiency of instructions based on user knowledge and context (Köhn et al., 2020).

3.3. Hierarchical Modular Networks for Control

Hierarchical modular networks realize instruction hierarchy in situated agents via a planner (mapping NL to procedural programs) and modular reactors (handling environmental feedback), representing tasks as hierarchically nested, compositional programs. This supports robust and efficient control in tasks such as embodied question answering and household manipulation (Zhou et al., 2021).

4. Instruction Hierarchy in LLMs: Safety and Robustness

4.1. Vulnerabilities and Baseline Limitations

LLMs are prone to prompt injection and role override attacks because traditional architectures treat all input instructions equally, lacking any principled hierarchy (Wallace et al., 19 Apr 2024, Wu et al., 9 Oct 2024, Zhang et al., 12 Feb 2025, Geng et al., 21 Feb 2025). Benchmarks like IHEval demonstrate that, given conflicting inputs (system message vs. user prompt), most open-source and proprietary models exhibit sharp performance degradation—often within 20–50 percentage points—compared to their baseline instruction-following accuracy, with only 48% accuracy in resolving conflicts for state-of-the-art systems (Zhang et al., 12 Feb 2025).

4.2. Architectural and Training Solutions

(a) Explicit Prioritization via Instruction Hierarchy

An explicit function $P(\cdot)$ maps instructions to privilege levels, and models are trained such that, for conflicting $I_1$, $I_2$,

$$\text{If } P(I_1) > P(I_2) \text{, follow } I_1; \text{ else, follow } I_2.$$

Training pipelines inject diverse, adversarial instruction sets to teach prioritization, yielding substantial increases in attack robustness with minimal task degradation (Wallace et al., 19 Apr 2024).

(b) Segment Embedding Approaches

Instructional Segment Embedding (ISE), inspired by BERT segment encoding, augments every token $x_m$ with a segment embedding indicating system/user/data/output role:

$$\text{Embedding}_m = \text{Tok}[x_m] + \text{Seg}[h_m]$$

with a segment table $\text{Seg} \in \mathbb{R}^{H \times D}$ (e.g., $H=4$). This embedding is preserved across all transformer layers, making privilege signals persistent and robust to injection and extraction manipulation, with observed gains in robust accuracy up to 18.68% (Wu et al., 9 Oct 2024).

(c) Intermediate Representation Augmentation

Augmented Intermediate Representations (AIR) inject layer-specific, trainable privilege embeddings at every transformer block:

$x'_{i,j} = x_{i,j} + s_j^{k}$

where $s_j^{k}$ is retrieved from a table $S_j$ for privilege level $k$ and block $j$. This approach provides between $1.6\times$ and $9.2\times$ lower attack success rates in gradient-based prompt injection without significant utility loss (Kariyappa et al., 25 May 2025).

(d) Surgical Alignment in Multi-Agent Systems

In multi-agent systems, fine-grained diagnostic metrics such as Contextualized Role Adherence Score (CRAS) are used to locate instruction misprioritization through attention drift analysis in model mid-layers. Surgical Alignment of Instruction Layers (SAIL) then applies token-weighted preference optimization via LoRA adapters only to these layers, increasing system-level instruction compliance by up to 5.6% on medical QA tasks (Wan et al., 27 Sep 2025).

4.3. Empirical Findings and Limitations

Despite such solutions, broad evaluations show that only architecture-level embedding strategies or direct intermediate representation injection yield robust instruction discrimination. Prompt engineering and standard fine-tuning offer, at best, modest and inconsistent improvements; constraint bias and explicit conflict recognition remain critical hurdles (Geng et al., 21 Feb 2025, Wu et al., 9 Oct 2024).

5. Data-Centric and Knowledge Hierarchies in Instruction Sets

5.1. Hierarchical Labeling for Dataset Construction

Large-scale instruction datasets can be systematically expanded in both “coverage” and “depth” using a hierarchical labeling system, with tags first generated and clustered by similarity and then mapped to domain-level categories (Du et al., 9 Jul 2025). Coverage (domain/topic representation) and depth (complexity, e.g., multi-skill or high-loss instructions) are critical for model generalizability. Statistical analyses reveal scale-free properties (degree distributions) and entropy-based measures to evaluate instruction set diversity.

5.2. Closed-Loop Data Evolution

Iterative closed-loop pipelines drive instruction diversity, incorporating informative seed selection (e.g., by token loss, tail tags, or multi-tagging), evolutionary data synthesis (by mutating instruction parameters), and deficiency feedback (oracle-based diagnosis triggers targeted synthesis) (Du et al., 9 Jul 2025).

6. Applications and Impact Across Domains

Instruction hierarchy is central to:

• Real-time and Embedded Systems: Safe WCET analysis, tight execution bounds, reliable scheduling (0807.0993).
• Parallel/Heterogeneous Programming: Scalable, portable code synthesis, analytics workflows (Srivastava et al., 2016).
• Human-Robot and Multi-Agent Interaction: Flexible and robust language grounding, hierarchical planning, and multi-level command resolution (Arumugam et al., 2017, Köhn et al., 2020, Zhou et al., 2021).
• Software Engineering: Automated code reordering, refactoring, and maintainability augmentation (Reiss et al., 2017).
• LLM Safety and Compliance: Resilience to adversarial instructions, improved robustness, conversational alignment, and reliable delegation in multi-agent environments (Wallace et al., 19 Apr 2024, Wu et al., 9 Oct 2024, Zhang et al., 12 Feb 2025, Geng et al., 21 Feb 2025, Kariyappa et al., 25 May 2025, Wan et al., 27 Sep 2025).

The future direction for instruction hierarchy research lies in refining architecture-level signals, formal robustness guarantees, and scalable, real-world evaluation across autonomous, conversational, and agentic LLM deployments.