💬 NLP

Localizing Anchoring Pathways in Language Models

This paper investigates the internal mechanisms of anchoring effects in 7B–8B Qwen and Llama models, revealing that edge-level attribution methods more accurately localize the relevant decision signals than node-level methods and that while these pathways are consistent across anchor directions within a model, they shift significantly between base and instruction-tuned variants.

Original authors: Hillary N. Owusu, Sarah Wiegreffe, Naomi H. Feldman

Published 2026-06-12

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CC BY 4.0

Original authors: Hillary N. Owusu, Sarah Wiegreffe, Naomi H. Feldman

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a large language model (LLM) as a super-smart, but slightly gullible, detective. You give it a riddle to solve, but you also slip a random, irrelevant number into the conversation—like telling the detective, "By the way, the lottery ticket stopped on 15," before asking, "How many days does it take for the moon to orbit Earth?"

Even though the detective knows the answer is 27 days, that random "15" might make them lean a little too hard toward 15. This is called anchoring. It's a cognitive bias where an irrelevant number pulls your judgment toward it.

This paper is like a team of mechanical engineers taking that detective apart to see exactly where in their brain the "gullibility" happens. They want to know: Which specific wires and switches inside the computer are carrying the signal that says, "Hey, that random number matters!"

Here is how they did it and what they found, explained simply:

1. The Setup: A Controlled Game

Instead of letting the detective write a long essay, the researchers turned the test into a multiple-choice game.

The Question: "How long is a moon orbit?" (Correct answer: 27 days).
The Trap: They added a sentence with a random number, either a "Low Anchor" (15) or a "High Anchor" (49).
The Goal: They measured how much the model's confidence shifted toward the wrong answer (15 or 49) just because that number was mentioned.

They confirmed that the models did get tricked, just like humans do.

2. The Method: Tracing the Wires

To find the "gullibility circuits," the researchers used a technique called Circuit Localization.

The Analogy: Imagine the model is a giant city with millions of roads (edges) connecting neighborhoods (nodes).
The Old Way: Researchers used to look at whole neighborhoods (nodes) to see where the traffic was heavy.
The New Way: This paper found that looking at the individual roads (edges) is much better. It's like realizing that the problem isn't the whole "Downtown" neighborhood, but specifically the one bridge connecting Downtown to the suburbs.

They found that edge-level methods (looking at the connections) were far more accurate at finding the bias than node-level methods (looking at the components alone). The "gullibility" isn't stuck in one specific part of the brain; it's in the pathway the information travels.

3. The Findings: What the Map Revealed

A. The "Low" and "High" Anchors use the same roads

Whether the model was tricked by a low number (15) or a high number (49), the traffic flowed through almost the exact same set of roads.

The Metaphor: It's like a river. Whether the water is flowing fast (high anchor) or slow (low anchor), it still uses the same riverbed. The model has a shared "susceptibility pathway" for being influenced by numbers, regardless of whether the number is big or small.

B. The "Base" vs. "Instruction-Tuned" Models

The researchers tested two versions of the same model:

Base Model: The raw, untrained detective.
Instruction-Tuned Model: The detective who has been trained to follow rules and answer questions politely.

The Surprise: While they use the same general "riverbed" (the same layers of the network), the specific roads that matter most changed after training.

The Metaphor: Imagine you teach a driver a new route. They still drive through the same city, but the specific streets they take to get to the destination have changed. The "instruction tuning" (the training) rewired the most important connections. A circuit that worked perfectly on the raw model didn't always work on the trained model.

4. The Big Picture

This paper proves that anchoring isn't just a "glitch" in the model's knowledge. It's a specific, mechanical process where irrelevant numbers hijack the model's decision-making pathways.

Key Takeaway: The bias travels through connections (edges), not just isolated parts.
Key Takeaway: Low and high anchors share the same "highway," but teaching the model new rules (instruction tuning) changes which exits on that highway are most important.

In short, the researchers mapped the "gullibility" inside the AI, showing us exactly which wires carry the signal when the model gets distracted by a random number. This helps us understand that the model isn't just "wrong"; it's following a specific, predictable path that leads it astray.

Technical Summary: Localizing Anchoring Pathways in Language Models

Problem Statement

Large Language Models (LLMs), like humans, exhibit anchoring bias, where an irrelevant numerical value in a prompt shifts subsequent judgments toward that value, even when the model possesses the correct factual knowledge. While prior work has established the existence of this behavioral phenomenon, it has largely treated the model as a black box, measuring the magnitude of the shift without explaining the internal mechanisms. This paper addresses the gap in mechanistic interpretability: specifically, identifying which internal pathways within an LLM carry the signal that causes an irrelevant anchor to compete with the correct answer during prediction.

Methodology

1. Controlled Task Setup

The authors adapted 100 numerical-estimation questions from the Open Anchoring Question Dataset (OpAQ) into a controlled multiple-choice format.

Prompt Structure: Each item includes a factual question, a ground-truth answer, and an irrelevant "slot machine" sentence containing either a low anchor, a high anchor, or a token-matched control (non-numeric string).
Answer Space: A fixed set of nine options is used across all conditions, containing the ground truth, the anchors, and intermediate values. The model is instructed to output only the answer letter.
Models Evaluated: Four open-weight decoder-only models from the Qwen2.5 and Llama-3.1 families:
- Base models: Qwen2.5-7B, Llama-3.1-8B.
- Instruction-tuned variants: Qwen2.5-7B-Instruct, Llama-3.1-8B-Instruct.

2. Metrics

Behavioral Metric: Normalized Expected Value (EV) shift measures the direction and magnitude of the shift in the model's probability distribution toward the anchor.
Attribution Metric: A logit-difference metric ( $m$ $m$ ) is defined as the difference between the logit of the correct answer and the logit of the active anchor answer ( $m = \text{logit}(y_{correct}) - \text{logit}(y_{anchor})$ $m = logit (y_{cor r ec t}) - logit (y_{an c h or})$ ).
- A decrease in $m$ indicates the anchor is becoming more competitive.
- The change in this metric ( $\Delta m$ ) between anchored and control prompts serves as the target for circuit localization.
- Validation confirmed that $\Delta m$ correlates strongly with behavioral EV shifts.

3. Circuit Localization Framework

The study employs attribution-based circuit localization to identify the minimal subgraph of the model responsible for the anchoring effect.

Graph Representation: The transformer is treated as a computation graph where nodes are components (attention heads, MLPs) and edges are directed pathways.
Methods Compared:
- Node Attribution Patching (NAP/NAP-IG): Scores individual components.
- Edge Attribution Patching (EAP/EAP-IG): Scores directed pathways between components.
- Integrated Gradients (IG): Variants (NAP-IG, EAP-IG) average gradients along an interpolation path to improve attribution quality.
Faithfulness Evaluation: The authors measure Circuit Performance Recovery (CPR). They retain the top- $k\%$ ranked edges/nodes from the "clean" (control) run and patch the rest with activations from the "corrupted" (anchored) run. A high CPR score indicates that the retained subgraph successfully recovers the model's unanchored behavior.

Key Contributions

Metric Validation: The paper establishes a validated answer-level metric (logit difference) that tracks behavioral anchoring, enabling the use of gradient-based attribution for circuit localization.
Edge vs. Node Localization: The study demonstrates that edge-level methods (EAP, EAP-IG) recover the anchoring signal significantly more faithfully than node-level methods (NAP, NAP-IG). This suggests the bias is better understood as a property of pathways between components rather than isolated "biased" components.
Structural Analysis of Circuits:
- Layer-wise Patterns: Qwen models concentrate attribution in mid-to-late layers, while Llama models concentrate it in earlier layers.
- Component Types: The top-ranked circuits are dominated by attention-to-attention edges (approx. 68–80% of selected edges), with significant involvement of attention-MLP connections, suggesting MLPs participate via attention-mediated pathways.
Transferability Findings:
- Within-Model: Low- and high-anchor circuits share substantial structure (approx. 66–71% shared edges) and transfer well across anchor contrasts within the same model.
- Cross-Variant: While base and instruction-tuned models share broad layer-wise attribution patterns, the specific sparse edges that matter most change after instruction tuning. Cross-variant transfer is less reliable, particularly for low-anchor contrasts and sparse circuits.

Results

Faithfulness: EAP-IG (Edge Attribution Patching with Integrated Gradients) emerged as the most faithful localization method, achieving CPR scores often exceeding 0.90 across models and conditions. In contrast, node-level methods (NAP) scored significantly lower (e.g., 0.36–0.67).
Anchoring Structure:
- Low- and high-anchor circuits within a single model are nearly identical in their layer-wise depth distribution (Pearson correlation > 0.99) and share roughly two-thirds of their top-ranked edges.
- Instruction tuning preserves the general depth of attribution but alters the specific sparse edges that drive the effect. For example, in Qwen-7B, cross-variant faithfulness for low-anchor contrasts dropped from 0.917 (matched) to 0.291 when using the instruction-tuned ranking.
Model Differences: Qwen models exhibit stronger behavioral anchoring and later-layer attribution compared to Llama models, which show earlier-layer concentration.

Significance and Claims

The paper claims to provide a mechanistic account of how anchoring-related decision signals are carried inside language models. By framing anchoring as a circuit localization problem, the authors move beyond measuring that a bias occurs to understanding how it is computed.

Key implications drawn by the authors include:

Pathway vs. Component: Anchoring is a pathway-level phenomenon; isolating specific "biased" nodes is less effective than identifying the flow of information between components.
Shared Mechanisms: The strong transfer between low and high anchors suggests a shared internal mechanism for anchor sensitivity, rather than distinct failure modes for different anchor directions.
Post-Training Sensitivity: The reduced transferability between base and instruction-tuned models indicates that post-training changes which specific pathways are critical for this bias, implying that mitigation strategies may need to be re-evaluated after fine-tuning.
Methodological Contribution: The work demonstrates the utility of applying circuit localization to cognitive biases, offering a framework to move from behavioral observation to mechanistic understanding of prompt-induced biases.

The authors remain modest, noting that their findings are specific to the multiple-choice formulation and a specific dataset (OpAQ), and that the identified circuits represent the mechanism for the validated logit-difference metric rather than every possible manifestation of anchoring in open-ended generation.