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Elucidating the Design Space of LM Data Attribution

Steven Yu, Sheng-Yu Wang, Kimia Hamidieh, Antonio Torralba, David Bau

arXiv:2610.40655v1cs.CL

TL;DR

Existing evaluations vary multiple dataset properties simultaneously, limiting diagnosis of attribution failures. The paper introduces controlled synthetic fact-tracing and tests changes to gradient loss and score aggregation, finding improved recall and counterfactual retraining performance.

  • Problem

    Existing attribution evaluations vary multiple dataset properties simultaneously, while retraining large models to verify attribution predictions is computationally prohibitive.

    Source: §1 · p. 1

  • Method

    CATT fine-tunes language models on synthetic fictitious facts and systematically varies dataset configurations to evaluate attribution across controlled fact-tracing tasks.

    Source: §1 · p. 1, §2.1 · p. 3

  • Results

    Top-k token aggregation with negative log-odds improves fact-tracing recall by 35 to 72 percentage points across multiple methods and settings, while negative log-odds improves FTRACE-TREX counterfactual retraining by up to 4.9×.

    Source: §1 · p. 2

  • Takeaways & Limitations

    Document-level attribution scores can be unreliable when causal evidence is highly localized, so attribution methods warrant caution in real-world settings.

    Source: §5 · p. 9

    The evaluation uses single-token predictions and single-task fine-tuning, leaving sequence-level dependencies and multi-task attribution unexplored.

    Source: §5 · p. 9

Abstract

from arXiv · show

Data attribution methods for Language Models (LMs) are typically evaluated using downstream tasks like fact retrieval. However, existing evaluations vary multiple dataset properties simultaneously, making it impossible to isolate exactly why an attribution algorithm fails. To diagnose these failures, we explore the design space of LLM data attribution, with a primary focus on evaluation. We introduce the Controlled Attribution Benchmark (CATT) for fact tracing, in which we fine-tune LLMs on entirely fictitious knowledge, providing unambiguous ground truth for attribution. This synthetic setup allows us to systematically alter one dataset configuration at a time, such as document redundancy and lexical distractors. With this configurable evaluation, we demonstrate that redundancy and distractors consistently degrade attribution performance. Rather than proposing a new estimator, we examine two design choices that are underexplored: the loss used to compute gradients and how per-token attribution scores are aggregated into a document score. We find that the true causal evidence within a training document is highly localized, but standard methods dilute this evidence into noise by averaging attribution scores across the entire document. We find that replacing standard cross-entropy loss gradients with the negative log-odds gradients surfaces the critical tokens from other uninformative ones. We can then aggregate only the top token scores to improve ground truth recall by 35 to 72 percentage points across multiple baselines on our diagnostic benchmark. The negative log-odds correction also generalizes to FTRACE-TREX, improving counterfactual retraining performance for every method we test, by up to 4.9x.

1 INTRODUCTION

Existing attribution benchmarks vary multiple dataset properties at once, making it difficult to diagnose why methods succeed or fail. CATT provides controlled fact-tracing evaluation, revealing diluted token evidence and improvements from changing gradient loss and document-score aggregation.

1 INTRODUCTION

  • CATT uses fictitious facts and varies dataset properties such as redundancy and lexical distractors to establish ground truth and diagnose attribution failures.Its two fact-tracing tasks are function bindings and routing rules.Source: §1 · p. 1, Figure 2 · p. 3
  • Redundancy and lexical distractors consistently degrade attribution, while relevant evidence is localized to a few tokens that document-wide averaging dilutes with background noise.The benchmark varies dataset complexity to isolate these effects.Source: §1 · p. 1
  • Existing fact-tracing benchmarks use distinct fixed datasets, producing conflicting comparisons and limited diagnostic insight into why attribution methods succeed or fail.Prior results differ on whether BM25 outperforms influence functions.Source: §1 · p. 2
  • Negative log-odds concentrates influence on relevant tokens, ranking the ground-truth document first rather than 582nd of 1,000 under cross-entropy.The comparison is shown for token scores normalized by the document’s largest token score.Source: Figure 1 · p. 2, §1 · p. 2
  • Top-k token aggregation with negative log-odds improves fact-tracing recall by 35 to 72 percentage points across multiple methods and dataset settings; negative log-odds improves FTRACE-TREX counterfactual retraining by up to 4.9×.The FTRACE-TREX gains apply to TRAK, EK-FAC, and Grad-Dot.Source: §1 · p. 2

2 CONTROLLED DIAGNOSIS OF LLM DATA ATTRIBUTION

The section introduces a configurable synthetic fact-tracing benchmark and uses it to examine how dataset complexity and attribution design choices affect performance.

2.1 CONFIGURABLE DESIGN SPACE FOR FACT TRACING DATASET

  • CATT varies task, fact set, documents per fact, distractor inclusion, and number of facts while fine-tuning models on synthetic facts.Redundancy means repeated factual support in different wording; distractors resemble queries but provide no answers.Source: §2.1 · pp. 3–4

2.2 CONTROLLED ATTRIBUTION BENCHMARK (CATT)

  • CATT tests atomic Function Bindings and compositional Routing Rules, using held-out query formats to test attribution to the synthetic facts.Function Bindings includes lexical distractors, whereas Routing Rules does not.Source: §2.2 · p. 4

2.3 EXAMINING ATTRIBUTION DESIGN SPACE VIA LOSS AND TOKENS

  • Layer-wise token attribution reveals localized evidence, and cross-entropy can suppress gradients for confidently predicted target tokens.Negative log-odds restores high attribution scores to confident tokens, redirecting document scores toward relevant tokens.Source: §2.3 · pp. 4–5
  • On Function Bindings, only TRAK and EK-FAC recover ground truth among gradient methods, both losing recall as documents per fact increase; distractors hurt both.On Rule Routings, no gradient-based method exceeds 0.32.Source: Figure 3 · p. 5
  • Averaging only top-k token scores is intended to prevent dilution; under cross-entropy, top-token selection alone yields small gains for all methods except EK-FAC.Pairing top-token aggregation with negative log-odds yields drastic improvements.Source: §2.3 · p. 5
  • For Grad-Dot with distractors, Recall@N rises from 0.01 under all-token cross-entropy to 0.30 with top-10 tokens, 0.35 with negative log-odds, and 1.00 combined.The comparison uses Function Bindings with N=50 documents per fact and |F|=50 facts.Source: Figure 4 · p. 6

3 EXPERIMENTS

The experiments diagnose how dataset complexity and token-level attribution affect fact tracing, then test whether the interventions transfer to an external benchmark. Negative log-odds and top-token aggregation improve CATT recall, while negative log-odds also improves remove-and-retrain results on FTRACE-TREX.

Diagnosing attribution failures

  • On Function Bindings, scaling from 1 to 50 documents per fact drops TRAK recall from ∼0.9 to below 0.1, while distractors push it nearly to zero.EK-FAC degrades less sharply, from 0.70 to 0.45; gradient methods struggle on Rule Routings, while BM25 performs strongly across settings.Source: §3 · p. 6

Token-level diagnosis and interventions

  • With negative log-odds, small token budgets substantially improve recall across CATT settings, but recall often declines as more tokens are retained.For Function Bindings, k = 10 gives nearly perfect recall for Grad-Dot, EK-FAC, and layerwise TracIn, including with distractors; Rule Routings remains harder and favors a larger optimal k.Source: Figure 6 · p. 7, §3 · p. 8
  • Averaging all token scores yields Recall@N of 0.01, versus 0.3 when averaging only the top 10, as irrelevant tokens dilute useful attribution signals.Negative log-odds lifts full-document recall to 0.35, and combining it with top-10 aggregation reaches 1.00 in the illustrated setting.Source: §3 · pp. 7–8
  • 35 to 72 percentage points: negative log-odds gradients plus top-k aggregation improve recall across six methods on CATT.On one setting, the combination raises recall to 1.00; the reported range is averaged over three tasks, N, and |F|.Source: §3 · p. 8
  • For a Rule Routings document, negative log-odds shifts top scores from irrelevant item names to answer-matching outcome tokens, moving its rank from 1499 to 12 of 1500.Cross-entropy favors item names, whereas negative log-odds favors outcome tokens.Source: Figure 5 · p. 7, §3 · p. 8

Generalization to other benchmarks

  • At the largest removal budget, negative log-odds raises TRAK’s accuracy drop from 8% to 40% (4.9×) on FTRACE-TREX.Negative log-odds improves results for TRAK, EK-FAC, and Grad-Dot at every removal budget; with both fixes, Grad-Dot rises from 7% to 23% and EK-FAC from 30% to 46%.Source: §3 · p. 8, Figure 7 · p. 8

4 RELATED WORKS

Prior work develops attribution estimators and evaluates them through proxy targets or retrieval benchmarks, but benchmark conclusions conflict when multiple dataset properties vary together. This paper uses controlled fact tracing and token-level analysis to examine evaluation and scoring choices.

Training Data Attribution

  • Prior attribution work scales influence estimates through Hessian approximations, gradient projections, training trajectories, or retraining on random subsets.Such methods are commonly justified by agreement with targets such as leave-one-out retraining, though those targets can be affected by training stochasticity.Source: §4 · p. 9

Token-level attribution

  • The paper uses per-token negative log-odds gradients and top-k aggregation to explain and address dilution in document-level attribution scores.Prior work has used token scores for visualization, while TrackStar discusses applying its loss conversion per token.Source: §4 · p. 9

Attribution evaluation

  • Retrieval benchmarks report conflicting comparisons between BM25 and gradient-based methods, but varying training corpora, queries, and tasks together prevents identifying the cause.The paper’s benchmark holds the training procedure fixed and changes one corpus property at a time.Source: §4 · p. 9

LLM fine-tuning

  • CATT differs by using fictitious facts and allowing redundancy, distractors, and fact counts to vary independently.Function Bindings use added vocabulary tokens, while Rule Routings teach arbitrary synthetic rules; fine-tuning uses LoRA.Source: §4 · p. 9

5 DISCUSSION, BROADER IMPACTS, AND LIMITATIONS

The authors caution that document-level attribution may be unreliable when causal evidence is localized, with implications for high-stakes uses. They also identify scope and tuning limitations and call for datasets where lexical overlap is not a shortcut.

Broader impacts

  • Document-level scores may be unreliable when causal evidence is highly localized, motivating caution in high-stakes attribution uses.The paper names copyright protection, equitable credit assignment, and tracing emergent misalignment as relevant domains.Source: §5 · p. 9

Limitations

  • The evaluation covers single-token predictions and single-task fine-tuning, leaving sequence-level rollouts and multi-task attribution unexplored.Top-k aggregation also adds a hyperparameter, and real-world settings lack ground-truth validation signals for choosing it dynamically.Source: §5 · pp. 9–10
  • Strong BM25 results motivate future datasets where surface-level text overlap is not a reliable shortcut.The authors also suggest extending the framework to multi-step reasoning, where factual support is scattered across multiple concepts.Source: §5 · p. 10

AI USE STATEMENT

The authors report using generative AI for synthetic data and paraphrases, writing, coding, and mathematical proofs, with human review described for the assisted outputs.

AI use statement

  • Claude Sonnet 4.5 generated CATT training documents and rule paraphrases; the authors manually inspected the text.LLM assistance was also used for writing and proofs, which were manually checked, and coding assistants helped implement and scale experiments whose code and outputs were reviewed.Source: AI USE STATEMENT · p. 10

REPRODUCIBILITY

The implementation used Qwen3.5-4B LoRA fine-tuning and a 2,400-GPU-hour attribution sweep. The gradient analysis shows how cross-entropy scales token gradients by model confidence, while negative-log-odds gradients remain bounded away from zero as confidence rises.

REPRODUCIBILITY

  • The attribution sweep used about 2,400 GPU-hours across single A100-80GB, H100, and H200 GPUs; the paper also provides code, corpora, queries, adapters, and attribution scores.The models were fine-tuned with LoRA using HuggingFace Transformers and PEFT on PyTorch.Source: REPRODUCIBILITY · p. 10

A.1 CROSS-ENTROPY VS. NEGATIVE LOG-ODDS GRADIENTS

  • Cross-entropy and negative-log-odds token gradients are collinear, but cross-entropy introduces a confidence factor of 1 − py+.Thus, the cross-entropy gradient shrinks as the correct-token probability rises, while the negative-log-odds gradient removes that factor.Source: §A.1 · pp. 13–14
  • As py+ approaches 1, the cross-entropy gradient is forced to vanish, whereas the negative-log-odds logit gradient remains bounded away from zero.A nonzero lower bound for the parameter gradient would require an additional assumption on Jθ.Source: §A.1 · p. 14

A.2 GRADIENT-BASED ATTRIBUTION METHODS

This section details gradient-based attribution implementations and the construction of the synthetic CATT benchmark, covering its controlled data grid, function-binding tasks, and rule-routing tasks. It also describes the rule-routing criterion and attribution-grid setup, along with task-specific fine-tuning configurations that control training exposure as corpus size changes.

A.2 GRADIENT-BASED ATTRIBUTION METHODS

  • NLO is a TRAK loss variant that drops the cross-entropy reweighting term after its removal improved top-10 results; queries always use negative-log-odds loss.The sign change applies to query and document features and cancels in their pairwise score, so NLO is a loss choice within TRAK rather than a separate attribution method.Source: §A.2 · pp. 14–15

B CATT BENCHMARK CONSTRUCTION AND FINE-TUNING

  • The main CATT experiments use nested corpora, varying document count while preserving existing examples, across 50 facts and task-specific document-count grids.Function Bindings uses N ∈ {1, 5, 10, 30, 50}; Rule Routings uses N ∈ {3, 5, 10, 30, 50} because N = 1 models perform near chance.Source: B CATT BENCHMARK CONSTRUCTION AND… · p. 16

B.1 FUNCTION BINDINGS

  • Function Bindings pairs synthetic function tokens with synthetic answer tokens; its distractors copy the query template and answer but refer to a different function.The distractor version adds one distractor per fact document, while leaving the original fact documents unchanged; synthetic answer tokens prevent pretrained numerical knowledge from helping.Source: §B.1 · p. 17

B.2 RULE ROUTINGS

  • Rule Routings assigns each category a binary queue rule determined by one of four Boolean properties, and training documents show eight assignments while queries use the eight held-out assignments.Documents vary in titles, nouns, ordering, and rule paraphrases but share the same worked cases; held-out nouns and assignments are excluded from training text.Source: §B.2 · p. 19
  • Rule Routings sends suitcases with a red strap to Birch and all others to Cedar; tornness, weight, and whether they are locked do not affect routing.Queries use held-out nouns, property combinations, and phrasing that differ from every training document.Source: §B.2 · pp. 20–21
  • Evaluation uses 200 attribution queries and 400 held-out prompts, reporting option-order accuracy, swapped-order accuracy, and selectivity under single-property flips.Selectivity is near 1 when the model applies the rule and near 0 when it gives a fixed answer per category, regardless of accuracy.Source: §B.2 · p. 21
  • At N = 1, Rule Routings models achieve 55% accuracy and 12% selectivity, so the attribution grid starts at N = 3.At one document per category, attribution scores would measure noise.Source: §B.2 · p. 21

B.3 FINE-TUNING

  • Function Bindings train embeddings and unembeddings for added tokens while freezing original vocabulary rows; Rule Routings train LoRA adapters alone.Both tasks use ordinary next-token cross-entropy over every document token, with no masking or special treatment for answer tokens.Source: §B.3 · p. 21
  • Training runs about 1,000 optimizer steps per cell; adding distractors keeps epochs fixed, so original documents receive the same number of passes while total steps double.As N grows, each document is seen fewer times; training-dynamics methods use eight evenly spaced checkpoints and average over seeds 1001 and 1002.Source: §B.3 · p. 21

B.4 RESULTING DATASETS AND MODELS

Held-out performance improves as training data per fact increases in both tasks, while retention and MMLU-Pro results show costs to general language ability. The appendix documents the shared attribution settings and curvature-estimation choices.

B.4 RESULTING DATASETS AND MODELS

  • 4–7× base retention perplexity occurs with distractors, compared with 2–4× from N = 5 onward without distractors and on Rule Routings.The N = 1 Function Bindings models are outliers at 7.5× without distractors and 188× with distractors; perplexity is only a coarse indicator of general-ability cost.Source: §B.4 · pp. 22–23
  • 100% Function Bindings accuracy is reached from N = 5 onward without distractors, while Rule Routings accuracy rises from 69% to 96% and selectivity from 39% to 90% as N grows from 3 to 50.Function Bindings averages 89% accuracy at N = 1; Table 5 summarizes held-out performance and retention perplexity.Source: §B.4 · p. 22, Table 5 · p. 23
  • Models at large N reach the highest held-out accuracy despite ending training with higher loss under the fixed step budget.Loss falls quickly in all three tasks; N = 50 receives four epochs versus 200 at N = 1. Figure 8 also plots accuracy, perplexity, and training curves.Source: Figure 8 · p. 24, §B.4 · p. 24
  • 16–30 points are lost on MMLU-Pro after fine-tuning, although every fine-tuned model remains above the 11.1% chance level.The reported scores use 5-shot answer-letter log-likelihood on the full test set; at least 99% of probability remains on valid answer letters.Source: Table 6 · p. 24, §B.4 · p. 24

C PRACTICAL CONSIDERATIONS FOR ATTRIBUTION METHODS

  • The reference cell contains 500 candidate documents and 200 queries, and methods sharing a job share a model pass.The appendix records method-specific implementation settings and reports costs jointly for methods run in the same job.Source: C PRACTICAL CONSIDERATIONS FOR… · p. 25, Table 7 · p. 25

C.1 SHARED IMPLEMENTATION DETAILS

  • Gradient methods differentiate only the 129.9M LoRA parameters; documents and queries are truncated to 512 and 128 tokens, respectively.Stored bf16 query gradients leave rankings effectively unchanged from fp32, with mean per-query Spearman 0.9999 for EK-FAC over 100 documents; methods use full gradients or projected representations.Source: §C.1 · p. 25

C.1.1 CURVATURE

  • Curvature uses the cross-entropy empirical Fisher from observed-label gradients, and changing the scoring loss changes query and document gradients but not the curvature estimate.Damping is method-specific: EK-FAC is effectively undamped, LoGra and TrackStar use a block-relative ridge, TRAK a Gram-matrix-relative ridge, and SOURCE none.Source: §C.1.1 · pp. 25–26

C.2 COMPUTE COST

Attribution-job costs generally grow with the number of candidate documents, but vary substantially by method and whether per-token terms are computed. Mixed hardware limits some sweep-wide runtime comparisons.

Runtime and complexity

  • Sweep-wide medians mix A100, H100, and H200 jobs, and hardware allocation was not random, so cross-method runtime comparisons can be misleading.The reported total is 2,426 GPU-hours over 843 jobs; the authors use |F| = 50 jobs on one 8×A100 host for like-for-like comparisons.Source: §C.2 · p. 26
  • On one A100, per-document cost slopes span about 14×, from 7.7 hours per 1,000 documents for EKFAC to 0.54 for dense TRAK.Every gradient method’s cost grows roughly linearly in the number of candidate documents M.Source: §C.2 · p. 27
  • Reported runtimes include 2.9 h for EK-FAC without per-token terms (about 4.8 h with them, fitted), 0.3 h for Dense TRAK, 2–3 minutes for RepSim, and seconds for BM25 on CPU.The layerwise-project job takes 0.4 h without per-token terms and 1.0 h with them.Source: §C.2 · p. 27
  • At M = 5,000, EK-FAC took 39 h per model, exact TracIn 28 h, Layerwise TracIn 24 h, and the layerwise-project job 6.6 h.Dense TRAK took 2.7 h; per-token terms made the layerwise-project job about 2.5× more expensive.Source: §C.2 · p. 27

Runtime by stage

  • EK-FAC scoring is dominated by per-document gradient, rotation, and contraction work, while layerwise-project methods avoid those costs but need a second corpus pass for per-token terms.At M = 2,500, the extra pass took 107 of 217 minutes in the reported layerwise-project stages.Source: §C.2 · pp. 27–28

D FULL RESULTS

Across the benchmark tasks, attribution performance depends strongly on task and scoring configuration. Log-odds top-token scoring improves retrieval on several tasks, while Rule Routings remains difficult for gradient methods and document weighting can fail sharply with distractors.

D FULL RESULTS

  • The full-document results use each method’s training-side loss, while the top-10 configuration averages its ten largest token-level log-odds terms when available.Recall@N measures recovery among the N highest-ranked documents; AUC measures pairwise ranking of ground-truth against other documents.Source: D FULL RESULTS · pp. 28–29

D.1 RECALL BY NUMBER OF DOCUMENTS

  • On Function Bindings, document-level Recall@N above 0.5 is limited to matched-width TRAK (0.76), Layerwise TRAK (0.62), and EK-FAC (0.59).With distractors, every document-level gradient method is below 0.2; on Rule Routings, no attribution method approaches BM25’s 1.00.Source: §D.1 · p. 29
  • With log-odds top-10 scoring, every method except TRAK variants reaches at least 0.92 on Function Bindings, while Grad-Dot, EK-FAC, and Layerwise TracIn reach 0.99–1.00 with distractors.On Rule Routings, BM25 reaches 1.00, while EK-FAC is the strongest gradient method at 0.55.Source: §D.1 · p. 29, Figure 10 · p. 30

D.2 AUC AND DECOY AUC

  • Top-10 scoring raises Function Bindings AUC for every method with per-token terms to at least 0.99, while document-level AUC can be high despite low Recall@N.On distractors, top-10 decoy AUC is 1.00 for every method with per-token terms except TrackStar; full-document log-odds gives SOURCE 0.15 and exact TracIn 0.13.Source: §D.2 · p. 29, Figure 10 · p. 30

D.3 EVERY SCORING VARIANT

  • Changing the loss matters before pooling: on Function Bindings, log-odds terms lift every method, whereas top-k cross-entropy pooling raises only EK-FAC above 0.22.With distractors, the full-document mean fails under either loss, while the log-odds sum reaches 0.85 for Grad-Dot and 0.99 for EK-FAC; Q weighting drops every method to 0.02 or below.Source: §D.3 · pp. 31–32
  • With distractors, Q weighting favors poorly fit decoys and reduces every method to 0.02 or below; TrackStar is an exception to top-10 gains, scoring 0.13 versus 0.18 for its full-document mean.The authors expect TrackStar’s inverse-whitened-norm weight to be large for short documents, but have not verified that explanation.Source: §D.3 · p. 32

D.4 SCORE DISTRIBUTIONS AND TOKEN TYPES ON THE OTHER TASKS

On the examined cells, changing from cross-entropy to negative log-odds substantially separates ground-truth documents on Function Bindings, while combining loss change and top-token selection helps Rule Routings. Negative log-odds also concentrates high token scores on answer or outcome tokens.

Score distributions

  • For Function Bindings, Recall@N rises from 0.11 with cross-entropy over all tokens to 1.00 with negative log-odds, and remains 1.00 with top-10 selection.On Rule Routings, Recall@N is 0.07 with cross-entropy over all tokens and 0.47 with negative log-odds top-10 scores.Source: §D.4 · p. 32

Token types

  • Under negative log-odds, answer tokens are enriched 5.1–11× on Function Bindings and 2.9–6.6× with distractors; no other token type exceeds 1.4× enrichment.Under cross-entropy, answer-token enrichment ranges from 0.2× to 1.3× on Function Bindings and 0.9× to 1.2× with distractors.Source: §D.4 · p. 33

D.5 NUMBER OF FACTS

The main trends persist across the tested fact-set sizes: document-level scores struggle with distractors, top-10 log-odds scoring recovers Function Bindings, and Rule Routings remains difficult for gradient methods. Some methods lose recall as facts are added.

D.5 NUMBER OF FACTS

  • On Rule Routings, at |F| = 25, no attribution method exceeds 0.3 at any N, while BM25 reaches 1.00, matching its result at |F| = 50.Source: §D.5 · p. 34
  • Across |F| ∈ {25, 50, 100}, Grad-Dot, EK-FAC, and Layerwise TracIn reach at least 0.99 on both Function Bindings tasks with top-10 log-odds scoring.With distractors, no document-level score exceeds 0.10 at any tested |F|.Source: §D.5 · pp. 33–34, Table 15 · p. 35
  • As |F| increases, some methods’ recall declines: EK-FAC falls from 0.78 to 0.70 to 0.56 on Rule Routings, while TrackStar stays at 0.25, 0.25, and 0.26.The |F| = 100 grid mostly covers N ≤10 and has incomplete coverage at N = 10.Source: §D.5 · pp. 33–34

E FTRACE-TREX

On FTRACE-TREX, negative log-odds improves remove-and-retrain accuracy drops for every tested method, while top-10 token pooling is roughly neutral. The evaluation compares equal-budget document removals against same-seed no-removal controls and also measures effects on related facts.

E FTRACE-TREX

  • FTRACE-TREX uses mT5-small on 8,437 novel facts, scoring answer tokens and testing published and negative-log-odds variants of EK-FAC and Grad-Dot.The 8,437 queries are facts the pretrained model gets wrong but the fine-tuned model gets right; gradients are summed over encoder input and decoder answer positions.Source: E FTRACE-TREX · pp. 35–36
  • The study removes documents round-robin across 50 facts at shared budgets, then compares retrained accuracy with same-seed no-removal controls.The largest budget, B = 11,522, equals the total number of proponents for those facts; retraining uses eight seeds for each removal set.Source: E FTRACE-TREX · p. 36
  • At B = 11,522, negative log-odds adds 32 ± 3 points to TRAK, 15 ± 1 to EK-FAC, and 16 ± 3 to Grad-Dot.These are paired-by-seed accuracy-drop gains; Table 16 reports drops on the 50 facts across removal budgets.Source: E FTRACE-TREX · p. 36, Table 16 · p. 36
  • Under negative log-odds, top-10 pooling adds 2 to 4 points to EK-FAC at every budget and changes Grad-Dot by −6 to +3.Top-10 document scores are the mean of the 10 largest per-position terms.Source: E FTRACE-TREX · p. 36
  • Removing every annotated proponent drops accuracy on the 50 facts by only 9 points, while removing BM25’s selections drops it by 15 points.BM25’s selection contains 76% of the proponents, yet its removal causes a smaller drop than removal of TRAK, EK-FAC, or Grad-Dot selections under negative log-odds.Source: E FTRACE-TREX · p. 37
  • Negative-log-odds rankings also lower accuracy on other facts sharing the relation by 8 points for Grad-Dot to 15 for EK-FAC, while other-relation facts are unaffected.The highest-ranked documents include examples teaching a relation’s answer pattern, not just evidence for one fact.Source: E FTRACE-TREX · p. 37

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