Deterministic Anchoring Effect

• Deterministic anchoring effect is a stable bias where initial values or static structures reproducibly direct subsequent judgments in tasks like syntactic annotation, LLM reasoning, and code-agent navigation.
• Empirical studies show that this effect can inflate performance metrics in parser reviews, shift LLM output distributions, and improve reproducibility in code agents via deterministic tagging.
• Mitigation strategies involve selective annotation methods and engineered static anchors to balance improvements in reproducibility with reductions in bias across different computational settings.

The deterministic anchoring effect denotes a class of stable anchoring phenomena in which an initial value or static structure systematically pulls subsequent judgments, annotations, or search trajectories toward itself. In the cited literature, the term appears in closely related but non-identical forms: as parser bias in syntactic annotation, where reviewers are drawn toward pre-existing parser output; as a deterministic manifestation of anchoring in LLMs, where irrelevant prompt content shifts output distributions and internal decision signals; and as deterministic anchoring in code agents, where static structural tags discipline repository navigation and reduce run-to-run variance (Berzak et al., 2016). Across these settings, the common feature is that the anchor does not merely correlate with the outcome; it changes the effective decision process in a reproducible direction.

1. Conceptual scope

Anchoring bias in cognitive psychology is the tendency of judgments to be drawn toward an initial value or “anchor,” even when that value is arbitrary or only weakly informative. Computational work extends this idea in two directions. One direction studies cases in which human or model judgments are pulled toward pre-existing outputs or irrelevant prompt numbers. The other studies engineered anchors that impose deterministic structure on otherwise stochastic search procedures.

The literature distinguishes these cases by mechanism rather than by vocabulary. In syntactic annotation, the anchor is the visible output of a tagger or parser. In LLM judgment tasks, the anchor is an irrelevant low or high value embedded in the prompt. In code agents, the anchor is static repository structure injected as plain-text comments. The resulting effects differ in valence: in annotation and LLM judgment they are typically treated as bias, whereas in code-agent navigation they are used deliberately to improve discipline and reproducibility (Lin et al., 25 Jun 2026).

Context	Anchor	Observable effect
Syntactic annotation	Prefilled parser output	Reviewers are pulled toward system decisions
LLM numerical reasoning	Irrelevant low or high prompt value	Output distribution shifts toward the anchor
Code-agent navigation	Static structure tags	Navigation becomes more disciplined and reproducible

This conceptual spread is important because the phrase does not refer to a single metric or single task family. Instead, it names a recurring pattern: deterministic conditioning by an initial structure that subsequently changes behavior, evaluation, or internal computation.

2. Parser bias in syntactic annotation

Berzak et al. explicitly term the effect the deterministic anchoring effect, or parser bias, in a study of human syntactic annotation workflows (Berzak et al., 2016). Their setting is standard corpus construction by human editing of automatic parser output. The core claim is that when annotators review prefilled analyses, their corrections are systematically pulled toward the presented system output.

The paper formalizes the bias through the discrepancy between parser accuracy on a purely human gold standard and on a gold standard produced by human review of that parser’s own output. If $A_h$ is the parser’s accuracy on “Human Gold” and $A_p$ is its accuracy on “Parser Gold,” then parser-specific anchoring is quantified by

$$\text{ErrorReduction}(P)=\frac{(1-A_h)-(1-A_p)}{(1-A_h)}=\frac{A_p-A_h}{1-A_h}\times 100\%.$$

The experiment used 360 sentences (6,979 tokens) from the Cambridge FCE learner corpus and five expert annotators trained over two months. “Human Gold” was produced from scratch with independent review; “Turbo Gold” and “RBG Gold” were obtained by review of the outputs of the Turbo and Stanford/RBG tagger-parser pairs. Evaluation used POS, UAS, LA, and LAS, with significance testing by McNemar’s test and blind quality comparisons by two-tailed $Z$ tests.

The quantitative pattern is unambiguous. Each parser scores approximately 1–4 points higher on its own review gold than on Human Gold, and each parser also performs about 1–2 points better on the other parser’s gold than on Human Gold. Overall error reductions relative to Human Gold range from about 33–36% for parsing and about 49% for tagging. For example, Turbo attains LAS 82.29 on Human Gold and 89.16 on Turbo Gold, while RBG attains LAS 82.05 on Human Gold and 87.87 on RBG Gold (Berzak et al., 2016).

The paper also shows that anchoring affects annotation quality, not only evaluation. In a blind ranking of tokens where the gold standards disagreed, judges preferred Human Gold over Turbo Gold at 64.3% for POS, 64.0% for HIND, and 61.5% for REL, and preferred Human Gold over RBG Gold at 56.7%, 61.4%, and 57.7%, respectively. The strongest degradation occurs when the reviewer approves a parser-specific decision: in those cases, judges prefer Human Gold at rates of 73–85% across POS, head, and label. By contrast, when both parsers agree and Human Gold differs, preference for Human Gold falls to chance, approximately 52–58%.

The recommended mitigation is correspondingly selective rather than absolute. The paper proposes pre-annotating only tokens on which multiple state-of-the-art parsers unanimously agree, having annotators review those consensus tokens and annotate all others from scratch. This treats consensus as a high-confidence anchor while avoiding the parser-specific bias associated with the largest quality losses.

3. Behavioral anchoring in LLMs

Recent LLM work treats anchoring as a stable shift in the model’s output distribution rather than as a mere sampling artifact. One study states that if a numerical or qualitative anchor is prepended or embedded in the prompt, the model’s output distribution systematically shifts toward that anchor, and that this is detectable under repeated runs and statistical testing rather than being reducible to decoding noise (Huang et al., 21 May 2025).

To benchmark this phenomenon, the SynAnchors dataset contains 100 questions: 60 semantic priming questions in a two-step “higher/lower” format and 40 numerical priming questions with an irrelevant number embedded directly in the prompt. The study evaluates models ranging from Qwen2.5-0.5B and Llama-3.2-1B to GPT-4o, GPT-4o-mini, DeepSeek-R1, and Qwen3-235B, using 100 runs per prompt, 15% trimming, removal of unextractable or null answers, and a minimum sample size of 30 (Huang et al., 21 May 2025).

Three metrics are used. The Anchor-Bias Score compares anchored and unanchored quantitative answers across repeated runs. The A-Index measures semantic priming intensity in the higher/lower paradigm. The Relative Error measures the mean absolute proportional deviation between anchored and original answers. Anchoring is called when $p<0.05$ and either $A\text{-Index}>0.4$ or $R\text{-Error}>0.2$.

The main empirical result is prevalence across widely used models, with substantial variation by scale and reasoning specialization. Total anchoring ratios range from 60.5% for Qwen2.5-0.5B down to 22.0% for Qwen3-235B and 25.0% for DeepSeek-R1. Tiny models often exceed the human-level A-Index range 0.4–0.6, with Qwen2.5-0.5B at 0.500 and Llama-3.2-1B at 0.618. Advanced models are milder, with GPT-4o at 0.340 and GPT-4o-mini at 0.475. Reasoning models are lowest, with Qwen3 at 0.321 and DeepSeek at 0.278. All reported cases satisfy $p<0.05$ (Huang et al., 21 May 2025).

A complementary line of work analyzes entire log-probability distributions over fixed targets $Y=\{0\%,1\%,\dots,100\%\}$ and introduces SoftEV and exact Shapley-value attribution over prompt fields. It reports robust anchoring effects in Gemma-2B, Phi-2, and Llama-2-7B, while smaller models such as GPT-2, Falcon-RW-1B, and GPT-Neo-125M show greater variability. The Anchoring Bias Sensitivity Score integrates behavioral and attributional evidence, and attributional effects vary across prompt designs, underscoring fragility in treating LLMs as human substitutes (Valencia-Clavijo, 7 Nov 2025).

A recurring finding across these studies is that anchoring in LLMs is measurable at the distributional level. This rules out the narrow interpretation that anchoring is only a superficial property of one decoded sample.

4. Mechanistic localization of anchoring pathways

Owusu et al. turn anchoring in LLMs into a circuit-localization problem by using a controlled nine-way multiple-choice setup with shared answer options (Owusu et al., 11 Jun 2026). Starting from 100 open-ended numerical questions, each item is converted into a task whose nine candidates include the ground-truth number, the low and high anchors, and evenly spaced intermediate values. Anchors are injected via an irrelevant slot-machine sentence such as “The slot machine stopped on 15.” or “The slot machine stopped on 49.” Controls replace the number with “XXXX” of the same token length. Behavioral analyses average over 20 random permutations of answer labels, and localization uses four cyclic rotations.

At the final answer position, the paper defines the correct–anchor logit difference

$$m=\mathrm{logit}(y_{\mathrm{correct}})-\mathrm{logit}(y_{\mathrm{anchor}}),$$

and then the anchored-versus-control contrast

$A_p$0

Lower $A_p$1 means that the anchor option has become more competitive with the correct answer, and $A_p$2 indicates that adding the anchor lowered the correct–anchor gap. Behavioral validation shows that $A_p$3 correlates with normalized expected-value shift with Spearman $A_p$4, and all $A_p$5 under both low and high anchors.

The localization framework compares node- and edge-level attribution methods. Node Attribution Patching (NAP) scores components such as attention heads and MLPs; Edge Attribution Patching (EAP) scores individual directed edges; integrated-gradient variants, NAP-IG and EAP-IG, average attributions over an embedding-interpolation path from control to anchored inputs. Faithfulness is summarized by Circuit Performance Recovery (CPR), the area under a recovery curve measuring how much of the control–anchor gap in $A_p$6 is recovered by a retained subgraph.

The decisive result is that edge-level methods recover the anchoring signal far more faithfully than node-level methods. Reported CPR ranges are 0.36–0.67 for NAP, 0.84–0.96 for EAP, 0.60–0.71 for NAP-IG, and 0.91–0.97 for EAP-IG. The paper further localizes attribution by depth: Qwen variants concentrate in mid-to-late layers with centroid approximately 60–70% depth, whereas Llama variants concentrate earlier, at approximately 30–40% depth. Low and high anchors have nearly identical layer profiles, with Pearson correlation greater than 0.99 and centroid difference below 0.01 relative depth. Component-type analysis shows that although about 95% of all possible edges are attention$A_p$7attention, the top 5% EAP-IG circuits contain only about 70–80% attention$A_p$8attention and proportionally more attention$A_p$9MLP edges.

Transfer results separate within-model regularity from post-training instability. Low- versus high-anchor circuits show Jaccard overlap 0.49–0.55, shared fraction 0.66–0.71, and cross-contrast CPR at 5% of 0.93–0.98, indicating largely overlapping sparse edge circuits within a model. Base versus instruction-tuned transfer is less reliable: at 5%, Jaccard is 0.47–0.49 and shared fraction 0.64–0.66, but sparse cross-variant CPR can collapse, as in Qwen-7B low from matched 0.917 to cross-variant 0.291. The paper interprets this as evidence that instruction tuning preserves the general layer region of anchoring pathways while reshuffling which particular edges matter most.

5. Deterministic anchoring in code agents

A distinct usage appears in repository-scale software agents. Lin et al. study whether lightweight static analysis can provide deterministic anchors for grep-first LLM-based code agents by injecting stable structural facts as plain-text comments (Lin et al., 25 Jun 2026). Here the anchor is not an irrelevant number but a deterministic annotation function applied to a repository snapshot. The baseline navigation policy depends solely on lexical relevance, while the anchored policy mixes structural and lexical signals:

$$\text{ErrorReduction}(P)=\frac{(1-A_h)-(1-A_p)}{(1-A_h)}=\frac{A_p-A_h}{1-A_h}\times 100\%.$$0

The implementation, CodeAnchor, emits comment blocks encoding CALLS, CALLED_BY, IMPORTS, BASE, DERIVED, and related relations. The baseline agent is OpenAI GPT-5.1-codex in a fixed “Codex” grep-first control loop exposing Search(Open), ApplyPatch, and RunTests. Evaluation is conducted on SWE-bench Lite ($$\text{ErrorReduction}(P)=\frac{(1-A_h)-(1-A_p)}{(1-A_h)}=\frac{A_p-A_h}{1-A_h}\times 100\%.$$1 Python issues) and SWE-bench Verified ($$\text{ErrorReduction}(P)=\frac{(1-A_h)-(1-A_p)}{(1-A_h)}=\frac{A_p-A_h}{1-A_h}\times 100\%.$$2), using Func@$$\text{ErrorReduction}(P)=\frac{(1-A_h)-(1-A_p)}{(1-A_h)}=\frac{A_p-A_h}{1-A_h}\times 100\%.$$3, Average Rounds, Link-Following Rate, Pass@1, and run-to-run variance.

The paper defines the deterministic anchoring effect as the observation that static structure helps less by making agents “smarter” and more by making navigation disciplined and reproducible. Quantitatively, Anchor-Topo improves function-level localization by +2.2 pp Func@5 and shortens trajectories by 1.6 interaction rounds on SWE-bench Lite; on Verified it yields +1.2 pp Func@5 and 1.5 fewer rounds. Link-following rate rises from 0.178 to 0.236 on Lite and from 0.147 to 0.209 on Verified. On a 50-task, 10-run stability study, mean per-task variance in Func@5 on Lite is halved from 0.00184 to 0.00050. Single-run Pass@1 on Lite Func@5 increases from 0.742 to 0.776, a gain of +3.4 pp, at the cost of about 10% more input tokens (Lin et al., 25 Jun 2026).

The paper also shows that the effect is scale-sensitive. Dense tags add context and rounds without improving Func@5 on Lite, while inverse-only tags hurt on small and medium repositories but match or slightly exceed Func@5 on hub-heavy Verified repositories, 0.6329 versus 0.6308, at approximately 9% token overhead. The recommended heuristics are correspondingly operational: default to lightweight topology on medium projects, prune forward edges in large hub-heavy repositories, and reserve dense tags for implicit-dependency cases.

6. Implications, misconceptions, and mitigation

A common misconception is that anchoring in model behavior is merely stochastic noise. The LLM literature rejects that interpretation directly: anchoring is described as a stable shift in the model’s expectations, detectable under repeated runs and statistical testing, and later work shows that it can be localized to sparse internal pathways and quantified by log-probability and attributional analyses (Huang et al., 21 May 2025). Another misconception is that anchoring is uniformly harmful. The code-agent literature shows the opposite for navigation tasks: deterministic anchors can improve localization, reduce rounds, raise link-following rates, and halve run-to-run variance when the anchor encodes useful static structure (Lin et al., 25 Jun 2026).

The harmful side remains clear in annotation and judgment settings. In syntactic annotation, parser-anchored review both inflates apparent parser performance and lowers annotation quality relative to purely human-derived gold. In LLM numerical reasoning, anchoring is not eliminated by conventional strategies, and reasoning offers only partial mitigation. On Llama-3.1-8B, the best reported Anti-DP result reduces the total anchoring ratio from 34.7% to 24.7%, the A-Index from 0.394 to 0.305, and the R-Error from 0.270 to 0.250; other strategies produce modest or inconsistent improvements, and none eliminates anchoring fully (Berzak et al., 2016).

The broader implication is methodological. Standard benchmark performance is not sufficient for evaluating trustworthiness when judgments can be pulled by irrelevant anchors, and gold standards are not necessarily neutral when they are produced under parser-anchored review. Conversely, when deterministic anchors encode valid structure, they can serve as a reproducibility mechanism rather than a bias source. This suggests that future work should continue to separate at least three questions that are often conflated: whether an anchor changes outputs, whether it changes internal computation, and whether that change is epistemically harmful or operationally beneficial.