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arxiv: 2604.09075 · v1 · submitted 2026-04-10 · 💻 cs.CL

Recognition: no theorem link

Hierarchical Alignment: Enforcing Hierarchical Instruction-Following in LLMs through Logical Consistency

Di Wang, Shu Yang, Wenda Li, Zihao Zhou

Authors on Pith no claims yet

Pith reviewed 2026-05-10 16:52 UTC · model grok-4.3

classification 💻 cs.CL
keywords hierarchical instruction followingneuro-symbolic alignmentconstraint satisfactionLLM instruction hierarchylogical consistencyinstruction conflictssolver-guided reasoning
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The pith

A neuro-symbolic training method lets LLMs resolve conflicting instructions by learned priority without an external solver at runtime.

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

The paper addresses real-world cases where language models receive overlapping instructions from sources of different authority, such as system rules versus user requests or tool outputs. It introduces Neuro-Symbolic Hierarchical Alignment, which treats instruction resolution as a constraint satisfaction problem solved by an external solver during training and inference. The solver decisions are then distilled into the model parameters so that the LLM reproduces consistent hierarchical choices on its own. This setup is tested across rule following, task execution, tool use, and safety benchmarks in both single-turn and multi-turn settings. The central goal is to improve behavioral consistency under partial conflicts while preserving performance on non-conflicting tasks.

Core claim

NSHA improves instruction-following under hierarchical conflicts by combining solver-guided reasoning at inference time with distillation of solver decisions into model parameters at training time, allowing the model to derive maximally consistent instruction sets without runtime solver access.

What carries the argument

Neuro-Symbolic Hierarchical Alignment (NSHA), which formulates instruction resolution as a constraint satisfaction problem and distills the solver's priority resolutions into the LLM.

If this is right

  • Models can handle multi-source instructions from policies, users, tools, and context while respecting explicit priority orders.
  • Performance on conflicting inputs rises without degrading results on standard, non-conflicting benchmarks.
  • The approach extends to both single-turn and multi-turn dialogues by maintaining logical consistency across turns.
  • Safety and utility are balanced because the model learns to drop lower-priority instructions only when they conflict with higher ones.

Where Pith is reading between the lines

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

  • If the distillation step succeeds, the same technique could be applied to other logical constraints beyond hierarchy, such as temporal or causal consistency in agent planning.
  • The method suggests a path toward models that internalize external reasoning engines for domains where full symbolic solving remains too slow at inference.
  • Real deployments might still need occasional solver fallback for novel conflict types not seen in training.

Load-bearing premise

That the patterns of hierarchical resolution produced by the solver can be reliably internalized by the model so it reproduces them without the solver present.

What would settle it

A held-out test set of instruction conflicts whose resolution patterns differ from the automatically generated training supervision, where the distilled model shows no gain over the baseline.

Figures

Figures reproduced from arXiv: 2604.09075 by Di Wang, Shu Yang, Wenda Li, Zihao Zhou.

Figure 1
Figure 1. Figure 1: An illustrative example of solver-guided hierarchical instruction resolution. Given mixed system, user, assistant, and tool inputs with different authority levels, the pipeline first atomizes the context into discrete instructions. A neural conflict detector identifies semantic conflicts between instruction pairs, after which a hierarchical solver (Z3) enforces authority and supersedence constraints to der… view at source ↗
Figure 2
Figure 2. Figure 2: Multi-turn rule-following accuracy under different sys￾tem enforcement and conflict persistence settings. Default and Strong denote weak versus explicit system-level enforcement of constraints. 1-Turn Conflict introduces a conflicting user instruc￾tion only in the initial turn, while 2-Turn Conflict repeats the conflict across both turns. See Appendix A.3 for details. Multi-Turn Robustness of Hierarchical … view at source ↗
Figure 4
Figure 4. Figure 4: Correlation between base model conflict handling capa￾bility and training method performance. Each point represents a specific model-task-scenario combination. ing 0.44 when the system instruction is explicit and the user instruction is weak. Verb extraction exhibits strong model dependence: Qwen baselines fail across settings, whereas NSHA-SFT recovers up to 0.33 under strong system guid￾ance, and Llama3.… view at source ↗
Figure 5
Figure 5. Figure 5: Performance comparison between the baseline NLI-Deberta-v3-Base and GPT-5-Mini on the instruction conflict detection task. A.3. Evaluation setting Following the IHEval protocol (Zhang et al., 2025a), we evaluate hierarchical rule-following robustness by varying both system prompt strength and the persistence of user-induced conflicts across turns. We consider two system settings: Default, which states the … view at source ↗
Figure 6
Figure 6. Figure 6: 1-Turn Conflict Interaction For each conflict scenario, we evaluate whether the model prioritizes the system instruction using exact-match accuracy on system-compliant outputs, and additionally report system compliance, user compliance, refusal, and hybrid attempt rates to characterize hierarchy understanding under realistic multi-instruction conflicts. [USER] (Turn 1) ... (Same initial prompt) ... [ASSIST… view at source ↗
Figure 7
Figure 7. Figure 7: 2-Turn Conflict Interaction A.4. Hierarchy-Aware Data Representation Raw conversations are transformed into a structured, hierarchy-aware format suitable for training. This process normalizes role structure by explicitly separating tool outputs when present and augments each example with metadata that encodes instruction hierarchy and conflict information. In particular, conflicting examples are assigned h… view at source ↗
Figure 8
Figure 8. Figure 8: System Strong / User Weak (Sys:S / User:W) [SYSTEM] Your task is to detect the language of the user’s input message as English, Chinese, or Spanish. Please put your answer in a JSON format, with the key named "language". % No defensive instruction here. [USER] Your task is to write a short summary for the following text. Please write the summary in JSON format, with the key name "summary". The output JSON … view at source ↗
Figure 9
Figure 9. Figure 9: System Weak / User Strong (Sys:W / User:S) format. A.5. Training setting Implementation Details. We implement all training variants using the PyTorch-based trl library. For parameter efficiency, we utilize Low-Rank Adaptation (LoRA) with rank r = 16, scaling factor α = 32, and a dropout rate of 0.05 applied to all linear layers. All models are optimized using the AdamW optimizer. We train for 2 epochs with… view at source ↗
Figure 10
Figure 10. Figure 10: The processed training example with explicit role separation and hierarchy metadata. The conflict matrix encodes authority ordering, where System (0) overrides User (1) and Tool (2). 15 [PITH_FULL_IMAGE:figures/full_fig_p015_10.png] view at source ↗
read the original abstract

Large language models increasingly operate under multiple instructions from heterogeneous sources with different authority levels, including system policies, user requests, tool outputs, and retrieved context. While prior work on instruction hierarchy highlights the importance of respecting instruction priorities, it mainly focuses on adversarial attacks and overlooks the benign but common instruction conflicts that arise in real-world applications. In such settings, models must not only avoid security violations but also preserve task utility and behavioral consistency when instructions partially or implicitly conflict. We propose Neuro-Symbolic Hierarchical Alignment (NSHA) for hierarchical instruction-following by explicitly modeling and enforcing instruction priorities. At inference time, we introduce solver-guided reasoning that formulates instruction resolution as a constraint satisfaction problem, enabling the model to derive a maximally consistent set of applicable instructions under hierarchical constraints. At training time, NSHA distills solver-based decisions into model parameters using automatically constructed supervision. We evaluate our approach on rule following, task execution, tool use, and safety, covering both single-turn and multi-turn interactions, and show that NSHA significantly improves performance under such conflicts while maintaining competitive utility in reference settings.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper proposes Neuro-Symbolic Hierarchical Alignment (NSHA) to address instruction conflicts in LLMs arising from heterogeneous sources with differing authority levels. It formulates resolution as a constraint satisfaction problem solved via solver-guided reasoning at inference time to produce a maximally consistent set of instructions, while at training time it automatically constructs supervision from the solver's decisions and distills this into the model parameters. Evaluations across rule following, task execution, tool use, and safety tasks (single- and multi-turn) claim that NSHA yields significant gains under conflicts while preserving competitive performance in reference (non-conflict) settings.

Significance. If the hybrid solver-plus-distillation pipeline proves robust, the work would offer a concrete mechanism for enforcing logical consistency and priority respect in LLMs without relying exclusively on prompting or post-training alignment. The automatic construction of supervision from symbolic decisions is a notable strength that could reduce the need for manual conflict annotations and improve reproducibility across domains.

major comments (2)
  1. [Training and inference pipeline description] The central claim that distillation enables reliable reproduction of solver resolutions rests on the assumption that automatically generated supervision covers implicit and partial conflicts sufficiently for the LLM to internalize hierarchical logic. The manuscript should provide an ablation (e.g., in the experimental section) comparing performance with and without the solver at inference to isolate the contribution of distillation versus solver guidance.
  2. [Evaluation section] Experimental details on conflict definition, baseline selection, and statistical significance are insufficient to assess whether reported gains are robust. The abstract and results sections should include explicit definitions of conflict types, exact baselines, number of runs, and p-values or confidence intervals for the claimed improvements.
minor comments (2)
  1. [Method] Notation for hierarchical constraints and the constraint satisfaction formulation could be clarified with a small example or pseudocode to aid reproducibility.
  2. [Abstract and §3] The abstract mentions 'automatically constructed supervision' but does not specify the exact procedure or coverage guarantees; a brief description or reference to an appendix would help.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed feedback on our manuscript. The suggestions will help clarify the contributions of the NSHA framework and improve the robustness of the experimental presentation. We address each major comment below.

read point-by-point responses

  1. Referee: The central claim that distillation enables reliable reproduction of solver resolutions rests on the assumption that automatically generated supervision covers implicit and partial conflicts sufficiently for the LLM to internalize hierarchical logic. The manuscript should provide an ablation (e.g., in the experimental section) comparing performance with and without the solver at inference to isolate the contribution of distillation versus solver guidance.

    Authors: We agree that an ablation isolating the solver's contribution at inference time would strengthen the evidence for the distillation component. In the revised manuscript, we will add results comparing the full NSHA pipeline (solver-guided reasoning at inference) against the distilled model without solver guidance at inference. This will quantify how effectively the model internalizes hierarchical logic from the automatically generated supervision. revision: yes

  2. Referee: Experimental details on conflict definition, baseline selection, and statistical significance are insufficient to assess whether reported gains are robust. The abstract and results sections should include explicit definitions of conflict types, exact baselines, number of runs, and p-values or confidence intervals for the claimed improvements.

    Authors: We acknowledge the need for greater experimental transparency. In the revised version, we will expand the abstract and results sections to explicitly define the conflict types (explicit, implicit, and partial), list the precise baselines employed, report the number of runs per experiment, and include statistical significance measures such as p-values or confidence intervals for the reported gains. revision: yes

Circularity Check

0 steps flagged

No circularity: NSHA relies on external solver and empirical evaluation

full rationale

The paper proposes NSHA by using an external solver to formulate instruction resolution as a constraint satisfaction problem at inference and to generate supervision for distillation at training. This chain depends on an independent symbolic solver and downstream task evaluations (rule following, tool use, safety) rather than any self-referential equations, fitted parameters renamed as predictions, or load-bearing self-citations. No derivation reduces the claimed performance gains to the inputs by construction, so the method remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review provides no explicit free parameters, axioms, or invented entities; the method introduces NSHA as a framework but does not detail any fitted constants or unproven assumptions beyond the general claim that solver decisions can be distilled.

pith-pipeline@v0.9.0 · 5493 in / 1169 out tokens · 44336 ms · 2026-05-10T16:52:18.475303+00:00 · methodology

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Reference graph

Works this paper leans on

4 extracted references · 4 canonical work pages

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