A Modular Dataset to Demonstrate LLM Abstraction Capability¶

Conference: ACL 2025
arXiv: 2503.17645
Code: None
Area: LLM/NLP
Keywords: LLM Reasoning, Internal Representations, Activation Classifiers, Intermediate Transformer Layers, Abstract Reasoning

TL;DR¶

This paper proposes the ArrangementPuzzle dataset and trains LLM activation classifiers, finding that the classifiers identify reasoning correctness with >80% accuracy. This reveals that LLMs encode abstract reasoning concepts distinguishing logical equivalence from semantic equivalence in middle-to-late Transformer layers.

Background & Motivation¶

Large language models (LLMs) demonstrate impressive capabilities, but they still frequently exhibit hallucinations and logical errors in reasoning tasks. A core question is: Do LLMs truly "understand" the reasoning process internally, or are they merely performing surface-level pattern matching? If models indeed internalize the distinction between correct and incorrect reasoning steps, it could be possible to correct reasoning errors by manipulating these internal representations.

However, existing studies lack a structured, verifiable reasoning dataset to systematically probe the internal representations of LLM reasoning. Most reasoning benchmarks (e.g., GSM8K, MATH) focus on the correctness of the final answer rather than the internal encoding of step-by-step reasoning. The core idea of this study is to design a modular puzzle dataset where each reasoning step can be automatically verified, and then train probing classifiers using the activation values of LLM intermediate layers to reveal the location and characteristics of internal representations of reasoning correctness.

Method¶

Overall Architecture¶

The entire research pipeline consists of three phases: (1) constructing the ArrangementPuzzle dataset, (2) collecting layer-wise activation values during LLM problem-solving, and (3) training probing classifiers to analyze the internal encoding of reasoning correctness in LLMs.

Key Designs¶

ArrangementPuzzle Dataset:
- Function: Provides a puzzle task with structured solutions and an automated, step-by-step verification mechanism.
- Mechanism: Each puzzle is defined by a set of modular arrangement rules. Whether each reasoning step is correct can be automatically determined via the rules without manual annotation. This modular design of the dataset enables precise control over difficulty and the number of reasoning steps.
- Design Motivation: Unlike natural language reasoning problems, each step of the puzzle has a clear correctness criterion, eliminating evaluation ambiguity. The modular design also allows researchers to systematically vary task complexity and observe changes in LLM reasoning performance.
Activation Probing Classifier:
- Function: Trains classifiers on the activation values of various LLM layers to predict whether the current reasoning step is correct.
- Mechanism: Given a reasoning step, the hidden state vector \(\mathbf{h}_l\) of each LLM layer is extracted, and a linear classifier \(f(\mathbf{h}_l) \rightarrow \{0, 1\}\) is trained to judge the correctness of the reasoning.
- Design Motivation: If a classifier's accuracy at a certain layer is significantly higher than chance, it indicates that the layer encodes information about reasoning correctness. Layer-wise comparison helps localize where the reasoning information is encoded.
Logical Equivalence vs. Semantic Equivalence Analysis:
- Function: Analyzes whether LLMs internally distinguish between the concepts of logical equivalence and semantic equivalence.
- Mechanism: Leveraging the structural characteristics of ArrangementPuzzle, sample pairs are constructed that are logically equivalent (different valid formulations of the same reasoning step) or semantically similar but logically different. The intermediate layer representations of the LLM are then analyzed to see if they can separate the two.
- Design Motivation: If the LLM only captures surface semantic similarity, it cannot distinguish between "seemingly correct" and "actually correct" reasoning, which is the root cause of hallucinations.

Loss & Training¶

The probing classifiers utilize simple linear models or shallow MLPs to prevent the classifiers themselves from learning complex reasoning capabilities, thereby ensuring that the detected information indeed originates from the LLM's internal representations rather than the classifier itself.

Key Experimental Results¶

Main Results¶

Metric	Middle-to-Late Layer Classifiers	Early Layer Classifiers	Random Baseline
Reasoning Correctness Prediction Accuracy	>80%	~60%	50%
Logical Equivalence Identification	Significantly higher than semantic equivalence	No obvious difference	-

Ablation Study¶

Configuration	Classification Accuracy	Description
All Layers	~80%	Richest integrated information
Middle-to-Late Layers Only (middle-late)	>80%	Highest concentration of reasoning information
Early Layers Only	~60%	Weaker reasoning information
Last Layer Only	Slightly lower than middle-to-late	Information might be diluted by output format encoding

Key Findings¶

The middle-to-late layers are the core region for encoding reasoning information, where classifiers achieve the highest accuracy.
LLMs indeed distinguish internally between correct and incorrect reasoning steps, implying that hallucinations might not stem from a lack of reasoning capacity, but rather from a failure to successfully exploit existing internal representations.
LLMs can distinguish between logical equivalence and semantic equivalence in their intermediate layers, indicating that their internal representations possess a certain level of abstract reasoning capability.
These findings hint at the possibility of correcting LLM reasoning errors through activation editing.

Highlights & Insights¶

Methodological Innovation: The modular design of ArrangementPuzzle allows reasoning correctness to be verified step-by-step automatically, addressing the limitation of existing benchmarks that can only evaluate the final answer.
Reusable Trick: The combination of a probing classifier and a structured reasoning task can be transferred to other scenarios for analyzing reasoning capabilities.
Inspiring Findings: Reasoning information is concentrated in the middle-to-late layers, which aligns with findings in representation engineering and activation steering, offering an intervention target for reasoning capabilities.

Limitations & Future Work¶

The paper is only 7 pages long, and the scale of the experiments is limited (model types and data scale are not detailed).
ArrangementPuzzle is a simple, synthetically constructed puzzle, which has a significant gap from the complexity of natural language reasoning.
Whether the high accuracy of the probing classifier implies that the information is "usable" still needs further verification (linear readability does not equal causal influence).
No activation intervention experiments were conducted to verify if modifying representations can indeed improve reasoning.

vs. Representation Probing (Belinkov 2022): Continues the classic probing methodology but innovatively applies it to step-by-step reasoning correctness determination.
vs. Representation Engineering (Zou et al. 2023): Ours finding that reasoning information localizes in the middle-to-late layers is consistent with findings in representation engineering where "concept vectors" are strongest in intermediate layers.
vs. Chain-of-Thought Analysis: Ours focuses on the internal encoding of the reasoning process rather than the external quality of the CoT text.

Rating¶

Novelty: ⭐⭐⭐⭐ The dataset design is clever, but the probing method itself is not new.
Experimental Thoroughness: ⭐⭐⭐ The 7-page limit constrains the depth and breadth of the experiments.
Writing Quality: ⭐⭐⭐⭐ Clear problem motivation and a complete logical chain.
Value: ⭐⭐⭐⭐ Provides an important empirical foundation for understanding and improving LLM reasoning.