Feature Resemblance: Towards a Theoretical Understanding of Analogical Reasoning in Transformers

Ruichen Xu; Wenjing Yan; Ying-Jun Angela Zhang

cs.CLMar 5, 2026

Feature Resemblance: Towards a Theoretical Understanding of Analogical Reasoning in Transformers

Authors: Ruichen Xu, Wenjing Yan, Ying-Jun Angela Zhang

Organizations: Department of Information Engineering, The Chinese University of Hong Kong, Hong Kong.

Abstract

Understanding reasoning in large language models is complicated by evaluations that conflate multiple reasoning types. We isolate analogical reasoning, where a model transfers an attribute between entities that share known properties, and study when such transfer can emerge from training. To make the problem analytically tractable, we study a minimal transformer-style abstraction that isolates how learned representations support analogical reasoning. Within this setting, we prove three key results. First, joint training on similarity and attribution premises enables analogical reasoning through aligned representations. Second, sequential training succeeds only when similarity structure is learned before specific attributes, revealing a curriculum asymmetry. Third, in our stylized setting, two-hop reasoning $(a \to b, b \to c \Rightarrow a \to c)$ can be viewed as analogical reasoning with identity bridges $(b=b)$ , which appear explicitly in training data. Together, these results reveal a unified mechanism: entities with shared properties become aligned in representation space, enabling property transfer through feature resemblance. Experiments with architectures up to 8B parameters show qualitative agreement with the theory and suggest that representational geometry plays an important role in analogical reasoning beyond the stylized model.

Figures & tables

Training tasks for Analogical Reasoning	Architecture	Training loss	Feature similarity	Success rate on $\mathcal{A}$
Joint training on $\biguplus_{k=1}^{\kappa}(\mathcal{S}_{1}\cup\mathcal{S}_{2})\biguplus\mathcal{S}_{3}$	GPT-2	0.0077 $\pm$ 1e-4	0.995 $\pm$ 6e-4	100% $\pm$ 0%
Joint training on $\biguplus_{k=1}^{\kappa}(\mathcal{S}_{1}\cup\mathcal{S}_{2})\biguplus\mathcal{S}_{3}$	One-layer	0.001 $\pm$ 5e-5	0.9202 $\pm$ 7e-4	100% $\pm$ 0%
Late training on the attribution premise $\mathcal{S}_{3}$	GPT-2	0.0845 $\pm$ 3e-4	0.7983 $\pm$ 0.027	100% $\pm$ 0%
Late training on the attribution premise $\mathcal{S}_{3}$	One-layer	0.0024 $\pm$ 0	0.9689 $\pm$ 4e-4	100% $\pm$ 0%
Late training on the similarity premise $\mathcal{S}_{2}$	GPT-2	0.0085 $\pm$ 1e-4	0.4326 $\pm$ 0.012	0.7% $\pm$ 0.471%
Late training on the similarity premise $\mathcal{S}_{2}$	One-layer	0.0061 $\pm$ 5e-5	0.0014 $\pm$ 3.7e-3	0% $\pm$ 0%

Table 1: Training loss, feature similarity, and success rate: mean

\pm

standard deviation of analogical reasoning and two-hop reasoning tasks over one-layer and GPT-2 transformers. GPT-2 is trained end-to-end with AdamW. We set

\kappa=3

and show the impact of

\kappa

in Appendix C .

Models	Tasks	Fea. Sim.	Success rate
Llama	Joint training	0.8174	73%
	Late on attribution	0.7990	86%
	Late on similarity	0.6431	53%
Qwen	Joint training	0.8488	85%
	Late on attribution	0.7971	72%
	Late on similarity	0.7455	33%

Table 2: Feature similarity and success rate over Llama-3-1B and Qwen-2.5-1.5B.

Tasks	Fea. Sim.	Success rate
Joint training	0.3785	84%
Late on Attribution	0.3757	75%
Late on Similarity	0.2704	34%

Table 3: Feature similarity and success rate over Qwen-3-8B.

Appendix figures & tables5 assets

Supplementary material from the paper’s appendix.

Appendix

Training tasks for Analogical Reasoning	Architecture	Training loss	Feature similarity	Success rate on $\mathcal{A}$
Joint training on $\biguplus_{k=1}^{\kappa}(\mathcal{S}_{1}\cup\mathcal{S}_{2})\biguplus\mathcal{S}_{3}$	One-layer	0.0133 $\pm$ 2e-4	0.9413 $\pm$ 3e-4	100% $\pm$ 0%
Late training on the attribution premise $\mathcal{S}_{3}$	One-layer	0.0198 $\pm$ 1e-4	0.7116 $\pm$ 2.2e-3	100% $\pm$ 0%
Late training on the similarity premise $\mathcal{S}_{2}$	One-layer	0.0138 $\pm$ 1e-4	0.4367 $\pm$ 1.2e-3	0.67% $\pm$ 0.47%

Appendix

Table 4: Training loss, feature similarity, and success rate: mean

\pm

standard deviation of analogical reasoning tasks over one-layer transformers. These results are under end-to-end training .

Values of $\kappa$	Architecture	Training loss	Feature similarity	Success rate on $\mathcal{A}$
$\kappa=1$	GPT-2	0.0294 $\pm$ 3e-4	0.9756 $\pm$ 5e-4	100% $\pm$ 0%
$\kappa=1$	One-layer	0.0079 $\pm$ 5e-5	0.6706 $\pm$ 9e-4	100% $\pm$ 0%
$\kappa=3$	GPT-2	0.0077 $\pm$ 1e-4	0.995 $\pm$ 6e-4	100% $\pm$ 0%
$\kappa=3$	One-layer	0.001 $\pm$ 5e-5	0.9202 $\pm$ 7e-4	100% $\pm$ 0%
$\kappa=5$	GPT-2	0.0039 $\pm$ 5e-4	0.9979 $\pm$ 3e-4	100% $\pm$ 0%
$\kappa=5$	One-layer	5e-4 $\pm$ 1e-4	0.9405 $\pm$ 2e-4	100% $\pm$ 0%

Appendix

Table 5: Training loss, feature similarity, and success rate: mean

\pm

standard deviation of analogical reasoning tasks over one-layer and GPT-2 transformers. These results are under end-to-end training .

Figure 1: Feature cosine similarity of data with the same labels of deep linear neural networks and GPT-2 trained on orthogonal data.

Subject 1	Subject 2	Aspect	Relation	Category
Apple	Pear	Tree	AtLocation	Fruit
Ant	Bee	Small	HasProperty	Insect
Eagle	Hawk	Hunting	CapableOf	Bird of Prey
Bed	Sofa	Resting	UsedFor	Furniture
Boots	Sneakers	Outfit	PartOf	Footwear

Appendix

Table 6: Dataset Sample Examples

Relation	Natural Language Template
AtLocation	[subject] is found in [Aspect]
MadeOf	[subject] is made of [Aspect]
UsedFor	[subject] is used for [Aspect]
CapableOf	[subject] is capable of [Aspect]
HasProperty	[subject] is [Aspect]
PartOf	[subject] is part of [Aspect]

Appendix

Table 7: Sentence Templates of Relations

Analogical Reasoning

Analogical reasoning studies how systems transfer relations and solutions between situations with shared structure, enabling inference beyond direct examples.

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Analogical reasoning is a hallmark of human intelligence, enabling us to solve new problems by transferring knowledge from one situation to another. Yet, developing artificial intelligence systems capable of robust human-like analogical reasoning has proven difficult. In this work, we train transformers using Meta-Learning for Compositionality (MLC) on an analogical reasoning task (letter-string analogies) and assess their generalization capabilities. We find that letter-string analogies become learnable when guiding the models to attend to the most informative problem elements, induced by including copy tasks in the training data. Furthermore, generalization to new alphabets improves when models are trained with more heterogeneous datasets. For the best training run, our 3-layer encoder-decoder model performs on par with frontier models on our letter-string analogy datasets. The MLC approach also enables some generalization to compositions of trained transformations, but not to completely novel transformations. To understand how the model solves the analogies, we identify an algorithm for one analogy task that approximates the model's computations. We verify this using interpretability analyses and show that head-level attention weights causally affect model output, allowing steering between different analogy tasks. We discuss the implications of our findings for generalization capabilities of larger models and the parallels to human analogical reasoning.

Abstract

Analogical Reasoning

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