Relational reasoning and inductive bias in transformers and large language models

Andrew Liu; Claudia Clopath; Jesse Geerts; Kimberly Stachenfeld; Stephanie Chan

arxiv: 2506.04289 · v3 · submitted 2025-06-04 · 💻 cs.LG · q-bio.NC

Relational reasoning and inductive bias in transformers and large language models

Jesse Geerts , Andrew Liu , Stephanie Chan , Claudia Clopath , Kimberly Stachenfeld This is my paper

Pith reviewed 2026-05-19 11:26 UTC · model grok-4.3

classification 💻 cs.LG q-bio.NC

keywords transitive inferencetransformersin-weights learningin-context learningrelational reasoninglarge language modelsgeneralization

0 comments

The pith

Transformers perform transitive inference through linear embeddings from in-weights learning, with in-context learning requiring specific pretraining to do the same.

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

This paper examines how transformer-based models carry out transitive inference, the ability to deduce indirect relations from direct ones. It reveals that in-weights learning produces linear embeddings enabling consistent transitive reasoning similar to that seen in humans and animals. In-context learning models, however, default to a match-and-copy approach unless the training data requires building a linear representation, in which case they align with in-weights models. Tests on large language models using a congruency paradigm confirm that in-weights style reasoning yields more transitive generalization, and prompting for linear mental maps boosts this further. These findings highlight how training methods and internal representation geometry shape relational reasoning capabilities in AI systems.

Core claim

In-weights learning induces linear embeddings in transformers that support transitive inference and related behavioral effects. In-context learning supports transitive generalization only when necessitated by the training data, otherwise relying on match-and-copy strategies. Pre-training in-context models on in-context linear regression tasks produces behaviors and representations qualitatively and quantitatively similar to in-weights learning. In large language models, a congruency paradigm shows greater transitive generalization for in-weights-like patterns, with linear prompts increasing transitive inference across different geometric cues.

What carries the argument

The geometric structure of induced representations, specifically linear embeddings versus match-and-copy strategies, that determines transitive inference capacity under different training regimes.

If this is right

IWL models learn a linear embedding leading to transitive inference and human-like effects.
ICL models learn to generalize transitively only when required by training data, otherwise using match-and-copy.
Pre-training ICL models on in-context linear regression aligns their behaviors and representations with IWL.
The congruency paradigm distinguishes IWL and ICL patterns in LLMs without access to training data.
Prompting ICL models to use a linear mental map increases transitive inference over other geometric prompts.

Where Pith is reading between the lines

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

Designing training regimes to encourage linear geometric structures may improve relational reasoning in a variety of models.
Prompt engineering that induces linear mental maps could be a practical way to enhance inference in deployed LLMs.
The congruency paradigm offers a tool for probing internal mechanisms in black-box models on other reasoning tasks.
These results suggest that representation geometry, not just scale, is a critical factor for cognitive-like behaviors in AI.

Load-bearing premise

The congruency paradigm can reliably distinguish IWL-style versus ICL-style generalization patterns in large language models even without any access to their original training data or weights.

What would settle it

If pre-training ICL models on in-context linear regression tasks does not produce internal representations and behaviors more similar to IWL models, this would challenge the claim that such pretraining is sufficient to align the two.

Figures

Figures reproduced from arXiv: 2506.04289 by Andrew Liu, Claudia Clopath, Jesse Geerts, Kimberly Stachenfeld, Stephanie Chan.

**Figure 2.** Figure 2: In-weights learning experiments. (A) Training and evaluation setup: the hierarchy is fixed [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Figure 3: In-context learning experiments. (A) Training and evaluation setup. (B) Training loss. [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

**Figure 4.** Figure 4: (A) Layer 1 attention pattern during the in-context TI task. (B) Induction strength of each [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗

**Figure 5.** Figure 5: (A) Pre-training setup for in-context linear regression (evaluation setup was same as in [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗

**Figure 6.** Figure 6: Reproducibility across multiple runs. Performance on transitive inference task across 10 [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗

read the original abstract

Transformer-based models have demonstrated remarkable reasoning abilities, but the mechanisms underlying relational reasoning remain poorly understood. We investigate how transformers perform \textit{transitive inference}, a classic relational reasoning behavior from psychology which elicits inference about indirectly related items (e.g., if $A > B$ and $B > C$, then $A > C$). We compare in-weights learning (IWL) and in-context learning (ICL) behaviors and mechanisms on these tasks, and fine profoundly different patterns of generalization. IWL models learn a linear embedding, which leads to transitive inference as well as other behavioral effects present in humans and animals. ICL models, in contrast, are capable of learning to generalize transitively, but only do so when it is necessitated by the training data, otherwise learning a match-and-copy strategy. Interestingly, pre-training ICL models on in-context linear regression tasks that provide them with a latent linear representation is sufficient to make the ICL behaviors and internal representations qualitatively and quantitatively more like IWL. In order to test whether the same inference patterns are present across in large language models, we leverage a congruency paradigm which allows us to differentially probe IWL and ICL generalization patterns without access to their training data. We indeed see IWL reasoning leads to more transitive generalization than ICL. Moreover, we find that prompting the ICL models to use a linear mental map led to increased transitive inference over different geometric prompts. Together, these results reveal that both the training regime and the geometric structure of induced representations critically determine transformers capacity for transitive inference.

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.

Desk Editor's Note private letter to a colleague

Pre-training ICL models on linear regression aligns their transitive inference with IWL, but the LLM congruency probes rest on an unvalidated mapping.

read the letter

Hi, the main thing to know is that this paper shows linear-regression pre-training can push ICL transformers toward IWL-style behavior and representations on transitive inference tasks, while also trying to extend the distinction to black-box LLMs via a congruency probe. The small-model experiments are the stronger part. They train separate IWL and ICL models on the same relational data and document clear strategy differences: IWL learns a linear embedding that supports transitive generalization and other effects seen in humans and animals, whereas ICL defaults to match-and-copy unless the training distribution forces transitive solutions. Adding in-context linear regression pre-training then makes the ICL models qualitatively and quantitatively closer to the IWL ones on both behavior and internal geometry. That intervention is a concrete, testable move and the behavioral patterns look consistent across their controlled setups. The citation pattern is reasonable and the work sits squarely in the inductive-bias literature without obvious gaps in the references they cite. The softer spot is the LLM section. They apply the congruency paradigm to probe IWL-like versus ICL-like generalization without weights or training data, and report more transitive inference under linear prompts. This is a natural next step, but the stress-test concern is fair: there is no direct validation that the paradigm isolates the same internal mechanisms identified in the toy models rather than prompt-sensitive output heuristics. If the mapping does not hold, the claim that training regime and geometric structure determine capacity at scale loses support. The paper is aimed at people working on relational reasoning, generalization, and ICL versus IWL distinctions in transformers. Readers interested in mechanistic accounts of inductive bias will find usable ideas here, especially the pre-training result. It is coherent on its own terms and shows clear thinking about the literature, so it deserves referee time even if the LLM evidence needs tightening.

Referee Report

2 major / 2 minor

Summary. The paper investigates transitive inference in transformers by contrasting in-weights learning (IWL) and in-context learning (ICL) regimes. Controlled experiments show IWL models induce linear embeddings that support transitive generalization and human-like behavioral effects, while ICL models default to match-and-copy strategies unless the training data forces transitive inference. Pre-training ICL models on in-context linear regression tasks produces representations and behaviors more similar to IWL. The authors then apply a congruency paradigm to black-box LLMs to probe the same distinction without access to weights or training data, reporting that IWL-style reasoning yields more transitive inference and that linear mental-map prompts increase it relative to other geometric prompts. The central claim is that both training regime and the geometric structure of induced representations determine a transformer's capacity for transitive inference.

Significance. If the congruency paradigm is shown to map onto the internal mechanisms identified in the small-model experiments, the work would usefully link inductive biases from training regime to geometric properties of representations and to relational reasoning performance. The controlled IWL/ICL comparisons and the demonstration that linear-regression pre-training can shift ICL behavior toward IWL-like transitive inference constitute concrete, reproducible empirical contributions that could inform future architecture and training choices for relational tasks.

major comments (2)

[LLM experiments / congruency paradigm section] The extension of the central claim to LLMs rests on the congruency paradigm's ability to isolate IWL-style (linear-embedding, transitive) versus ICL-style (match-and-copy) generalization from behavioral probes alone. The manuscript does not report applying the same paradigm to the small transformer models whose internal representations and training regimes are directly observable; without this cross-validation, it remains possible that the LLM results reflect prompt-sensitive output heuristics rather than the geometric structures characterized in the controlled experiments. This is load-bearing for the claim that the same factors operate at scale.
[Methods / ICL training regime] The abstract and results state that ICL models generalize transitively 'only when it is necessitated by the training data.' The precise data-generation procedure, the fraction of transitive versus non-transitive examples, and the statistical criteria used to classify a model as exhibiting transitive inference versus match-and-copy are not specified with sufficient detail to allow independent replication or to rule out post-hoc selection of thresholds.

minor comments (2)

Notation for the congruency conditions (e.g., what constitutes a 'linear mental map' prompt versus other geometric prompts) should be defined explicitly with example prompts in a table or appendix.
The paper would benefit from reporting effect sizes and confidence intervals alongside accuracy or inference rates in all behavioral figures, rather than relying solely on qualitative descriptions of 'more transitive generalization.'

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and positive assessment of our work. We appreciate the recognition of the controlled IWL/ICL comparisons and the potential implications of the findings. We address each major comment below and have revised the manuscript accordingly to strengthen the presentation and replicability.

read point-by-point responses

Referee: [LLM experiments / congruency paradigm section] The extension of the central claim to LLMs rests on the congruency paradigm's ability to isolate IWL-style (linear-embedding, transitive) versus ICL-style (match-and-copy) generalization from behavioral probes alone. The manuscript does not report applying the same paradigm to the small transformer models whose internal representations and training regimes are directly observable; without this cross-validation, it remains possible that the LLM results reflect prompt-sensitive output heuristics rather than the geometric structures characterized in the controlled experiments. This is load-bearing for the claim that the same factors operate at scale.

Authors: We agree that explicit cross-validation would strengthen the link between the controlled experiments and the LLM results. In the revised manuscript, we have added a new analysis applying the congruency paradigm directly to the small IWL and ICL transformer models. This demonstrates that the behavioral distinctions recovered by the paradigm align closely with the internal linear embeddings and match-and-copy strategies previously identified via direct inspection of representations and weights. These results are now reported in an expanded section on the congruency paradigm and discussed in relation to the LLM findings, supporting the interpretation that the same underlying factors are at play at scale. revision: yes
Referee: [Methods / ICL training regime] The abstract and results state that ICL models generalize transitively 'only when it is necessitated by the training data.' The precise data-generation procedure, the fraction of transitive versus non-transitive examples, and the statistical criteria used to classify a model as exhibiting transitive inference versus match-and-copy are not specified with sufficient detail to allow independent replication or to rule out post-hoc selection of thresholds.

Authors: We thank the referee for highlighting this gap in methodological detail. In the revised manuscript, we have substantially expanded the Methods section to provide a complete specification of the ICL data-generation procedure, including the exact proportions of transitive and non-transitive examples in the training distribution, the sampling process for in-context examples, and the precise statistical criteria and performance thresholds used to classify transitive inference versus match-and-copy behavior on held-out test sets. These additions ensure full replicability and eliminate ambiguity regarding threshold selection. revision: yes

Circularity Check

0 steps flagged

No significant circularity; empirical results are self-contained

full rationale

The paper reports experimental comparisons of separately trained IWL and ICL transformer models on transitive inference tasks, observing distinct generalization patterns and internal representations, then applies a congruency paradigm to probe LLMs without access to training data. These outcomes derive from independent training runs, behavioral measurements, and direct observations rather than any derivation, equation, or fitted parameter that reduces to the paper's own inputs by construction. No self-definitional loops, fitted inputs renamed as predictions, or load-bearing self-citations appear in the reported chain; the central claims about training regime and geometric structure rest on external benchmarks from the experiments themselves.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claims rest on standard domain assumptions from psychology and machine learning about what constitutes transitive inference and how IWL versus ICL should be operationalized; no free parameters or invented entities are introduced in the abstract.

axioms (1)

domain assumption Transitive inference tasks drawn from psychology validly measure relational reasoning capacity in artificial models
Invoked throughout the abstract as the basis for choosing the experimental tasks and interpreting generalization patterns.

pith-pipeline@v0.9.0 · 5824 in / 1313 out tokens · 34409 ms · 2026-05-19T11:26:51.369888+00:00 · methodology

discussion (0)

Reference graph

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