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Representational Analysis of Binding in Language Models

Qin Dai, Benjamin Heinzerling, Kentaro Inui

arXiv:2409.05448v3cs.CL

TL;DR

Entity tracking depends on binding entities to their attributes, while the Binding ID account raises questions about how ordering information relates to binding. The paper analyzes activations and edits an ordering-encoding subspace; interventions shift which attribute a model binds to an entity, with the subspace reported across several model families.

  • Problem

    Entity tracking requires binding entities to attributes, and the Binding ID account raises whether entities’ OI-PC representations are consistent.

    Source: §1 · p. 1, §4.6 · p. 7

  • Method

    The authors use PCA and ICA to analyze entity-tracking activations, then intervene along the localized OI subspace to test its role in binding.

    Source: §1 · p. 2, §4.3 · p. 5

  • Results

    Editing along OI-PC shifts attribute choices: the original attribute’s logit difference falls as other attributes rise, and the OI subspace is reported across multiple LM families.

    Source: §1 · p. 2, §4.3 · p. 5

  • Takeaways & Limitations

    The authors conclude that a low-rank activation subspace encoding ordering information serves as a prototype of Binding IDs and causally determines binding.

    Source: §6 · p. 9

    The analysis uses a synthesized entity-tracking dataset, so real-world entity binding remains unexamined.

    Source: Limitations · p. 10

Abstract

from arXiv · show

Entity tracking is essential for complex reasoning. To perform in-context entity tracking, language models (LMs) must bind an entity to its attribute (e.g., bind a container to its content) to recall attribute for a given entity. For example, given a context mentioning ``The coffee is in Box Z, the stone is in Box M, the map is in Box H'', to infer ``Box Z contains the coffee'' later, LMs must bind ``Box Z'' to ``coffee''. To explain the binding behaviour of LMs, existing research introduces a Binding ID mechanism and states that LMs use a abstract concept called Binding ID (BI) to internally mark entity-attribute pairs. However, they have not captured the Ordering ID (OI) from entity activations that directly determines the binding behaviour. In this work, we provide a novel view of the BI mechanism by localizing OI and proving the causality between OI and binding behaviour. Specifically, by leveraging dimension reduction methods (e.g., PCA), we discover that there exists a low-rank subspace in the activations of LMs, that primarily encodes the order (i.e., OI) of entity and attribute. Moreover, we also discover the causal effect of OI on binding that when editing representations along the OI encoding direction, LMs tend to bind a given entity to other attributes accordingly. For example, by patching activations along the OI encoding direction we can make the LM to infer ``Box Z contains the stone'' and ``Box Z contains the map''.

1 Introduction

Entity tracking requires models to bind entities to attributes so they can later retrieve the right information. This work identifies ordering information in activations as a causal influence on binding and offers a revised view of the Binding ID mechanism.

1 Introduction

  • Entity tracking supports complex reasoning by requiring a model to retain and retrieve information associated with an entity.Source: §1 · p. 1
  • Prior Binding ID accounts describe BI as marking entity-attribute pairs, but do not capture ordering information in entity activations that affects binding (Feng and Steinhardt, 2023).Source: §1 · p. 1
  • OI information occupies a low-rank activation subspace that can causally alter binding, leading models to infer a different attribute for a given entity.Patching along the OI-encoding principal component can change Box Z’s inferred content from coffee to stone or map.Source: §1 · p. 2
  • The OI subspace associated with binding is reported across Llama2, Llama3, Qwen1.5, Pythia, and code-fine-tuned Float-7B.The authors describe it as primarily encoding the order index of entities and attributes in context.Source: §1 · p. 2

2 Finding OI Subspace

The method localizes Ordering ID information by examining entity-token activations and identifying directions that encode order. PCA is the primary approach, with other dimension-reduction methods also applied.

2 Finding OI Subspace

  • The method extracts query activations for entity tokens and arranges them as rows in a relation-specific activation matrix.Each row corresponds to an entity token’s activation.Source: §2 · p. 2
  • The approach also applies Independent Component Analysis alongside PCA to capture the OI subspace.Source: §2 · p. 3
  • The working hypothesis is that entities with the same OI cluster together despite differing in semantic meaning, with OI encoded as directions in the subspace.Source: §2 · p. 3
  • PCA is used to identify principal directions in the activation matrix, with its first c directions designated as the OI direction subspace.Source: §2 · p. 3

3 OI Subspace Visualization

Layer-wise visualizations show that OI is more clearly organized in middle-layer activations than in other layers. Similar patterns are reported across several model families.

3 OI Subspace Visualization

  • The visualization projects entity activations into two dimensions, with each point representing an entity and colors indicating OI.Source: §3 · p. 3
  • Middle layers, especially layer 8, show a visible direction along which OI increases, while other layers have tangled distributions.Source: §3 · p. 3
  • Similar OI distribution patterns are reported for Llama3-8B, Float-7B, Qwen1.5, and Pythia, in addition to Llama2-7B.Source: §3 · p. 3

4 Causal Interventions on OI Subspace

The section tests whether intervening along the OI subspace changes binding, then examines how that subspace relates to position, pair consistency, and relational binding. Across direct editing and activation steering, interventions shift the attributes LMs infer, while analyses distinguish OI encoding from absolute position and binding relation.

4.1 Activation Patching

  • Activation patching edits representations directly along OI-PC to test whether changing that direction alters model output and binding computation.The approach differs from common activation patching, which replaces activations using corrupted inputs.Source: §4 · p. 3, §4.1 · pp. 3–4

4.2 Setting

  • The experiments use entity-tracking contexts with seven entity-attribute pairs and evaluate interventions using logit difference and logit flip.The dataset asks the model to infer the attribute associated with a queried box.Source: §4.2 · p. 4

4.3 Results: Direct Editing OI Subspace

  • Adding one OI-PC step changes the inferred attribute from “coffee” to “stone”; doubling the step shifts it to “map,” though some attributes repeat or are skipped.OI occupies continuous ranges on OI-PC, so an edit can leave an entity within its original range or skip a neighboring range.Source: Table 1 · p. 4, §4.3 · p. 5
  • Increasing OI-PC intervention steps lowers the original attribute’s logit difference and raises the matching target attribute’s logit difference and output proportion, supporting a causal effect on binding.At three steps, BI_3 attributes have the highest logit difference and become the major answers.Source: §4.3 · pp. 5–6, Figure 3 · p. 5, Figure 4 · p. 7

4.4 Results: Activation Steering on OI Subspace

  • Activation steering toward BI 3 increases the logit difference and answer proportion for a3, matching the direct-editing trend and supporting an OI-subspace role in binding.The reported steering result is on the entity-tracking dataset; other datasets are reported in the appendix.Source: §4.4 · p. 6

4.5 OI Subspace and Position

  • With positional information varied while OI is preserved, OI-PC distributions remain similar; filler-word tests also show high correlation with OI but almost zero correlation with position.Together, these tests indicate that OI-PC does not simply encode absolute token position.Source: §4.5 · pp. 6–7

4.6 Consistency of OI Subspace

  • Related entity-attribute pairs tend to have smaller OI-PC distances across binding patterns, and PC1-based distance performs significantly better than distances from other PCs.A threshold selected on development data is used to classify potentially related pairs in a test set.Source: §4.6 · p. 8

4.7 OI Subspace and Relatedness

  • Non-related pairs retain strong OI-PC correlation despite a slight decrease from related pairs, suggesting OI-PC primarily encodes order rather than binding relation.The authors describe the relational information in OI-PC as limited.Source: §4.7 · p. 9

5 Related Work

The paper extends linear-representation research by finding that language models can linearly encode Ordering ID (OI) along an OI-increasing direction in activations.

Linear Representation

  • Multiple language models, including Llama2, linearly encode OI along an OI-increasing activation direction.The section also describes OI-PC distance classification and OI-PC correlations between attributes and corresponding entities.Source: §5 · p. 9

6 Conclusion and Future Work

The paper studies in-context binding and proposes that a low-rank activation subspace encodes ordering information and serves as a prototype for Binding IDs that causally determine binding. Future work includes more realistic settings, interaction with pretrained factual knowledge, and further mechanistic analysis.

6 Conclusion and Future Work

  • The paper studies in-context binding, a skill underlying complex reasoning and natural language understanding tasks.Source: §6 · p. 9
  • A low-rank LM activation subspace primarily encodes ordering information and serves as a Binding ID prototype that causally determines binding.Source: §6 · p. 9
  • Future work includes analyzing the OI subspace in more realistic settings, its interaction with pretrained factual knowledge, and its mechanistic basis.Source: §6 · p. 9

Limitations

The study identifies limits in task coverage, PCA explanation, relation coverage, and dataset realism, and it restricts activation analysis to query tokens while leaving OI–BI interaction and the subspace-generating mechanism unresolved.

Limitations

  • The analysis covers attribute prediction but not entity inference, and offers no theoretical account of why PCA captures the OI subspace.Source: Limitations · p. 10
  • The study does not analyze how predicates affect the OI subspace or how intervention results vary by predicate type.Source: Limitations · p. 10
  • The adopted entity-tracking dataset is synthesized, so analysis on real-world data remains necessary for understanding binding and tracking in reality.Source: Limitations · p. 10
  • Analysis is limited to query-part activations; the OI–BI interaction is not directly observed, and the subspace's generation and use circuit remain unexplained.Source: Limitations · p. 10

Ethical Statement

The authors use publicly available entity-tracking datasets and language models according to their intended research purposes, and report no ethical concern from human-annotation or semantic bias in their synthetic datasets.

Ethical Statement

  • The authors report no ethical concern from human-annotation or semantic bias because their synthetic datasets follow existing dataset patterns and use sampled one-token names and concepts.Source: Ethical Statement · p. 10

A.1 Other Related Work

The related work distinguishes localization of pretrained factual relations in model weights from analysis of in-context relations in activations. It also notes that prior accounts of binding and entity-tracking circuits did not capture ordering information in entity activations.

Knowledge Localization

  • Knowledge-localization work studies factual relations stored in model weights, whereas this paper analyzes in-context relations in activations.The cited studies address relation localization and editing in pretrained models.Source: §A.1 · p. 13

Mechanistic Interpretability

  • Prior circuit work includes identifying an entity-tracking circuit, while Feng and Steinhardt (2023) proposed a Binding ID mechanism for entity-attribute pairs.Their account did not capture Ordering ID information from entity activations.Source: §A.1 · p. 13
  • The stated gap is that prior Binding ID accounts omit entity-activation Ordering ID information that directly determines binding behaviour.Source: §A.1 · p. 13

A.2 Partial least squares regression and PCA

The section compares PCA with supervised PLS regression as ways to capture Ordering ID. Both methods’ first directions score close to one on the target entity’s OI.

A.2 Partial least squares regression and PCA

  • Near one, the regression score for both the first PCA component and first PLS direction indicates that each contains almost all target-entity OI information.Source: §A.2 · p. 13, Figure 11 · p. 13
  • PLS is supervised dimension reduction that maximizes feature-score covariability, while PCA is described as unsupervised dimension reduction.Source: §A.2 · p. 13
  • Figure 11 presents regression curves for PCA and PLS as the visual comparison of their OI scores.Source: Figure 11 · p. 13, §A.2 · p. 13

A.3 ICA for OI Subspace

The appendix reports that OI-subspace interventions affect binding across model settings, including a fine-tuned model and a dataset with interjections. It also examines ICA, layer sensitivity, and visualizations or interventions across several model families and relations.

A.3 ICA for OI Subspace

  • ICA yields a subspace distribution generally similar to PCA and produces intervention results similar to PCA-based intervention.The authors conclude ICA can also capture the OI subspace computationally.Source: Figure 12 · p. 14, Figure 13 · p. 14, §A.3 · p. 14

A.4 Layer-wise Intervention

  • Layers 7–15, especially layer 8, significantly affect binding computation and overlap with layers that clearly encode OI.Source: Figure 14 · p. 15, §A.4 · p. 15

A.5 Layer-wise Embedding Visualization on Llama3-8B and Float-7B; A.6 OI Subspace on other LM Families

A.7 Case Study on Llama2-7B

  • Directed OI-PC activation patching reports inferred attributes for Llama2-7B across the sell, apply, move, bring, and push datasets.The table captions indicate that color denotes BI.Source: Table 7 · p. 18, Table 8 · p. 18, Table 9 · p. 19

A.8 Activation Steering on Llama2-7B

A.9 Results on Fine-Tuned LM

  • Around 10, Float-7B’s maximum LD for a4 is twice Llama2-7B’s around 5, and Float-7B is more sensitive to OI-subspace intervention.The reported intervention results are similar to those on Llama2-7B.Source: Figure 20 · p. 22, §A.9 · p. 22, Figure 21 · p. 23

A.10 Activation Patching on Llama3-8B

A.11 New Dataset with Interjections

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