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Technical Manual for Toolkit for Confidence-Corpus Consistency via Fine-Tuning on a Fabricated Corpus

José Luciano Verçosa Marques, Frederico Jorge Heitmann, Daniel Omar Perez, Reinaldo Cesar, Marcelo Vinicius de Paula, Tárcio André dos Santos Barros

arXiv:2609.28747v1cs.CLcs.AIcs.LG

TL;DR

The manual addresses whether a model’s confidence tracks corpus consistency rather than factual correctness. It documents an addition-based fine-tuning toolkit to test that prediction, but reports no outcome from a specific run.

  • Problem

    The manual asks whether a model’s confidence tracks consistency with its training corpus rather than correspondence with fact.

    Source: §1 · p. 2

  • Method

    The toolkit tests this prediction by fine-tuning a small causal language model on fabricated facts in an exhaustive single-digit addition domain.

    Source: §1 · p. 2, §10 · p. 28

  • Results

    The manuscript does not report or interpret the outcome of a specific fine-tuning run.

    Source: §7 · p. 25

  • Takeaways & Limitations

    The toolkit provides a concrete, reproducible observation with which to test arguments about confidence and correctness-indifference.

    Source: §1 · p. 2

    Its output is a point estimate for a specific model, fabricated-fact draw, and training run, not a claim across domains, models, or repeated draws.

    Source: §8 · pp. 26–27

Abstract

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A language model's confidence in an answer is often read as a proxy for how well it knows the corresponding fact. This manual documents an open toolkit built to test that reading directly: a small causal language model is fine-tuned on a corpus that consistently asserts one fabricated arithmetic answer for each of the 81 single-digit addition pairs, and its post-fine-tuning confidence in each fabricated answer is compared against its own pre-fine-tuning confidence in the corresponding true answer, using an unchanged measurement procedure throughout. We describe and justify every pipeline stage, fact-space generation, token-length-aware confidence measurement, baseline validation, corpus construction, fine-tuning, and paired before/after comparison, together with the confound each is meant to rule out, among them tokenization asymmetry between single- and double-digit answers and the difference between an answer merely losing its edge and one being actively suppressed. This manuscript is a methodological and implementation reference: it documents the instrument and does not report or interpret the outcome of any specific run. The toolkit and its pinned dependency environment are archived separately (Section 9) under a persistent identifier, to be cited as an instrument by work that produces and interprets empirical results with it.

1. Introduction

The introduction frames a testable question: whether a model’s confidence follows corpus consistency rather than factual correctness. It presents an exhaustive addition-based fine-tuning intervention and a paired confidence comparison, while defining the manual as an instrument rather than a report of a run’s outcome.

1. Introduction

  • The central prediction is that repeatedly asserting a false fact can give it a confidence signature indistinguishable in kind from a correctly learned fact’s.The test intervenes on training data rather than asking only whether hidden representations correlate with correctness.Source: §1 · p. 2
  • The toolkit uses all 81 single-digit addition pairs, each with one true answer and sixteen false candidates, as a small, exhaustive fact domain.Its narrow scope is intended to make facts and candidate answers unambiguous and auditable.Source: §1 · p. 2
  • It measures baseline confidence in each true sum, trains on one repeatedly asserted fabricated answer per pair, then remeasures every candidate with the same procedure.The paired comparison is each true sum’s pre-fine-tuning confidence against the trained-on fabricated sum’s post-fine-tuning confidence.Source: §1 · p. 3
  • The manuscript documents and justifies the toolkit’s design and implementation but does not present or interpret an empirical outcome from a specific fine-tuning run.It is intended as a methodological and implementation reference.Source: §1 · p. 3

2. Intended Uses and Potential Contributions

The toolkit is presented as an instrument for making questions about confidence, correctness, and corpus consistency tractable. Its contributions include an intervention-based empirical handle, a reusable fabricated-corpus construction, and a small auditable testbed, with broader validation beyond its stated scope.

Intended Uses and Potential Contributions

  • The toolkit is an instrument, not a claim; its value lies in making questions tractable rather than in a specific answer it has produced.The manuscript presents the instrument as a way to test arguments about model confidence, not as an empirical result.Source: §2 · p. 3
  • Fine-tuning the corpus itself complements probes that ask whether a representation-space index correlates with correctness.The intervention asks what happens to the model’s confidence when a false fact is repeatedly asserted in training data.Source: §2 · pp. 3–4
  • The small, exhaustive, unambiguous testbed makes candidate answers, fabricated facts, and measured confidence values enumerable and auditable by hand.The fact domain is 81 single-digit sums with one true answer per pair.Source: §2 · p. 4
  • A concrete, reproducible confidence comparison offers an empirical handle on symbol-grounding and correctness-indifference arguments, including those advanced by Hicks et al. (2024).The comparison asks whether confidence toward a corpus-reinforced falsehood is distinguishable from confidence toward a fact learned correctly during pretraining.Source: §2 · p. 4
  • The exhaustive fact-space and repeated-fabrication pipeline can be reused to study how repetition or fabrication strength relates to overwriting pretrained facts.This construction is described as reusable independently of the manual’s specific comparison.Source: §2 · p. 4
  • Scaling across more fact domains or models, or statistically validating repeated fine-tuning runs, is beyond what one toolkit run or this manual undertakes.The manual states that boundary explicitly.Source: §2 · p. 4

3. Background and Related Work

The background asks whether model confidence tracks meaning or instead corpus consistency, and presents arithmetic as a testbed for examining that question. It situates the toolkit among work on arithmetic computation, numerical confounds, and small curated-corpus models.

3.1. Classical Foundations

  • The section frames a test of whether confidence tracks corpus consistency rather than correspondence with fact, a question motivated by debates about meaning and symbol grounding.It proposes manipulating the training corpus and observing confidence.Source: §3.1 · p. 5

3.2.1. Arithmetic as a probe of internal computation

  • Arithmetic offers unambiguous answers and evidence of identifiable computation, making it a meaningful domain for testing fabricated facts against pretraining-acquired answers.Stolfo et al. (2023) trace operand information through attention and MLP modules to the predicted result, contrasting arithmetic with retrieval tasks.Source: §3.2.1 · p. 6

3.2.2. Tokenization and pretraining frequency as confounds in numerical reasoning

  • Numerical outputs can reflect tokenization and corpus-frequency effects unrelated to the arithmetic fact itself; Singh and Strouse (2024) find arithmetic accuracy changes with number tokenization, motivating controls in confidence comparisons.Source: §3.2.2 · p. 6

3.2.3. Small, curated-corpus language models

  • The toolkit uses small causal language models because their training text can shape their assertions, while the default model is selected for single-GPU fine-tuning and arithmetic competence.Li et al. (2023) provide a larger-scale precedent in which curated synthetic training text yields reasoning behavior comparable to larger models.Source: §3.2.3 · p. 7

3.2.4. Where does this toolkit stand?

  • The identified gap is direct testing of whether confidence tracks corpus consistency; the toolkit fine-tunes on fabricated facts and compares confidence with its own pre-fine-tuning confidence in corresponding facts.The comparison uses an unchanged measurement procedure.Source: §3.2.4 · p. 7

4. Design Principles

The design principles make the fabricated-fact comparison exhaustive and stable, control measurement differences, and distinguish a fabricated answer gaining confidence from a true answer being suppressed. They also document the practical consequence of mutating the model in place.

4.1. An exhaustive, unambiguous fact domain

  • The fact domain comprises all 81 single-digit addition pairs, each with one unambiguous true answer, enabling exhaustive scoring when baseline arithmetic competence is confirmed.This supports treating pre-fine-tuning confidence in the true sum as a real-fact baseline rather than a guess.Source: §4.1 · p. 8

4.2. One fixed fabrication per fact, not a resampled one

  • Each pair receives one wrong answer sampled under a fixed seed and retained across measurement, corpus construction, fine-tuning, and comparison, so the intervention remains stable.Changing a fabrication between stages would prevent attributing post-fine-tuning confidence to a specific intervention.Source: §4.2 · p. 8

4.3. Token-length-aware confidence measurement

  • Single-digit candidates tokenize to two tokens and double-digit candidates to three, so the toolkit uses mean per-token log-probability to avoid length-driven confidence penalties.The function also reports summed log-probability.Source: §4.3 · pp. 8–9

4.4. One measurement procedure, used unchanged on both sides

  • The same confidence-measurement function is used unchanged before and after fine-tuning for true and fabricated answers, preventing measurement changes from explaining comparison differences.The procedure also keeps teacher-forcing, log-probability aggregation, and candidate enumeration consistent.Source: §4.4 · p. 9

4.5. Repetition as the fine-tuning signal

  • Each fabricated fact is repeated a fixed number of times because one exposure may not compete with pretrained arithmetic; sufficient repetition is an empirical, run-specific setting.The repetition count is not assumed to work as a fixed constant at every scale.Source: §4.5 · p. 9

4.6. Two contexts, three confidence numbers

  • The comparison tracks pre-fine-tuning confidence in the true sum, then post-fine-tuning confidence in both fabricated and true sums, distinguishing lost advantage from active suppression.The true-answer post-fine-tuning value is needed to distinguish these outcomes.Source: §4.6 · p. 9

4.7. One base model per run, mutated in place

  • Fine-tuning mutates the sole model object in place, so a clean pre-fine-tuning baseline after fine-tuning requires restarting the runtime and rerunning the pipeline.The manual describes this as a simplicity trade, not an oversight.Source: §4.7 · p. 10

5. The Toolkit

This section documents the reference notebook’s seven-stage toolkit pipeline, from fact-space generation and confidence measurement through baseline validation, fabricated-corpus construction, and fine-tuning. It also describes padding-excluded fine-tuning loss, unchanged post-fine-tuning confidence measurement, and the paired comparison and visualization of before-and-after distributions.

5.1. Fact-space generation and model setup

  • The toolkit generates all 81 arithmetic pairs before measurement, using pair-specific prompts throughout; its declared roster contains causal LMs small enough for a free-tier cloud GPU.Each later stage reads the prompt directly from the shared fact-space declaration.Source: §5.1 · pp. 11–12

5.2. Confidence measurement

  • A single teacher-forced function scores all 17 candidates per pair, returning summed and per-token mean log-probabilities; later distributions use the mean for token-length comparability.Teacher forcing scores candidates whether or not the model would generate them, and reusing the function guarantees the same measurement procedure throughout.Source: §5.2 · pp. 12–13

5.3. Baseline measurement and validation

  • Before fine-tuning, the toolkit scores 17 candidates for each of 81 pairs and confirms that values 2–9 use two tokens while 10–18 use three.Per-pair normalization uses mean rather than total log-probability to avoid structurally penalizing two-digit answers under this tokenizer.Source: §5.3 · pp. 13–14

5.4. Fabricated corpus construction

  • For each pair, the toolkit samples one incorrect candidate uniformly, fixes it with a seeded generator, then repeats and shuffles the fabricated facts into training texts.The same sampled fact is used for corpus construction, fine-tuning, and the final comparison without downstream resampling.Source: §5.4 · pp. 15–16

5.5. Fine-tuning

  • Fine-tuning wraps texts in a PyTorch (Paszke et al., 2019) Dataset/DataLoader and uses causal language-model loss with AdamW, excluding padding positions.Because training mutates the model in place, restoring a clean baseline requires restarting the runtime and rerunning the pipeline from the top.Source: §5.5 · p. 16
  • Fine-tuning excludes padding positions from the loss by assigning them the ignored label -100, so the model is not trained to predict pad tokens as content.This follows the Hugging Face Transformers convention for an ignored index.Source: §5.5 · p. 18

5.6. Post-fine-tuning measurement

  • After fine-tuning, the toolkit reruns the same measurement over 81 pairs and 17 candidate values, normalizing results into per-pair distributions for direct comparison.The measurement differs only in the model object and added fabricated-value bookkeeping.Source: §5.6 · pp. 18–19

5.7. Comparison and visualization

  • The comparison assembles each pair’s pre-fine-tuning confidence in the true sum, post-fine-tuning confidence in the fabricated value, and post-fine-tuning confidence in the true sum.Source: §5.7 · p. 19
  • The visualization places full 17-value distributions before and after fine-tuning side by side, highlighting the context-correct answer and outlining the model’s arg-max.Figure 2 illustrates the output format only; its example confidence shifts are not reported, interpreted, or generalized as findings.Source: §5.7 · p. 20, Figure 2 · p. 23

6. Implementation and Reproducibility

The reference implementation specifies supported model choices, software and hardware requirements, and run procedures that shape reproducibility and comparison. It is designed for small causal decoders and requires a clean rerun to compare models or fabricate a new fact set.

6.1. Supported model families

  • The candidate models are small causal decoders spanning two model families and two pretraining regimes, and compatible Hugging Face causal-language-model interfaces can be substituted.The reference roster is selected to be small enough for fine-tuning on a single free-tier cloud GPU.Source: §6.1 · p. 24

6.2. Software dependencies

  • The sequential reference notebook uses Transformers and PyTorch for model loading, scoring, and fine-tuning, with pinned dependencies archived alongside the toolkit.Pandas/numpy support confidence tabulation and normalization, while matplotlib produces paired visualizations.Source: §6.2 · p. 24

6.3. Hardware requirements

  • Fine-tuning at the stated 0.5–1.5B-parameter scale is impractical on CPU, while a free-tier Google Colab GPU suffices for the default Qwen2.5-0.5B configuration.The notebook selects whichever device is available and is intended in practice to run on a CUDA-enabled GPU.Source: §6.3 · p. 24

6.4. Determinism

  • A seeded generator makes the fabricated fact set reproducible, but training-specific randomness is not fixed, so exact post-fine-tuning numbers may differ across runs.Reproducing the same corpus and pipeline structure is distinct from reproducing a specific run’s exact numbers.Source: §6.4 · p. 25
  • Each run fine-tunes one model in place; comparing models or drawing another fabricated fact set requires a clean restart and a full pipeline rerun.Partial reruns are not the prescribed way to make either comparison.Source: §6.4 · p. 25

7. Interpreting the Toolkit’s Output

The toolkit presents three confidence values per addition pair to assess fabricated-answer uptake and possible suppression of the true answer, while leaving run-specific outcomes to empirical work.

7. Interpreting the Toolkit’s Output

  • For each of 81 addition pairs, the comparison table reports pre-fine-tuning confidence in the true sum and post-fine-tuning confidence in both the fabricated and true sums.The first two values are intended to be comparable in kind, not merely both high.Source: §7 · p. 25
  • The post-fine-tuning true-sum confidence helps distinguish a fabricated answer merely outranking the true answer from active suppression of the true answer.High confidence in the fabricated answer alone cannot distinguish those cases.Source: §7 · p. 25
  • Paired before-and-after charts show confidence across all 17 candidate values for each pair, with accent-colored and outlined bars marking the relevant values and the model’s arg-max.When those bars do not coincide, the chart surfaces a difference between the model’s top prediction and the context-correct answer.Source: §7 · p. 26
  • This manual explains how to read the comparison table and charts but does not report or interpret the outcome of any specific run.Run-specific outputs are left to empirical work using the toolkit.Source: §7 · pp. 25–26

8. Scope and Limitations

The toolkit’s scope is a controlled, single-run comparison; its design and resource boundaries limit statistical, cross-domain, and cross-model conclusions.

8. Scope and Limitations

  • All tested facts are single-digit addition; whether the confidence pattern extends to other enumerable domains or open-ended factual claims is untested.The toolkit does not assume that the pattern generalizes beyond this fact domain.Source: §8 · p. 26
  • Candidate base models span roughly 0.5 to 1.5 billion parameters, and cross-model or cross-scale comparison requires a clean full-pipeline rerun for each model.Such comparisons are not automated or aggregated within a single run.Source: §8 · p. 26
  • Fine-tuning is not repeated across seeds, and comparison-table values are point estimates for a specific model, fabricated-fact draw, and training run—not statistically validated effect sizes.The fabricated-fact draw is seeded, but the fine-tuning procedure is not additionally seeded and no confidence intervals are reported.Source: §8 · pp. 26–27
  • The repetition count, learning rate, and epoch count are fixed constants for one model-corpus combination, so the toolkit does not characterize outcome sensitivity to them.The toolkit states that its controlled comparison remains useful within these boundaries, but does not support broader generalization across domains, models, or repeated draws.Source: §8 · p. 27
  • Only one randomly chosen wrong answer is fabricated per pair, so the toolkit does not test whether a fabricated answer’s relative implausibility affects its absorption..Source: §8 · p. 27
  • Fine-tuning at a practical epoch count is infeasible on CPU, so an end-to-end run requires local or cloud GPU access..Source: §8 · p. 27

9. Data and Code Availability

The toolkit’s source code, pinned dependency environment, and documentation are archived separately, with citation guidance distinguishing instrument use from design rationale.

9. Data and Code Availability

  • The toolkit’s source code, pinned dependency environment, and documentation are archived under a persistent identifier..Source: §9 · p. 27
  • The toolkit is released under a Creative Commons Attribution 4.0 International license, and the manuscript is intended for archival under the same license..Source: §9 · p. 27
  • Cite the archived toolkit when reporting results produced with it, and cite the manuscript when referring to its design rationale..Source: §9 · p. 28

10. Conclusion

The toolkit tests whether fine-tuning on fabricated arithmetic facts changes confidence relative to the model’s own pre-fine-tuning confidence in true facts. It specifies a controlled measurement and comparison, but leaves the results of any particular run to empirical work.

10. Conclusion

  • The motivating prediction is that a sufficiently reinforced corpus-fabricated falsehood can acquire a confidence signature indistinguishable in kind from a pretraining-acquired fact.The proposed test concerns whether confidence tracks corpus consistency rather than correspondence with fact.Source: §10 · p. 28
  • The toolkit fine-tunes a small causal language model on an exhaustively enumerated fabricated arithmetic corpus and compares post-tuning confidence with the model’s own pre-tuning confidence under an unchanged measurement procedure.The manual justifies design choices including token-length-aware confidence measurement.Source: §10 · p. 28
  • A three-number comparison is designed to distinguish a fabricated answer outranking the true answer from active suppression of the true answer.The instrument’s readout for a particular model and fabricated-fact draw is an empirical question addressed by work building on the toolkit.Source: §10 · p. 28
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